Mixing efficiency

                                                                                                                           Mixing Efficiency #Challenge 1                        

 

Aim

To compare mixing Efficiency through mixing tees to check which turbulence model is better k-epsilon or k-omega

 

Introduction

In this challenge using Steady state simulation we compare the mixing effectiveness when a fluid through a hot inlet and cold inlet mixes through mixing tees come together under different cases  based on the mixing tee, We run the cases with k-epsilon and k-omega SST model and finalizes which one is better and why.

Theory

The mixing tees experience turbulence and thermal mixing at the tee joint. This project comprises of mixing of two water streams of different temperature in a T-junction. In this challenge thermal mixing phenomena has been observed in two different test case scenarios. First test case is with short tee with momentum ratios 2 and 4 and Second case with Longer mixing tee joint with momentum ratios 2 and 4.This Project was done with ANSYS 2019 R3 student version. We use  k-epsilon and k-omega SST model turbulence model for the simulation. The applications for mixing tees are uncountable, for example especially for normal hot baths where mixing of hot and cold water happens ,here we can control the water temperature or in power plant cooling system the application are many.

Solving and modelling approach

The model tee joint is downloaded from the link. There are two models one is short tee model other one is longer tee model. The purpose of solving the model is to check the cases in which maximum mixing are happening.

                                                                                               

The first step is importing the geometry to Space claim, here we extract the Wet volume of the mixing Tee using Volume extract. Assigning the boundaries the model is opened up for meshing. Here we are going with tetrahedral mesh. The element size is changed from default to 5e-3.The meshed model is open for pre-processing. For pre-processing we configure the Fluent launcher with double precision and in serial, also with steady state Pressure-based solver with absolute velocity formulation. Afterwards initial boundary conditions are assigned i.e. with inlet velocity, temperature and other parameters. By selecting the turbulence model we initialise the solver and input the number of iteration we desire and calculate. The plots including residual plots are generated, from the graph we can determine the convergence, the velocity, temperature also which model prevails. Later on closing the fluent we need to do the post processes, by opening the cfd post we can see the contour plots of temperature and the velocity.

Steady state pressure based setting                                                          Both k-epsilon and K-omega turbulance model

   

For pre-processing, Steady-state pressure based Solver is used. Along with hybrid initialisation

In these simulations the number of iterations given is 350 with time scale factor of 1 now referring to the cases of tees. 

meshed short tee

       

 The element size given for short tee is 0.005 or 5e-3 and the elements was 14247 with 3142 nodes.From the element metrics we can say that the mesh quality is good as most of the element metrics are 0.7 and above also the mesh is tetrahedral

                                      

For pre-processing, Steady-state pressure based Solver is used. Along with hybrid initialisation.In this simulation the number of iterations given is 350 with time scale factor of 1 now referring to the cases of tees. We have two cases

Case 1:A)Short mixing tee, for Momentum ratio 2:Hot Inlet velocity of 3m/s and cold inlet velocity of 6m/s, with k epsilon (Realizable) model;

                      Residual Plot                                                                                            Area-Weighted Average of temperature (30.25 c)                   

                            

              Area-weighted Average of velocity(m/s)                                                      Standard Deviation of the temperature

                       

 

            Contour Plot for Temperature                                                                              Contour Plot For Velocity

                              

          B)Short mixing tee, for Momentum ratio 2:Hot Inlet velocity of 3m/s and cold inlet velocity of 6m/s, with k omega (SST) model;

              Residual Plot                                                                                                    Area-Weighted Average of temperature(30.25 c)

                           

             Area-Weighted Average of Velocity(4.5075 m/s)                                             Standard deviation of temperature(2)

                    

            Contour Plot  for Temperature                                                                             Contour Plot for Velocity

                      

     

 

 

   C)Short mixing tee, for Momentum ratio 4:Hot Inlet velocity of 3m/s and cold inlet velocity of 12m/s, with k - Epsilon (Realizable)model;

 

             Residual Plot                                                                                                                 Area-Weighted Average of temperature (27.5 c)

                 

 

          Area-weighted Average of velocity                                                                                                Standard deviation plot for temperature

                      

 

             Contour Plots for Temperature                                                                                                            Contour Plots for Velocity

                        

 

       C)Short mixing tee, for Momentum ratio 4:Hot Inlet velocity of 3m/s and cold inlet velocity of 12m/s, with k - Omega (SST)model;

         Residual plot                                                                                                       Area-Weighted Average of Temperature (27.5 c)

                     

 

         Area-Weighted Average of Velocity                                                                       Standard Deviation of Temperature

                      

 

         Contour Plot for Temperature                                                                                       Contour Plot for Velocity

                             

 

Analysis

Comparing the moment ratio 2 and moment ratio 4 to find which turbulence model is effective ,we compare them with the standard deviation charts.Here we can use temperature Standard plot into account.

