Experimental and numerical study of the thermal and hydraulic effect ...

Abstract

Today’s telecommunication cabinets use Electro Magnetic Compliance (EMC) screens in order to reduce electromagnetic noise that can cause some miss functions in electronic equipment. Many radio base stations (RBSs) use a 90-degree building architecture: the flow inlet is perpendicular to the EMC screen, which creates a complex flow, with a 90-degree air turn, expansions, compressions, perforated plates and PCBs. It is of great interest to study how the EMC screen interacts with the rest of components and analyze the total pressure drop and how much the flow pattern changes due to the placement of the screen. Velocity, pressure and temperature measurements as well as flow pattern visualizations have been carried out to gain good insight into the flow and heat transfer characteristics in a subrack model of an RBS. Furthermore, these measurements have been very useful for validating detailed CFD models and evaluating several turbulence models. Nowadays, industrial competition has caused a substantial decrease in the time-to-market of products. This fact makes the use of compact models in the first stages of the design process of vital importance. Accurate and fast compact models can to a great extent decrease the time for design, and thus for production. Hence, to determine the correlations between the pressure drop and flow pattern on the PCBs as a function of the geometry and the Reynolds number, based on a detailed CFD parametric study, was one objective. Furthermore, the development of a compact model using a porous media approach (using two directional-loss coefficients) has been accomplished. Two correlations of these directional loss coefficients were found as a function of the geometry and Reynolds number.

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Acknowledgements

First I would like to thank my supervisor Professor Bahram Moshfegh and co-supervisor Dr Hans Jonsson for all their help with this thesis. Without you, this thesis would not have been accomplished. Thanks, Bahram, for employing me and giving me the opportunity to work in this beautiful area. Thanks also for all your comments and discussions about results and analyses. Although our offices were in different cities, you were always available to find some time to discuss the project wherever you were. Thanks, Hans, for all your supervising work and for the encouragement during these years. I would like to thank Professor Carlos Bastero, Professor Miguel Angel Serna and Professor Tomás Gómez Acebo from TECNUN (University of Navarra) who trusted in me and decided to give me a scholarship to come to KTH. Also thanks to Professor Björn Palm and Associate professor Per Lundqvist, who accepted me in their division at KTH. Thanks, Björn, for helping me at the beginning of my stay in Sweden and because you always have your door opened and available to help anyone who comes by. And Per, for being always of good humor!! Thanks to the KK Foundation, Sweden and Antonio Aranzabal Foundation, Spain for economically supporting this project. Thanks to Mr Mikael Ardvisson and Dr Jukka Rantala and their staff teams at Ericsson and Nokia, respectively, for participating in this project and for all the good comments during all the presentations at Kista and Helsinki. Thanks to everybody at the Applied Thermodynamic division at KTH: Prof. Eric Granryd, Tim, Jaime, Claudi, Peter, Joachim, Anders, Rathmat, Oxana, Wimol, Cecilia, Samer, Branko, Rashid, Jan-Erik, Erik, Åke, Nabil, Yang, Emilio, Getachew, Shota, Teclemariam, Primal, Richard, Wahib, and of course our technicians, Benny S. and Benny A., the computer support team, Tony and Birger, and our efficient secretaries, Inga and Susy and in a special way to Miguel Castiella for the help with the visualizations. It has been a pleasure to enjoy a lot of meals, coffee times, kart driving, excursions and all kinds of football with all of you. It has been such an enriching experience. Thanks!!! 2

Thanks also to everybody at the Department of Technology and Built Environment, University of Gävle: Daniel, Ulf, Samuel and Sofia. It always felt so familiar to be with you during my short visits there. Special thanks to Dr Mathias Cehlin, who always finds some time to help everybody with the experimental stuff and to the most efficient technician I have ever met: Larry Smith, who did such nice work with the test rig. Thanks to Hans Lundström for all the help with the hot-wire anemometers, Tommy Gaude for the good work with the perforated plates, Beth Chapple for the English corrections, Mrs Eva Wännström, our helpful secretary and again Mathias and Daniel for reading carefully the manuscript of the thesis. I extend also my gratitude to Associate Professors Alejandro Rivas and Juan Carlos Ramos that lead the Fluid Flow and Thermal Engineering Division of TECNUN (University of Navarra) and taught me in my undergraduate studies, and to the rest of the nice people in that Division with whom I am working now: Gorka, Jon, Mireia and Juan. I would like to thank everybody with whom I have lived during these years in the best residence hall in the world (it is not an exaggeration): Lärkstaden Studiecentrum. All of you have really made me enjoy this stay in Sweden. You are my family in Sweden. At last but not least, thanks to my parents Luis Miguel and Rosa María, and my sisters Judith, María Elena and Beatriz for everything: for life, love and all the encouragement during these years and many other things! To you this thesis is dedicated! Raúl Antón Remírez Stockholm, October 2006

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Table of Contents 1

Introduction ............................................................................................ 10 1.1

Thermal Management of Electronic Systems........................... 10

1.2

Radio Base Station: A Cooling Building Architecture............. 11

1.3

Electromagnetic Compliance ...................................................... 12

1.4 Motivation for This Study ........................................................... 13 1.4.1 General reasons......................................................................... 13 1.4.2 Complex flow phenomena...................................................... 14 1.4.3 Compact modelling .................................................................. 14 1.5

Aim of the Study ........................................................................... 15

1.6

Methods .......................................................................................... 15

1.7

Limitations...................................................................................... 16

1.8

Research Process ........................................................................... 17

1.9 Literature Survey ........................................................................... 19 1.9.1 Perforated plates ....................................................................... 19 1.9.2 EMC screens ............................................................................. 19 1.9.3 CFD and experiments in electronic systems with screens. 20 1.9.4 Compact model......................................................................... 20 2

Experiments ............................................................................................ 22 2.1 Experimental Set-up ..................................................................... 22 2.1.1 Wind tunnel ............................................................................... 22 2.1.2 EMC screens ............................................................................. 24 2.2

Data Reduction.............................................................................. 25

2.3 Velocity ........................................................................................... 26 2.3.1 Experimental procedure—inlet profile................................. 26 2.3.2 Experimental procedure—interior points ............................ 26 2.3.3 Uncertainty Analysis................................................................. 27 2.4 Pressure........................................................................................... 28 2.4.1 Experimental procedure .......................................................... 28 2.4.2 Uncertainty Analysis................................................................. 28 2.5 Temperature................................................................................... 29 2.5.1 Experimental procedure .......................................................... 29 2.5.2 Uncertainty Analysis................................................................. 30 2.6 4

Flow Pattern................................................................................... 33

2.6.1 2.6.2 3

Smoke visualization.................................................................. 33 Uncertainty Analysis................................................................. 35

Computational Fluid Dynamics ........................................................... 36 3.1

Introduction to the CFD Method .............................................. 36

3.2

Turbulence ..................................................................................... 37

3.3

Turbulence modelling................................................................... 38

3.4 Two-equation models................................................................... 41 3.4.1 The Standard kH Model ........................................................... 41 3.4.2 The RNG kH Model ................................................................. 41 3.4.3 The Realizable kH Model ......................................................... 41 3.4.4 The standard kZ Model........................................................... 42 3.4.5 The Shear Stress Transport (SST) kZ Model....................... 42 3.5 Wall Treatments ............................................................................ 42 3.5.1 Enhanced wall treatment......................................................... 42 3.6

Boundary Conditions.................................................................... 43

3.7 Numerical aspects ......................................................................... 46 3.7.1 Numerical schemes .................................................................. 47 3.7.2 Mesh density sensitivity ........................................................... 47 3.7.3 Convergence criteria................................................................. 48 3.7.4 Validation of the numerical models....................................... 49 4

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Validation of the numerical detailed models...................................... 50 4.1

Velocity and pressure.................................................................... 50

4.2

Inlet velocity profiles .................................................................... 51

4.3

Flow Pattern................................................................................... 53

4.4

Temperature................................................................................... 54

Correlations for pressure drop, flow pattern and compact model. 56 5.1

Data Reduction.............................................................................. 57

5.2 Pressure drop and flow pattern correlations based on the detailed CFD parametric study ................................................................. 60 5.2.1 Total pressure drop .................................................................. 60 5.2.2 Dimensionless wetted area...................................................... 61 5.2.3 RMS* factor ............................................................................... 62 5.3 Methodology to develop a compact model based on a porous media approach ........................................................................................... 63 5

5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 6

Methodology and validation ................................................... 63 Correlation for two directional loss coefficients ................. 66 Mesh density and CPU savings .............................................. 69 A comment on the uncertainty of the correlations............. 69 Accuracy of the compact model ............................................ 70

Summary of papers ................................................................................ 72 6.1 Paper I............................................................................................. 73 6.1.1 Outline........................................................................................ 73 6.1.2 Conclusions and discussion .................................................... 73 6.2 Paper II ........................................................................................... 74 6.2.1 Outline........................................................................................ 74 6.2.2 Conclusions and discussion .................................................... 74 6.3 Paper III.......................................................................................... 75 6.3.1 Outline........................................................................................ 75 6.3.2 Conclusions and discussion .................................................... 75 6.4 Paper IV.......................................................................................... 76 6.4.1 Outline........................................................................................ 76 6.4.2 Conclusions and discussion .................................................... 77 6.5 Paper V ........................................................................................... 78 6.5.1 Outline........................................................................................ 78 6.5.2 Conclusions and discussion .................................................... 79 6.6 Paper VI.......................................................................................... 80 6.6.1 Outline........................................................................................ 80 6.6.2 Conclusions and discussion .................................................... 80 6.7 Paper VII ........................................................................................ 80 6.7.1 Outline........................................................................................ 80 6.7.2 Conclusions and discussion .................................................... 81

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Conclusions ............................................................................................. 82 7.1

Conclusions from the Results ..................................................... 82

7.2

Design Tools.................................................................................. 83

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Suggestions for further work................................................................ 86

9

References ............................................................................................... 88

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This thesis is based on the following papers: Paper I

Antón R., Jonsson H., Moshfegh B. 2004. Modelling of EMC screens for radio base stations Part 1: Experimental parametric study. Proc ITHERM 04, Las Vegas, Nevada, 1-4 June.

Paper II

Antón R., Castiella M., Jonsson H. and Moshfegh B. 2005. Smoke and CFD visualization of the flow after an EMC screen in a sub-rack model. Proc THERMINIC 05, Belgirate, Italy, 27-30 September.

Paper III

Antón R., Jonsson H., Moshfegh B. 2004. Modelling of EMC screens for radio base stations Part 2: Evaluation of turbulence models. Proc ITHERM 04, Las Vegas, Nevada, 1-4 June.

Paper IV

Antón R., Jonsson H., Moshfegh B. 2006. Detailed CFD modelling of EMC screen for radio base stations, A benchmark study. IEEE Transactions on Components and Electronic Packaging (accepted with minor revision).

Paper V

Antón R., Jonsson H., Moshfegh B. 2006. Detailed CFD modelling of EMC screen for radio base stations: A conjugate heat transfer problem. International Journal of Heat Exchangers (accepted for publication with some revisions).

Paper VI

Antón R., Jonsson H., Moshfegh B. 2006. Detailed CFD modelling of EMC screen for radio base stations: A parametric study. Submitted to IEEE Transactions on Components and Packaging Technologies.

Paper VII

Antón R., Jonsson H., Moshfegh B. 2006. Compact CFD modelling of EMC screen for radio base stations: A porous media approach and a correlation for the directional loss coefficients. IEEE Transactions on Components and Packaging Technologies (accepted with revisions).

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Other publications not included here, since they are out of the scope of the thesis: Antón R., Jonsson H., and Palm B. 2002. Modelling of air conditioning systems for cooling of data centers. Proc ITHERM 02, San Ciego, California, 30 May-1 June. Antón R., Palm B., 2002. Spray cooling, an overview of methods and possibilities. Proc ScandTherm 2002, Stockholm, Sweden, 17 June.

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Nomenclature A, area a, inlet height Ainlet, inlet area Apcb, cross sectional area between two PCBs b, gap between sub-rack inlet and EMC screen D, hole diameter d, sub-rack depth h, heat transfer coefficient k, turbulent kinetic energy n, number of holes between 2 PCBs p, pressure P, average pressure p', fluctuating pressure P , modified kinematic pressure q, heat flux Q , heat flow S, hole spacing t. temperature T, average temperature t', fluctuating temperature tpcb, PCB thickness ts, screen thickness u, velocity U, average velocity u', fluctuating velocity Wslot, distance between 2 PCBs x, coordinate along the sub-rack depth z, coordinate along the sub-rack height 'p, pressure difference 'T, temperature difference Dthermal diffusivity Hscreen porosity Hdissipation rate of turbulence kinetic energy Qdynamic viscosity U density

m2 m m2 m2 m m m W/m2 ºC m2/s2 Pa Pa Pa m2/s2 W/m2 W m ºC ºC ºC m m m/s m/s m/s m m m Pa ºC m2/s - m2/s3 m2/s kg/m3

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1 Introduction

1.1 Thermal Management of Electronic Systems Thermal management of electronic systems is one of the bottlenecks in today’s electronic industry. The increasing clock speeds and miniaturization implies a huge increase in the heat dissipation per unit area in electronic systems. It is a real challenge to cool electronic components in an efficient way. Air is still the most common method for cooling electronics, due to safety reasons and availability. For some highdissipation cases, liquid cooling cannot be avoided any more, since there is no way to cool very high heat fluxes with air. However, most electronics are still cooled by air. Thermal management consists of reducing failures due to thermal-related problems in such a way that a good level of reliability is achieved. This means assuring the good performance and long life of the electronic product. The normal way to achieve this is to make sure that the junction temperature of all electronic components is not excessive. Heat dissipation from a surface may be described by Newton’s law of cooling: Q

hA'T

According to this law, there are four ways to try to improve thermal management. One way is to reduce the heat dissipation, for example reducing the voltage in the electronic components, as has been done during the last few decades (Kim and Kim, 2004). A second way is to increase the heat transfer coefficient (see Figure 1a). A lot of research has also been performed in this direction: air jet impingement (Rundström and Moshfegh, 2006), liquid cooling, etc. A third way is by increasing the dissipation area (Jonsson and Moshfegh, 2001), e.g. see heat sinks in Figure 1b, and the fourth way is to increase the temperature 10

difference by reducing the surrounding temperature (see Figure 1c) or to use new materials inside the components that withstand higher temperatures. To ensure that the junction temperature is not excessive, there must be an adequate heat transfer coefficient on the surfaces of the chips and a correct temperature surrounding the component. The correct component ambient temperature will be achieved only if there is good thermal management on the board level. In order to achieve a convenient inlet temperature on the board level, good thermal management should be achieved at the sub-rack level as well as at the cabinet level. This chain of temperature level requirements eventually leads to achieving the right temperature in the surroundings of the cabinet: room temperature. To set the room temperature to a particular value will normally be accomplished by using air conditioning units. 4 3

2

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1

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a) Spray cooling

b) Heat sink

c) Active cooling in a data center

Figure 1. Several ways to increase the cooling in an electronic system.

This thesis is focused on the system level: a sub-rack of a radio base station. However, the analysis that has been performed in this thesis is not only valid for a RBS but also for all the telecommunication sub-racks with a cooling architecture in which the airflow makes a 90 degrees turn.

