Mixing efficiency

The steady state simulation of each of the two geometries with momentum ratios of 2 and 4 has been performed for 400 iterations using the k-epsion turbulence model.

Solver - Fluent

Post processing- CFD post and MS excel

Selection for the k-epsion model was done based on two reasons

1. We are interested in the outlet area temperature and not on the temperature of any area very close to the wall in the viscous sublayer . Therefore the use of k-omega is not required.

2. The standard deviation obtained from the k-epsilon model gave a better result than the k-omega (lesser standard deviation)

Result Table

Geometry	Momentum Ratio	Cell count	Average outlet tempertaure(C)	Standard deviation at the outlet	Number of iterations
Long	2	767214	30.6079	1.2812	425
Long	4	767214	27.4157	1.0780	400
Short	2	578212	30.5682	2.0172	350
Short	4	578212	27.4561	1.5689	425

Mesh independent study:

The short geometry with a momentum ratio of 2 was taken . Initial mesh was created by using max face size as 1mm(578212) , and later it was modified to 0.75 mm(1131809) and the average temperatures were compared.

Mesh with 0.75mm - 30.5789

Mesh with 1mm- 30.5682

With the difference 0.01 , the mesh chosen for the simulations gives satisfactory results.

The higher the momentum ratio , the cooler is the outlet temperature of the air .

The effect of the length appears to be inconsistent for the two momentum ratios as for momentum ratio-4 , the outlet temperature is lower for a longer geometry and for the momentum ratio of 2 the outlet temperature is higher for the longer geometry . According to my findings the difference of the turbulent kinetic energy between the short and long case for the momentum of 4 is 0.31086 m2/s2 and the same for momentum of 2 is 0.106111 m2/s2 . The difference is three times more in the case of momentum of 4 , this accounts for the counter-intuitive result of the momentum 4 case . Therefore - the shorter the length of the geometry the cooler is the outlet temperature if the inlet velocity is sufficently low , however for a large inlet velocity the turbulence induced reverses the result.

Convergence plots for the residual , Area weighted average temperature on the outlet.

1. Long , momentum-4

2.Long Momentum -2

3.Short momentum ratio-4

4. Short momentum -2

Contor plots

1. Long momentum-4

2.Long momentum-2

3. Short momentum-4

4. Short momentum-2