INTRODUCTION. A pulsating heat pipe (PHP) [1] is a passive and extremely efficient way of exchanging heat between a hot source and a cold one.
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CFD simulation of a Pulsating Heat Pipe using ANSYS FLUENT Technical Report · July 2016
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1 author: Umberto Costa Bitencourt Illinois Institute of Technology 2 PUBLICATIONS 0 CITATIONS SEE PROFILE
Available from: Umberto Costa Bitencourt Retrieved on: 29 August 2016
CFD SIMULATION OF A PULSATING HEAT PIPE USING ANSYS FLUENT
A PAPER SUBMITTED AS A PART OF A RESEARCH PROJECT ENTITULED “DEVELOPMENT OF A PULSATING HEAT PIPE FOR ENHANCED HEAT TRANSFER” By UMBERTO COSTA BITENCOURT under orientation of PROF. ALI KHOUNSARY
DEPARTMENT OF PHYSICS ILLINOIS INSTITUTE OF TECHNOLOGY JULY 2016
1. INTRODUCTION A pulsating heat pipe (PHP) [1] is a passive and extremely efficient way of exchanging heat between a hot source and a cold one. The simulation of a 2D single loop pulsating heat pipe using ANSYS FLUENT 17.1 is proposed on this article. After doing a lot of research on the theme it can be noticed that not many articles actually explain how to simulate a pulsating heat pipe. For this reason, the main point of this article is to make anyone to be able to reproduce this simulation. This approach starts with the simplifying assumptions to carry out the simulation, and then its procedure is shown step by step which are also explained physically as they are introduced.
2. PHYSICAL CHARACTERISTICS AND ASSUMPTIONS The pulsating heat pipe analyzed here is a pretty simple one. First, it has only one loop, second the analysis is carried out using a 2D model. The filling ratio is 50 %, which is the ratio between the volume of liquid used and the total volume, but this number can be changed very easily. Three phases are utilized: water liquid, water vapor and air. 2.1. GEOMETRY The geometry dimensions are shown in the image 1, it is already shown with half of its volume filled with liquid water (this is defined at the end).
Image 1: Geometry dimensions in mm
2.2. BOUNDARY CONDITIONS The boundary conditions are defined as in the image 2. The heat flux is very high because the walls are too thin, they will be set as 0.5 mm later. The basic process of a PHP is that, when
the water heats up at the bottom part of the pulsating heat pipe, it increases its temperature, vaporizing at around 35 °C (because there is a vacuum inside the pipe), and consequently rises up. When it rises all the way up it touches the condenser and its temperature decreases, making it condense and now it goes down again.
Image 2: Boundary conditions
3. MOVING TO ANSYS FLUENT The next sessions show a step by step procedure of how the simulation is done. Most of the steps come with some physical insight explaining the reason of using specific features.
3.1.GENERAL PROPERTIES The transient model was chosen since there is a dependence on time and there is no steady state for a pulsating heat pipe. The gravity was set as 9.81 m/s² in the negative y direction. Nothing else was changed from the default.
Image 4: General properties of the model
3.2.SETTING UP THE MODELS
The flow inside a pulsating heat pipe is called slug flow which is characterized for a liquid–gas flow in which the gas phase exists as large bubbles separated by liquid “slugs” [2]. For this kind of flow the VOF (volume of fluid) approach is the most adequate because it tracks the interface of the phases, which is very important to describe this flow [3].
Image 5: Models utilized for the analysis
Clicking on multiphase twice, the properties are set as shown in the image 6. The three Eulerian phases are air, water vapor and water liquid, even though there is a vacuum inside the pipe, which is defined later, air is still defined as one of the phases. The reason for including a phase with air is that if only water liquid and vapor are defined, the calculation starts as if there is already water vapor inside the pipe. The implicit Body Force box was checked as well.
Image 6: Defining the multiphase model
Plus, the energy equation was turned on to allow heat transfer between the phases and the flow is laminar with the viscous heating box checked. The viscous heating is turned because it includes the effect of transformation of friction on the walls into heat. To show that the flow is laminar a conservative assumption is made. It assumes a velocity of 1 m/s, which is high, and then calculate the Reynolds number using the formula: Re =
𝜌𝑉𝐷 𝜇
Where:
𝜌 is the liquid water density = 992 kg/m³ (at 39 °C) V is the liquid water velocity = 1 m/s D is the diameter of the pipe = 2 mm
𝜇 is the liquid water viscosity = 8.90 × 10−4 Pa.s (at 25 °C) Using those values, the Reynolds number is calculated as Re = 2230. As Re < 2300 then the flow is laminar [4].
Image 7: Defining the viscous model
3.3.IMPORTING THE MATERIALS
The next step is to import the materials needed from the fluent library. To do that, click on materials and then on Create/Edit.
Image 8: Opening ANSYS materials Database
After clicking on Fluent Database the materials can be copied, and then they will be displayed on the first window (Image 8). The materials selected here are only the fluids (Water liquid and water vapor), since aluminum is already default for the solid parts as well as air is for fluids.
Image 9: Selecting materials
3.4. DEFINING THE PHASES AND THEIR INTERACTIONS Now that the materials were imported, come back to the Models, and then following the steps shown in the image 10, define which material corresponds to each of the three phases.
