Week 4 - CHT Analysis on Exhaust port

Objective :

  In this challenge,

1.  We will ,give a brief description of why and where a CHT analysis is used.

2.  We wil simulate both fluid flow and also the heat transfer to the solid i.e., CHT Analysis on an Exhaust port

3. Then we will calculate the wall heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas.

4. We will verify the HTC predictions from the simulations are right? And mention the factors that the accuracy of the prediction depend on.

 Conjugate Heat Transfer (CHT) analysis :

Conjugate Heat Transfer analysis allows for the simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them and transported via conduction within solids and adiditionally via convection within fluid domains.Conjugate heat transfer analysis can accurately predict heat transfer by simultaneous solving all the relevant solid and flow field heat transfer processes.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. Conjugate heat transfer is observed in many situationsfor example: conduction through solids, free and forced convection in the gases/fluids and thermal radiation.

• The three main modes of heat transfer:
  ‐ Conduction is heat transfer that occurs when a temperature difference exists across a stationary medium.
  ‐ Convection is the heat transfer between a surface and a moving fluid when there is a temperature difference between the two.
  ‐ Radiation(thermal radiation) is the emission of energy in the form of electromagnetic waves. In the absence of an intervening medium ,there is net heat transfer by radiation between two surfaces at different temperatures.

Conduction :

• Conduction is thermal energy transmission through solid or fluid by the action of translational, rotational and vibrational motion of atoms and molecules.
• Molecular collisions transfer energy from more energetic molecules to less energetic ones. Higher temperature = Increased atomic/molecular motion
• Conduction occurs in all fluid and solid media.
•  Due to the Second Law of thermodynamics, heat must always be conducted from higher to lower temperatures.
•  Conduction problems often involve fluid flows at the boundaries of the solid, which serve as a mechanism for heating or cooling the solid.
• Conduction is the transfer of energy from more energetic to the less energetic particles of a substance via interactions between the particles at molecular levels due to a temperature difference.
• Temperature at any point can be associated with the energy of random translational, internal rotational and vibrational motions of gas molecules.
• Molecular collisions transfer energy from more energetic molecules to less energetic ones .
• Higher molecular energies are associated with higher temperatures, and the energy transfer always occurs in the direction of decreasing temperature in the presence of a temperature gradient.
• The mechanism of conduction is the same for liquids as the molecules are closely spaced and the molecular interactions are stronger and more frequent than gases.
•  In the case of solids, conduction is associated with atomic activity in the form of lattice vibrations. In the case of an electrical conductor, the translational motion of free electrons also contributes to energy transfer.
• The heat transfer process can be quantified in terms of appropriate rate equations which are used to compute the amount of energy being transferred per unit time.
•  In the case of heat conduction, the rate equation is Fourier’s law. For a one-dimensional plane wall
  this is expressed as            

                                      

• Here,
  ‐ 𝑞_𝑥^′′(𝑊/𝑚^2) is the heat transfer rate per unit area in the x-direction.
  ‐ 𝑘 is the thermal conductivity (𝑊/𝑚𝐾) and is a characteristic of the wall material.
  ‐ The negative sign signifies the fact that the heat transfer is in the opposite direction of the temperature gradient

Convection :

• Convection is transfer of heat by the combination of the bulk motion of a fluid and random molecular motion (diffusion).
• Heat is transferred to/from the fluid via conduction at walls.
• Fluid carries thermal energy to other parts of the system.
• Heat transfer only due to the bulk motion of the fluid (no diffusion) is referred to as advection.
•  Convection heat transfer can be classified into:
•  Forced convection:  Flow is caused by external means, such as by a fan, a pump or atmospheric winds.
• Free (or natural) convection: Flow is induced by buoyancy forces, caused by density differences due to the temperature variations in the fluid.
•  Mixed (combined) connection: Forced and natural convection can also exist if both external driving forces and buoyancy forces exist.
• Heat transfer by convection is rooted in the idea that the heat transfer rate is proportional to the temperature difference between a fluid and a heated/cooled body.
•  This idea is called Newton’s Law of Cooling. The parameter governing the rate of heat transfer is the heat transfer coefficient, usually denoted ℎ.

                            

          Here,  𝑞′′ = Convective heat flux
                     𝑇𝑠= Temperature of the solid surface
                    𝑇∞= Temperature of the fluid

•  One of the central problems in convection is determining the heat transfer coefficient for a given flow field.
• The heat transfer coefficient depends on the conditions in the boundary layer, and it is affected by the surface geometry, the nature of the fluid flow and various fluid thermodynamic and transport properties.

