Multi-Physics CFD Simulations in Engineering - Springer Link

Journal of Thermal Science Vol.22, No.4 (2013) 287−293

DOI: 10.1007/s11630-013-0626-x

Article ID: 1003-2169(2013)04-0287-07

Multi-Physics CFD Simulations in Engineering Makoto Yamamoto Tokyo University of Science, Department of Mechanical Engineering 6-3-1 Niijuku, Katsushika-ku, Tokyo, 125-8585, Japan © Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2013

Nowadays Computational Fluid Dynamics (CFD) software is adopted as a design and analysis tool in a great number of engineering fields. We can say that single-physics CFD has been sufficiently matured in the practical point of view. The main target of existing CFD software is single-phase flows such as water and air. However, many multi-physics problems exist in engineering. Most of them consist of flow and other physics, and the interactions between different physics are very important. Obviously, multi-physics phenomena are critical in developing machines and processes. A multi-physics phenomenon seems to be very complex, and it is so difficult to be predicted by adding other physics to flow phenomenon. Therefore, multi-physics CFD techniques are still under research and development. This would be caused from the facts that processing speed of current computers is not fast enough for conducting a multi-physics simulation, and furthermore physical models except for flow physics have not been suitably established. Therefore, in near future, we have to develop various physical models and efficient CFD techniques, in order to success multi-physics simulations in engineering. In the present paper, I will describe the present states of multi-physics CFD simulations, and then show some numerical results such as ice accretion and electro-chemical machining process of a three-dimensional compressor blade which were obtained in my laboratory. Multi-physics CFD simulations would be a key technology in near future.

Keywords: Computational fluid dynamics, Multi-physics, Engineering problems

Introduction Nowadays Computational Fluid Dynamics (CFD) software is adopted as a design and analysis tool in a great number of engineering fields such as automobile, turbo-machinery, aerospace, ship building, medical engineering, electric engineering, civil engineering, architecture and many others. We can say that single-physics CFD has been sufficiently matured in the practical point of view. The main target of existing CFD software is single-phase flows such as water and air. Every single-phase flow includes single physics (i.e. fluid dynamics or aerodynamics). On the other hand, many multi-physics

problems exist in engineering as well as science. Most of multi-physics phenomena consist of flow and other physics, and the interactions between different physics are very important. Fluid/structure interaction, solid/ liquid, gas/liquid and gas/solid two-phase flows, conjugate heat transfer, reactive and combusting flows, ice accretion, particle deposition, erosion, chemical machining and so on are all multi-physics phenomena related to flow physics. Obviously, such phenomena are critical in developing machines and processes. However, from the technical view point of CFD, a multi-physics phenomenon seems to be very complex, and it becomes so difficult to be predicted by adding other physics to flow phe-

Received: March 2013 Makoto Yamamoto: Professor www.springerlink.com

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nomenon. Therefore, most of multi-physics problems have not been solved yet. In other words, a multi-physics CFD technique is still under research and development. This would be caused from the facts that processing speed of current computers is not fast enough for carrying out a multi-physics simulation, and furthermore physical models except for flow physics have not been sufficiently established. As everyone knows, turbulence models such as Reynolds-Averaged Navier-Stokes Simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) have been fully developed, and we can use any suitable model with considering the computational load, accuracy and model complexity. This is an ideal situation for CFD. However, for the non-flow physics, we can use either a micro-scale model based on a first principle, or a macro-scale model based on experimental measurements (i.e. empiricism). These models often prevent us from doing a multi- physics CFD simulation. Therefore, in near future, we have to develop various physical models and efficient CFD techniques, in order to success multi-physics simulations in engineering. Taking into account the present state of the art in CFD, multi-physics CFD simulations would be a key technology in near future. In the present paper, I will describe the present states of multi-physics CFD simulations, and then show some numerical results such as ice accretion, electro-chemical machining process of a compressor blade and some others which were obtained in my laboratory. The numerical results clearly indicate that Weak Coupling strategy is promising in a lot of multi-physics CFD simulations.