1.2 Radio Base Station: A Cooling Building Architecture In a telecommunication network (e.g. a mobile telephone network), the RBSs are the nodes of the network, where wireless signals are received and transmitted. The RBSs have several shelves called sub-racks (see Figure 2b), filled with cards with electronic components (see Figure 2c). These boards are the power board assemblies (PBAs) where components are mounted on printed circuit boards (PCBs). In most of the cases, RBSs are cooled by forced air convection. 11

a) Cabinet level

b) Sub-rack level

c) Board level

Figure 2. Several levels in the thermal management of a cabinet.

In a typical RBS building architecture, the sub-racks are cooled individually, in such a way that the same amount of fresh air enters into each sub-rack. At the top of the sub-rack, several blowers (a radial fan tray) that suck the air (a pull configuration, see Figure 2b) are placed. Furthermore, two Electro Magnetic Compliance (EMC) screens are placed at the inlet and the outlet of the sub-rack slots. The function of this EMC screen is to decrease electromagnetic noise for safety and good performance reasons. In a sub-rack (see Figure 2b), the air first enters through the inlet and makes a 90-degree turn while impinging and going through the EMC screen. Then the air flows past the electronic components, thereby removing the heat. The air finally goes through the second EMC screen and is drawn out by the fans and ejected to the back chimney of the cabinet, ending in the cabinet surroundings. This pull configuration is more typical than the push configuration (where axial fans are placed in the inlet plenum), since it creates a more uniform flow over the PCBs.

1.3 Electromagnetic Compliance The desire to reduce the size of electronic systems results in closer placement of many electronic components. This proximity may create problems due to electromagnetic interference. Noise is an undesired electrical signal in a circuit; interference is the effect of the noise. Noise should be reduced to a level at which it does not create interference. Requirements for electromagnetic compatibility demand that electronic equipment works properly in its electromagnetic environment and that the equipment is not a source of electromagnetic interference. 12

A way to control the propagation of magnetic fields is by means of a shield. A shield may be a metallic perforated plate that efficiently hinders electromagnetic radiation going through it. In a sub-rack, this means to hinder electromagnetic radiation from leaving the sub-rack and electrical disturbances from entering it. The ideal shield would be to completely enclose the electronics in a metallic box. However, this prevents cooling, so there should be some apertures, although this means some electromagnetic leakage. The level of leakage of electromagnetic radiation from the shield depends mainly on three parameters (Ott, 1988): the maximum linear dimension, the wave impedance (ratio of the electrical and magnetic fields) and the frequency of the source. A typical shield is a perforated plate (an EMC screen). It has small openings but enough free area that permits cooling of the electronic systems. For commercial products, a good rule of thumb is to avoid openings greater than 1/20 of a wavelength.

1.4 Motivation for This Study There are three different motivations for this thesis: general reasons related to the selection of fans and to flow distribution problems, as well as a wish to study complex flow phenomena that appear in this building architecture and finally to develop compact models for a more efficient design process.

1.4.1 General reasons It is important to know the pressure drops in the RBS cabinet in order to know which size of fans are required. In general, the pressure loss in a system increases with an increase in the flow rate, and it is important to match the pressure increase of the fan to the pressure losses caused by the flow through the system. It is therefore important to identify where those pressure losses occur. For low screen porosities, the pressure drop is mainly due to the low porosity of the screen. In this case, the volume before the EMC screen has a tendency to act more as a plenum, and therefore the EMC screen behaves as a honeycomb flow straightener. This leads to a more uniform flow distribution (flow pattern) after the screen. On the other hand, high porosity EMC screens lack this feature, and thus a less uniform flow pattern is obtained between the PCBs. 13

The reason why information about the flow pattern is so important is that high dissipative components should be placed in locations with high velocity (i.e., in the bulk flow), and not in areas with very low velocities. This is a consequence of the strong dependence between the heat transfer coefficient and the velocity.

1.4.2 Complex flow phenomena According to a recent article (Joshi et al., 2002), there are still gaps in system level modeling. One of the main issues to be solved is to eliminate uncertainty in input parameters like the screen pressure loss coefficient. For complex flows as in an RBS sub-rack, it is difficult to calculate the pressure drop and to predict the flow pattern in between the PCBs. To simply add pressure loss coefficients for flow obstacles in the flow path will in general produce inaccurate results for flow obstacles placed close to each other, due to such factors as hydraulic interference between the obstacles (Smith, 1971; Fried and Idelchik, 1989). Since the air entering the sub-rack makes a 90-degree turn, the flow does not impinge the screen at the same velocity. The impinge angle may also vary along the sub-rack depth, as shown in Figure 3. Furthermore, the flow will experience a sudden change in direction after colliding with the interior faces of the EMC screen holes.

Figure 3 Non uniform velocity profile (coloured by velocity magnitude) before and after the EMC screen

1.4.3 Compact modelling Nowadays, when the design time is cut due to industrial competition, thermal management engineers do not have as much time as they want to analyze the thermal problems. In order to have an efficient design process, computers performing simulations of the behavior of the designed system are often utilized. Thanks to the increasing speed of computers, it is now possible to perform detailed computational fluid 14

dynamics (CFD) simulations. Moreover, much more information can be extracted from the CFD simulations than would be possible with normal experimental investigations. However, it is a challenge to choose the proper turbulence model, near wall treatment and mesh strategy for a particular application, and it is also quite a time-consuming activity. Therefore, engineers tend to minimize their models by employing compact models of certain components, e.g. heat sinks, components or, as in this case, EMC screens. The importance and benefits of compact models are many. Primarily, the use of compact models reduces the time needed to get a good design for a given application and an accurate compact model of an EMC screen would be of great importance and benefit to the industry.

1.5 Aim of the Study This thesis is focused on analyzing the heat and fluid flow inside an RBS sub-rack, and mainly analyzing the effect of the first EMC screen on the flow pattern, pressure drop and temperature field in a PCB sub-rack. The ultimate goal is to predict the total pressure drop and the flow details after the EMC screen in a PCB slot of a RBS sub-rack by means of a fast and accurate tool either based on correlations or by a CFD compact model based on a porous media approach.

1.6 Methods There are two main methods to study an electronic system or a flow problem in general: experimental and theoretical. To use the experimental method is very time consuming; normally one does not get a whole field measurement, but local or average data are obtained. Many times, it is necessary to study the system at a reduced scale. Other times, in order to get more accurate measurements, a wind tunnel is used, or a simplified model is built. Anyway, experiments are still the most reliable method. Hence, the experimental method is not only used to gain insight into the heat and fluid flow in the system but it is very often used to check the validity of a numerical result. A theoretical method is based on the laws of nature. Sometimes, it is possible to get an analytical solution, but many times a numerical solution is needed, due either to the mathematical complexity of the laws (e.g. nonlinear partial differential equations) or the complexity of the geometry where the laws are applied. This numerical approach implies an approximation of the analytical solution and thus it should be validated by experiments. 15

The positive feature of the theoretical approach is that we obtain detailed information about the whole domain (sometimes the discretized domain), it is relatively cheap and fast. Hence, it is interesting to work with both methods: to validate several CFD models by experiments and then a larger range in the analyzed parameters may be studied by CFD. This has been the approach in the present thesis.

1.7 Limitations In the present case, the reference values have been the experimental studies. These studies were not performed in a real RBS sub-rack but in a model inside a wind tunnel. The size of the sub-rack model is close to standard RBS sub-racks. The position of the model is horizontal, i.e., the PCBs are horizontal. In reality, the normal position is vertical. The reason why the sub-rack was placed horizontally was that an entrance duct of one meter was placed at the entrance of the sub-rack model, as can be seen in Figure 4. The entrance duct was used to get low turbulence intensity level (fully turbulent developed flow) in order to have reliable hot-wire measurements. Due to the 90-degree turn, the velocity profiles at the inlet of the sub-rack are neither uniform nor symmetric and it was important to measure these profiles in order to use accurate boundary conditions in the numerical study. This approach is beneficial, since the profiles at the inlet of the sub-rack are asymmetric. However, this is also a limitation, because in reality there is no entrance duct, and the flow would not always be perpendicular, which may affect the pressure drop. Anyway, it is thought to be a good approximation, and a repeatable method.

Figure 4. Wind tunnel set-up.

Another approximation is that the sub-rack model analyzed in this thesis lacks swirl boundary conditions at the outlet. It is supposed that the second screen (not studied in this work) will break the swirl produced by the blowers at the top of the sub-rack. In Nevelsteen et al. (2006) the axial fans are parallel to the screens and they are set in a push configuration. They studied the interaction of the fan swirl and an EMC 16

screen. It can be seen from their results that the swirl is actually reduced after the EMC screens. Although the building architecture studied in this thesis is a pull configuration, Nevelsteen et al.’s results can justify this approximation.

1.8 Research Process The process of the thesis is depicted in Figure 5. First an experimental parametric study was done (paper I, and the experimental part of paper II). In the experimental study, pressure and velocity measurements were performed at several locations before and after the screen for several velocities, sub-rack geometries, as well as screen porosities. The influence of these parameters on the flow pattern was also studied using the smoke-wire technique. All these experiments were used to validate detailed CFD models, and at the same time to evaluate different turbulence models and near wall treatments used in the numerical investigations in papers III and IV. Experimental Parametric Study To validate Detailed CFD Parametric Study (velocity profile at the inlet of the subrack)

Detailed CFD Parametric Study (uniform velocity profile at the inlet of the entrance duct) Comprehensive Detailed CFD Parametric Study (uniform velocity profile at the inlet of the entrance duct)

To validate

To validate Compact model of the EMC screen by a porous media approach Comprehensive Compact CFD Parametric Study (uniform velocity profile at the inlet of the entrance duct)

To create

Design Tools

Figure 5. Research process.

In CFD simulations, accurate boundary conditions are needed. In order to use accurate boundary conditions, the velocity and turbulence 17

intensity profiles at the inlet of the sub-rack were used (paper III). In order to acquire reliable measurements, an entrance duct was placed before the sub-rack inlet in such a way that the profiles were fully developed turbulent profiles. It was interesting to study the influence of different geometrical parameters and velocities for a greater range. However, the velocity profiles were needed at the sub-rack inlet and thus the study was not possible to perform. However, it was shown in paper IV that by increasing the CFD model using an entrance duct of 0.5 meters and using uniform velocity and turbulence intensity profiles at the inlet of the entrance duct, a good prediction of the velocity and turbulence intensity profiles at the inlet of the sub-rack was achieved. A comprehensive parametric study could be performed with this approach, as was done in paper VI. Before performing this parametric study, an evaluation of turbulence models using an enhanced wall treatment (see details in section 3.5.1) was done in paper IV. The best of these models was also used for the analysis of the conjugate heat transfer as a function of several parameters (paper V). After that, a large number of isothermal detailed CFD simulations were done and correlations were developed to predict the total pressure drop. Furthermore, to characterize the flow pattern after the screen, two parameters were defined that account for the wetted area and the flow uniformity after the screen. Correlations for these two parameters were also developed. Since it can actually be said that these correlations are some kind of compact model, the objective of the thesis was partially fulfilled. However, a further step could be done: to try to create a compact model using a porous media approach (paper VII) and to validate the model by means of the comprehensive detailed CFD parametric study. The aim of the compact model is to obtain the pressure loss coefficients of a volume hydraulical impedance that defines the EMC screen. The use of these pressure loss coefficients provides an accurate prediction of the pressure drop and the flow pattern after the screen. Correlations that predict the two directional loss coefficients as a function of the geometry and Reynolds number were developed. One positive aspect to this porous media approach is that the model can be completed by setting electronic components and other devices, but knowing that the flow pattern and pressure drop due to the 90-degree turn and screen porosity to be predicted faster and more accurately. The last step was to develop programs in a user-friendly environment that give all the information (pressure drops, flow pattern and directional loss coefficients) in a fast 18

way and as a function of the geometrical parameters: inlet height, PCB thickness, screen thickness, distance between inlet and screen, screen porosity, distance between two PCBs, and the Reynolds number.

1.9 Literature Survey There are enormous numbers of papers that focus on thermal management of electronics equipment. There are also plenty of papers that analyze the pressure drop through perforated plates. However, very little has been written about the effect of an EMC screen in a building architecture in which the flow makes a 90-degree turn and impinges the screen at an angle from the normal plane. To the best of my knowledge, there are no compact models for EMC screens for these configurations.

1.9.1 Perforated plates The pressure drop through perforated plates has been extensively studied by Idelchik (1994), who wrote a handbook for pressure loss coefficients that is very often used in the thermal management community. Other authors that have studied this issue are Carrothers and Baines (1965) and Smith (1971). Carrothers and Baines found the pressure drop through an inclined screen proportional to the square of the velocity component perpendicular to the screen. Smith published a book with the state of the art for correlations of the pressure drop through perforated plates, in which with the aid of experimental visualization he shows that porosity and screen thickness are the most important parameters for the prediction of pressure drop at high Reynolds numbers. Furthermore, Gan and Riffat (1997) analyzed the pressure drop through perforated plates experimentally and numerically. They also showed how the dimensionless pressure drop through the screens decreases as the ratio of screen thickness and hole diameter increases.

1.9.2 EMC screens There have been earlier attempts to model EMC screens for particular cases, as in Nevelsteen et al. (2006), where the screens close to axial fans were modelled by a compact model with three directional loss coefficients. Baelmans et al. (2003) analyzed experimentally the distance of influence by the screen, remarking on the difficulty of predicting the flow beside components placed close to the screen when the screen is modelled by means of hydraulic surface resistance. No correlations were developed in these works. Kordyban (2000) emphasized the need to use volume hydraulic impedance and not planar impedance to model EMC 19

screens or filters. He stated also that using a volume hydraulic impedance with only one coefficient is wrong. A one-coefficient model would reduce the velocity component perpendicular to the screen but not the other component, and thus the inclined flow would turn to the wrong direction. It was also stated that on some occasions the in-plane pressure loss coefficient may be larger than the perpendicular loss coefficient, however no correlations were developed in his study either. Akella and Ortega (2005) analyzed the pressure loss coefficients in a slot (1 RU card passage). In this case the air was perpendicular to the screens. They measured the pressure loss coefficient for the first screen, for the board populated with electronic components, and finally for the second screen. They said that there may be interaction between the different components, but if these interactions are small a flow network modeling (FNM) approach would be viable for this case. They showed also that the pressure loss coefficients were influenced very little by the Reynolds number. Bejan et al. (1995) used the intersection-of-asymptotes method applied to the cooling of stacks of plates shielded by porous screens, but in this case the air flow was also perpendicular to the EMC screens.

1.9.3 CFD and experiments in electronic systems with screens Many studies have been performed numerically by means of CFD, for example Nakamura and Komura (1996), Biswas et al. (1999) and Tahmaspur and Berhe (2002). Nakamura and Komura studied the airflow in a sub-rack with and without EMC screens. The study used CFD and measurement techniques such as LDA (Laser Doppler Anemometry). Biswas et al. also performed experiments and CFD simulations in an electronic box in which there were grilles, however these grilles were modelled using pressure loss coefficients from a handbook. Tahmaspur and Berhe compared honeycomb and perforated vents in a TW-150 Passive Optical Network. They did a detailed model of the perforated plate in order to estimate the pressure loss coefficient of that screen in that application.