Radiation Heat Transfer :

• Thermal radiation heat transfer is the emission of energy via electromagnetic waves.
•  All matter at a nonzero temperature emits thermal radiation.
•  This emission is due to changes in the electron configurations of the atoms or molecules, and the energy is transported via electromagnetic waves (or photons).
• Radiation intensity depends on body temperature and surface characteristics.
• Unlike conduction or convection, radiation does not require the presence of a material medium and can occur in a vacuum.
•  Radiation is an important mode of heat transfer at high temperatures.
•  It is also the only mode of heat transfer in outer space, and this is how the solar energy reaches Earth.

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. An accurate description of heat transfer modes, material properties, flow regimes, and geometrical configurations enables the analysis of temperature fields and heat transfer. Such a description is also the starting point for a numerical simulation that can be used to predict conjugate heat transfer effects or to test different configurations in order, for example, to improve thermal performances of a given application.

 Introduction : 

Here our objective is to simulate the flow through it as the flow is going through manifold it is going to exchange heat with the solid,we want to simulate that process.We are going to do this by initially assuming that the flow is comming through the exhaust which is basically through all the four inlets and we are giving or going to assume that the fluid isreally very hot and thats going to heat the solid pipe from inside and on the external surface we are assuming that htere is a particular heat transfer .So inreal world scenario as your engine is air cooled as it is exposed to air and air which is near to the port has particular heat transfer coefficient and tha would be provided as input and that value depends on the external air reynolds number.We can simualate it and find the value but here we are just giving the value as input i.e, heat transfer coefficient for the outer wall boundary condition.Then by aking these assumptions into consideration we start the simulation.

Solution procedure :

• We wil simulate both fluid flow and also the heat transfer to the solid i.e., CHT Analysis on an Exhaust port with the steady state .Then for solving we follow the below procedure :   

                 1)Geometry setup 

                 2)Meshing

                 3) Problem setup

                 4)Solving

                 5)Post processing

• Then we calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas.

Simulating the flow with the Steady case :

In the ANSYS work bench we first open the fluent module by drag and drop.The we follow the procedure we have mentioned above

1) Geometry setup :

• In fluent module we have to open spaceClaim and import the geometry.
• if you look closely to the geometry it has solid part .So first let us extract the fluid volume.For that we have to go to,

        prepare -> volume extract -> select edge selection -> then select all the edges of inlet and outlet -> then click ok.fluid volume will be created .

• Then after the volume has created then in the design  change the name of the components i.e., fluidvolume to fluid and solid volume to solid. 
• Then if you open meshing and mesh you will see that the mesh is fine,but when you zoom it at the inlets or outlet you will see that the mesh is non conformal ,meaning that one particular vertex of solid part is not connected exactly with the fluid vertex or element.And if you have conformal mesh i.e., when the edges are connected exactly then only the heat is going to transfer smoothly.You may also see physical gap if it non conformal mesh.For CHT simulation we should not have such kind of mesh,We shold have both of the volume overlap perfectly,inorder to fix that we need to share topology.

                                               

• In order to all of this to work as one component we need to make sure that share topology is set to share.Only then these two individual blocks going to exchange information i.e., the meshing is going to be uniform and with perfect connectivity.So we need to fix this.                           
• For that in properties enable share for share topology,But before that we need to do important step to follow.We need to take two volumes and move into a new component ,and this is the final geometry which consists of solid volume and fluid volume and then delete the old empty components.Now enable the share toplology and then go work bench and click share .This is very important if you dont do this step you will not see the single interface between them.So this particular step takes care of creating the interfaces,so that you will have one interface between your solid volume or block and fluid block.Once you have done this you will see the pink circles at the interface,that basically tells you where the things are being shared.Basically what this means is that you will have a sharing between inner wall of solid and outer layer of fluid will have a common interface and bounds of share is one.This is only interface you will see.

                                            

• Now if you open meshing and you will see that there is perfect mesh connectivity and the interface is shared perfectly.This is exactly how we need to make meshes for CHT simulation.                              
• This completes the creation of geometry.Then we close the spaceClaim ,the progress will be saved automatically.

2) Meshing :

• For meshing we open Meshing,where we mesh our model so that we can use it to solve our model.
• In general it is always good to name the surfaces before meshing. So let us do that.
• We first select the entity by using the entity selection by using faces so that we can provide name for our entity selection.

        steps : select the edge you want to name  by using edge selection -> then press N -> name the selection.

