Conjugate Heat Transfer Simulation

Aim:

To setup flow through pipe and simulate Conjugate Heat Transfer(CHT).

Objective:

1.To setup flow through pipe.

2.Perform Grid dependence test with 3 different grid size.

3.Effect of supercycle stage interval on output.

 

Introduction:

CONJUGATE HEAT TRANSFER:

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 study of Heat Transfer, the rate of transferred heat is directly proportional to the temperature difference between the bodies. 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. 

Significance of y+:

The y+ value denotes where in the y+ vs u+ curve we are with respect to the cell size. It is undesirable to have a cell size that leads to a y+ of between 10 to 30 since the modelling of flows transitioning from laminar to turbulent is not easy and is still being researched. Due to this fact, it is better to have a y+ of less than 10 meaning we'd be at the laminar region or have a y+ of greater than 30 where we can go with a wall function and still achieve results. The y+ value can be used as a marker based on which we can decide on the base grid size and make a decision based on the computing power as to whether the grid needs to be refined further or coarsened.

 

Problem Desciption:

Geometry:

Geometry is created in CONVERGE studio with center1 (0,0,0) and center2 (0,0,0.2)  with inner radius of 0.015 m and outer radius of 0.02m.

         

Geomtry with different Region according to materials:

Region with ID 0 represents Air and with ID 1 represent Solid.

        

 

Case Setup:

Material:  predefined Mixture : Air

Species:    Gas = O2,N2

                Solid = Alluminium

 

Run Parameters:  Solver = Transient

Simulation Time parameter: Start Time =0 s

                                         End Time = 0.5 s

                                         Initial Time Step = 1e-7

                                         Minimum Time Step = 1e-7 s

                                         Maximum Time Step = 1 s

Initial velocity Calculation:

Inlet Reynolds number should be 7,000.

At 25 deg C,properties of air are

Density = 1.184 kg/m^3

Dynamic Viscosity = 1.86e-5 Pa.s

radius of Cylinder = 0.015 m

 

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

7000 = (1.184*V*0.03)/(1.86e-5)

V = 3.665 m/s

 

Region & Initialisation:

Stream ID:0     Fluid Region

                       Velocity= 3.665 m/s (Z-direction)

                       temperature = 300 K

                       Preassure = 101325 Pa

                       Species = Air (O2,N2)

Stream ID:1     Solid Region

                       temperature = 300K

 

Boundary Conditions:

1.Solid Outer Wall(Solid region):  Type : Wall

                                                    Velocity : Slip

                                                    Temperature: heat Flux

                                                                       Flux: -10000 (negative value shows heat is going inside the system)

2.Thickness(Solid region):      Type : wall

                                              Velocity: Slip

                                              Temperature: Zero normal gradient

3.Inlet (Fluid Region):     Type : INFLOW

                                      Velocity: 3.665 m/s (Z-derection)

                                      Preassure: Zero normal gradient

                                      Species : Air(O2,N2)

4.Outlet (Fluid Region):   Type : OUtFLOW

                                       Preassure: 101325 Pa

                                      Temperature: 300 K

                                      Species : Air(O2,N2)

5.Intreface :

Interface is boundary type that separates two types of material or phases.

Forward Region:     Region:Fluid Region

                               Velocity: Law of Wall

                               Temperature: Law of Wall

Reverse Region:     Region:Solid Region

                               Velocity: Slip

                               Temperature: Specified Value

 

Turbulence Model: RNG k-

$\mathrm{Super-Cycle\; Modelling:}$

Super Cycling is method used by CONVERGE to deal with conjugate heat transfer problem. Time required for fluid solver to reach steady state is much smaller than that taken by solid solver hence it will create the problem for solid side solver as it will not reach steady state in provided time. Hence we need to pause fluid solver until solid solver reach steady state.

To understand Super cycling effect, Set supercyle stage interval to 0.01,0.02 and 0.03.

                

 

Base Grid:

To conduct grid dependecy test,set the grid size to 0.004,0.003 and 0.002 m.

 

Result:

Grid Dependency test:

As the mesh size reduced from 0.004m to 0.002 m, the mesh becomes finer.

               

                                                                       fig: Mesh at 0.004 m

              

                                                                         Fig: Mesh at 0.003 m

             

                                                                    Fig: Mesh at 0.002 m

 

Temperature plots for Fluid and Solid region:

Following temperature plots are taken at super cycle stage of 0.03.Outlet Temperature for fluid and solid region is diferent.fluid solver tends to converge at lower temperature than solid solvers.Temperature profile in fluid region is looking fully Transient.

            

            

 

Total Cell Count:

As the grid size decreases total cell count increases.

for grid size 4mm,cell count is ~5000

for grid size 4mm,cell count is ~10000

for grid size 4mm,cell count is ~35000

            

Y+:

Grid size 0.004m:

            
                     

Grid size 0.003m: 

           

 

Grid size 0.002m: 

          

 

Effect of supercycle stage interval:

Super Cycling is method used by CONVERGE to deal with conjugate heat transfer problem. Time required for fluid solver to reach steady state is much smaller than that taken by solid solver hence it will create the problem for solid side solver as it will not reach steady state in provided time. Hence we need to pause fluid solver until solid solver reach steady state.

Here,transient solver will solve both fluid and solid region for initial steps and stores the heat transfer coeficient and temperature at interface boundary condition.Then it freezes the Transient solver and time average the heat transfer coefficient at interface Boundary and run steady state solver for solid region untill it reaches steady state. 

 

         

                                                                          Fig: Fluid Region Temperature plot

        

       

                                                                             Fig: Fluid Region Temperature plot

Animation:

Case 1: Grid size =0.004 m

Velocity Contour:

      

 

Preassure Contour:

      

 

Temperature Contour:

      

 

Case 2: Grid size =0.003 m

Velocity Contour:

      

 

Preassure Contour:

      

Temperature Contour:

      

 

Case 3: Grid size =0.002 m

Velocity Contour:

      

Preassure Contour:

      

Temperature Contour: