Week 6: Conjugate Heat Transfer Simulation

Objective:

• Setup a flow simulation through a pipe
• Inlet Reynolds number should be 7,000
• 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
• Add Y+ to your post.in file
• Start with an initial base grid
• Run grid dependence test on 3 grids and show that the outlet temperature converges to
  a particular value
• Set supercyle stage interval to 0.01,0.02 and 0.03

The term conjugate heat transfer (CHT) is used to describe processes which involvevariations of temperature within solids and fluids, due to thermal interaction betweenthe solids and fluids. The exchange of thermal energy between the two physical bodiesis called study of Heat Transfer, the rate of transferred heat is directly proportional to thetemperature difference between the bodies. A typical example is the heating or coolingof a solid object by the flow of air in which it is immersed and some other exampleincludes conduction through solids, free and forced convection in the gases/fluids andthermal radiation.Typical applications of this analysis type exist as, but are not limitedto, the simulation of heat exchangers, cooling of electronic equipment, and general-purpose cooling and heating systems.

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

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

Modes of heat transfer:

• Conduction: diffusion of heat due to temperature gradients. A measure of the amount ofconduction for a given gradient is the heat conductivity.
• Convection: when heat is carried away by moving fluid. The flow can either be causedby external influences, forced convection; or by buoyancy forces, natural convection.Convective heat transfer is tightly coupled to the fluid flow solution.
• Radiation: transfer of energy by electromagnetic waves between surfaces with differenttemperatures, separated by a medium that is at least partially transparent to the(infrared) radiation. Radiation is especially important at high temperatures, e.g. duringcombustion processes, but can also have a measurable effect at room temperatures.
• An accurate description of heat transfer modes, material properties, flow regimes, andgeometrical configurations enables the analysis of temperature fields and heat transfer.

Typical design problems involve the determination:

• Overall heat transfer coefficient, e.g. for a car radiator.
• Highest (or lowest) temperature in a system, e.g. in a gas turbine, chemical reactionvessels, food ovens.
• Temperature distribution (related to thermal stress), e.g. in the walls of a spacecraft.
• Temperature response in time dependent heating/cooling problems, e.g. enginecooling, or how fast does a car heat up in the sun and how is it affected by the shape ofthe windshield?
• The fluid flow and heat transfer problems can be tightly coupled through the convectionterm in the energy equation and when physical properties are temperature dependent.While analytical solutions exist for some simple problems, we must rely oncomputational methods to solve most industrially relevant applications.
• Mechanisms and the interactions between those mechanisms, which our engineers can perform without hassle. Critical cooling applications often rely on multiple thermalprotection techniques, including internal cooling, external film cooling, etc. which areefficiently used by our analysis to cool components and limit the use of coolant. We doextensive support for Motor and Battery CHT Analysis to get optimized design for Highvoltage systems. Conjugate Heat Transfer analysis provides the temperaturedistribution in solid and coolant of the engine and clear insight on velocity distributionand mechanism of heat transfer of coolant. Results of CHT analysis become input tostructural simulations as thermal loads.

We have a wide experience in Engine CHT Analysis for various type of engines like Bikes,Passenger Cars, Racing cars, Commercial Vehicles, Marine, Agricultural equipment andEarth-moving equipment etc.

Mathematical Modeling:

The flow of thermal energy from matter occupying one region in space to matteroccupying a different region in space is known as heat transfer. Heat transfer can occurby three main methods:

• Conduction
• Convection
• Radiation

Physical models involving conduction and/or convection only are the simplest whilebuoyancy-driven flow or natural convection and radiation models are more complex.

Super Cycling Concept:

Super cycling is a technique which is used in Converge studio in the case of conjugateheat transfer problems with a solid and liquid regions. Main poblem is that both solverscannot run at the same speed since solving in fluid domain is much faster owing to thetime scale difference for heat transfer in liquids as compared to the solids. This causesproblems during the solution given that the solid side solver would not have reached asteady state/convergene in the time the liquid solver does. This is where the concept ofsuper cycling is based.

The basic idea of super cycling is that the solver for the fluid domain is paused until thesolver for the solid domain converges. The following steps are involved in performing thesuper cycling

• Solve the fluid and the solid together with the transient solver. store the instantaneousHeat transfer coefficients and temperature on the interface during process.
• Freeze the fluid solver. Time-averages the Heat transfer coefficients and temperaturesand applies them as boundary conditions at the interface.
• Solves the solid temperature until it reaches steady-state.
• Update the solid temp field and unfreezes the fluid solver.
• Repets until the solid temp converges.

Geometry dimensions:

Inner diameter = 0.03 m
Thickness diameter = 0.01 m
Length of pipe = 0.2 m

A diagnosis check is performed to check for errors.

Diagnosis check1- After geometry setup

The non-manifold problems occur due to the presence of three surfaces of a triangularelement in contact with each other which are not recommended in ordinary simulationsbut are unavoidable in CHT analysis. This error will automatically disappear after thecase setup procedure as Converge identifies this simulation to be a CHT analysis.

Diagnosis check2

Case-setup

• In order to begin the case-setup, click on the case-setup and click begin case-setup and click Time based.
• Then click on Materials and select Air to be predefined mixtures. Also enable the solid simulation and species.

Then open the Gas simulation and Global transport parameters and retain the defaultsetting. Then open the species tab, in the Query available list choose the Aluminum as a solid species. Then goto gas and in the Query available list, choose N2 and O2 as a gas species.

Then click on the Run Parameter under the Simulation Parameter and choose the transient solver under the solver tab and then choose the Full Hydrodynmic under the simulation mode . And then choose the Compressible under the Gas flow solver.

