Conjugate Heat Transfer Simulation of Flow

Conjugate Heat Transfer Simulation

Objective: Baseline configuration

• Setup a flow simulation through a pipe
• Inlet Reynolds number should be 7,000

• HINT: Use the below formula to calculate velocity for corresponding value of REYNOLD NUMBER and give DIRICHLET BC for velocity at inlet and specify the value for velocity calculated at INLET BC using below formula ,

Re = (rho*V*D)/(Dynamic viscosity)

• Turbulence modelling - K-Epsilon
• Supercycling parameters - same as in the video

Additional 3D outputs

• Add Y+ to your post.in file

Grid dependence test

• Start with an initial base grid
• Run grid dependence test on 3 grids and show that the outlet temperature converges to a particular value

Effect of supercycle stage interval

• Set supercyle stage interval to 0.01,0.02 and 0.03
• For these three values, how does the total simulation time compare against the baseline configuration

It is expected to show the mesh generation using PARAVIEW.

Also create an animation and upload it on You tube and provide the You tube link for an animaion in your report.

Theory:

Conjugate Heat Transfer and its Significance:

The term conjugate heat transfer (CHT) is used to describe processes which involve variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids. The exchange of thermal energy between the two physical bodies is called the study of Heat Transfer, the rate of transferred heat is directly proportional to the temperature difference between the bodies. A typical example is the heating or cooling of a solid object by the flow of air in which it is immersed and some other example includes conduction through solids, free and forced convection in the gases/fluids and thermal radiation.

CHT simulation is more suitable for structural analysis of the Engine as the Red heated region of the engine is highly prone to structural damage due to fatigue.

Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas in fluids, convection usually dominates. Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers. Forced convection is the most common way to achieve high heat transfer rate. In some applications, the performances are further improved by combining convection with phase change (for example liquid water to vapor phase change).

Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls, and because solids are usually immersed in a fluid.

The fluid flow and heat transfer problems can be tightly coupled through the convection term in the energy equation and when physical properties are temperature dependent. While analytical solutions exist for some simple problems, we must rely on computational methods to solve most industrially relevant applications.

CHT can be performed to improve cooling performance of the water jacket and increase engine life. Advancements in cooling for applications such as gas turbines components require improved understanding of the complex heat transfer mechanisms and the interactions between those mechanisms. Critical cooling applications often rely on multiple thermal protection techniques, including internal cooling, external film cooling, etc. which are efficiently used by CHT analysis to cool components and limit the use of coolant. For Motor and Battery CHT Analysis to get optimized design for High voltage systems. Conjugate Heat Transfer analysis provides the temperature distribution in solid and coolant of the engine and clear insight on velocity distribution and mechanism of heat transfer of coolant. Results of CHT analysis become input to structural simulations as thermal loads.

CHT Analysis for various types of engines like Bikes, Passenger Cars, Racing cars, Commercial Vehicles, Marine, Agricultural equipment and Earth-moving equipment etc.

Modes of heat transfer

• Conduction: diffusion of heat due to temperature gradients. A measure of the amount of conduction for a given gradient is the heat conductivity.

The rate of Heat transfer in conduction is given by the Fourier’s law:

Qc= -K*(dT/dx)

Where, Qc is (Heat flux=Q/A )which is rate of heat flow per m^2 of heat area normal to the direction of heat flow.

K is constant known as Thermal conductivity.

dT/dx is the change in Temperature only along one direction in x.

• Convection: when heat is carried away by moving fluid. The flow can either be caused by external influences, forced convection; or by buoyancy forces, natural convection. Convective heat transfer is tightly coupled to the fluid flow solution.

The convection is of two types: Forced Convection and Natural Convection.

In Forced Conevction, the fluid is forced to flow over a solid surfaces by external means such as fan, pump or atmospheric wind.

When the fluid motion is caused by the buoyancy forces that are induced by the density differences due to the variation in temperature in fluid, the convection is called Natural or Forced Convection.

Thus, heat transfer rate Qconv=h¯⋅A⋅(Ts−T∞)

Where, Qconv is the rate of Heat transfer by Convection.

A is the Heat transfer area.

h¯ is the average convective Heat transfer coefficient over the area A.

Ts is the surface temperature and Tinfinity is the temperature of fluid.