1.9.4 Compact model Nakayama et al. (2001 and 2004) present a methodology in which, after spending time in developing detailed models, one can compress the information in a database and create compact models. The compact models can then be used to find a design in which the junction 20

temperature is not exceeded. Compact models have been developed not only for electronic packages like in Vinke and Lasance (1997), but also for subsystems like heat sinks. Narasimhan et al. (2003) developed a compact model of heat sinks using a porous media approach that was based on a boundary layer model between the plate fins of the heat sinks. Recently Kim and Kim (2004a) have developed a compact model based on a volume average technique, which has been applied for straight fin heat sinks as well as for pin fin heat sinks (Kim et al. 2004b). Another approach to shorten the design time is optimization methods, such as in Parry et. al. (2004), where a methodology is developed for getting the best design that fulfils an objective function and subject to some constraints, in which some of them may be integers like in the case of an optimized heat sink. Another way of compact modelling is flow network modelling, with early works like Butterbaugh and Kang (1995). Kowalski and Radmehr (2000) analyzed the flow in a cabinet in which they combine a flow network analysis together with some CFD simulations for some details (to get the impedance curve of the axial fans that they used). However, it should be emphasized that this method cannot be used when there is hydraulic interference between the different flow components. It is used between locations in which the pressure is uniform, without gradients, for some complex geometry may cause inaccuracies with this method.

21

2 Experiments

The experimental measurements in this thesis have two purposes. The first goal is to gain insight into the hydraulic and thermal behavior of the flow inside the sub-rack model. The second objective is to use the experimental measurements as a reference with which to validate the detailed CFD predictions.

2.1 Experimental Set-up The experiments were performed in a sub-rack model inside a wind tunnel. In the following section the wind tunnel is presented.

2.1.1 Wind tunnel The general layout of the wind tunnel is shown in Figure 6. Screen

Fan

Inlet Subrack Laminar flow element

Entrance duct

Figure 6. Wind tunnel layout.

The wind tunnel walls are made of Plexiglass. The air velocity is controlled by frequency regulation of the electric power driving the fan.

22

A sub-rack was modelled by means of Plexiglass plates (4 mm thick) as is shown in Figure 7 and Figure 8 (all the dimensions in mm). There are a total of 14 PCB dummies.

Figure 7. A detailed view of the sub-rack slots.

x 15

280

z

265.5 Inlet

1000 Top view

d

50

Side view

Screen

Figure 8. Sub-rack model.

Two models were built with the same dimensions except for the depth, d, which was either 200 mm or 260 mm. 23

The size of the commercial sub-racks follows the standards for electronic packaging that have been developed by the International Electrotechnical Commission (IEC). The employed unit for the height of the sub-rack is U=44.45 mm (17.5 in). The typical values for the subrack height are 3U, 6U and 9U. The corresponding PCB heights for these sub-racks are (in mm): 100, 233 and 366. In the model for this thesis, the PCB height was always 280 mm. The typical PCB depths for these sub-racks are 160, 220 and 280 mm. In the model for this thesis, the PCB depth was either 200 mm or 260 mm. A typical distance between two PCBs is 3×5.08 mm (3×2 in); in the model for this work it was 14 mm. As can be seen, the tested sub-rack geometry is close to that of commercial sub-racks and based upon discussions with Nokia and Ericsson. A commercial sub-rack appears in Figure 9.

Perforated plates

Figure 9. A typical commercial 6U subrack.

2.1.2 EMC screens Stainless steel screens (1 mm thickness) with 60° staggered circular holes were used (see Figure 10). The location of the screen is indicated in Figure 8. Three different porosities, H, have been used for the screen, shown in Table 1 The EMC screens were manufactured with a Computer Numerical Controlled (CNC) drilling machine. After the drilling a sand blaster was used to remove the remaining steel debris in a few holes.

24

Table 1. Screen characteristics

D (mm) S (mm) 3.25 1.25 3.50 1.00 3.75 0.75

D+S (mm) 4.5 4.5 4.5

H (%) 46.9 54.3 62.2

The porosity in the above table is calculated according to: H

nSD 2 / 4Wslot d

(1) 4

S

D 18

Figure 10. Model of the screen and PCB slot.

2.2 Data Reduction The following nomenclature designates the different geometries and velocities: V1, V2, V3, V4, and V5 are the five velocities studied in the wind tunnel. V1 is the minimum (1.5 m/s) and V5 is the maximum (7.5 m/s). More details follow in Boundary conditions (section 3.6). p1, p2, and p3 are the three screen porosities (see Table 1. Screen characteristics) studied. p1 is the maximum porosity (62.2%) and p3 is the minimum porosity (46.9%). q1, q2, and q3 are the heat fluxes used in the PCBs. q1 is the minimum heat flux (266.5 W/m2) and q3 is the maximum one (431.5 W/m2). More details can be found in Boundary conditions (section 3.6). S designates the short model, i.e., sub-rack depth equal to 200 mm; L refers to the large model, i.e., sub-rack depth 260 mm. 25

2.3 Velocity 2.3.1 Experimental procedure—inlet profile The system was always allowed to stabilize for approximately two minutes before taking the measurements with a cross hot-wire anemometer. The sample frequency used was 4 kHz and the sample time 20 sec. The average velocity and turbulence intensity were always obtained.

Figure 11. Traversing system used to measure the velocity profiles at the inlet of the sub-rack.

Twenty-one measurements along the inlet width were measured in order to get an accurate profile. A Mitutoyo traversing system (see Figure 11) was used with 0.01 mm digital resolution and 0.254 mm accuracy. The accuracy for the point closest to the wall may be worse. These profiles were used through the project; the average of those velocity profiles agrees ±5% with the laminar flow element. The laminar flow element measures the average velocity in the whole sub-rack, but the hot-wire measurements were done at the middle of the sub-rack and thus some disagreement with the laminar element was expected.

2.3.2 Experimental procedure—interior points When measuring the local velocities, the positioning of the probe was done manually. First the probe was put in its position, and then the control system for the wind tunnel cycled through five preset wind tunnel velocities. The wind tunnel was then turned off, the probe moved to its new position, and the local velocities for the five preset wind 26

tunnel velocities were obtained as described earlier. The sample frequency and the sample time were 4 kHz and 20 sec, respectively. The measurements before the screen were done along half of the depth of the screen (locations b1, b2 and b3 in Figure 12). z L

R a5

a3 a4

a1 a2

1a 2a 3a 4a 5a 6a 7a 8a 9a 10a Subrack Inlet

Entrance duct inlet

b1

Flow direction T

b3

1b 2b 3b 4b 5b 6b 7b 8b 9b 10b z x

Figure 12. locations.

b2

Pressure

EMC screen

x

velocity point pressure tap

and

velocity

The velocity measurements after the screen were done at 14.5 cm behind the screen (locations a1, a2, a3, a4 and a5 in Figure 12) making sure that the turbulence intensity was below 25%. The velocity measurements before the screen were performed at a distance about 21 mm perpendicular from the screen. Although it is not stated in paper I, some of the velocity measurements after the screen (a2, a3, a4 and a5) may not be trustworthy because of the obstacle that the hot-wire body probe produces on the flow. However, it is believed that the first reading (a1), in which the probe body is just 2 mm, can be trusted.

2.3.3 Uncertainty Analysis The Dantec calibration unit was used to calibrate the probe with a fourth-order polynomial curve and with linearization errors less than ±1%. During tests, the air temperature at the wind tunnel inlet was kept at around 21°C. Recalling that the wind tunnel is turned on and off for each position of a local velocity measurement, the repeatability of the wind tunnel should also be considered. The velocity was measured during several days at several occasions and the estimated uncertainty in the velocity is ±2.5%. In Table 2 the total estimated uncertainty is calculated as the square root of the sum of the squares of the maximum error of the hot-wire anemometer and wind tunnel repeatability. 27

Table 2. Summary of the total estimated uncertainty for the velocity measurements

Maximum error from calibration ±1% Wind tunnel repeatability ±2.5% Total ±2.7% In papers I to V the same velocity boundary conditions were used. This boundary condition comes from the hot-wire anemometer measurements. As the thermal and pressure measurements were done on different occasions, the wind tunnel repeatability should be taken into account. A flow laminar element (see Figure 6) was used as a checking device, making sure that the velocity was within the wind tunnel repeatability, as it actually was.

2.4 Pressure 2.4.1 Experimental procedure The pressure taps are placed flush at the middle of the sub-rack bottom wall at 65 mm before the screen, and flush in a PCB at 101.5 mm after the screen (see Figure 12). The pressure transducer is connected to a Campbell scientific 21X logger, which saves the data in the computer. The pressure measurement procedure described here is slightly different from the one used in paper I, where some valves were used. Some small leakage was found in some valves that were used for pressure measurements in paper I. Hence, the pressure measurements were repeated but without the valves. A pressure reading consisted of an average of 500 samples that were taken over 40 seconds. This process was repeated 5 times, once every minute to make up one series. Three series were obtained every ten minutes. Then the average of all the 15 values was taken.

2.4.2 Uncertainty Analysis The pressure taps are connected to an Autotran 750 pressure transducer by approximately 0.8 meters of tubing. The accuracy (maximum error) according to the manufacturer is ±1% of the full-scale reading of 25 Pa. For the highest velocity (if pressure readings were larger than 25 Pa) a similar pressure transducer with a full-scale reading of 100 Pa was used; the accuracy in this case was also ±1% of the full-scale reading. According to the measurements the pressure uncertainty (twice the standard deviation) ranges from an average of ±0.2 Pa at the lowest 28

velocity (V1§1.6m/s) to an average of ±0.5 Pa at the highest velocity (V5§7.5m/s). Since the velocity and pressure drop measurements were not obtained simultaneously, the repeatability of the wind tunnel may also affect the pressure drop measurement uncertainty. The pressure drop is approximately proportional to the square of the velocity. Hence, there is an uncertainty in the pressure drop due to the wind tunnel repeatability being estimated to twice the wind tunnel repeatability, i.e., ±5% (as shown above). The total estimated uncertainty is calculated as the square root of the sum of the squares of the maximum error of the pressure transducer, twice the wind tunnel repeatability and an average uncertainty during a run of the wind tunnel, i.e., around 0.3 Pa for the lowest velocity and 1.5 Pa for the highest velocity.

2.5 Temperature In this section, temperature measurement on a PCB dummy used in paper V is discussed.

2.5.1 Experimental procedure The temperature was measured using type T thermocouples connected to a Campbell scientific 21X logger via a Campbell multiplexer. Sixteen thermocouples were attached, eight at each side of the PCB (in order to duplicate the eight measurement locations). The thermocouple tips were soldered to the copper inside a 0.5u1mm channel. After the thermocouple attachment to the copper, the thermocouple channel was filled with conductive grease, leaving a smooth PCB surface. See paper V for more details and the location coordinates of the thermocouples. A PCB consisted of two copper plates of around 2 mm thickness in which had been milled a 0.4×1.5 mm channel (see Figure 13). In one of them, an electrically insulated heater cable (0.6 mm diameter) is placed and finally both plates are glued with epoxy and the help of a hydraulic press. In five of the fifteen PCBs the same heat flux was applied. The heat applied in each of them was the same, because the same length of heater cable was used and due to the serial connection, meaning the same current passed through each of the PCBs. Five heated PCBs were used to achieve heat symmetry conditions in the PCB in which the measurements took place (the one in the middle of the five).

29

The measurements were done automatically in such a way that a logger takes 10 samples (once every minute) if and only if the difference in temperature between two consecutive series is less than 0.05ºC in all the measurement locations at the same time. At this time steady state was assumed.

Figure 13. Details of a half PCB with the milled channel and the copper PCBs inside the sub-rack model.

2.5.2 Uncertainty Analysis The uncertainty of the thermocouples was estimated after calibration in an ice bath to ±0.1ºC. The uncertainty in the measurements is calculated by twice the standard deviation of the 10 temperature samples taken at each point; an average of this uncertainty for all the points and cases is equal to ±0.2ºC. As thermocouples were set at both sides of the PCB, at the same distance from the center plane of the PCB, the average difference between both sides’ measurements for all the locations and cases was ±0.2ºC. The total estimated temperature uncertainty is determined by the square root of the square of the previous uncertainties and is equal to ±0.3ºC. The heat losses were calculated by a three-dimensional CFD conduction analysis. The heat transfer coefficient on the PCB surface and the bulk temperature inside the PCB slot were taken into account. These two parameters were obtained from the detailed PCB slot model. Furthermore, the temperature between the double walls at both sides of the model was measured by thermocouples and a heat transfer coefficient (natural convection and radiation) equal to 6 W/m2K was assumed. In Figure 14 a detail of the model used to calculate the heat 30

losses is presented. The model size was 385,000 cells and the double precision Fluent solver was used. Plexiglass Copper

Heater Air Figure 14. 3D conduction pressure losses model (model in figure is mirrored around the symmetry plane and thus contains 385,000 x 2 cells).

The estimated heat losses are defined as the heat leaving through the plexiglass out of the sub-rack model and expressed as a percentage of the heat load applied to the PCB. Initially, the radiation was neglected, and the error due to this assumption has been estimated and also expressed as a percentage of the heat load applied to the PCB. These losses (conduction and radiation) ranged between 1.4% for the maximum velocity cases and 3.8% for the minimum velocity cases. Some further simulations have been done that take into consideration these conduction and radiation heat losses in order to quantify the error in the PCB temperature prediction. As can be seen in Table 3, the predictions for the high velocity (V5) are even closer to the experimental measurements, but for the low velocity level a worse result is obtained. The average disagreement in Table 3 is defined as the average disagreement of the temperature measured and predicted at the eight locations. Anyway, these heat losses do not give rise to a large uncertainty in the prediction of temperature. Table 3.Temperature average disagreement (% in ºC) between experiments and CFD predictions (RNG kH model), taking into consideration the heat losses

p2-V5-q1 (%)

p2-V5-q3 (%)

p2-V1-q1 (%)

p2-V1-q3 (%)

Nominal case

2.40

1.96

-4.60

-3.02

Nominal case without heat losses

1.9

1.24

-6.69

-5.75

31

Further, the temperature and velocity measurements were not taken simultaneously. This means that the repeatability of the wind tunnel should be considered. As stated before, the velocity was measured during several days at several occasions and the estimated repeatability is 2.5% of the velocity. Further simulations have been performed in order to study the average disagreement in the eight temperature locations when the velocity is varied ±2.5% of its nominal value in 4 cases: maximum and minimum value of the analyzed velocities and heat fluxes with the intermediate screen porosity. In Table 4, the average temperature disagreement at eight locations between the experimental values and CFD predictions, in which the nominal velocity is increased or decreased by 2.5%, are shown. It can be inferred that this uncertainty in the velocity does not give rise to a large uncertainty in the prediction of the temperature. Table 4.Temperature average disagreement (% in ºC) between experiments and CFD predictions (RNG kH model) with a change in the nominal velocity by 2.5%

p2-V5-q1 (%)

p2-V5-q3 (%)

p2-V1-q1 (%)

p2-V1-q3 (%)

Nominal velocity

2.40

1.96

-4.60

-3.02

Nominal velocity +2.5%

1.83

1.13

-5.57

-4.19

Nominal velocity -2.5%

3.11

2.83

-3.58

-1.79

The natural convection was ignored due to the position of the PCBs in the test rig. They were placed horizontally and that means that the Grashoff number is very small if we compare it with the square of the Reynolds number ( Gr Re 2 was always less than 0.059); thus, natural convection was ignored. Anyway, it was examined whether natural convection would be important if the PCBs were placed vertically as in reality. That was not the case studied in paper V, however it is interesting to know if large differences may be expected or not. In order to study that, the worst case (S-p1-V1-q3) was investigated, taking into consideration the gravity and still using the incompressible ideal gas model to calculate the density of the air. The average temperature difference over the whole PCB with 32

and without taking into consideration the buoyancy effect in the vertical PCB was equal to 1.3ºC (or 1.7%). Once the porosity increases, the input heat flux is reduced, or the inlet velocity is increased this difference is greatly reduced. At medium or high velocities the effect of buoyancy can totally be ignored.