• Then open the Gas simulation and Global transport parameters and retain the defaultsetting. Then open the species tab, in the Query available list choose the Aluminum as a solid species. Then goto gas and in the Query available list , choose N2 and O2 as agas species.
• Then click on the Run Parameter under the Simulation Parameter and choose the transient solver under the solver tab and then choose the Full Hydrodynmic under the simulation mode. And then choose the Compressible under the Gas flow solver.

Boundary Conditions:

• Outer solid wall:

• Solid wall:

• Inlet

• Outlet:

• Interface:

Forward side boundary condition

Reverse side boundary condition:

Regions and Initializations:

• In the fluid region set the stream-id as 0 and velocity condition as (0,0,0). Temperatureinitial condition as 300K and pressure condition as 101325 pa.

• In the solid region set the stream-id as 1. Set the temperature boundary condition as 300K. Specify the boundary condition as Aluminum with a mass fraction of 1.00.
• Then go to physical modelling and enable the turbulence and super cycling modelling.

• The first option is to set the initial time at which the super-cycle begins storing data. Thiscan be set from 0 to any value less than or equal to the total simulation time.
• The solvers used for the solid region can be a steady or transient solver that isindependent of the solver set in the run parameters window and can be steady or transient.
• The time length fo each cycle determines the intervals at which the fluid domain ispaused and the solid domain solved for. This inteval is taken into account after the initialpause of the fluid solver at 1.
• The CFL number, SIE tolerance and relaxation factors are solver parameters that aregiven for the purpose of accuracy and speed of the solver.
• An output point must be defined in the solid region to let the solver know at which thetemperature 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.
• We are running the simulation using three base grid which is 0.001, 0.002, 0.003.

• Output files

1.Grid size = 0.001

Mesh plot 0.001:

Pressure contour 0.001:

Pressure animation:

Velocity contour 0.001:

Velocity animation:

Y plus contour for 0.001:

Y plus animation for 0.001:

Temperature contour 0.001:

SC_AVG_HTC at Mesh 0.001

2.Grid size – 0.002:

Mesh plot:

Pressure contour 0.002:

Pressure animation:

Velocity contour:

Velocity animation:

Y plus contour:

Y plus animation:

Temperature contour:

SC_AVG_HTC at Mesh 0.002

3.Grid size = 0.003

Mesh plot 0.003:

Pressure contour 0.003:

Pressure animation:

Velocity contour for 0.003:

Velocity animation:

Y plus contour for 0.003:

Y plus animation:

Temperature contour for 0.003:

SC_AVG_HTC at Mesh 0.003

Results:

Effect of supercycle stage interval

Fluid Side Mean temperature

Table

Supercycle stage intervel Temperature value

0.01 358.622

0.02 358.129

0.03 356.986

Solid Side Mean Temperature

Table:

Supercycle stage interval Temperature value

0.01 704.614

0.02 701.658

0.03 692.928

Supercycle at the monitor point

In the above reults, we set the different values of supercycle stage interval. The timelength for each cycle stage from supercycling modelling to 0.01, 0.02 and 0.03. In thesupercycling mode converge continue to solve both the fluid and solid equations andstores the heat transfer coefficient and near-wall fluid cell temperatures for a timeequal to the supercycle stage interval. In the start converge solves both fluid and solidequations together using the transient solver (but does not store the solid heat transferdata ) from the start of the simulation until the supercycle start time in order to developthe fluid flow field. At supercycle start time converge begins storing values for a heattransfer coefficient and near wall temperature for each cell at the solid/fluid interface,one value for each time-step.

In the above plots, we can easily observe that setting the lower value of supercyclestage interval converges to the exact values of temperatures. Basically we increase thevalue of supercycle stage interval.

Time at mesh 0.001:

Time at mesh 0.002:

Time at mesh 0.003:

Conclusion:

Results discussion of mesh independency:

In this challenge we have performed the conjugate heat transfer analysis in a solid pipe.
We have performed the grid independency test with 0.001m, 0.002m, 0.003m. From the above plots, we can clearly say that the as the mesh finer, the accuracy in the results increases. But when the mesh goes more finer and finer the computational cost has been increased.

Mesh size 0.001 0.002 0.003

Fluid mean temperature(K) 353.285 351.738 345.402

Solid mean temperature(K) 665.76 745.452 823.746

Computational time used by program(S) 21389.76925 1287.318420 346.041404

As summarized in the above table, as the mesh becomes finer we got the values which is near to the exact solution. At the 0.001 mesh we can observe that it takes too much time as
compared to the other ones.

Results discussion of the effect of supercycle stage:

We set the supercycle stage interval, i.e time length for each cycle stage from supercycle modelling is used 0.01, 0.02 and 0.03. And for smallar value of supercycle stage
interval the convergence is achieved faster. A monitor point is also create in the solid thickness boundary to observe the effects of super cycling. The plot shows that the steady state
solver is employed in the solid region at fixed intervals of time (i.e. the super-cycle stage interval) and the results are compared while the transient solver computing the fluid flow is
temporarily paused. Super-cycling is done as the heat flow in the solids when depicted by a transient solver, is time consuming. Hence it is better to apply steady-state analysis for the
heat transfer through the solid while studying the behaviour of fluid flow through the pipe.

Temperature profile in the solid region

As we mentioned above, the steady state solver is employed in the solid region resulting in the sudden increase in temperature at various time intervals. This does not represent
the actual temperature flow in the solid and only the steady-state temperature. Note that the increase in the temperature in the solid regions is due to the heat flux added to the solid outer wall.

Temperature profile in the fluid region

The transient solver is used to simulate the flow in the fluid region and hence the actual increase in the temperature is observed in this case. The increase in temperature is due to the
transfer of heat from the solid to the fluid.