• In the similar way we name our inlets,outlet,and for outer face just double click on the outer part any where and ANSYS mesher will automatically select the faces we require and we name it ass outer wall convection(Since we are going to use convective BC for it), and dyou can see additional walls like flangs which have not selected you cn name them or even if you dont name what ANSYS mesher will do is it is going to automatically import those into fluent  as a wall by default these walls will have adiabatic BC,which is exactly what we want.
• Then next thing to do is to mesh.We click the mesh option in the side window and create our base line mesh.We then refine mesh.Let's mesh the geometry .Once the mesh has done we need to see what are the things we have to refine.Let us refine one by one .Let us start with creating inflation layer.

a) Inflation :

• Inflation layer helps us to create a body fitted mesh.It means it creates a layer of mesh same as the geometry.
• Since at the interface it is very important and we want to calculate the heat transfer at that place we need to take that region and create inflation layers so that flow is captured exactly and the values are calculated exactly.
• To do this we first with selecting  fluid part  and naming it as inflation layer.
• In the global mesh select inflation option  and in that for use automatic inflation - select all faces in the choosen named selection and for named selection - select the inflation layer which we have just named.
• And for inflation option we use first layer thickness and we give this based on y+ value and the turbulence model we use.Here we use k-omega SST turbulence model so y+ should be in between 0.1 to 5.Lets calculate the first layer thickness.

1.  U∞ = freestream velocity = 5 m/s
2.     ρ = freestream density     = 1.225 kg/m3
3.     μ = dynamic viscosity       = 0.000017894 kg/m s 
4.    L  =diameter of the inlet(m) = 0.1662206 m
5.    desired y+ = 1

 =>    Then Reynolds number,  Re  =   (ρ*U∞*L)/μ = (1.225*5*0.1662206)/ 0.000017894 =56896.2319

 =>  skin friction coefficient, C_f    =  (0.026)/Re ^1/7 = 0.026/(56896.2319)^1/7 = 0.00544096214

 =>   wall shear stress, Tau_wall   =  (C_f*ρ*U∞^2)/2  = (0.00544096214*1.225*(5)^2)/2 =0.08331473276

 =>   friction velocity , U_friction   =  (Tau_wall/ρ)^1/2 = (0.08331473276/1.225)^1/2 = 0.26079115541

=> Therefore, first layer thickness , Δs =  (y+ * μ)/(U_friction*ρ) = (1*0.000017894)/(0.26079115541*1.225) = 0.0000560116653 m = 0.0560116653 mm

•  Now we got the  first layer thickness ,let us give the above first layer thickness and maximum of 10 growth layers and with a growth ratio of 1.2 for inflation layers.                                                           

•  Clear the generated data and we have to mesh again.By this we have completed the meshing process then we have to update or generate the mesh again.You can observe formation of inflation layers.

                                                                                                                          

b) Sizing(Body sizing) :

• We are making the mesh of inside fluid domain finer by using sizing.To do this,
• Right click on mesh => sizing => in geometry -we select inner fluid volume by hiding outer component and give size 22 mm  => Then generate mesh again you will see inner fluid volume is refined finer.

                                             

• Below is the view of the final mesh.

                                             

•  Now we have to check the quality of the mesh.steps : mesh ->quality-> mesh metric-> Element quality                                               
• Here our minimum quality is around 15 %,so we can move further for our solution setup.

3) Problem Setup :

• To set up our problem we open Fluent and setup inital conditions , boundary conditions material etc.,
• We first start with checking the mesh quality using perform mesh check under domain.If no error is seen in console window then we can proceed further.
• Then we move move to setting up physics where we select the solver ,viscous model ,initial and boundary conditions etc.,
• We use a steady state pressure based solver to solve our model.

Physics :

General :

                      Solver type      :      pressure based

                          time            :      steady state

       velocity formulation         :       absolute

 models  :

                       viscous model  :       k-omega SST

 Material  :                   Fluid  :  Air

                                    Solid : aluminum

 Zones :

                  Cell zone : In cell zones you will see fluid volume,it is of type fluid with material air and solid volume it is of type solid with material aluminum.

  Boundary conditions :We will basically give our boundary conditions here such as inlet velocity and outlet conditions.

      we   give,

  Inlet  :  

                          velocity        :     5 m/sec

                        temperature   :   700K

 Outlet  :

                       pressure outlet : gauge pressure = 0 pa

Outer wall convection  :      

                                type : wall    

                 Theremal conditions => convection  : Heat transfer coefficient = 20 W/m^2 K

Flanges or Support :  

                                 type : wall 

                           Theremal conditions =>Heat flux : Heat flux = 0 W/m^2 (Adiabatic walls)

• Now if you check other BC they are just wall boundaries we are not changing anything we are going to ignore them.
• Now we are almost ready to run the simulation ,but as the solution is being solved we want to moniter different flow quantities while the solution is being generated ,we create contour for this.But before that we have to initialize the domain.We use the Hybrid initialization , this provides a very good initial condition .
• Now we want to see the temperature contour.
• For contour -> go to solutions tab -> graphics  -> contour  -> in contour of : select temperature under that select static temperature  -> select the outer walls and press save /display.
• Then you can see the initial values for temperature for whole domain which is obtained by initialization which is not the final one.
• Then we want to create animation so that we can see how the temperature is varying over the domain when problem is being solved.
• For that,

           steps : Activities -> solution animation -> select temperature contour,which we have created -> preview -> set the required view and use active  -> and name it as temperature animation.