2.6 Flow Pattern 2.6.1 Smoke visualization The smoke-wire technique consists of coating the stretched wires with oil and heating them up. After heating them, the oil evaporates and immediately after that the oil condenses, forming smoke-like microdroplets. The smoke was illuminated by xenon light. The visualized flow pattern was recorded on video. The experimental set-up is presented in Figure 15.

Figure 15. Experimental set-up.

33

Five wires were placed in the middle between two PCB dummies that are located in the middle of the sub-rack model (see Figure 16). d w 5 wire 5 w 4 wire 4

Bulk flow

z coordinate

w 3 wire 3

c

Frontier point Recirculation Bulk flow

w 2 wire 2 w 1 wire 1

b a x coordinate

Figure 16. Location of the wires after the screen.

The procedure for generating smoke is presented in Figure 17. First, the wires were inserted inside the sub-rack through 0.6 mm holes. Two cotton pieces with oil were attached at the plexiglass walls. The wire was long enough (more than twice the distance between the cotton pieces) to be easily moved and impregnated with oil. In this way, it was not necessary to open the wind tunnel in order to impregnate the wire with oil.

Flow

Syringe Wire

Weight Cotton is stuck on the wall

Horizontal wire movement in order to wet the wire

F i g u r e 1 7 . E x p e r i m e n t a l p r o c e d u re i n t h e s m o k e - w i r e t e c h n i q u e .

The objective of the videos was to identify the frontier line between the bulk flow with a high velocity level and the reversed flow (recirculation) with a low velocity level (see Figure 16). This frontier line is a function of several parameters. Some of those parameters are analyzed: the velocity level, the ratio between the inlet and the depth of the sub-rack, and the screen porosity. The frontier line is identified by five points (see w1-w5 in Figure 16). These points are defined as having the z34

component of the velocity equal to zero. In order to making it easier to see the frontier point, a black paper was placed on the PCB dummy. Another technique based on tufts (see Figure 18) was used, giving results very similar to CFD predictions. However, the uncertainty was difficult to estimate (Castiella, 2005), and the technique could only be used for high velocities.

Figure 18: Flow visualization using tufts.

2.6.2 Uncertainty Analysis First it was studied whether the position of the camera influenced the measured frontier points. After 60 videos it was concluded that this factor was of little importance due to the fact that the wires are close to the PCB. Actually, the uncertainty of the camera position was estimated to be up to about 0.5 cm (twice the standard deviation of the frontier point values observed in the videos). Furthermore, in order to decrease the uncertainty, each wire was recorded between two and five times. The uncertainty of wires 1 to 4 (and depth equal to 200 mm) in the observed values is around 0.5 cm (twice the standard deviation of the observed values of the five videos that were recorded per wire), for the wire 5; at the outlet and for the large case (d=260 mm), the estimated uncertainty increases up to 0.5–1 cm. The estimated total uncertainty for the first four wires and the short model (depth equal to 200 mm) is 0.71 cm and for the fifth wire and the large model is around 1 cm.

35

3 Computational Fluid Dynamics

3.1 Introduction to the CFD Method Computational fluid dynamics (CFD) is a way to calculate the fluid and heat flow in any geometrical domain by numerical methods. It can be called a whole-field method because it provides all the information in the whole numerical domain. The numerical domain is the result of discretizing the continuum domain in a set of volumes or points. Nowadays, CFD is a method that has vastly increased its use in industry due to the increase of computational capability in terms of memory and processors. Many papers that use CFD predictions for both chip level and system level of electronic equipment can be found. However, there is still a need to check the validity of the numerical models, turbulence models and mesh density distributions by experimental measurements. Most CFD software packages have three elements: the preprocessor, the solver and the postprocessor. The preprocessor is the software that is used to generate the geometry and the mesh (the discretized domain) and finally to set the boundary conditions. Then the solver applies numerical methods in order to convert the partial differential equations into a set of algebraic equations applied to the nodes of the mesh that can be solved by an iterative process. The third element is the postprocessor, which provides the ability to visualize the results. It also provides the tools to calculate e.g. mean values for a specified sub-domain. Fluid flow is governed by conservation laws: mass and momentum, (for non-isothermal flow the energy equation is added) together with some relations between fluid properties (e.g. the ideal gas law) and other relations: e.g. a linear relation between stress and strain (Newtonian fluids). The momentum equations are also known as the Navier-Stokes equations. The problem is that these equations are nonlinear partial differential equations that need to be solved by numerical methods. The continuity equation, the Navier-Stokes equations and the energy 36

equation for steady state incompressible flow can be written in the following form: wui wxi



w u j ui wx j



w u jT wx j

(2)

0



wP  Q’ 2ui wxi

D’ 2T

(3)

(4)

3.2 Turbulence At high Reynolds numbers, instabilities appear in the laminar flow that ends up in the turbulent regime. Turbulence is characterized by threedimensional chaotic flow with a high mixing capacity, thus increasing the momentum and heat exchange in the flow. It is also characterized by a huge spectrum of length, velocity and time scales (or eddies). The large scales are the energy-bearing eddies; they extract the turbulent kinetic energy from the main flow (due to main velocity gradients), and correlate well with the main flow and are thus anisotropic. Its characteristic length scale is related to the geometry of the domain. The large eddies form smaller eddies by a vortex-stretching mechanism. These smaller eddies receive the energy from the large energy-bearing eddies and transfer it successively to smaller and smaller eddies. This phenomenon, known as energy cascade, ends up in the smallest eddies that are dissipated into heat (internal energy) by the action of molecular viscosity. The length scale of the smallest eddies, also known as the Kolmogorov scale, depends on the value of the molecular viscosity and is considered isotropic. The production of turbulent kinetic energy depends on the generation of the large energy-bearing eddies (due to the main velocity gradients). The rate of dissipation of the turbulent kinetic energy into internal energy depends to a certain extent on the production and thus also of the large eddies. If the rate of production is equal to the rate of dissipation, the flow is in a state of equilibrium. When performing design work, what is interesting to know is not the instantaneous flow variables but, often, the mean quantities. Normally 37

this is what is measured when doing experimental investigations. This idea ends up in the Reynolds decomposition. This consists of decomposing the instantaneous flow variables (velocity, pressure, temperature…) into a mean value and a fluctuating value, as is indicated in equation 5. The mean value is a time-averaged value or an ensemble average. The mean value of the fluctuation terms is zero, but the mean value of a product of fluctuation terms is not zero. U i  u ic

ui

(5)

p P  pc t T  tc

If we apply equation 5 to equations 1–3, the Reynolds average NavierStokes (RANS) equation appears. In the present study, the flow is assumed to be steady-state, threedimensional, incompressible and turbulent. The buoyancy effect and radiation heat transfer are also assumed to be negligible. With these assumptions, and based on the Reynolds decomposition, the governing equations for the conservation of mass, momentum and energy are given by wU i wxi

0





w U jU i wx j



w U jT wx j



(6)



wP w  Q’ 2U i   uicu cj wxi wx j

D’ 2T 



w  u cj t c wx j







(7)

(8)

where P is the modified kinematic pressure and the unknowns,

u icu cj

and uict c , constitute the second-moment statistical correlation or socalled Reynolds stresses and turbulent heat fluxes.

3.3 Turbulence modelling The instantaneous real flow contains a very large length and time scale range. Hence, it requires a very fine mesh and time step in order to solve the Navier-Stokes equations. Nowadays, this is possible for simple geometries at low Reynolds numbers, but anyway a large number of 38

computers and a large amount of computational time are required, something that the industry still cannot afford. To resolve directly (without turbulence modeling) the instantaneous Navier-Stokes equations is called Direct Numerical Simulation (DNS). Some advanced turbulence models called Large Eddy Simulation (LES) also resolve the instantaneous flow variables, but only for the large eddies. For the small eddies, modeling is employed to resolve the time-averaged values of the flow variables. LES is also computationally very time demanding and thus is seldom used in industry. The RANS equations are not a closed set of equations; due to the nonlinear term of the original set of equations, a new term called the Reynolds stresses appears and thus new unknowns are added to the equation system. Actually, the Reynolds stresses are a symmetry tensor and thus, six new unknowns appear. These Reynolds stresses represent the increase in the momentum transfer due to the turbulence (correlations between fluctuating velocities). We have a closure problem due to a larger number of unknowns (13) than number of equations (5), and thus turbulence modeling is required. Turbulence modeling is the way to solve the closure problem, i.e., how to specify the Reynolds stresses and turbulent heat fluxes. One way to solve the closure problem is to use the Reynolds Stress Model (RSM). The RSM, (see Launder et al., 1975), or the so-called second-momentum model, is one of the most sophisticated tools currently used by engineers to predict turbulent flows. The aim is to solve the transport equations for the transport of the Reynolds stresses, u icu cj . The stress components are solved by a transport equation. A linear pressure-strain model available in Fluent 6.1 is used in the simulations. This model is not as computationally time demanding as the LES. The most popular model to approximate the Reynolds stresses is the eddy-viscosity turbulence model. The eddy-viscosity model is based on the Boussinesq assumption that makes an analogy between turbulent stresses and viscous stresses (given by Newton’s friction law). Therefore, the Reynolds stresses are proportionally related to the velocity gradients (strain) by an eddy-viscosity model for turbulence, and the turbulent heat fluxes are modelled using the eddy-diffusivity hypothesis in analogy with the eddy-viscosity hypothesis for the Reynolds stresses. uicu cj

2 2Q t Sij  G ijk 3

(9)

39

u ict c



Q t wT V t wxi

(10)

where Qt is the eddy viscosity, k is turbulent kinetic energy, Vt is the turbulent Prandtl number (which is constant in the present study and equal to 0.85) and Sij 0.5(wU i / wx j  wU j / wxi ) . The kinematic eddy viscosity by dimensional analyses can be expressed as the product of a turbulent length and velocity scale (using an analogy with the kinetic theory of gases). Several models have been implemented depending on the way to supply the velocity and length scale. These models range from the so-called zero-equation model to the two-equation models. In zero-equation models, the length scale is based on geometry and the velocity scale is calculated by an algebraic relationship. In the one-equation models, one transport equation is solved in order to calculate the velocity scale (normally, an equation for k is solved) and the length scale is calculated by an algebraic relationship. Finally, in the two-equation models, the platform of transport equations may be closed by two additional transport equations of two parameters related with the turbulent length and velocity scale. This model implies that the length and velocity scales of the mean flow and of the turbulence are proportional, and can be related by means of dimensional reasoning to turbulent kinetic energy, k, and one length-scale-related parameter like its dissipation rate, H, u=k0.5, l=k1.5H. Considering the above assumption, the turbulent eddy viscosity can be derived as, vt=CPk2H, and it is valid only when local isotropy in the turbulence field is assumed. H is given by H Q

wuic wuic wx j wx j

(11)

Thus, the two-equation eddy-viscosity model requires two additional transport equations for k and Hor another scale-related parameter like time scale Z Hk) to solve the spatial and temporal variation of the local velocity scale and the length scale.

40

3.4 Two-equation models This section is a summary of the two-equation turbulence models employed in this thesis. More details of each of them can be found in the papers or in the cited references.

3.4.1 The Standard kH Model The standard kH model (Launder and Spalding, 1974) employs, as has been already explained in the previous section, two transport equations for k and H. The employed closure coefficients V k , V H , CH 1 , CH 2 , C P have been empirically found based on several benchmark studies. w (U j k wx j

where S w (U j H wx j

w wx j

2S

ª§ Q t · wk º 2 ¸¸ «¨¨Q  » Q t S  H V k ¹ wx j » ¬«© ¼

(12)

S ij

0.5

ij

w wx j

ª§ Q t · wH º H H2 2 ¸¸ «¨¨Q  »  CH1 Q t S  CH 2 k k V ε ¹ wx j ¼» ¬«©

(13)

3.4.2 The RNG kH Model The coefficients of the standard kH are determined from a number of case studies of simple turbulent flows. Thus the kH has limited applicability, which yields poor performance for cases with complex flows. This poor performance is suspected to be due to inaccuracies in the H-equation. The Renormalization Group kH model (RNG; Yakhot et al., 1992) introduces an additional term in the H-equation and several of the standard-model coefficients are adjusted, which improves its performance in cases like streamline curvature (Yin et al., 1996), sudden expansion (Koronaki et al., 2000) and back-facing step (Speziale and Thangam 1992). The basic idea is to systematically filter out the smallscale turbulence to a degree that the remaining scales can be resolved (this is applied in large eddy simulations). This is done by the parameter K, which is the ratio between the time scales of the turbulence and the mean flow.

3.4.3 The Realizable kH Model In the Realizable kH Model (Shih et al., 1995), realizable means that by numerical clipping, which is introduced in the code, one can remove non-physical values of variables, e.g. negative normal stresses, from the 41

predictions and the Schwartz inequality for turbulent shear stresses is fulfilled. To achieve the realizability effect, the CP is no longer constant but a function of the turbulence fields, mean strain, and rotation rates. As this model includes the effects of mean rotation in the definition of the turbulent viscosity, it works better than the standard kH model for flows with streamline curvature. The k equation is identical to the standard model and the Hequation is based on the dynamic equation of the mean-square vorticity fluctuation at high Reynolds number.

3.4.4 The standard kZ Model The original kZ model (Wilcox, 1988) is based on model transport for the turbulent kinetic energy, k, and the specific dissipation rate, Z = H/k. The quantity Z may be taken as an inverse time scale of the large eddies. The model that has been used is the standard kZ model with low Re effects (Wilcox, 1998), where damping functions are used (see further details in Wilcox, 1998, and Fluent Inc., 2003).

3.4.5 The Shear Stress Transport (SST) kZ Model The original SST kZ model (Menter, 1994) blends the original kZ model in the inner layer and the kH model in the outer layer. In this way it is a model with good performance in boundary layer flows and does not suffer from the sensitivity to free stream values. The blending will take place in the wake region of the boundary layer. In order to blend the kH model and kZ model, the kH model has been transformed into kZ equations, and this causes a new term to arise: a cross-diffusion term.

3.5 Wall Treatments In this thesis, the main wall treatment that has been used is the enhanced wall treatment. It will be briefly described in this section.

3.5.1 Enhanced wall treatment For high Re models (i.e., kH, RNG kH and Realizable kH), the enhanced wall function (EW) was used as a wall treatment. The EW subdivides the near wall region into a viscous sub-layer and a fully turbulent flow. In the viscous sub-layer region a one-equation turbulence model is used (only the k equation is solved) and H is computed algebraically (see Wolfshtein, 1969). But in the fully turbulent flow the two-equation high Re models are used and thus H is computed from a transport equation. Finally, the 42

two sets of H equations are blended. The term wall distance turbulence Reynolds number ( Re y U k y / P ) is introduced to compute the interface between the two layers. For more information see Fluent 6.1 (2003).