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pling strategy. Each physics which is included in a multi-physics problem has characteristic scales of time, space, velocity and so on. Figure 1 illustrates time-scales of a multiphysics phenomenon. As shown in Fig.1(a), when two time-scales overlap or neighbor with each other, these two physics strongly interact, and thus we must take into account the interaction of these two physics simultaneously. This means that computation becomes very heavy and thus too time-consuming in the practical point of view. We call this type phenomenon as a “Strong Coupling” problem. On the other hand, as shown in Fig.1(b), when one time-scale is far from the other, these two physics do not interact, and thus we can neglect the interaction between them. Since each physics can be computed separately, the computational cost does not become so high. We refer this type of phenomenon a “Weak Coupling” problem.

Fig.1

Coupling between Two Physics

Numerical Results and Discussion Multi-Physics CFD with Weak Coupling Strategy There are two strategies to simulate a multi-physics phenomenon. One is "Strong Coupling", and the other is "Weak Coupling". Each can be employed in CFD, based on time-scales of physics embedded in a problem. That is, if a time-scale of one physics is nearly the same as that of the other physics, we have to use Strong Coupling to take into account the interaction between the two physics. Fluid/structure interaction is the typical problem. On the other hand, if one time-scale is quite different from that of the other one, Weak Coupling can be applied. Erosion is one of such problems. Taking into account the present computer performance (i.e. processing speed and memory size), Strong Coupling is a little difficult to be used in engineering design processes. Therefore, I am focusing on Weak Coupling method, and it has been applied to a number of multi-physics CFD simulations in various engineering fields. We have successfully simulated sand erosion, ice accretion on a jet engine, particle deposition on a turbine blade, electro-chemical machining process of a compressor blade and so on, with using Weak Cou-

Based on the concept described above, we have been challenging multi-physics CFD simulations, especially in engineering fields, with using a “Weak Coupling” strategy. Two examples are presented below. The first example is ice accretion phenomena on a fan blade in a jet engine, and the second one is electro-chemical machining process of a compressor blade. Example 1: Ice accretion phenomena on fan blade The first example is ice accretion on a fan blade. Ice accretion is a phenomenon where super-cooled water droplets impinge and accrete on a body. It is a typical multi-physics phenomenon which consists of three physics; flow, droplet and surface deformation. Ice accretion has two types of ice shape. The first is called ‘rime ice’ which is formed at low temperature (lower than −10°C). Under rime ice condition, droplets freeze at the impingement point instantly. The second one is called ‘graze ice’ which is generated at 0 to -10°C. Under graze ice condition, droplets gradually freeze with running along a body surface (so-called runback). When ice ac-

Makoto Yamamoto

Multi-Physics CFD Simulations In Engineering

cretes on an aircraft wing, it remarkably affects on the performance by increasing drag and reducing lift, and it may cause a serious accident. On a jet engine, ice accretion disturbs the inlet flow, and separated ice pieces can give mechanical damages to the compressor and the casing. Many instances of accidents due to ice accretion have been reported until now. Obviously, it is essential to deeply understand the mechanisms of ice accretion. Moreover, the estimation of ice accretion is necessary to avoid accidents and is useful to reduce both the cost and the design period in the design phase of aircrafts and jet engines. However, experimental investigations are very difficult, because it is not easy to reproduce ice accretion conditions repeatedly in a wind tunnel. Therefore, CFD is expected to be a useful tool to predict ice accretion phenomenon in design processes. We developed a three-dimensional ice accretion code. Based on the weak coupling strategy, it is composed of iterative computations for fully-developed turbulent flow, droplet trajectory, thermodynamics of ice formation and grid modification. Fig.2 illustrates the flow chart. Each governing equation is solved in the rotating frame of reference. The rotor flow field is obtained from the threedimensional numerical solution to the compressible Reynolds-averaged continuity, Navier- Stokes, energy equations and the high-Reynolds- number type k-ε turbulence model. Droplet trajectory calculation based on the Lagrangian approach is performed to estimate the droplet collection efficiency on a fan blade. When super-cooled water droplets impinge on a body, ice deposits on the surface by heat transfer among the water, the gas and the solid surface. On rime ice condition, droplets freeze at the impingement points instantly. On graze ice condition, droplets runback along the body because of the small heat transfer. To estimate the freezing rate of droplets and ice thickness, mass and energy balances are calculated in each control volume on the solid surface. In this study,