Standard deviation in momentum 2:

In Plot below we can see from k omega,the standard deviation of temperature can be approximated as 2 While In case of k epsilon the standard deviation is 1.5 this indicates the k epsilon model is reliable and provides us with the closest value to the real life problems

 Std of Temperature for k-epsilon model                                                                                        Std of Temperature for K-omega model

      v/s   

From this plot  we can conclude that in k-omega the errors are more than k-epsilon Turbulence model. Indicating k-epsilon as the adequate model for case 2 simulation.

 

Case 2:A)Long mixing tee, for Momentum ratio 2:Hot Inlet velocity of 3m/s and cold inlet velocity of 6m/s, with k epsilon (Realizable) model;

    Residual plot                                                                                                                        Area-Weighted Average of temperature (30.255 c)

                                                                                                                                    

 

   Area-Weighted Average of velocity (4.5m/s)                                                       Standard deviation of temperature (0.9)

   

 Contour Plot For Temperature                                                                          Contour Plot For Velocity

             

 

   B)Long mixing tee, for Momentum ratio 4:Hot Inlet velocity of 3m/s and cold inlet velocity of 12m/s, with k epsilon (Realizable) model;

 

   Residual Plot                                                                                               Area-Weighted Average of temperature(27.5c)

    

 

 Area-Weighted Average of Velocity (6.01m/s)                                                           Standard deviation of Temperature(0.68)

   

 Contour Plots for Temperature                                                                                   Contour Plots for velocity

       

 

 Result

 

 Comparisson Table for cases

 

Case	Cell Count	Average Outlet temperature (c)	No. of iteration to converge
1	Short tee
Momentum ratio 2	14247	30.25	152
Momentum ratio 4	14247	27.25	148
2	Long tee
Momentum ratio 2	17771	30.255	162
Momentum ratio 4	17771	27.5	127

 

                                                                                                                                                                                                                 

                  

                                                            From this we can conclude that length of the tee doesn’t play much role in temperature difference. All that makes the difference is the velocity of the air coming through the cold inlet. i.e. with momentum ratio 2 and 4,the one with more momentum ratio that is the higher the cold air velocity the better and more efficient in temperature mixing thereby reducing the overall temperature resulting the desired temperature.

    

Mesh Independance study (on Long tee momntum ratio 4):

While performing mesh independence study on Long Tee making the mesh finer, we can see the results given below:

Element  size of mesh is reduced to 3 e-3 or 0.003.with  number of elements 56373,From the graph metrics we are able to analyse that the mesh is fine

                   

 

Image of the meshed long tee

 

Residual plots                                                                                                                    Area-Weighted Average of temperature(27.5c)

    

 

Area-Weighted Average of Velocity  (5.995m/s)                                                                                    Standard deviation of Temperature(0.4)

   

Contour Plot for temperature     (k)                                                                             Contour Plot for Velocity   

    

 

Temperature contour plot for the whole Pipe (k)

 

 

Conclusion

By performing mesh independence For Long tee with momentum ratio , that is inlet x=3m/s and inlet y=12m/s.With the same turbulence model-epsilon(Realizable) model. The models with mesh grid size 5e-3 ( the old model)and 3e-3(refined new model) ,we can see that the one with finer mesh can produce better result.Inorder to prove this, all we need is to consider the standard deviation charts.

Std chart of temperature for element size 5e-3 (old Long mixing Tee with moment ratio 4)v/s std chart of temperature for element 3e-3(newly meshed refined long mixing tee with momentum ratio 4)

Std of temperature (3e-3, Refined mesh)       (0.4)                                                               Std of temperature (5e-3, previous mesh) (0.65)

    

From this two graph we can conclude that the refined mesh model(3e-3) has standard deviation of 0.4 while 5e-3 have 0.65.This indicates that the Refined meshed model is better and closer to the original value. Therefore From this project  we can conclude that The parameters like Mesh refinement plays an important role in CFD.Also it seems that the length of the tees doesn’t significantly cause  temperature reduction but when it comes to momentum ratios or the high velocity of the cold air these parameters can literally change the output temperature. Now we came to conclusion that k-epsilon(Realizable) turbulence models was indeed better than k-omega SST