• In solution method we use SIMPLE .

    4) Solving :

• Give iterations such that your solution is converged.
• Run the simulation until the steady state is reached.Lets run for 200 iterations ,we can find the solution is converged.
• Then we can see that in the residual plot that residuals dropping and reach a steady state after 100 iterations.
• Then let us post process the results.

5)Post processing :

Residuals plot :

•  You can observe from the below plot the residuals has converged after 100 iterations.                                                                           

                                          

                                                        

Temperature contour :

• The below plot is the temperature contour on exhaust port.

                                       

• Then if you think about the results we have,the idea is simple ,we have hot exhaust gases comming in,they are at very high temperature 700k then if you look at the solid metal temperature close to the inlets,the temperature is 474K but if you check in a place where all pipes meet the temperature is around 557K.Now you would have assumed that the temperature of solid is high at the inlet as the fluid enters with high temperature there but actually it is not,the hifh temperature is at the outlet pipe the reason for this is because of convection.To explain more about this let use streamlines.

Streamline plot :

• Here in the below streamline plot you can see that streamlines coloured with velocity.

                                            

• You can see that the velocity is low at the at the inlets compared to outlet this is because of mass conservation.i.e., at each inlet you have particular mass flow rate and all of these inlets diameter are pretty similar and so we can say that velocity from all the inlets is pretty much same and as A*V is the volume flowrate  and as there are four inlets  and one outlet and all those incomming air needs to flow out through one outlet,which means the velocity of the air is going to be very very high at the outlet pipe and now because of this higher velocity there will be higher reynolds number which means there is higher heat transfer coefficient, which means there is going to be higher heat transfer from fluid to solid. and this is why solid temperature at the outlet is higher.
• Now we will insert a plane at the outlet to show the wall heat transfer coefficient i.e., it is a quantity that is calculated only at the outlet walls adjacent to the fluid and if you see that contour in the below image you will observe that the heat transfer is high at the curve section in the outlet pipe,that is because where the velocity is also highest ,in other words if we plot the velocity contour in the same cut plane you will see that the velocity is highest at the curved section , so that is the reason the heat transfer coefficient is highest at that location.Since the fluid is hot that's why that is the place where maximum amount of heat transfer from fluid to solid takes place which results in higher temperature of solid at that particular location.

Velocity contour :

• In the below contour you can see the velocity is higher in the outlet pipe than inlet pipe.

             

• In the below contour you can see clearly how the velocity is varying while fluid is approaching from inlet pipe to outlet pipe.

                                     

Heat transfer coefficient contour :

• In the below contour you can see the heat transfer coefficient is high in the outlet pipe than in the inlet pipe,So thats the reason for high temperature in the outlet pipe than at the inlet.

                                    

Verifying the HTC predictions from the simulations :

• The Nusselt number is the ratio of convective to conductive heat transfer across a boundary.

                    

• where h is the  convective heat transfer coefficient of the flow, L is the characteristic length, k is the thermal conductivity of the fluid.
• Then this Nusselt number is related to Reynolds number i.e.,

                                                 

• Where ,

                           

              and u is the flow speed (m/s)

• So if you observe heat transfer coefficinet is directly proportional to the Reynolds number (also to the velocity). So if you increase the velocity then there will be increase in the convective heat transfer coefficient. That's what we have proved above and if you want you can run another simulation by increasing the reynolds number of the flow then you will observe there will be increase in the overall convective heat transfer coefficient or at a particular location than in the previous low reynolds number simulation.

Factors that the accuracy of the prediction depend on :

• The factors that the accuracy of the prediction depend on are 
• We need to make sure that share topology is set to share.Only then  the meshing is going to be uniform and with perfect connectivity.
• We need to select exact turbulent model.As it is wall bounded flow k- omega SST will be very much suitable.And when selecting the turbulence model selecting exact Y+ value also important.
•  We need to enable share(share prep) in the work bench and click share .This is very important if you dont do this step you will not see the single interface between them.So this particular step takes care of creating the interfaces ,so that you will have one interface between your solid volume or block and fluid block. 
• We need to give exact heat transfer coefficient for the outer boundary.Then only we get the overall accurate solution.
• While giving the values,like for inflation layers or any other values with decimal values,give the exact values or else it may lead to round off error.
• Since at the interface it is very important as we want to calculate the heat transfer at that place we need to take that region and create inflation layers so that flow is captured exactly and the values are calculated exactly