• Radiation: transfer of energy by electromagnetic waves between surfaces with different temperatures, separated by a medium that is at least partially transparent to the (infrared) radiation. Radiation is especially important at high temperatures, e.g. during combustion processes, but can also have a measurable effect at room temperatures.

Heat Transfer Coefficient(HTC) and its Prediction

Heat transfer coefficient, often denoted by hx or h¯h¯ and measured in Wattm2⋅K, is a quantitative characteristic of convective heat transfer, typically between a surface and a medium, which relates heat flux qs,x˙′′with the temperature difference between the surface and the medium. For steady state heat transfer i.e. when ∂T∂t=0,

qs,x˙′′=hx⋅(Ts−T∞)

Here hx is the localized heat transfer coefficient at x, Ts is the surface temperature of the object from which heat is being transferred, and T∞ is the ambient temperature.

The overall heat transfer coefficient can be calculated as follows:

h¯=∫Ahx⋅dAh¯=∫Ahx⋅dA

Thus, heat transfer rate q˙=h¯⋅A⋅(Ts−T∞)

There is one more equation which relates heat flux with the temperature gradient:

Heat transfer coefficient for Conduction

q˙′′=−kf(∂T∂y)

Here, kf is the thermal conductivity of the medium (unit: Wattm⋅K), which measures its ability to conduct heat.

Combining the equations and multiplying by length of the surface, we get a dimensionless number called Nusselt Number Nu which is the ratio of heat transferred through convection to the heat transferred through conduction. In simple terms, it tells us how much the heat transfer is enhanced due to fluid motion. Hence HTC is depend on Nussselt number.

Nusselt Number(Nu)= Convection Heat transfer/ Conduction Heat Transfer.

`Nu¯=(h¯⋅L)/(kf)`

A lot of calculations related to heat transfer coefficient can be done by using certain statistically established correlations involving the Nusselt number and other dimensionless numbers like Reynolds number and Prandtl number.

Factors affecting HTC:

1. Velocity of the fluid.
2. Density of the fluid.
3. Viscosity of the fluid.
4. conductivity of the fluid.
5. Characteristic length of the heat transfer area.
6. Heat capacity of the fluid.
7. Temperature difference between the hot and cold body.
8. Mean film temperature of the fluid.

Super Cycle Modelling:(The article is taken from skill lync website)

Super-cycling is a method used by CONVERGE Studio in the case of conjugate heat transfer problems with a solid and liquid regions.

The integral problem here is that both solvers cannot run at the same speed since solving in the fluid domain is much faster owing to the time scale difference for heat transfer in liquids as compared to solids. This causes problems during the solution given that the solid side solver would not have reached a steady state/convergence in the time the liquid solver does. This is where the concept of super-cycling can be used.

The basic idea of super-cycling is that the solver for the fluid domain is paused until the solver for the solid domain converges. This pausing is done in intervals that can be set by the user and will be explained below.

Super-cycling in Converge:

1.The first option is to set the initial time at which the super-cycle solver begins storing data. This can be set from 0 to any value less than or equal to the total simulation time-> 0.05s,/ 0.1s

2.The solver used for the solid region can be a steady or transient solver that is independent of the solver set in the run parameters window and can be steady or transient.->0.01s, /0.02s, /0.03s, /0.05s

3.The time length for each cycle determines the intervals at which the fluid domain is paused and the solid domain solved for. This interval is taken into account after the initial pause of the fluid solver at 1.

4.The CFL number, SIE tolerance and relaxation factors are solver parameters that are given for the purpose of accuracy and speed of the solver.

5.An output point must be defined in the solid region to let the solver know at which point the temperature data must be calculated. This point must be given in the solid domain as the solver runs for the solid domain and once this value converges, the fluid domain solver is continued. At 0.18m in z-column from the inlet

• Conduction CFL number 100
• Relaxation factor 1.4

In order to better understand what is happening during super-cycling, consider the following scale.

The scale shows the super-cycle steps from start to end of the solver,

Initially, for 0.1s, both the solvers are run. At the first interval, 0.1s, the fluid solver is paused and the solid side solver is continued to run towards convergence. As mentioned in point 2, the super-cycle solver is used in this case and the solid side solver is run to the steady state using a steady or transient solver.