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numerical simulations were conducted on an engine fan blade as shown in Fig.3. We used an overlapping grid system. Figure 4 exhibits the computational grid for the fan blade consisting of an H-type of 800,000 grid points along the flow path (main grid) and an O-type of 260,000 grid points around the blade (sub grid).

Fig.3

Fig.4

Schematic of Fan

Computational Grids

We computed two cases and compared the results, in order to clarify the effect of operating condition on ice accretion phenomena. One is a cruising condition, and the other is a climb-up condition. Table 1 lists the computational conditions. The total pressure, the total temperature and the Mach number at the inlet are averaged from the tip to the hub. LWC means the liquid water content of droplets, and MVD is the median volume diameter of a droplet. Table 1

Computational Condition of Ice Accretion Cruising

Fig.2

Flow Chart of Ice Accretion Simulation

Climb-up

Total pressure [kPa]

101.32

Total temperature [K]

253.15

Mach number

0.40

Rotating speed [r/min]

4291

0.48 4880

LWC [g/m3]

1.0

MVD [µm]

20.0

Icing time [s]

5.0

Figure 5 illustrates the collection efficiency distributions on each condition. P.S., L.E., and S.S. in the figure denote the pressure side, the leading edge and the suction

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side, respectively. We can confirm that the collection efficiency on the climb-up condition is larger than that on the cruising condition. This is due to the larger rational speed, and thus the relative velocity is higher on the climb-up condition. On both conditions, the droplet impingements concentrate on the leading edge, and the impingements are significant on the hub side. There is no impingement on the suction side, but it can be seen that a number of droplets impinge near the hub of the pressure side. The amount of impingements decreases gradually with increasing the radial location. This is because the blade gets thinner, and its camber becomes smaller on the higher radial location, resulting in few or no droplet impingements.

is higher than that on the cruising condition, the area where ice layer forms is smaller. The reason why ice does not form on the tip side even if droplets impinge there is that the static temperature is higher than the freezing point. The volume of ice results in the larger amount of ice on the cruising condition (1528 mm3 in the cruising condition and 1431 mm3 in the climb-up condition).

Fig.6

Fig.5

Collection Efficiency Distributions

Figure 6 shows the distribution of the local ice thickness on each condition. It can be seen that the thickest ice accretes near the hub due to the largest collection efficiency in both cases. Comparing the results on the cruising and the climb-up conditions, the local maximum ice thickness on the climb-up condition is thicker than that on the cruising condition (approximately 0.93 mm on the cruising, and 1.60 mm on the climb-up condition). In addition, the amount of ice accretion decreases with increasing the radial position. Ice forms up to the approximately 70% span on the cruising condition, while on the climb-up condition, ice cannot be seen at the higher location than the 50% span. This is because the surface temperature becomes higher as the rotational speed increases. Since the surface temperature on the climb-up condition

Ice Thickness Distributions

Three-dimensional multi-physics CFD simulations of ice accretion on a jet engine fan blade were conducted. Two operating conditions (cruising and climb-up) were simulated and the results were compared. Through the present multi-physics simulations, the effect of operating condition on ice accretion phenomena was numerically clarified. It was confirmed that ice accretion on the fan blade is remarkable around the leading edge and on the pressure side near the hub. Example 2: Electro-chemical machining process The second example is electro-chemical machining process of a compressor blade. Electro-chemical machining (ECM) is one of advanced machining technologies. Gussef originally proposed and designed the ECM procedure in 1929. Since then, ECM has been developed and employed in highly specialized fields such as aerospace, aeronautics, defense and medicine. In recent years, ECM has been used in the automobile and turbo-machinery industries because it has no tool wear and can machine difficult-to-cut metals and complex geometries