3.6 Boundary Conditions Several CFD models have been developed during this project. A summary of the level of detail, geometry, and thermal details is shown in Table 5. Table 5. CFD models

Model I Model II Model III Model IV

Detailed or compact screen? Detailed Detailed Detailed Compact

Isothermal? Yes Yes No Yes

Entrance duct No Yes Yes Yes

Detailed model means that the screen holes have been modeled in detailed. Compact model means that the screen has been modeled as volume hydraulic impedance with several pressure loss coefficients and a coarser mesh. The boundary conditions are summarized in Table 6 and Figure 19. Table 6. Some boundary conditions of the CFD models

Inlet Inlet tempera turbulence Density ture intensity Model From Exp: From Exp: 21ºC 1.2 I Profile Profile Inlet velocity

Model II

Uniform

21ºC

Uniform*

Model III

Uniform

From Exp. (§21ºC)

Uniform*

Model IV

Uniform

21ºC

Uniform*

Pressure outlet Uniform: Set to 0

Uniform: Set to 0 (except small 1.2 profile for V5** in papers II and IV) Incompr Uniform: Set to 0 essible except small ideal gas profile for V5 1.2

Uniform: Set to 0 43

*

Turbulence intensity was set equal to 10%.

**

For the high velocity level (V5), a small pressure gradient was measured at the outlet. However, at the low velocity level (V1) there was no pressure gradient and a uniform pressure outlet boundary condition was used.

In Table 7, the pressure difference (in Pa) measured and used as a boundary condition in the simulations with the high velocity level is shown. Table 7. L-R pressure difference (Pa) at the outlet and V5 S-p1-V5 1.5

S-p2-V5 0.915

S-P3-V5 1.06

L-P1-V5 1.78

Due to symmetry conditions, only half of the PCB slot was modelled with the same dimensions and boundary conditions as in the experimental model. The dimensions of half of the slot for the four models are shown in Figure 19. Pressure Outlet

Pressure Outlet

W slot/2

9 mm

Symmetry boundary condition

Front walls

Bottom wall

Back walls

Apcb/2

Symmetry boundary condition 65 mm

Velocity Inlet PCB walls Symmetry plane

=280 mm

280 mm

Back walls

50 mm Symmetry plane

D

a+b

Front walls

Bottom wall Symmetry plane

500mm

D PCB walls Symmetry plane

ts

Model I

44

Subrack inlet

a

Velocity Inlet ts

Models II and III

Ainlet/2

Pressure Outlet W

slot/2

c=280 mm

Apcb / 2

Back walls Symmetry boundary condition

a+b

PCB

Front walls Subrack inlet A /2 inlet

a Bottom wall Symmetry plane

500mm

EMC screen PCB walls Symmetry plane

Velocity Inlet

Porous Media Volume ts

Model IV

Figure 19. Geometry of the employed CFD models.

The depths of the sub-racks used in the CFD predictions are summarized in Table 8. Table 8. Sub-rack depth employed in the CFD models

Model I

Model II

200 and 260

200 and 260 (papers II, III, IV) §212 (paper VI)

Model III Model IV

200

§212

In Table 9 the magnitude of the average inlet velocity is shown for the cases simulated in CFD. The average is obtained, as has been already said, by doing an area-weighted average from the hot-wire measurements along the inlet width of the sub-rack. Table 9. Average inlet velocities

S-p1-V1 S-p1-V3 S-p1-V5 S-p2-V1 S-p2-V3 S-p2-V5 Inlet velocity (m/s) 1.61 4.44 7.49 1.65 4.43 7.57 S-p3-V1 S-p3-V3 S-p3-V5 L-p1-V2 L-p1-V5 Inlet velocity (m/s) 1.60 4.42 7.31 3.21 7.66

In Table 10, the thermo-physical properties of the solid materials for model III are shown. 45

Table 10. Thermo-physical properties of the solid materials

Steel Copper

Density (kg/m3) 8030 8900

Specific heat, cp, J/kgK 502.5 385

Thermal conductivity, W/mK 16.3 395

In the middle plane of the PCB is set a uniform heat flux boundary condition. For the rest of the walls (front walls and back walls, see Figure 5) an adiabatic boundary condition is used. For the outlet boundary condition the possible reversed flow temperature was set 4 degrees higher than the ambient temperature (V5) and 6 degrees higher than the ambient temperature (V3). Four heat fluxes were applied to the mid-plane of the PCB in the CFD model. The first three of the following heat fluxes (W/m2) are the same as those in the experiments: 266.5, 353.3, 431.5 and 537.6.

3.7 Numerical aspects To numerically solve the flow domain, first the continuum geometry should be discretized, and then also the differential equations by approximating the equations using the values at the discrete points. There are three well-known ways to discretize: the finite difference method, the finite element method, and the finite volume method. The finite difference method is based on a differential form of the conservation equations, where the derivatives are replaced by an approximation based on truncated Taylor series expansions. The finite element method approximates locally the studied variable by a low order polynomial, and then one substitutes that polynomial in the differential equation. As it is an approximation, a residual is generated. The objective is to minimize that residual. For this purpose, weighting functions will be used in the solution procedure. The finite volume method is based on the integral form of the conservation equations. Then derivatives are substituted by profile assumptions, yielding a set of algebraic equations This integral approach makes sure that conservation is fulfilled in each of the volumes in which the domain is divided into and thus also in the whole domain. The finite volume method employed by the commercial CFD software Fluent has been used throughout the thesis.

46

3.7.1 Numerical schemes Fluent 6.1 was used for the simulations. The governing equations were solved with a segregated scheme. The momentum, turbulent kinetic energy and turbulent energy dissipation equations were solved with second order upwind schemes. The pressure-velocity-coupling algorithm SIMPLE was used to solve the continuity equation. The central difference scheme is used for the diffusion terms and the second order upwind scheme is used for the advective terms in all the papers. Furthermore, for the continuity equation (the pressure equation) a second order scheme is used in all the detailed simulations and the PRESTO scheme (PREssure STaggered Option, see details in Fluent 6.1, 2003) for the compact model. The PRESTO scheme uses the discrete continuity balance for a staggered control volume about the face to compute the staggered pressure; it is analogous to the staggered grid approach described by Patankar (1980). After the discretization, a set of algebraic equations are obtained that are solved by iterative procedures. In order to stabilize the iterative procedure, it is convenient that the studied variable does not change abruptly and thus relaxation techniques are used. In this case a linear relaxation is used. This adds a factor between the variable value at i and i1 iteration to calculate a new value for the ith iteration, e.g. vi,new= Dvi+ (1-D)vi-1. The following under-relaxation factors have been used for the pressure, momentum, turbulent kinetic energy, the dissipation rate of turbulent kinetic energy and energy: 0.3, 0.7, 0.8, 0.8 and 1. The simulation was conducted on a workstation (2.5 GHz).

3.7.2 Mesh density sensitivity After a study of the mesh distribution, it was seen that a finer mesh before and after the screen was required in order to get a correct flow pattern. The modelling of the EMC screen was also studied. It was shown that just one layer of volumes in the screen was not enough to get a correct flow pattern. A model of the screen (1 mm thickness) using five layers obtained the best results. The mesh density sensibility was also checked by using a mesh with almost double the number of cells. It was shown that the difference in the local velocities was negligible. For the pressure drop some differences were encountered, but as these were not large, it was decided to continue with the original mesh. 47

Figure 20. Mesh details in the detailed (above) and compact models (left).

3.7.3 Convergence criteria For all turbulence models, 7000 iterations were shown to be enough in order to reach convergence. This was checked by running 3000 extra iterations for all turbulence models (S-p1) and for both velocity levels. The relative difference, after those extra iterations, in the total static pressure drop was always less than 0.5% (except for one case: SST kZ model for V5) and in the local velocity after the screen was always less than 0.5%. The non-dimensional residuals of all the variables were always less than 1.5×10-6 (after 10000 iterations) for the kHmodels (V1 and V5) and kZ model (V1). However, for the kZ models (V5) the nondimensional residuals were just less than 1×10-4. For the compact model, between 1250 and 2500 iterations were required to get a convergence result. In the compact model, convergence was assumed when all the non-dimensional residuals were less than 1×10-5. However for a few of them, the non-dimensional residuals were just less than 5×10-5.

48

3.7.4 Validation of the numerical models There are always differences between a numerical solution and reality. This may be due to numerical errors caused by discretization errors, or it may that the chosen turbulence model is not suitable for a particular situation, the geometry simplifications, etc. The fact is that it is necessary to validate the numerical solution. There are normally three ways to do it. The first is to compare with an analytical solution, but there is no analytical solution for complex geometries and flows. Another way is to refine the mesh until a mesh independent solution is obtained, and the third way is by comparing with experimental measurements. However, it should be emphasized that measurements are not free of errors and uncertainties. The way to validate the CFD simulations in the present thesis has been by experimental measurements (pressure, local velocities, flow patterns and temperature).

49

4 Validation of the numerical detailed models

In this chapter, the validation of the detailed CFD model against the experiments will be presented. After evaluation of the five two-equation models, presented in the previous Chapter, against the experimental measurements, the kH RNG model was the one that performs best. Thus, all the CFD values in this and in the following Chapters are based on simulations that use the kH RNG model. It is intended to show the velocity and pressure agreement with some experimental measurements in locations before and after the screen. After that, some flow pattern features between CFD and smoke-wire visualizations will be compared. Finally, the temperature predicted by CFD and measured by thermocouples at eight locations of the PCB will be shown. This section is intended to validate the detailed model from hydraulic and thermal points of view for the range of parameters shown in Table 11. Table 11. Range of parameters analyzed in the experimental model

a/d 0.19 to 0.25

V (m/s) 1.5 to 7.5

H (%) 47 to 62

q (W/m2) 260-430

In this project, several models have been developed. Model I was an interesting intermediate model that paved the way for a better approach: Model II. Model II was the one used in the parametric study and the one that the compact model has been based on. Therefore, Model II should be validated in the present Chapter.

4.1 Velocity and pressure In paper IV the velocity magnitude and static pressure drops at several locations before and after the screen were compared with the CFD predictions. An average disagreement around 5% was found for the 50

velocity magnitude. This comparison was based on an average between the four measurement locations (a1,b1,b2 and b3 in Figure 12) in 20 cases (the combinations between V1, V5, p1, p2, p3, S and L). From the pressure drop point of view, the total static pressure drop is of interest; however, this is difficult to measure since the pressure profile at the sub-rack inlet is non-uniform. In order to validate the pressure field, it was decided to take pressure drop measurements before and after the inlet of the sub-rack and after the screen, in places where the pressure gradients were smaller than at the inlet of the sub-rack and to make the measurement more reliable. Furthermore, it was not physically possible to measure right at the sub-rack inlet due to the location of the traversing system used for the velocity measurements. An average disagreement of 5–10% for the static pressure drop was encountered between the CFD predictions and the experimental measurements. This comparison was based on an average of four pressure drop locations close to the inlet and outlet (between pressure taps T and L, between T and R, between 1b and L, and between 1b and 1a, see Figure 12) in 20 cases (the combinations between V1, V5, p1, p2, p3, S and L).

4.2 Inlet velocity profiles In Figure 21, Figure 22, and Figure 23, the flow at the inlet of the subrack is shown. As can be seen, the flow just before the inlet can be considered almost perpendicular to the inlet. The velocity in these figures was the minimum velocity, but it is expected that with a higher Reynolds number, the flow would be also perpendicular to the inlet, due to the higher inertia of the flow. And thus, it is shown that only one component-velocity profile is needed to characterize the boundary condition. Inlet of the sub-rack

51

Fi g u r e 2 1 . F l o w p a t t e r n a t t h e i n l e t o f t h e s u b - r a c k . E a c h f r a m e i s separated by 0.065 sec. Short model, p1, V1. Inlet of the sub-rack

Figure 22. Flow pattern at the inlet of the sub-rack. Each frame is separated by 0.065 sec. Short model, p3, V1.

Inlet of the sub-rack

Figure 23. Flow pattern at the inlet of the sub-rack. Each frame is separated by 0.065 sec. Large model, p1, V1.

The result of using uniform velocity and turbulence intensity profiles (always 10%) at the entrance duct inlet (see Figure 5) was validated by a comparison between CFD and experimental values of the velocity and turbulence intensity profiles at the inlet of the sub-rack. The agreement between the measured and predicted profiles at the sub-rack inlet, presented in Figure 24 and Figure 25, not only validates the velocity and turbulence intensity at that location but also shows that an entrance duct of 500 mm in length is enough to get fully turbulent developed flow at the sub-rack inlet. The results are rarely sensitive to turbulence intensity and hydraulic diameter at the inlet boundary conditions.

52

ti-exp v-exp

50

1.6 1.4

40

1.2 1

30

0.8 20

0.6 0.4

10

0.2 0

0 0

0.01

0.02

0.03

0.04

0.05

Position z (m)

Bottom plane

ti-cfd

v-exp

60

1.8

Velocity v (m/s)

Turbulence intensity ti (%)

v-cfd 2

9 8

50

7 6

40

5

30

4

20

3 2

10

1

0 0

0.01

0.02

0.03

0.04

0 0.05

Position z (m)

Bottom plane

Figure 24. Experimental vs. RNG. v and turbulence intensity profiles at the inlet cross-section of the sub-rack (S-p1-V1).

v-cfd

Velocity v(m/s)

ti-cfd

Turbulence intensity ti (%)

ti-exp 60

Figure 25. Experimental vs. RNG. v and turbulence intensity profiles at the inlet cross-section of the sub-rack (Sp1-V5).

4.3 Flow Pattern In Figure 26–Figure 29, the PCB area is depicted and the frontier line between the bulk flow and the recirculation (see w1–w5 in Figure 16) is shown. Both the line seen in the flow visualization (see section 2.5) and the line predicted by CFD are presented. 275

250

250

225

225

200 CFD Smoke

175 150 125 100 75

PCB height (mm), z coordinate

PCB height (mm), z coordinate

275

200

150 125 100 75

50

50

25

25

0

CFD Smoke

175

0 0

25

50

75 100 125 150 175 200

PCB depth (mm), x coordinate

Figure 26. Validation for the following case: depth=200 mm, V1= 1.60m/s, porosity 1=62.2%. See x and z coordinates in Figure 16.

0

25

50

75 100 125 150 175 200

PCB depth (mm), x coordinate

Figure 27. Validation for the following case: depth=200 mm, V5=7.50 m/s, porosity 1=62.2%.See x and z coordinates in Figure 16.

53

275

250

250

PCB height (mm), z coordinate

225 200 CFD Smoke

175 150 125 100 75

PCB depth (mm), z coordinate

275

225 200

CFD Smoke

175 150 125 100 75

50

50

25

25 0

0 0

25

50

75 100 125 150 175 200

PCB depth (mm), x coordinate

Figure 28. Validation for the following case: depth=200 mm, V5=7.50 m/s, porosity 3= 46.9%. See x and z coordinates in Figure 16.

0

25 50 75 100 125 150 175 200 225 250 PCB depth (mm), x coordinate

Figure 29. Validation for the following case: depth=260 mm, V2=3.2 m/s, porosity 1=62.2%. See x and z coordinates in Figure 16.

It can be concluded from Figure 26 through Figure 29 that the detailed CFD model is able to predict the right change in direction when the inclined flow collides with the interior face of the holes. Thus it is a model that could be used to predict how large the bulk flow area is (see Figure 16), which is an important parameter when placing electronic components on a PCB.