Once the solid side reaches convergence, the fluid solver is restarted. Both solvers run up to the second interval, in this case, 0.05s at which point the same process occurs and super-cycle data is collected. Super-cycle data is the temperature that is measured inside the solid as mentioned in point 5.

This process is continued till the simulation end time. The intervals must be chosen based on the simulation time and can be set to any value. Super-cycling is only meant to speed up the simulation and if the simulation is run without super-cycling, the convergence of the data will take a long time.

Y-plus: It's important that the mesh near the wall is properly sized to ensure accurate simulation of the flowfield. By knowing the Y+ (1-5 for laminar flow & 30-10,000 for Turbulent flow) value, the height of the first mesh cell off the wall can be calculated.

Simulation:

The following Simulation tools will be incorporated:

1.Converge studio:- To pre-process the data that needs to simulate the case. It plays an important role in generating important 3d input files only using GUI. It does not run simulation directly, however it generates inputs files which use to run the simulation.

2. Cygwin:- Cygwin is a collection of GNU and open-source tools that provide the functionality similar to Linux distribution on windows.
3. Converge msmpi 3.0:- To run the simulation using these input files in Cygwin in series or in parallel.
4. Post convert:- To convert all the output files which are processed by converge msmpi into the files which will be readable for post-processing in Paraview.
5. Paraview :- To post-processing to obtain the contour, plots, etc. It is an open-source, multi-platform data analysis and visualization software.

Geometry Setup:

• Create a hollow cylinder with some thickness

• Boundary Flagging

Case Setup/Simulation Setup:

MATERIAL:

Gas Simulation:

• As only air is our working medium hence uncheck Reaction Mechanism.
• Predifined mixture: air
• Enable species(not in mech.dat) as we want to assign the participating species of Air like O2 and N2

Solid Simualtion:

• Click predifeined (under solid database)
• Click dat to load the database of aluminium properties like temperature, density, specific heat , conductivity.

Global Transport Properties

• Terbulent Prandtl number: 0.9
• Terbulent Schmidt number: 0.78

Species:

• Click Solid
• Click on Quary available list and add Aluminium.
• Click on Gas species and add O2 and N2

SIMULATION PARAMETER:

Run Parameter:

• Solver: Pressure-based Transient
• Simulation Mode: Full Hydrodynamic
• Gas flow Solver: Compressible (as air is working medium)

Simulation Time Parameter:

• End time: 0.5s
• Start time: 0s
• Initial time step: 1e-07 s
• Minimum time step: 1e-07 s
• Maximum time step: 1 s

REGION & INITIALIZATION:

• Click on Region and Initialization and add 2 Regions.
• Region 0 as Fluid region-Stream ID 0: temperature 300k; Pressure 101325 Pa
• Species Air
• Region 1 as Solid Region - Stream ID 1:
• Species Aluminium.

BOUNDARY:

• Naming: Select faces and name as Solid outer wall, Solid thickness, Inlet, Outlet.
• Bounday condition:

Solid Outer wall:

• BOUNDARY TYPE: wall
• Wall motion type: stationary
• Velocity BC: Slip as the flow is Turbuelent in which there is very very less Viscous-laminar region hence we neglect this region so as viscous effect.
• Temperature BC: Heat flux= -10,000 (negative sign indicates heat accepted by the system)

Solid Thickness:

• BOUNDARY TYPE: wall
• Wall motion type: stationary
• Velocity BC: Slip as the flow is Turbuelent in which there is very very less Viscous-laminar region hence we neglect this region so as viscous effect.
• Temperature BC: Neumann BC as the heat transfer takes place from the outer wall to the wall thickness.

Inlet:

• Bounady Type: Inflow
• Pressure BC: Zero normal gradient(Neumann BC)- As we don’t know the value of pressure at a given velocity. So by assigning a Neumann Boundary condition, the pressure at a given velocity value will be calculated by Converge itself.
• Velocity BC: 5m/s
• Species Boundary condition: air

Outlet:

• Boundary type: OUTFLOW
• Pressure BC: 101325 Pa
• Velocity BC: Zero normal gradient(Neumann BC)- As we don’t know the value of velocity.

