steady-state simulations on the mixing tee geometry

Aim:

To set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C.

Use the k-epsilon and k-omega SST model for the first case and based on your judgment use the more suitable model for further cases.

Given:

• Case 1
  • Short mixing tee with a hot inlet velocity of 3m/s.
  • Momentum ratio of 2, 4.
• Case 2
  • Long mixing tee with a hot inlet velocity of 3m/s.
  • Momentum ratio of 2, 4.
• Momentum ratio = velocity at cold inlet / velocity at hot inlet

Expected Results:

• Velocity and temperature contour plots on the cut planes along and across the pipe.
• Velocity and temperature line plots along and across the length of the pipe.
• Perform Mesh independent study for any one case.
• Discuss the effect of length and momentum ratio on results.

End Reports:

The standard deviation of temperature at the outlet has been plotted and viewed to understand the effective mixing of the cold air with hot air and also to consider for the optimum design.

The area weighted temperature is plotted to understand the nrt average temperature at the outlet.

Choosing k-epsilon or k-omega SST model for case:1:

k-omega residual plot:

k-epsilon residual plot:

k–omega (k–ω) turbulence model is a common two-equation turbulance model, that is used as a closure for the RANS equations. The model attempts to predict turbulance by two partial difference equation for two variables, k and ω, with the first variable being the turbulance kinetic energy (k) while the second (ω) is the specific rate of dissipation (of the turbulence kinetic energy k into internal thermal energy).

K-epsilon (k-ε) turbulence model is the most common model used in CFD to simulate mean flow characteristics for turbulant flow conditions. It is a two equation model that gives a general description of turbulance by means of two transport equations (PDEs). The original impetus for the K-epsilon model was to improve the mixing length model, as well as to find an alternative to algebraically prescribing turbulent length scales in moderate to high complexity flows.

From above Residuals k-epsilon is much more converged than k-omega ,so k-epsilon model was to improve the mixing length model.

CASE :1 :

Short Mixing tee:

Mesh profile:

Momentum Ratio 2:

Residual plot:

Weighted average of temperature:

Standard deviation:

The standard deviation is seen to br nearly 1.5 which is low . hence mixing is efficient and temperature is nearly uniform.

Along the pipe:

Temperature plot:

Velocity plot:

Across the pipe:

Temperature plot:

Velocity plot:

MOMENTUM ratio 4:

Residual plot:

Standard deviation:

Weighted average of temperature:

Along the pipe:

Temperature plot:

V

Velocity plot:

Across the pipe:

temperature plot:

Velocity plot:

Case :2:

Long Mixing tee:

Mesh profile:

Momentum ratio 2:

Residual plot:

Weighted average of temperature:

Standard deviation:

Along the pipe:

Temperature plot:

velocity plot:

Across the plane:

Temperature plot:

Velocity plot:

Momentum ratio 4:

Residual plot:

Weighted average of temperature:

Standard deviation:

Along the pipe:

Temperature plot:

Velocity plot:

Across the pipe:

Temperature plot:

Velocity plot:

Mesh independent study for any one case:

Conclusions:

The higher velocity has had a better mixing and as the mass floe rate of cold air is higher ,the temperature at the outlet is also less compared to other cases.

since there is a concern for the number of elements in the ansys academic version , a finer grid could be used to perform the grid dependency test perfectly.

it is seen that iterations more than 300 does not significantly change the results and convergence is easily achieved using 300 ietrations. but at lower ietrations loke 250, it can be seen that the convergence is not fully achieved as gradients are seen to be very prominent.

1. increasing the length of the model did not result in much change in temperature hence it is not good option to select the long model as it increases the cost without much effect.

2. increase in momentum ratio has resulted in decrease in average outlet temperature and the time taken for convergence is also seen to increase.

The shorter model if found to be more optimal to use and the momentum ratio is seen to play a huge role in the outlet temperature and increase in momentum ratio has resulted in decrease in average outlet temperature.