4.4 Temperature Figure 30 shows the temperature increase (temperature minus inlet temperature) for the eight measured locations and for eight cases. Further, the inlet temperature (ºC) and the PCB heat flux (W/m2) for each of these cases are shown. A comparison between the CFD temperature increase (inside square) and the experimental values (without square) is presented as well. The maximum and minimum velocity levels, screen porosity and heat flux can be distinguished in these eight cases. From a qualitative point of view, it can be observed that the CFD predictions follow the same tendency as the experimental measurements. The temperature gradients along the x and z directions (see the coordinates in Figure 2) are satisfactorily predicted. The model seems to predict the temperature field fairly well for an extensive range for the three parameters (screen porosity, inlet velocity and heat flux). The average deviations from the experimental temperature values are less than 4%. 54

a) p3-V1-q1 36.6 34

35.5 8 33.3

3

36.1 33

34.8 32.2 7

2

34.9 31.6

1

34.1 30.8

4

b) p1-V1-q1 37.4 35.6

36.1 8 34.6

3

37.2 34.9

35.5 33.6 7

33.4 30.7 6

2

36.3 33.9

32.4 29.8 5

1

35.9 33.4

4

d) p1-V1-q3

54.7 8 54.3

4 61.1 58.4

59.2 8 56.8

3

55.5 53.8

53.6 52.5 7

60.8 3 57.2

58.2 55.2 7

34.2 32.3 6

2

53.6 51.6

51.4 50.1 6

56.2 53 6

33.3 31.4 5

1

52.5 50.3

49.8 48.6 5

59.4 2 55.6 58.7 1 54.8

54.7 51.6 5

Tinlet=21.0

Tinlet=20.8

Tinlet=22.2

Tinlet=21.3

qPCB=266

qPCB=263.9

qPCB=431.1

qPCB=431.5

e) p3-V5-q1 13 13.7

12 8 12.9

3

12.7 13.4

11.5 12.3 7

2

11.7 12.5

10.4 11.4 6

1

10.8 11.9

9.5 10.9 5

4

c) p3-V1-q3 56.3 55.4

4

f) p1-V5-q1 13.2 14.2

12.2 8 12.8

3

13.3 13.9

11.8 12.2 7

2

12.6 13.3

10.9 11.5 6

1

12.1 12.9

10.2 11 5

4

g) p3-V5-q3 20.7 22.7

19.3 8 20.9

3

20.4 22

18.4 19.9 7

2

18.7 20.6

16.6 18.6 6

1

17.3 19.6

15.3 17.7 5

4

h) p1-V5-q3 22.5 22.9

20.9 8 20.8

3

22.7 22.5

20.3 19.9 7

2

21.6 21.5

18.8 18.7 6

1

20.8 20.9

17.5 17.8 5

4

Tinlet=21.2

Tinlet=20.7

Tinlet=22.5

Tinlet=20.9

qPCB=266.2

qPCB=263.7

qPCB=431.7

qPCB=432.1

F i g u r e 3 0 . A c o m p a r i s o n o f t h e t e m p e r a t u r e i n c r e m e n t s (temperature minus inlet temperature) b e t w e e n e x p e r i m e n t a l a n d C F D v a l u e s ( i n s i d e b o x e s ) f o r s e v e r a l velocities, porosities and heat fluxes.

55

5 Cor relations for pressure drop, f low patter n and compact model

Using the detailed model that has been experimentally validated in the previous Chapter, a larger parametric study based on 174 detailed CFD cases was performed. Based on this detailed CFD parametric study, correlations for the pressure drop and two flow pattern coefficients were developed. Furthermore, the detailed parametric study was used as a reference to develop a compact model for the screen based on a twocoefficient volume hydraulic resistance. Seven parameters were studied: velocity, inlet height, screen porosity, PCB thickness, inlet-screen gap, distance between two PCBs and screen thickness. The nomenclature of the analyzed parameter is shown in Figure 31. d

z

f x

S

tpcb

Bulk flow c Recirculation Bulk flow b a

D Wslot

ts

Figure 31. Parameters used in the parametric study.

Each parameter may take four different values. The total number of possible combinations is more than 16,000 simulations (47 possible choices). Due to the fact that each of the detailed simulations took between 1.5 and 4 days to converge (using a 2.5 GHz processor), it was not reasonable to try the whole set of combinations. Instead, 174 simulations were performed. Each of the four possible values of each 56

parameter was used in at least 14 simulations. Further, all the possible combinations between any two parameters (with the rest of the parameters able to take any value) from Table 12 and Table 13 have been used in at least one simulation. The same 174 cases have been performed using the porous media approach. Table 12. Analyzed parameters (geometrical dimensions in mm); d=209.79 mm and Wslot=14.25 mm

a 20 35 50 65

H(%) 64.3 49.2 36.2 25.1

b 1.1 5 10 15 20

ts 0.5 1 1.5 2

tpcb 1 2 3 4

v (m/s) 1.5 4 6.5 9

Table 13. Analyzed parameters (geometrical dimensions in mm); d § 214 mm and Hscreen=60%

Wslot 13.5 16.5 22.5 25.5

a 20 35 50 65

b 5 10 15 20

ts 0.5 1 1.5 2

tpcb 1 2 3 4

v (m/s) 1.5 4 6.5 9

d 214.3 214.3 214.3 213.9

Note that in Table 13, d (sub-rack depth) can be considered constant because of the negligible difference in its values.

5.1 Data Reduction It is interesting to predict the total pressure drop, but in a typical subrack configuration this should be divided between a static pressure drop and a dynamic pressure drop. Due to the deceleration imposed by the screen and the change between the cross-section area at the inlet and at the outlet, the velocities at those faces are different and should be taken into consideration to predict the total pressure drop. Therefore, the pressure drop has been divided into static and dynamic pressure drops. The total static pressure drop 'ps is defined as the weighted area average of the static pressure profile at the inlet, less the average static pressure at the outlet. That implies that the total static pressure drop depends to a large extent on the static pressure profile at the inlet of the sub-rack. The dimensionless static pressure drop is defined by 57

'p s

'p s*

2 0.5Uvinlet

The dynamic pressure drop, 'pd , is defined as the weighted average of the dynamic pressure at the inlet, minus the weighted average of the dynamic pressure along the area of the outlet through which the bulk flow is going out, i.e., outlet area minus area in which there is reversed flow (see parameter, f, in Figure 31). The dynamic pressure in the area in which reversed flow exists is ignored due to the very low velocities. The dimensionless dynamic pressure drop is defined by 'p d 2 0.5 Uv inlet

'p d*

The dimensionless wetted area, Aw* is the ratio of the area after the screen in which the bulk flow is present to the total area. The bulk flow is defined as that in which the z- velocity-component is larger than zero (see Figure 3). It has been analyzed in a plane inside the boundary layer along the PCB and thus after the screen. Aw*

Aw Apcb

0 d Aw* d 1

Another interesting parameter is the normalized RMS (root mean square) factor; i.e., how uniform the flow after the screen is. From a mathematical point of view, it is calculated as a normalized standard deviation around the mean velocity. It shows how large the velocity gradients along the x direction on three planes perpendicular to the zcoordinate are at 1.5 cm, 14 cm (half height) and 28 cm (at the outlet) after the screen (see Figure 16). Briefly, the smaller the velocity gradients are, the more homogeneous the flow and the smaller the RMS* will be. The analyzed RMS* is the average of the three cited planes and it is calculated for each plane in the following way: n

¦ A (v i

i

 v pcb ) 2

i 1

RMS *

A pcb

RMS * t 0

v pcb

vpcb corresponds to the velocity in the PCB slot with an RMS* factor equal to zero. 58

v pcb

Ainlet vinlet A pcb

The RMS* factor and the wetted area are complementary values. The former gives an idea of how uniform the flow after the screen is, and the latter shows the percentage of the area without recirculation but does not supply information about the evenness of the flow pattern after the screen. The nomenclature employed for the geometrical parameters is depicted in Figure 31. In order to convey the importance of this factor, Figure 32 shows four simplified qualitative examples (velocity profiles along the x-coordinate) with quantitative values of the normalized RMS* factor. The four examples are based on the same vpcb but with different RMS* values. As can be seen, the wetted area ratio for the first three examples in Figure 32 is the same, but the RMS* factors are different. V

V RMS*=0

RMS*=0.25

Aw*=1

Aw*=1

Vpcb

Vpcb d

V

x

0.75 V pcb

1.25 Vpcb d

x

V RMS*=0.5 Aw*=1

1.5 V pcb

0.5 Vpcb d

RMS*=1 Aw*=0.5

2 Vpcb x

d

x

Figure 32. Quantitative RMS* values from four simplified flow patterns with the same mean velocity (vpcb).

59

5.2 Pressure drop and flow pattern correlations based on the detailed CFD parametric study 5.2.1 Total pressure drop Five parameters are of importance in predicting the dimensionless total pressure drop; nine constants are used. As can be seen in Table 14, the porosity and the ratio a/d are the main parameters to predict the total pressure drop. The achieved R2 value is 0.99223 (see Figure 33) and all the predicted values are inside the ±15% of the observed values. The Reynolds number is defined in the following way: Re Uvinlet d h P , where the hydraulic diameter is based on the inlet area used in the CFD model:

dh

2(Wslot  t pcb )a (Wslot  t pcb )  2a

n6 ª Re n1 t n2 a n3§ t ·n5 W ºª a n8 º § · § s · § · ¨ pcb ¸ § slot · § · n7 n8 'pt* C«¨ ¸ ¨ ¸ ¨ ¸ ¨ ¨ ¸ H »«C¨ ¸  F H » ¸ «© 10000¹ © d ¹ © d ¹ © d ¹ © d ¹ »¬« © d ¹ ¼» ¬ ¼

Table 14. Correlation parameters for the 'pt* correlation

C

n1

n2

n3

n5

1.34860 -0.02207 -0.04466 -0.34363 0.08657

F

n6

n7

n8

0.26918 -0.13107 -2.04307 2.28047

60

5

4 Predicted values

+/- 10% 3

2

1

0 0

1

2 3 Observed values

4

5

Figure 33. Evaluation of the correlation for the total essure drop, R2 = 0.99223.

5.2.2 Dimensionless wetted area The following correlation is not applied when b is less than 5 mm; it is therefore based on 154 simulations (the simulations with a value of b equal to 1.1 mm have been discarded). The reason for this is that the low-pressure zone in the corner between b (see Figure 31) and the screen almost disappears, and thus the recirculation zone after the screen produced due to this low pressure greatly decreases. No good correlation was obtained with such a small b value. The main parameters are the ratios a/d and ts/d; the rest of parameters have a similar relative importance. In this case also the ratio b/d is not important. The nine constants that are used appear in Table 15. The obtained R2 is equal to 0.94201 (see Figure 34). All the predicted values have a disagreement of less than 22% of the observed values and most are within ±10%, see Figure 34. AW*

n6 ª Re n1 t n2 a n3 § t ·n5 W ºª a n8 º § · § · § s · § · ¨ pcb ¸ § slot · n7 n8 C«¨ ¨ ¸ H »«C¨ ¸  F H » ¸ ¨ ¸ ¨ ¸ ¨ ¸ «© 10000¹ © d ¹ © d ¹ © d ¹ © d ¹ »« © d ¹ »¼ ¬ ¼¬

Table 15. Correlation parameters for the Aw* correlation

C

n1

n2

n3

n5

9.11556632 -0.09088 0.09596

0.91549

0.08392

F

n6

n8

-9.018978

-0.24372 -1.07545 -0.012546

n7

61

1.2 1 Predicted values

+/- 10% 0.8 0.6 0.4 0.2 0 0

0.2

0.4 0.6 0.8 Observed values

1

Figure 34. Evaluation of the correlation dimensionless wetted area, R2 = 0.94201.

1.2

for

the

5.2.3 RMS* factor For this case, the simulations with a value of b equal to 1.1 mm were not taken in consideration either, and thus the correlation is based on 154 simulations. The ratio a/d and the porosity are the main parameters, with the nine constants that appear in Table 16. The achieved R2 is also good: 0.98096 (see Figure 35). Most of the values have a disagreement less than 20% of all the observed values and a majority of those are within ±10%, see Figure 35. RMS*

ºª a n8 ª Re n1§ t ·n2 a n3 § t ·n5 § W ·n6 º § · § · s § · ¨ pcb ¸ n7 n8 C«¨ ¨ slot ¸ H »«C¨ ¸  F H » ¸ ¨ ¸ ¨ ¸ ¨ ¸ »« © d ¹ «© 10000¹ © d ¹ © d ¹ © d ¹ © d ¹ »¼ ¼¬ ¬

Table 16. Correlation parameters for the RMS* correlation

62

C

n1

n2

n3

n5

0.36143

0.07993

-0.22809

4.80997

-0.16161

F

n6

n7

n8

0.13339

0.23425

0.93894

-5.52688

2 +/- 10% Predicted values

1.5

1

0.5

0 0

0.5

1 1.5 Observed values

2

Figure 35. Evaluation of the correlation for the RMS* factor, R2 = 0.98096.

5.3 Methodology to develop a compact model based on a porous media approach 5.3.1 Methodology and validation The objective is to achieve two pressure loss coefficients that define the screen in such a way that the total pressure drop and flow pattern after the screen would be well defined and accurately predicted by these two parameters. The approach is a porous media model that uses a volume hydraulic impedance defined by two directional loss coefficients. The porous media volume acts as a momentum sink in the momentum equation: That momentum sink in general is due to viscous losses (proportional to the velocity) and inertial losses (proportional to the velocity squared) that take place in the porous media volume. In the case of the analyzed perforated plates with a small thickness (between 0.5 and 2 mm), the viscous losses can be ignored compared to the inertial losses and thus we can define the momentum sink as: Si

1 § · ¨ Cij v mag v j ¸ 2 © ¹

63

§ C xx ¨ ¨ 0 ¨ 0 ©

C ij

0

0 · ¸ 0 0 ¸ 0 C zz ¸¹

Cij physically represents pressure loss coefficients per unit of length, i.e. §1 · Cij ¨ Uv j vmag ¸ ©2 ¹

’p pmedia

Due to the volume blockage of the screen is not physically present in the porous model, the velocity formulation that has been used and that Fluent uses by default in the porous media is a superficial velocity based on the volumetric flow rate that ensures the continuity of the velocity vectors across the porous volume interface and thus is not a physical velocity (the velocity inside the holes). One of the coefficients, Czz (see Figure 36), is related to the inertia losses in the screen. These inertial losses are mainly the contraction and expansion that the flow suffers when approaching and just after passing through the screen holes. The second parameter is related to the resistance that the screen does to the flow; it is the coefficient that straightens the flow and is a function of the screen thickness, hole diameter, and flow angle, although other parameters may affect this opposition in some way. d

z

f x

Porous model

Czz

Bulk flow c Recirculation Bulk flow

Cxx ts

b a

Figure 36. Pressure loss coefficients in the volume hydraulic model.

The methodology that was employed was an iterative process. First, it was based on a first approximation and then further corrections (either extrapolations or interpolations of the previous estimated coefficients) until a good agreement with the analyzed outputs ('pt*, AW*, and RMS*) was found, having always as a reference the detailed model. 64

A summary of the employed methodology is shown in Figure 37, and more in detail can be found in paper VII.

Step I

Step II

5 first initial Cxx and Czz New estimation of Cxx and Czz The best Cxx and Czz from all the runs are taken

Step III

Average disagreement for the outputs less than 5%?