Inteface:

• Boundary type: INTERFACE
• Forward Boundary-Fluid region- (If the normal are pointing toward the fluid region, then the forward boundary for Fluid and it becomes Reverse boundary for other phase i.e solid)
• Velocity BC: Law of the wall. (as flow is Turbulent)
• Temperature BC: law of wall.
• Reverse region: Solid region
• Velocity BC: Slip
• Temperature BC: Specified value

Assign Fluid region for Inlet and Outlet

Solid region for Solid outer wall and Solid thickness.

Turbulence model:

• RNG k-epsilon

Base grid:

• dx=0.004m; dy=0.004m; dz=0.004m.
• dx=0.003m; dy=0.003m; dz=0.003m
• dx=0.002m; dy=0.002m; dz=0.002m

Enable Super Cycle Modelling:

Post-variable selection:

Post-processing: Assign y-plus

Output files:

Time interval for writing 3d output data files=0.005s

Time interval for writing text output files=1e-6s

Export input files and Running the Simulation:

Now we have successfully setup the Case and need to export the input files to run the Simulation.

Run the Simulation in Cygwin using parallel processor.

Post Converting:

Now we need to convert all the output files which are processed by converge msmpi into the files which will be readable for post-processing in Paraview

Paraview:

We need to Post-process the output files to obtain the contour.

Results:

CASE(1): Different mesh size but constant supercycle stage interval

Contour at constant different Mesh size as 4mm, 3mm & 2mm and at constant Supercycle stage intervals as 0.05s:

Mesh:

The Mesh is getting finer as the grid size decreases.

Velocity Contour:

As the flow enters inside the cylinder, at some portion of inlet upto certain horizontal direction the viscosity effect near the wall is very small, but as the flow progresses, the vicous effect takes place, due to which velocity is minimum at the outlet wall portion and is maximum at the center of the cylinder.

As the mesh size, decreases we can see the visibility of the viscosity more clear.

Temperature contour:

As the friction near the wall at outlet increases, the temperature also increases, where its minimum at the center of the cylinder.

Y plus:

As the mesh becomes finer, the y plus value decreases. That means the first cell size at the Fluid and Solid Interface decreases, hence the cell counts increases which help to capture the physics of flowfield more accurately near the wall.

Plots at constant different Mesh size as 4mm, 3mm & 2mm and at constant Supercycle stage intervals as 0.05s:

Total cell counts:

The Mesh is getting finer as the grid size decreases and cell counts increases 5000, 10000, & 35000 approximately.

Mean Temperature of Solid region:

For all the mesh sizes, we can see that the temperature is updating at the same interval of time, 0.05s, and finally converges at 0.4s. However, over the entire path (transient) and at the endpoint (final converged point) the temperatures are different. The temperature is due to the introduction of heat flux to the Solid outer cylinder wall.

Mean Temperature of the fluid(gas) region:

For all the mesh sizes, we can see that the temperature is updating at the same interval of time, 0.05s, and finally converges at 0.4s. However, over the entire path (transient) and at the endpoint (final converged point) the temperatures are different. There is a Heat transfer between Solid wall and fluid taking place.

CASE(2): Different supercycle stage interval but constant mesh size

Mean Temperature of Solid region:

The different supercycle stage intervals for solid region of 0.01s,0.02s, & 0.03s, in which the less interval SC is converging faster than the large interval. However, the final convergence temperature for all the intervals is the same.

Mean Temperature of the fluid(gas) region:

The different supercycle stage intervals for a fluid region of 0.01s,0.02s, & 0.03s, in which the less interval SC is converging faster than the large interval. However, the final convergence temperature for all the intervals is the same.

Animation:

Velocity:

The temperature of Fluid is maximum at the wall due to friction and Heat transfer from the Solid surface. The velocity of Fluid is maximum at the center of the cylinder, whereas it is minimum near the wall due to viscosity.

Conclusion:

• Super-cycling helps to reduce overall simulation time.
• By knowing the Y+ value the first cell height of the mesh near the Boundary or Interface of the wall can be calculated. As the Mesh size decreases, the y+ decreases, cell size also decreases, and cell counts increase.
• The temperature of Fluid is maximum at the wall due to friction and Heat transfer from the Solid surface.
• The velocity of Fluid is maximum at the center of the cylinder, whereas it is minimum near the wall due to viscosity.
• As the Super-cycling time interval is less, the temperature plot converges faster.
• As the mesh becomes finer, the accuracy of the temperature result increases.