Steady-state simulations on the mixing tee geometry

STEADY-STATE SIMULATION ON MIXING TEE GEOMETRY

Objective:

• To set up a steady state simulation to determine the mixing effectiveness of the two different configurations of the mixing tee provided
• To find out the average outlet temperature of air in the two cases
• To perform a mesh independent study in any one case
• To discuss the effect of length and momentum ratio on the effectiveness of mixing

Theory:

A mixing tee is a device which is used in many diffusion or mixing processes.Mixing Tee utilizes a specifically engineered internal geometries to efficiently ix two fluid streams into a combined stream.The mixing tee are more commonly used in HVAC applications where the cold air from the air conditioner is mixed with the ambient air from the outside thus,providing a suitable temperature for air at the outlet for better human comfort.

Simulation:

1.Geometry:

Two geometries have been provided and their 3D geometries have been provided below:

• Case 1: Mixing Tee with short pipe

The dimension of the model has been provided below:

• Case 2:Mixing Tee with Long pipe

The dimenson of the same has been provided below:

But,for the simulation only the fluid domain has been used from the above geometries.This is obtained from the volume extraction option from the spaceclaim.

• Fluid domain for the short pipe mixing tee

• Fluid domain for the long pipe mixing tee

2.Meshing:

Case 1.Mixing Tee with short pipe

• Cell Count:1,83,451
• Orthogonal Quality of mesh elements: 0.787
• Size of meshing element: 5 mm.
• Type of element:Tetrahedral

Case 2.Mixing Tee with long Pipe

NOTE: Grid independence study has been made in the above configuration of the mixing tee.Hence as a baseline simulation,the geometry has been meshed with a mesh having lower number of cell count.

• Cell count:15,737
• Type of element: Tetrahedral
• Orthogonal qualtiy: 0.77

The named selection of the geometry has been made and is shown below:

3.Setup:

The simulation set up a was done for two cases ,for the mixing tee with short pipe and the with long pipe and within each case 2 more cases arises with different momentum ratios and each cases has been discussed below:

• Momentum ratio is defines as the ratio of the velocity at cold inlet the velocity at hot inlet,ie for our case momentum ratio is given by:

Momentum Ratio= velocity at inlet_y/velocity at inlet_x

Details of setup:

• Solver type: Pressure-based
• Material:Fluid - Air
• Energy equation is kept on
• Turbulence Model: k-epsilon realizable (for tee with momentum ratio 2) & k-omega SST (for tee with momentum ratio 4)

Boundary conditions:

• inlet_x: - velocity inlet: 3m/s

- Temperature: `36^o`

• inlet_y:- velocity inlet: 6m/s( tee with momentum ratio 2) & 12 m/s (tee with momentum ratio 4)

- Temperature:`19^o`

• outlet : Pressure-outlet
• wall : No slip condition.

Initial Condition: Hybrid Initialisation

Number of Iterations : 500

Time step method: Automatic.

4.Solution:

CASE 1 : MIXING TEE WITH SHORT PIPE

1.1 MOMENTUM RATIO 2:

1.1.A Residual Plot:

• Solution converged at about 300 iterations.

1.1.B Temperature contour along the plane of pipe:

1.1.C Velocity contour along the plane of pipe:

1.1.D Temperature contour across the pipe:

1.1.E Velocity variation across the pipe:

1.1.F Temperature line plot along the pipe:

1.1.G Velocity line plot along the pipe:

1.2 MOMENTUM RATIO 4:

1.2.A Residual Plot:

• Solution converges for an iteration of 179.

1.2.B Temperature contour along the plane of the pipe:

1.2.C Velocity contour along the plane of the pipe:

1.2.D Temperature contour across the plane of pipe:

1.2.E Velocity contour across the plane of pipe:

1.2.F Temperature line plot along the pipe:

1.2.G Velocity line plot along the pipe:

• By running the simulation by both the turbulence modesl ie, k-epsilon & k-omega SST the end result that we obtained is almost same
• But if we are using the k-epsilon SST turbulence model,we are obtaining faster convergence for the solution than that of the k-epsilon realizable turbulence model
• Thus, for the next set of simulation we would be using the k-omega SST turbulence model for the analysis.

Result:

• The average outlet temperature obtained are as follows:

- Momentum Ratio 2 : Average outlet Temperature = 303.27 K

Standard Deviation of Temperature at outlet = 1.9 K

- Momentum Ration 4: Average outlet Temperature = 300.68 K

Standard deviation of Temperature at outlet = 2 K

• Thus it can be inferred from the above data that , increasing the momentum ratio reduces temperature at the outlet.

CASE 2: MIXING TEE WITH LONG PIPE:

2.1 MOMENTUM RATIO 2 :

2.1.A Residual Plot:

• The solution converged at 34 iterations.

2.1.B Average temperature at outlet Plot:

2.1.C Standard Deviation of Temperature at Outlet:

2.1.D Temperature contour along the pipe:

2.1.E Velocity contour along the pipe:

2.1.F: Temperature contour across the pipe:

2.1.G Velocity contour across the pipe:

2.1.H Temperature line plot along the pipe:

2.1.I Velocity line plot along the pipe:

2.2 MOMENTUM RATIO 4:

2.2.A Residual Plot:

• Solution converged at about 157 iterations

2.2.B Average Temperature plot at outlet:

2.2.C Standard deviation of temperature at outlet:

2.2.D Temperature contour along the Pipe:

2.2.E Velocity contour along the pipe:

2.2.F Temperature contour across the pipe:

2.2.G Velocity contour across the pipe:

2.2.H Temeprature line plot along the pipe:

2.2.I Velocity line plot along the pipe:

• A grid independence study has been made by making the average outlet temperature and the standard deviation of the outlet temperature as the output parameters,and a graph has been plotted by changing the number of grid points to see how it varied the output.Further details of the files has been provided at the link provided.

• Plot between the number of mesh nodes/grid points and outlet temperature of mixing tee for momentum ratio of 2

• Plot between the number of mesh nodes or grid points and outlet temperature of the mixing tee for momentum ratio of 4

NOTE: From the above plots we can infer that as the number of mesh nodes is increasing,in this particular case the variation of temperature at the outlet is very less.Thus at a lower cell count and lower number of grid points we could obtain a descent result with minimum variation from the optimum value.

5.RESULT:

• The table above summarises the results that are obtained from the cases that we have simulated.

1. It was found that the turbulence model k-omega SST turns out to converge the solution quickly than the k-epsilon model,but the result obtained from both the model turns out to be similar.
2. Since our primary aim was to obtain the average outlet temperature of the mixing tee, the results we got from the case 1 and case 2 are similar irrespective of the length of the tee.Hence it is preferable to use mixing tee with short pipe for the thermal mixing applications.
3. Higher the momentum ratio,the cold fluid inlet velocity is higher compared to the hot inlet velocity,so the amount of the cold fluid entering in the Tee will be also higher relative to the amount of hot fluid entering.Thus,due to the higher cold inlet velocity the turbulence experienced will be higher and therby the outlet temperature drops.Therefore higher the momentum ratio higher will be the efficiency of the mixing tee.
4. Mesh independence study showed that with a relatively lower number of cell count also,we could achieve near to optimum result,thus reducing the compututational cost.

Thank You

Arjun