No

Yes

Is it possible to get a correlation for both Cxx and Czz?

Yes Correlation for Cxx and Czz, as a function of the geometrical parameters and Re

No Step IV

Fix one coefficient, for example Cxx, according to a correlation based on step III Validate correlation looking at the outputs (' Pt*,

Step V

RMS* and Aw*) based on the coefficients from the correlation vs. outputs from detailed model

Figure 37. Employed methodology.

65

As the coefficients are in some way coupled, it was necessary to fix one of the coefficients by one correlation and then to correct the other coefficient by further estimations (or correction of the coefficients). Finally, it was possible to also obtain a correlation for the second coefficient. 5.3.2

Correlation for two directional loss coefficients

The correlation for Cxx is presented below. The coefficients that are used in the correlation are presented in Table 17. ª Re n1 t n2 a n3 b n4 § t ·n5 º § · § s · § · § · ¨ pcb ¸ n6 » Cxx C«¨  H ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ «© 10000¹ © d ¹ © d ¹ © d ¹ © d ¸¹ » ¬ ¼ Table 17. Correlation parameters for the Cxx correlation

C

n1

n2

n3

50000

0.091301

1.285787

-0.982199

n4

n5

n6

-0.237446

-0.269083

0.392687

This correlation shows the way in which the parameters affect the inplane directional loss coefficient: an increase of Re and a decrease of a and b makes the impact of the flow more perpendicular to the interior face of the holes and thus it implies an increase of Cxx—the larger the screen thickness (ts) and porosity (H) are, the larger the diameter and the interior face area, and thus it means an increase of Cxx. An increase of the PCB thickness (tpcb) seems to provoke the flow to impinge less in some holes and the Cxx decreases. The correlation for Czz is presented below. The coefficients used in that correlation are presented in Table 18. Czz

ª§ Re ·n1§ t ·n2 º n3 C«¨ ¸ ¨¨ s ¸¸ H » «¬© 10000¹ © d ¹ »¼

Table 18. Correlation parameters for the Czz correlation

66

C

n1

n2

n3

10.19002

-0.038945

-0.80090

-2.32410

It is clear that the porosity is the parameter of most influence; a decrease in porosity implies an increase of the Czz coefficient. The influence of the screen thickness is not negligible and the influence of the Re number is very small. It is important to emphasize that these two correlations should not be applied out of the range of Table 12 and Table 13.

Predicted values by the correlation

As the Cxx coefficients were fixed by means of a correlation, the values predicted by the correlation for Cxx are of course the same (R2=1) as the ones used in the original compact model (see paper VII). These Cxx coefficients range between 200 and 9000.

30000

20000

10000

0 0

10000 20000 30000 Original set of estimated values

Figure 38. Original set of estimated Czz values vs. Czz values predicted by the Czz correlation (R2=0.98).

However, the values of Czz predicted by the correlation for Czz are not the same (R2=0.987) as those of the original compact model (see paper VII and Figure 38) and should be validated by checking the outputs. In Figure 39, Figure 40, and Figure 41, the 'pt*, Aw* and RMS* values from both the detailed model and the model that uses the values from the correlations are shown.

67

5

3 Based on compact model (using the correlations)

Based on compact model (using the correlations)

+/-10% 4

3

2

1

2

1

0

0 0

1

2

3

4

5

Figure 39.'pt*: Detailed model vs. compact model (using Cxx and Czz values predicted by the correlations).

1

+/-10% RMS

0.75

Figure 40. RMS*: Detailed model vs. compact model (using Cxx and Czz values predicted by the correlations).

'pt*

0.5 0.25 0 0

0.25

0.5

3

2

Table 19. Average disagreement between the detailed model and the compact model that uses the loss coefficients from the correlations

1.25 1

0

Based on the detailed model

Based on the detailed model

Based on compact model (using the correlations)

+/-10%

0.75

1

1.25

(%) Average 3.1 disagreement: Maximum 14.2 disagreement:

Aw* (%) 6.4

RMS* (%) 9.2

24.7

39.4

Based on the detailed model

Figure 41. Aw*Detailed model vs. compact model (using Cxx and Czz values predicted by the correlations)

In Table 19 (above) the average disagreement (for the 174 cases) between the detailed model and the compact model that uses the pressure loss coefficients predicted by the correlations is presented for the three outputs. As can be seen, good agreement between the detailed model and the compact model that uses the coefficients from the correlations has been achieved. It is important to remember that the correlations that have been developed were using an entrance duct in the numerical model. When 68

using correlations for design, it will be interesting to also use an entrance duct. As has been said, this is a good way to use better boundary conditions than just uniform profiles.

5.3.3 Mesh density and CPU savings The same y+ (with values close to 1) values as in the detailed model were always used. The amount of layers used in the thickness of the EMC screen in the compact model was the same that in the detailed model. For the rest of the model a coarser mesh was used, except in the proximity before the screen where a finer mesh is used. The coarser mesh was found after several mesh density investigations. It was found that the maximum size of the cell, in order to achieve good convergence for all simulated cases, was a cell size with dimensions 1.9 mm × 1.9 mm × 1.9 mm. The mesh size for the present is around one-fifth compared to the detailed model, where it was between 750,000 and 2,000,000 cells. The fact that the mesh quality is very good—only orthogonal hexaedrals—helps to speed up the convergence and thus the number of iterations needed to converge is reduced to at least one-third that of the needed iterations with the detailed model. Due to the mesh reduction, mainly due to not modelling the screen in detail, the computing time is reduced to 1.5–5.5 hours, or in other words around 5% of the CPU time needed for the detailed model.

5.3.4 A comment on the uncertainty of the correlations In paper VII the deviation of the outputs predicted using the pressure loss coefficients from the correlations compared with those from the original compact model and finally with those from the detailed model was shown. However, it should be highlighted that the detailed model used in paper VI (parametric study) was experimentally validated as has been already shown in chapter 6, but it was not validated for the whole range of parameters but only for those that appear in Table 6. Rather, the point of paper VI was to try to get some correlations using a similar CFD model (i.e., a similar mesh density distribution in the models) that had obtained good experimental validation. To some extent, the point of the paper VI was to extend the range of the parameters with the confidence that a similarly good agreement with reality could be expected. However, as a consequence of the employed method, for those values out of the range of Table 11, no experimental validation has been conducted.

69

5.3.5 Accuracy of the compact model Three examples of the velocity field in the symmetry plane between two PCBs (after the EMC screen) are shown in Figure 42. The velocity fields of the detailed model, compact model (using the two directional loss coefficients from the correlations) and a compact model that only uses one coefficient are compared. Detailed

Compact with 1directional coefficient

Compact with 2directional coefficient

2

4.5

1.9

4.28

1.8

4.05

1.7

3.83

1.6

3.60

1.5 1.4

3.38 3.15

1.3

2.92

1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4

2.70 2.47 2.25 2.03 1.80 1.58 1.35 1.13 0.9

0.3 0.2

0.68

0.1

0.45

0.0

0.22 0.0

ParametersH=0.251, a=50 mm, b=15 mm, ts=2 mm, v=4 m/s, tpcb=2 mm and Wslot=14.25 mm 1.3 0.8

0.76

1.23

0.72

1.17 1.11

0.68 0.64

1.04

0.60 0.56 0.52

0.98 0.91

0.48

0.78

0.44

0.72

0.40 0.36 0.32

0.66

0.28

0.46 0.39

0.24 0.20

0.85

0.59 0.52

0.16

0.33 0.26

0.12 0.08 0.04

0.20 0.13 0.07

0.0

00

Parameters:H=0.492, a=35 mm, b=10 mm, ts=1.5 mm, v=1.5 m/s, tpcb=3 mm and Wslot=14.25 mm 6.5 6.18 5.85 5.53 5.20 4.88 4.55 4.22 3.90 3.58 3.25 2.92 2.60 2.28 1.85 1.63 1.30 0.98 0.65 0.33 0.0

8.25 7.84 7.43 7.01 6.60 6.19 5.78 5.36 4.95 4.54 4.13 3.71 3.30 2.89 2.47 2.06 1.65 1.24 0.83 0.41 00

Parameters:H=0.6, a=50 mm, b=15 mm, ts=1 mm, v=9 m/s,tpc b=2 mm and Wslot=13.5 mm Figure 42. Comparison of the velocity field over the PCB between the detailed model, the compact model with two coefficients and a compact model with one

70

In the figure caption, the velocity and the geometrical parameters used for the three different cases are written. As can be seen these parameters are quite different for each case. The colour scale is the same for the detailed model and the two-coefficient compact model; for the onecoefficient compact model, another colour scale was required. The first example in Figure 42 is a case with low porosity and a thick screen (2 mm). In this case, the one-coefficient compact model predicts the flow pattern poorly. For the third example, the flow pattern in the one-coefficient compact model is better predicted, due to the smaller screen thickness. However, the velocity magnitude is still poorly predicted. The agreement in the flow pattern between the detailed model and the two-coefficient compact model is very good. However, as already mentioned, the one-coefficient compact model is not able to predict the flow pattern. These figures also validate the representation of the flow pattern after the screen by means of RMS* and Aw*. When the agreement of RMS* and Aw* between the compact model and the detailed model is good, then the whole flow pattern also agrees well.

71

6 Summar y of papers

This chapter presents a brief outline and discussion of each of the seven papers included in this thesis. Also, an overall view of the CFD models used in the papers is shown in Table 20 and of the employed parameters in Table 21. Table 20. CFD models used in the papers

Paper II III IV V VI VII CFD Model II I II II III IV Table 21. Employed parameters in the papers

V1 V2 V3 V4 × × × × × × × × × × Another range × × Another range

Paper I Paper II Paper III Paper IV Paper V Paper VI Paper VII

V5 p1 p2 p3 S L q1-2-3 × × × × × × × × × × × × × × × × × × × × × × × × Another range Another range × × × × × × Another range Another range

Further, Table 22 indicates whether experimental work or CFD simulations were used for writing each of the papers. Table 22. The kind of work employed in each of the papers

Paper I Paper II Exp. CFD

72

× ×

Paper III

Paper IV

Paper V

Paper VI

Paper VII

× ×

× ×

×

× ×

×

6.1 Paper I 6.1.1 Outline A sub-rack model was built inside a wind tunnel in order to be able to make experimental measurements. An experimental parametric study was performed on a sub-rack model inside a wind tunnel with isothermal conditions. Hot-wire anemometry was used to measure the local velocity at several locations before and after the EMC screen, as well as the profile at the inlet of the sub-rack. The static pressure drop at several locations before and after the screen was also measured. Finally, the smoke-wire technique was used to identify some recirculation areas. Apart from the insight provided by these measurements, these results were accomplished to validate the CFD models. The uncertainty of the velocity and pressure measurements was also shown.

6.1.2 Conclusions and discussion The importance of this paper lies in its being the experimental parametric study that will be the reference to validate future CFD papers. Some figures related the degree of asymmetry in the velocity profiles at the inlet of the sub-rack to the screen porosity and sub-rack depth. The lower the porosity and the sub-rack depth, the less symmetric the velocity profiles at the inlet. By measuring the local velocities before the screen, it was clear that a nonuniform velocity profile will impinge on the screen. It was also shown that the velocity angle of the flow before the screen depends mainly on the geometry (ratio inlet height and sub-rack depth). It was also observed in the velocity angles that the larger the cited ratio and the smaller the porosity, the closer to the sub-rack inlet the flow will turn into the screen. The relation between the velocity magnitude at locations before and after the screen as a function of the distance from the sub-rack inlet and a coefficient related to the porosity was shown. The pressure drop through the screen at several locations along the sub-rack depth was also shown. In those figures, it can be observed how the pressure drop mainly depends on the porosity and the geometry (ratio inlet height and subrack depth). The lower the porosity and the larger the cited ratio, the larger the pressure drop through the screen. Other comments: Although, it is not stated in the paper, some of the velocity measurements after the screen (a2, a3, a4 and a5) may not be trustworthy 73

because of the obstacle that the hot-wire probe body produces on the flow. However the first reading, in which the probe body is just 2 mm, is believed to be trustworthy. Furthermore, it was later discovered that the pressure drop measurements at some locations were slightly wrong due to some leakages in valves. This will be further discussed in the summary of paper IV.

6.2 Paper II 6.2.1 Outline The flow pattern after the perforated plate was studied extensively using the wire-smoke technique. Several videos were recorded for all possible combinations of the following parameters: velocity, sub-rack depth and screen porosity. This study was performed not only to get insight into the proportion between the bulk flow and the recirculation, but also to validate the flow pattern obtained using the detailed CFD model. The detailed CFD model using the RNG kH model shows good agreement with the experimental results. The experimental uncertainty is also discussed.

6.2.2 Conclusions and discussion In the experimental parametric analysis, it can be seen that for low velocities the bulk flow area (or wetted area) covers most of the PCB. Probably the flow for the minimum velocity is in transition, or at least not fully turbulent, hence the bulk flow is wider at the outlet. At high velocities, the reason the bulk flow does not distribute across the outlet area is believed to be the large inertia of the flow. In the case of the smallest velocity, the inertia forces are not large enough to maintain this uneven distribution and the flow is hence distributed more evenly. It is also shown that the bulk flow area (or wetted area) increases with a decrease in porosity and with an increase of the ratio inlet height and sub-rack depth. It can be seen that the detailed CFD model is able to predict the right change in direction when the inclined flow collides with the interior face of the holes. Thus it is a model that could be used to predict how large the bulk flow area is, which is an important parameter when placing electronic components on a PCB.

74

6.3 Paper III 6.3.1 Outline A steady state three-dimensional CFD model was used in order to predict the details of the air-flow paths and the pressure field. The flow was assumed to be isothermal, turbulent, and incompressible. The velocity and turbulence intensity profiles at the inlet of the sub-rack were used for boundary conditions. Two different meshes were employed, one with a y+ close to 1 when using the enhanced wall treatment and low velocities, another with a y+ close to 10 when using the standard wall function (Launder and Spalding, 1974) with high velocities. Four two-equation turbulence models, together with the Reynolds Stress Model, were evaluated. The reference in the validation process was the experimental values from paper I. A third coarser mesh that used the standard wall function and a hydraulic surface impedance was used with two pressure loss coefficients. These loss coefficients were taken from a correlation for a thin perforated plate with flow perpendicular to the screen at high Reynolds numbers.

6.3.2 Conclusions and discussion This paper is an intermediate step in order to get a good CFD model to make a parametric study. The results show that for most of the tested turbulence models with the right wall treatment, the influence on the prediction of pressure drop and velocity field is small. If the y+ is correct, the choice of wall treatments does not influence the prediction of the pressure and velocity fields. The pressure field through the screen is over-predicted by about 15% and the average velocity deviation evaluated at several locations before and after the screen is less than 10%. Since, for the objectives of the thesis, it was necessary to conduct a larger parametric detailed CFD analysis, it was decided to use the enhanced wall treatment. To use the standard wall treatment means to create a specific mesh close to the walls for each of the velocity values of a future parametric study, in such a way that the y+ is bigger than 10–15. However, the standard wall treatment is very sensitive regarding the y+ value of the first cell. It was decided that if a parametric study was going to be conducted in the future (paper VI) the enhanced wall treatment would be a better decision, since one could design the mesh in such a way that the y+, independently of the velocity, would always be less or around 1. Then, one can use the same mesh and 75

the enhanced wall treatment for all the velocity ranges without tailoring the mesh close to the walls as a function of the inlet velocity. This decision was applied in model II, III and IV. Convergence problems were encountered when using the Reynolds stress model with low velocities and enhanced wall treatment. In any case, there were not large differences between the RSM and the twoequation models. So another decision was made for future papers: not to use the RSM, due to the large increase in computational time required. For the range of porosities investigated, an almost linear relation between the dimensionless pressure drop and the screen porosity was observed. However, this cannot be generalized for a larger screen porosity range. The dimensionless static pressure drop seems constant for most of the velocities used in the present study. At low velocities the path lines of the flow occupy most of the PCB surface, however at high velocities, due to the high inertial forces of the flow, the bulk flow that leaves the PCB does not occupy the whole PCB surface and recirculation with low velocity levels clearly appears. Finally, it was shown that modelling the screen as a hydraulic planar impedance does not capture the flow pattern after the screen.