Image 10: Defining the three phases
The phases are defined as in the table 1:
Phase 1- Primary phase 2- Secondary phase 3- Secondary phase
Fluid Water vapor Water liquid Air Table 1: Description of the phases
As an example, clicking twice on phase 1, it can be defined as shown in the figure 11, it is a good habit to name the phases with their actual names. This process is repeated for the other two phases.
Image 11: Defining the primary phase
Now, the interactions between the phases need to be defined. Clicking twice on phase interactions, there are only two possible interactions: Mass transfer and surface tension. Both play an important role in a PHP. First, the mass transfer accounts the effects of condensation and evaporation happening inside the pipe, second the surface tension is important because the tube diameter is very small and the liquid ends up sticking to the walls (as expected). To set up the mass transfer, follow the image 12. Then, clicking on edit, the saturation temperature, which is the temperature that the liquid starts to turn to vapor and the vapor to liquid, is defined as 35 °C (308 K) at a pressure of Pa.
Image 12: Setting up the mass transfer mechanism
To set up the surface tension, follow the image 13. Even though the surface tension changes with temperature, here it is considered constant (0.07 N/m), for simplification purposes, which is approximately the surface tension of water at 39 °C. Wall adhesion must be included since the main feature of a PHP is the fact that the water sticks to the walls.
Image 13: Setting up the surface tension
3.5. CELL ZONE CONDITIONS On this section the vacuum inside the pipe is introduced. Clicking on “Cell Zone Conditions” and then on “Operating Conditions” set the “Operating Pressure” as 4000 (this is the saturation pressure of the water at a saturation temperature of 29 °C, as defined in the image 12) as shown in the image 14. The other parameters used are the default ones.
Image 14: Including the vacuum effect
3.6. BOUNDARY CONDITIONS Following the scheme from the image 2 the boundary conditions are introduced to ANSYS. Named selections should be created during the meshing to facilitate this step. After clicking on “Boundary Conditions” the window that popped up should look like the image 15.
Image 15: Boundary conditions
Again, following the image 2, the boundary conditions are defined. As an example, let’s set the evaporator conditions. Clicking on “evaporator”, its type is “wall”, then clicking on edit, configure it as in the image 16. The Wall Thickness used here is 0.5 mm.
Image 16: Boundary condition for the evaporator
3.7. INITIALIZING SIMULATION AND PATCHING LIQUID AND AIR POSITIONS After configuring the other two boundary conditions the last step before starting the simulation is initializing it and attribute initial positions for the liquid and air for the beginning of the simulation as shown in the image 1. Configure the initialization window as shown in the image 16 and hit “Initialize”. Set the liquid and air volume fractions as zero because in the next step they are going to be patched.
Image 17: Initializing solution
After initializing, under the group “Adapt” hit “Mark/Adapt Cells” and then “Region…” as in the image 18.
Image 18: Mark/Adapt Cells localization
The main point of marking cells is to create regions that later will be filled with one of the phases. For this simulation, two regions will be marked, the bottom half for water liquid and the top half for air. As an example let’s mark the liquid water region. The first thing to do is define the coordinates that the region will sweep and then hit “Mark”. To make sure everything is right hit “Manage…” and the regions created will be under the Registers tab, click on one of them and then “Display”. The geometry should turn to red as in the image 19. Do the same for the air region.
Image 19: Marking liquid water region
The last thing to do is patch these two regions. This only can be done if you initialized the simulation before. Hit “Patch…” and configure it as in the image 20. Selecting the phase liquid and the variable as “Volume Fraction” with its value of one, basically it’s been told to the software that initially that region filled with only liquid water. The same process is repeated to the top part, which is filled with air.
Image 20: Patching regions
When both patching are done, the work can be checked on the tab “Results”, clicking on “Graphics” and then on “Contours” twice. After the new window pops up, follow the image 21 to see the phases on the geometry.
Image 21: Checking the phases distribution
3.8.RUNNING THE SIMULATION The biggest issue with simulation of multiphase flows is that the time step needs to be sufficiently small to capture the movement of the particles, and at the same time it needs to be big to reduce the computational time. For the simulation purposed here, different time steps were used and their main issues are summarized in the table 2. At the end, a time step of 5x10-4 s was the best choice since all the others were diverging. Furthermore, the number of steps was chosen as the number needed to have 6 seconds of simulation.
Time step (s) 0.1 0.01 0.001 0.0005
Issue Diverges very fast Diverges Diverges after some time Takes a long time but doesn’t diverge Table 2: Issues for different time steps
Image 22: Running the simulation
4. RESULTS The computational time was around 20 hours, using a laptop with 4 cores. Maybe this approach is not the best one, however the results seem adequate. As expected: a) The water sticks to the walls b) Liquid columns are formed c) The fluid oscillates The following images are a synthesis of the results. In the image 23 there is a legend to better understand the image 24.
Image 23: Legend for the next images
Image 24: Liquid distribution at t = 1 s, 2 s, 3 s and 5.7 s respectively
5. REFERENCES
[1] Akachi H., U. S. patent # 4921041, 1990. [2] Wikipedia, Slug flow. [3] LearnCAx, Introduction to Multiphase flow modeling in ANSYS FLUENT. [4] Wikipedia, Reynolds number. [5] Ashutosh Kr Singh, Numerical Analysis of Performance of Closed Loop Pulsating Heat Pipe