Makoto Yamamoto

Multi-Physics CFD Simulations In Engineering

geometries with relatively high accuracy and extremely smooth surfaces manufactured. However, ECM still has some problems with the efficient tool design, electrolyte processing, and disposal of metal hydroxide sludge. In order to solve these problems, a numerical simulation so-called CFD (Computational Fluid Dynamics) is expected to be a powerful and helpful tool in near future. However, a numerical code has not been established that can satisfactorily predict this machining process, including the thermal fields, electric fields, complex flow natures such as the generation of hydrogen bubbles and metal hydroxide sludge (i.e. three-phase effect), temperature increase by Joule heating, three-dimensionality of the flow and flow separation. Fig.7 shows the schematic of ECM process.

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(a) Entire Domain (Last Step)

(b) Enlarged View around Blade (Last Step)

Fig.9 Fig.7

Schematic of Electro-Chemical Machining

In the present study, the flow field was assumed to be incompressible, laminar and three-phase. That is, the electrolyte flow, hydrogen bubbles and metal hydroxide sludge were considered. Moreover, Joule heating due to the electric field between the tool and the blade surface was considered. A weak coupling method was adopted, because the void fractions are low on average and the strong coupling method is time consuming and unavailable for the ECM process. Therefore, the flow field is governed by the equations of continuity, Navier-Stokes, energy and transport of volume fractions of the hydrogen bubbles and metal hydroxide sludge. We simulated a three-dimensional compressor blade. Figure 8 shows the schematic view of ECM for a threedimensional compressor blade. A metal block is initially held by the tools, then the tools are moved towards the

Fig.8

Schematic of ECM for 3D Compressor Blade

Computational Grid

center, and the compressor blade is produced. The computational domain for this simulation was separated into two parts: the inlet channel and the gap passage around the blade. We employed a H-type structure grid for each region. To calculate these two regions with an exchange of flow information, we adopted the overset grid method. Furthermore, by dividing the machining process into 65 steps, the temporal changes of the flow and the blade geometry were simulated. The step-number of 65 was determined by finding a solution that was step-number independent. Through the preliminary computations, we found that, when the 201x41x61 (about 5×105) grid system was used, the final shape around the mid-chord region has a deviation by less than 1% from that in the finest grid case. Therefore, in the present computation, we employed approximately 7×105 grid points in the initial step and 5×105 in the last step. Figure 9 shows the typical grid system. It should be noted that the inter-electrode-gap is highly three-dimensional (an order of 1 [mm] in the first step and an order of 0.1 [mm] in the last step), and the minimum grid size was approximately 1[ μ m] in the final step. Four cases were computed. In Case 1, no flow effect is considered. In Case 2, the electric field, Joule heat, hydrogen bubbles and hydroxide sludge were considered for a Reynolds number of 500. The Reynolds number was defined based on the chord length and the maximum velocity at the inlet. Case 3 was the same as Case 2, but the Reynolds number was 1000. This condition is nearly

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the same as that in the experiment. Case 4 was also the same as Case 2, but the Reynolds number was 2000. The Reynolds number was changed to clarify the effect of the Reynolds number on the ECM process. It should be noted that the workpiece material was nickel alloy, the machining time was 500 [s]. First, the predicted blade shapes are compared with the experimental data in Fig.10. As shown in this figures, the pressure and suction sides are reasonably predicted, but the leading and the trailing edges are over-dissolved. However, when all the physics are included and the Reynolds number matches that of the experiment (Case 3), this prediction is obviously the best. Therefore, Joule heating and hydrogen bubbles are important effects in the compressor blade simulation. Over-dissolution occurs around the leading and trailing edges due to simplification of the tool configuration there. Comparing the results in Cases 2, 3 and 4, we can confirm that, if the Reynolds number is sufficiently high, the solution does not strongly depend on the Reynolds number because hydrogen bubbles are not accumulated by the high-speed flow. Fig.11 shows the velocity and H2 void fraction contours at different spanwise sections, and the dissolution volume distribution on the metal surface. The left and right figures show the pressure and suction sides, respec-