6.4 Paper IV 6.4.1 Outline The objective of this paper was to investigate the performance of five well-known turbulence models, in order to find a model that predicts the details of the flow pattern through an EMC screen. The turbulence models investigated in the present study are five different eddy-viscosity models: the standard kƥ model, the RNG kƥ model, the realizable kƥ model, the standard kƹ model, as well as the SST kƹ model. A steady-state three-dimensional detailed model was used in order to evaluate the details of the air flow paths and the pressure field. The flow was assumed to be isothermal, turbulent, and incompressible. A general model that covers a considerable range of velocities and geometries was validated experimentally by wind tunnel measurements. 76

6.4.2 Conclusions and discussion There are several differences between this paper and paper III. In this paper the same mesh was used both for low velocity levels and for high velocity levels. The y+ value was always less than or around 1. In this paper, uniform velocity and turbulence intensity profiles are used at the entrance of a 500 mm duct. It was earlier observed that this duct length was enough to satisfactorily predict the velocity and turbulence intensity profiles at the inlet of the sub-rack. In this paper, the Reynolds Stress Model was not used, since it gives some convergence problems. The mesh used in this paper is finer than that of paper III. It was also seen that the standard wall treatment had more tendency to delay the separation point than using the enhanced wall treatment; that is also why it was decided to use the enhanced wall treatment for the walls. An evaluation of five two-equation turbulence models was presented. The evaluation was performed by comparison with the experimental values. It was shown that the kH model predicts fairly well the total static pressure drop and the velocity field at several locations before and after the screen. Several velocities, sub-rack geometries and screen porosities were used in the evaluation. The RNG kH model was the best among the analyzed turbulence models. It is believed that the poor performance of the kZ models in predicting the pressure drop is not in the model but in the mesh. Although a finer mesh was used for the kZ models, it seems that a further refinement of the mesh is required. Furthermore, the converged non-dimensional residuals were just below 1×10-4 for this case and thus a bit high. When using the RNG kH model, the total static pressure drop deviates about 5–10% and the average velocity deviation evaluated at several locations before and after the screen is around 5%. A general model that covers a considerable range of velocities and geometries and that uses uniform velocity and turbulence intensity profiles was validated experimentally. The same mesh distribution strategy can be used to study a broader range of geometrical parameters and Reynolds numbers (paper VI). Comments A uniform 10% turbulence intensity level for the reversed flow (at very low velocities) of the outlet boundary condition was used in this and successive articles with good results. Anyway, it is a parameter that has little influence on the flow, probably due to the low velocity level of the reversed flow. 77

Some leakage was found in some valves that had been used for pressure measurements in paper I. Hence, the pressure measurements were repeated but without the valves. Similar results were found for half of the pressure drop measurements and thus good repeatability (when it was done one year later). In Figure 43 and Figure 44 the difference can be seen for several configurations (pressure drop in y axis and dimensionless distance from the inlet at the x-axis): 'p 30 (Pa)

'p 40 (Pa) 35

25

30

20

25 20

15

15

exp-without valves

10

exp-without valves

10 exp-with valves

5

exp-with valves

5 0

0 0

0.2

0.4

0.6

0.8

x*=x/d Figure 43. Pressure measurements with and without valves. Case: p1-V5.

1

0

0.2

0.4

0.6

0.8

1

x*=x/d Figure 44. Pressure measurements with and without valves. Case: p3-V5.

6.5 Paper V 6.5.1 Outline The objective of this paper was to perform an experimental as well as CFD investigation of the conjugate heat transfer problem in a sub-rack slot model. A steady-state three-dimensional detailed model was used in order to evaluate the details of the air flow paths and the temperature field. A general model that covers a considerable range of velocities, screen porosities and heat fluxes was validated experimentally by wind tunnel measurements. The result shows that the RNG kƥ model used with the correct y+ and mesh strategy predicts the temperature field fairly well. The average temperature deviation evaluated at several locations is less than 4% compared to experimental data. The influence of the velocity, screen porosity, heat flux, and presence of the EMC screen on the PCB temperature field is discussed.

78

6.5.2 Conclusions and discussion Placing an EMC screen in the sub-rack is something that cannot be avoided in a sub-rack design. It is often seen as negative from the cooling point of view, since it is a flow obstacle. However, in this paper it is shown that the screen creates a more uniform flow, and this fact increase the cooling capacity of the PCB. For the same reason, the larger the porosity is, the more even the flow after the screen is and the better the cooling capacity. This can be illustrated in Figure 45:

~V0/10 Velocity profile

V0

~2xV1

V1

PCB

Low in plane heat conduction

CASE A

High in plane heat conduction

CASE B

Figure 45. An example of the velocity profiles and in-plane heat conduction in a PCB with a uniform and a non-uniform flow pattern.

In the very uneven flow case (case B), the velocity on the left side is a tenth of the velocity on the left side of the even flow case (case A). This creates in case B a conduction of heat in the PCB from left to right: more heat will be dissipated on the right side (high velocity side). But in case A, the conduction heat inside the PCB is much less (due to the even flow). This means that case A has much higher capacity to cool since the velocity is 10 times bigger than in case B and on the right side may also have more capacity to cool: although the velocity is almost half of the one that in case B, the amount of heat to dissipate is much less due to the reduction of the internal heat conduction inside the PCB. From an overall point of view, a more even flow has more capacity to cool when there is a uniform heat flux at the middle of the copper PCB. The result shows that the RNG kƥ model used with correct y+ and mesh strategy predicts the temperature field fairly well. The average temperature deviation evaluated at several locations is less than 4% compared to experimental data. This detailed model (the same as the one in paper IV) also has the capacity to predict the temperature field for a broad range of velocities, screen porosities, and heat fluxes.

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6.6 Paper VI 6.6.1 Outline Once the detailed CFD model was validated from the hydraulic point of view in papers II and IV, a larger parametric study was performed to investigate the flow after an EMC screen and between two PCBs of a radio base station sub-rack using the detailed CFD model (with entrance duct). Seven parameters were investigated: velocity, inlet height, screen porosity, PCB thickness, distance between two PCBs, inlet-screen gap and screen thickness. For this study, 174 cases were simulated; based on their results, correlations for the static and dynamic pressure drop, the percentage of dimensionless wetted area, Aw* , and the RMS* factor (a parameter describing the flow uniformity along the PCB) after the screen were reported as a function of six geometrical dimensionless parameters and the Reynolds number. The objective of this paper was to make a parametric study of the hydraulic resistance and flow pattern. The parametric study is carried out using a detailed three-dimensional model of a PCB slot. The detailed model was partially experimentally validated in paper IV.

6.6.2 Conclusions and discussion The correlations, that are based on 174 three dimensional simulations, yield good results for the total pressure drop, in which the values are predicted within the interval of ±15%. For the Aw* , all the predicted values are within the interval of ±22% of the observed values. Finally, for the RMS* factor, the majority of the values also have a disagreement of less than ±20% of the observed values. These last two parameters are believed to provide a correct picture of the flow pattern after the screen. These correlations are believed to be useful tools for predicting pressure drop and flow pattern for this kind of sub-rack building architecture.

6.7 Paper VII 6.7.1 Outline A methodology to obtain the directional pressure loss coefficients in a porous media model of an EMC screen in a radio base station is presented. The directional loss coefficients of this compact model are validated against a detailed CFD (paper VI) model not only by 80

comparing the total pressure drop but also by evaluating the flow pattern after the screen. The detailed model was partially validated in paper IV. A parametric study is conducted for 174 cases. Seven parameters were investigated: velocity, inlet height, screen porosity, PCB thickness, inletscreen gap, distance between two PCBs and screen thickness. Based on the compact model parametric study, two correlations for the directional loss coefficients are developed as a function of the Reynolds number and some of the above mentioned geometrical parameters.

6.7.2 Conclusions and discussion The average disagreement between the initial compact model and the compact model that uses the directional loss coefficients from the correlations was less than 3.5% for 'pt* and Aw* and less than 6% for RMS*. The average disagreement with a detailed model from paper VI was 3.1% for 'pt*, and less than 6.5% and 9.5% for Aw*and RMS*, respectively. It has also been shown that a compact model with only one coefficient does not have the capacity to accurately predict the pressure drop and flow pattern after the screen. The use of these correlations may be a good guideline for improvements in the prediction of flows with this kind of building architecture. Furthermore, this model may be completed with electronic components and other devices, knowing that the pressure drop as well as the flow pattern in the PCB slot due to the presence of the EMC screen are done more accurately than using simple planar resistance or with a volume hydraulic resistance that uses only one coefficient.

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7 Conclusions

7.1 Conclusions from the Results This work has attempted to advance one step forward in the analysis of electronic systems with a 90-degrees cooling architecture, in particular sub-racks of radio base stations. The influence of EMC screens at the inlet of the slots in sub-rack configurations in which the inlet cross section is perpendicular to the screen has been analyzed. In particular, the hydraulic and thermal behavior as a function of several parameters has been presented. The following conclusions can be drawn from this project: A detailed CFD model is an accurate approach to study the fluid flow and heat transfer behavior for complex flows. To the best knowledge of the author, no detailed model of EMC screens has been used before in a parametric study. It is important to use a correct mesh density and turbulence model. The kH turbulence models predicted well the velocity and pressure drops. The RNG kH model predicted best the velocity and pressure drop at several locations. The kZ models need more mesh density than kHmodels, for the same mesh density kZ models over-predict the pressure drop, due to the lack of a higher mesh density close to the walls. The EMC screen is something necessary in order to reduce the electromagnetic noise. But in addition to the known drawback of the associated pressure, there is also an advantage. The EMC screen works as a flow straightener, which makes a more uniform flow after the screen, normally increasing the overall cooling over the PCB. Due to this straightening effect, the study found how the pressure drop and flow pattern is affected by the screen. Two parameters (Aw*and RMS*) were defined in order to characterize the flow pattern after the screen. 82

Five correlations were implemented to calculate the static, dynamic and total pressure drop, as well as for the two flow pattern parameters. These correlations are expressed as a function of the geometry and Reynolds number. A one-coefficient compact model, using both planar and volume hydraulic resistance, was shown not to have the capacity to predict the correct flow pattern after the screen. This study showed that a porous media approach based on a volume hydraulic impedance compact model that uses two directional loss coefficients has the capacity to predict well the total pressure drop and the flow pattern after the screen, while greatly reducing the needed CPU time. Furthermore, two correlations for the two directional loss coefficients were presented as a function of the geometry and Reynolds number. The parameters found to be more important to define the in-plane pressure loss coefficient are the screen thickness and the ratio of the inlet height and sub-rack depth. For the pressure loss coefficient perpendicular to the screen, the important parameters are the porosity and screen thickness. The Reynolds number in general has little influence on both coefficients. It has also been shown that the static pressure drop is mainly a function of the porosity and the ratio inlet height to sub-rack depth and both flow pattern parameters (Aw*and RMS*) are very much related to the porosity and screen thickness. It is believed that these results can help thermal designers to have a better idea about the pressure drops and flow pattern changes due to the EMC screen in a 90-degree sub-rack building architecture.

7.2 Design Tools Fast design is one of the most important issues in today’s design process. There have been many attempts to create an efficient methodology to get the design parameters in the shortest time. Several modelling techniques have been developed and are used at different stages of the design cycle of the product. Different approaches to the problem have been analyzed in recent years. One way to shorten the time to market is to work with compact models. Once the compact model has been developed, the design time can be greatly reduced. 83

One of the aims of the project was to develop design tools. A fast design tool was implemented using EES (Engineering Equation Solver). EES is software that permits you to perform parametric analysis in an easy way and to create a user-friendly graphical interface for your program (see more details about EES at www.fchart.com). Software based on the correlations from paper VI is shown in Figure 46. &

Figure 46. User-friendly software that predicts the pressure drop and flow pattern.

The software gives the total pressure drop, wetted area and RMS* factor (these are the output variables) for whatever combination of the input parameters: Reynolds number and the geometrical variables, which are inlet height, screen porosity, PCB thickness, screen thickness, distance between two PCBs and the gap between inlet and screen placement. Furthermore, one may choose a range of values for the input variables and see the result of the chosen output in a diagram. Similarly, a second part of the software based on the correlations developed in paper VII is presented in Figure 47. Once the geometrical dimensions and inlet velocity are supplied to the program, the directional loss coefficients for a compact model similar to those used in paper VII are calculated.

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Figure 47. User-friendly software that predicts the pressure loss coefficients as a function of the geometry and Reynolds number.

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8 Sug gestions for fur ther work

The competitive market has demanded a faster design process in the production of electronics in general and electronic systems in particular. It would be useful to continue to develop fast and accurate compact models that give good guidelines to designers and thermal management engineers. From the heat transfer point of view, a suggestion to continue with this project would be a fast design tool that would allow the freedom to place the electronic components in any location. The modelling of the components on the PCB would be represented by an approximation that accounts for the component thickness and the components’ heat load. This, together with the hydraulic compact model developed in this thesis, would be an even better tool with which accurate and very fast results might be obtained. That means that the PCB surface would be divided into rectangles with different roughness and heat loads. Furthermore, the mesh of the model could be driven from an Excel worksheet, as could the boundary conditions set on the CFD solver, providing a fast and friendly environment to build the models. There is still work to be done with the compact model. For example, one must study how robust the model is and if the model is boundarycondition independent for that geometry. Some preliminary analyses show that the model is not dependent on the boundary condition; however more work should be performed in order to confirm it. A larger experimental analysis would be also desired in order to validate a broader range of parameters. A natural continuation of the project would be to study the interaction of the second EMC screen and the fans. Thanks to the second EMC the flow in the PCB slots may not have the swirl created by the fans’ tray or blowers (that is why this thesis has neglected swirl in the boundary conditions), because the second screen may break this swirl. However, in breaking this swirl and the fact of the closeness of an obstacle (the perforated plate) to the fan inlet, would greatly affect the fan 86

performance curve. It would be very interesting to study experimentally how much the performance of the fan/fans is affected by a perforated plate. An experimental parametric study could be done, studying the effect of velocity, screen porosity, and distance between the screen and the fan. From this experimental study, a compact model of the fan could be used with the new corrected performance curve. This would be also another step to speed up the analysis of the whole electronic system. Another natural continuation of this thesis may be the study of the flow uniformity after the screen, using a screen whose porosity varies along the sub-rack depth and an implementation of a compact model for this kind of screen. This methodology could be applied to the perforated tiles in data centers or in other fields in which perforated plates are present.

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