Mixing efficiency
AIM: To set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 360C & the Cold inlet is at 190C.
GEOMETRY:
Fig 1 Long Mixing Tee Fig 2 Short Mixing Tee
THEORY:
In industrial process engineering mixing is a unit operation that involves manipulation of a heterogeneous physical system with the intent to make it more homogenous. Familiar examples include pumping of the water in a swimming pool to homogenize the water temperature, and the stirring of pancake batter to eliminate lumps (deagglomeration). Mixing is performed to allow heat and/or mass transfer to occur between one or more streams, components or phases.
Mixing Tee joints are important flow control devices. It is called Tee joint because it splits the flow and the angle between them is 90 degrees
Grid Dependency Test
A CFD Solution can never be trusted unless we check whether the result depends on the grid or not. or else we have any experimental data. The output result of a coarser mesh and finer mesh can neither be the same. So up to what extent, we need to vary the mesh to get the accepted level of tolerance, can be found out from Grid Independence test.
This is done by varying the mesh size from coarse to fine and checking the output result for each mesh. When varying the mesh does not affect the result much then we can stop and select that minimum mesh size for our final solution output.
In this case we are comparing the Geometry with 3 different mesh sizes
Mesh size = 0.0050
Mesh size = 0.0025
Mesh size = 0.0010
The governing Fluid Dynamics equations are solved in each and every cell, so more the number of cells more equations we have to solve which takes more simulation time. If we increase the number of cells the compute time does not incease linearly, but it increases quadratic way as well. As we add more cells in the Geometry the solver will take more iterations to converge, but if the number of cells are less the solution can converge very fast. As the mesh becomes finer with each and every increment we should get converged solution, which means the standard deviation of temperature at the outlet reaches a steady value as we progressively refine the mesh. When this happens the solution is said to be grid converged.
We get nearly the same residual plots, Standard deviation at the outlet, Temperature and Velocity contour for both the mesh size of 0.0025 and 0.0010.
In this case for future solution output we have considered mesh size 0.0025
SHORT MIXING TEE
K- epsilon Model
For K -epsilon model we have considered 2 cases considering momentum ratio in to account.
Case 1: Short mixing tee with a hot inlet velocity of 3m/s, cold inlet velocity of 6m/s. Momentum ratio of 2.
Area weighted Average
In interative solution, the calculation starts with the estimation of the physical quantities(pressure, temperature, velocity). In every iteration the value of these quantities are updated with respect to the previous iterative values. In case of converged steady state solution one must expected to see these quantities do not change and expected to remain same.
- From the above graph we can easily identify that the area weighted average of temperature at the outlet boundary is approximately equalt to 30.23 degree celsius
Standard Deviation
As the mesh becomes finer with each and every increment we get a converged solution, which means the Standard deviation of the outlet temperature should reach a steady value as we are progressively refining the mesh. When this happens the solution is said to be grid converged.
From the above graph we can clearly see that the Standard deviation of temperature at the outlet boundaryn reaches a steady state at 2.12 degree celsius
Residual results
Residuals quantifies the error in the solution of the system of the equations The residuals plot shows the difference between the successive solution of the equation. In iterative solution the residual will never be exactly be equal to zero. Lower the residual value more numerically accurate the solution is.
In the above graph we can easily see that the solution converges at 225 iterations
Numerical value of Area weighted average and Standard Deviation
Post processing results
Temperature Contour
Velocity Contour
3D Temperature contours 3D Velocity Contours
Temperature contour across the length of mixing Tee Velocity contour across the length of mixing Tee
Case 2: Short mixing tee with a hot inlet velocity of 3m/s, cold inlet velocity of 12m/s. Momentum ratio of 4.
Area weighted Average
From the above graph we can easily identify that the area weighted average of temperature at the outlet boundary is approximately equalt to 27.65 degree celsius
Standard Deviation
From the above graph we can clearly see that the Standard deviation of temperature at the outlet boundaryn reaches a steady state at 1.23 degree celsius
Residual results
From the above graph we can clearly see that the solution converges at 200 iterations
Post processing results
Temperature Contour
Velocity Contour
3D Temperature contours 3D Velocity Contours
Temperature contour across the length of mixing Tee Velocity contour across the length of mixing Tee
K- omega Model
For K -omega model we have considered 2 cases considering momentum ratio in to account.
Case 3: Short mixing tee with a hot inlet velocity of 3m/s, cold inlet velocity of 6m/s. Momentum ratio of 2.