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tively. It is apparent that the flow is highly three-dimensional, and the high dissolution region corresponds to the narrow gap in each section. This figure indicates that the gap size between the workpiece and the tool is the primary parameter in the ECM process for a compressor blade. Moreover, as can be expected, the low-speed region corresponds to the region with a high void fraction

Fig.10

Comparison of Predicted Blade Shapes

Fig.11 Contours of Velocity and H2 Void Fraction at Different Spanwise Sections and Dissolved Volume Distribution on Blade Surface (Top: 81% Span, Middle: 61% Span, Bottom: 40% Span, at 25th Stage)

Makoto Yamamoto

Multi-Physics CFD Simulations In Engineering

of hydrogen and a high temperature (not shown here). In other words, hydrogen bubbles reside and accumulate in the low-speed region. In the present study, the multi-physics ECM process for a two-dimensional flat plate and a three- dimensional compressor blade were simulated, and the characteristics of the flow between the tool and the workpiece surface were investigated by observing the computed flow fields. The multi-physics CFD results lead to the following conclusions. (1) Joule heating and hydrogen bubbles are very important in the ECM process. (2) The interaction of Joule heating and hydrogen bubbles is the primary determinant of workpiece dissolution. (3) The effect of metal hydroxide sludge is negligible. (4) In the three-dimensional simulation of the compressor blade, Joule heating and hydrogen bubbles strongly influence the flow nature, and thus essential. (5) Joule heating and hydrogen bubbles cause the flow nature to be highly non-uniform. (6) The non-uniform flow nature leads to the nonuniform dissolution of the workpiece surface. (7) Hydrogen bubbles reside and accumulate in the low-speed region. Through this study, we can confirm that multi- physics CFD simulation is very useful to understand the phenomena in electro-chemical machining process, and it would be a good design tool.

Summary Multi-physics CFD simulation is a key technology in near future. In the present paper, I explained the coupling strategies for multi-physics CFD simulations, and de-

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scribed that a weak coupling method is very attractive in various engineering fields. Then, two examples which have successfully been investigated in our laboratory were exhibited. One is ice accretion phenomena on a fan blade in a jet engine, and the other is electro-chemical machining process of a compressor blade. It was clearly indicated that a multi-physics CFD simulation is very useful, and the weak coupling method is promising for the simulation of multi-physics phenomena.

References [1] W.B.Wright, R.W.Gent and D.Guffond, DRA / NASA / ONERA Collaboration on Icing Research: Part II-Prediction of Airfoil Ice Accretion, NASA CR-202349, 1997 [2] W.B.Wright, Validation Results for LEWICE3.0, NASA CR 2005-213561, 2005 [3] M.Yamamoto et al., Development and Verification of Unified Ice Accretion Model for Multiphysics Icing Simulation, Computational Methods for Coupled Problem in Science and Engineering II, edited by E.Onate, CIMNE, Barcelona, Spain, 2007, pp.524-527 [4] Hourng,L.W. and Chang,C.S., 1993, “Numerical Simulation of Electrochemical Drilling”, J. Applied Electrochemistry, 23, pp.316−321 [5] Kozak,J., 1998, “Mathematical Models for Computer Simulation of Electrochemical Machining Processes”, J. Material Processing Technology, 76, pp.170−175 [6] Van Damme,S., Nelissen,G., Van den Bossche,B., and Deconinck,J., 2006, “Numerical Model for Predicting the Efficiency Behavior during Pulsed Electrochemical Machining of Steel in NaNO3”, J. Applied Electrochemistry, 36, pp.1−10

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