Area Weighted Average
From the above graph we can easily identify that the area weighted average of temperature at the outlet boundary is approximately equalt to 30.35 degree celsius
Standard Deviation
From the above graph we can easily identify that the standard deviation of temperature at the outlet boundary is approximately equalt to 2.5 degree celsius
Residual results
From the above graph we can see that the solution converges at 550 iterations
Post processing results
Temperature Contour
Velocity Contour
3D Temperature contours 3D Velocity Contours
Temperature contour across the length of mixing Tee Velocity contour across the length of mixing Tee
Case 4 : Short mixing tee with a hot inlet velocity of 3m/s, cold inlet velocity of 12m/s. Momentum ratio of 4.
Area Weighted Average
From the above graph we can easily identify that the area weighted average of temperature at the outlet boundary is approximately equalt to 27.68 degree celsius
Standard Deviation
From the above graph we can easily identify that the standard deviation of temperature at the outlet boundary is approximately equalt to 1.61 degree celsius
Residual results
From the above graph we can see that solution converges at 690 iterations
Post processing results
Temperature Contour
Velocity Contour
3D Temperature contours 3D Velocity Contours
Temperature contour across the length of mixing Tee Velocity contour across the length of mixing Tee
The results of all the above cases are tabulated as below
K-epsilon (k-ε) turbulence model is the most common model used in Computational Fluid Dynamics(CFD) to simulate mean flow characteristics for turbulent flow conditions. It is a two equation model that gives a general description of turbulence by means of two partial Difference Equations. k-ε model focuses on the mechanisms that affect the turbulent kinetic energy.
- The realizable - model contains a new formulation for the turbulent viscosity. The term "realizable'' means that the model satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of turbulent flows.
An immediate benefit of the realizable - model is that it more accurately predicts the spreading rate of both planar and round jets. It is also likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation.
K-omega(k-w) SST model The SST k-omega turbulence model is a two-equation eddy-viscosity model that is used for many aerodynamic applications. The SST models exhibit less sensitivity to free stream conditions (flow outside the boundary layer) than many other turbulence models.
The shear stress limiter helps the k-omega model avoid a build-up of excessive turbulent kinetic energy near stagnation points. The SST k-ω model does produce a bit too large turbulence levels in regions with large normal strain, like stagnation regions and regions with strong acceleration.
Conclusion for selection of model
The k-ε model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. whereas k-ω Solves one equation for turbulent kinetic energy k and a second equation for the specific turbulent dissipation rate (or turbulent frequency) ω. This model performs significantly better under adverse pressure gradient conditions. So k-w model is selected for calculatoin in Long Mixing Tee.
LONG MIXING TEE
K-omega model
In case of k-omega model we have 2 cases considering the momentum ratio in to account
Case 5 : Long mixing tee with a hot inlet velocity of 3m/s, cold inlet velocity of 6m/s. Momentum ratio of 2.
Geometry
Area weighted Average
From the above graph we can clearly see that the area weighted average of temperature at the outlet boundary is equalt to 30.479 degree celsius
Standard Deviation
From the above graph we can clearly see that the standard deviation of temperature at the outlet boundary is equal to 1.920 degree celsius
Residual results
From the above graph we can clearly see that the solution conveges at 300 iterations
Numerical value of Area weighted average and Standard Deviation
Post processing results
Temperature Contour
Velocity Contour
3D Temperature contours 3D Velocity Contours
Temperature contour across the length of mixing Tee Velocity contour across the length of mixing Tee
Case 6 : Long mixing tee with a hot inlet velocity of 3m/s, cold inlet velocity of 12m/s. Momentum ratio of 4.
Geometry
Area Weighted Average
From the above graph we can clearly see that the Area Weighted Average of temperature at the oulet bounday is equal to 27.57 degree celsius
Standard Deviation
From the above graph we can see that the the Standard Deviation of temperature at the outlet boundary is 1.46 degree celsius
Residual results
From the above graph we can clearly see that the solution converges at 490 iterations
Numerical value of Area weighted average and Standard Deviation
Post processing results
Temperature Contour
Velocity Contour
3D Temperature contours 3D Velocity Contours
Temperature contour across the length of mixing Tee Velocity contour across the length of mixing Tee
The results of above 2 cases are tabulated as below
OBSERVATIONS:
1] Increasing the Momentum ratio from 2 to 4 causes more mixing in the T_junction and results in better mixing efficiency.
2] Increasing the length of mixing tee after the T_junction improves the diffusion coefficient.
3] The standard Deviation of the temperature at the outlet is more for k-ω SST model than - model.