Week 1- Mixing Tee

OBJECTIVE:

For this challenge, we have created two versions of the mixing tee. One of them is longer than the other.

Our job is to set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36⁰C & the Cold inlet is at 10⁰C.

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. Giving the reason for choosing a suitable model is compulsory.

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

INTRODUCTION:

The function of mixing Tee is to provide proper mixing of quantities to get the desired result at the outlet.

CASE 1:

• Short mixing Tee with a hot inlet velocity of 3m/s
• Momentum ratio of 2,4

CASE 1.1:

• Short mixing Tee with a hot inlet velocity of 3m/s
• Momentum ratio of 2

SETUPS	SHORT TEE (MR=2 AND HOT INLET VELOCITY = 3m/s)
	K-EPSILON	K-OMEGA
SOLVER TYPE	Pressure based	Pressure based
VELOCITY FORMULATION	Absolute	Absolute
TIME	Steady	Steady
VISCOUS MODEL	Realizable K-epsilon with standard wall function	K-omega SST model
MATERIAL	Air	Air
CELL ZONES	Fluid type : air	Fluid type : air
BOUNDARIES	· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 6m/s Temperature – 100c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls	· Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature - 360c · Inlet_y (velocity inlet) Velocity magnitude 6m/s Temperature – 100c · Outlet (pressure outlet) Gauge pressure – 0 pa · Walls – stationary walls

ANALYTICAL SOLUTION:

MOMENTUM RATIO 2:

• Mass of hot fluid (m_h) = rho*a*V_h = 997*0.0009*3 = 2.69 kg/s
• Mass of cold fluid (m_c) = rho*a*V_c = 997*0.0009*6 = 1.35 kg/s
• Temperature of mixture (T_mixture) = (m_h*T_h + m_c*T_c)/(m_c + m_h) = 30.319⁰c = 303.319k

MOMENTUM RATIO 4:

• Mass of hot fluid (m_h) = rho*a*V_h = 997*0.0009*3 = 2.69 kg/s
• Mass of cold fluid (m_c) = rho*a*V_c = 997*0.0009*12 = 2.3928 kg/s
• Temperature of mixture (T_mixture) = (m_h*T_h + m_c*T_c)/(m_c + m_h) = 27.99⁰c = 300.99k

CONCLUSION:

AVERAGE OUTLET TEMPERATURE:

On comparing the both models with analytical solution we got nearly the same results.

ITERATIONS TO CONVERGE:

No. of iterations taken to converge is less for Realisable K-epsilon model than K-omega SST model.

STANDARD DEVIATION:

The standard deviation of k-epsilon model is less than k-omega model which shows the better mixing efficiency in k-epsilon model.

So based on the above observations the K-epsilon turbulence model is predicting the results accurately in less no. of iterations. So we can use realisable k-epsilon model for

case 2-long tee

SUMMARY:

	LONG TEE (MR = 2)	LONG TEE (MR = 4)
AVERAGE OUTLET TEMPERATURE [K]	303.367	300.449
STANDARD DEVIATION	1.2	0.8
NO OF ITERATIONS	180	130

COMPARISON OF BOTH LONG AND SHORT TEE:

K-EPSILON REALIZABLE MODEL
GEOMETRY	MOMENTUM RATIO	CELL COUNT	AVERAGE OUTLET TEMPERATURE [K]	NO. OF ITERATIONS	STANDARD DEVIATION
SHORT TEE	2	12583	303.413	150	1.5
SHORT TEE	4	12583	300.396	130	1.1
LONG TEE	2	15368	303.367	180	1.2
LONG TEE	4	15368	300.449	130	0.8

OVERALL DISCUSSION:

AVERAGE OUTLET TEMPERATURE:

Irrespective of length of the mixing Tee, the average outlet temperature on both cases are quite same.

MOMENTUM RATIO:

• As momentum ratio increases, the velocity of cold inlet fluid increases and due to high relative velocity between the fluid it experiences higher turbulence and therefore the outlet fluid temperature decreases.
• For momentum ratio 2, the average outlet fluid temperature is 303k whereas for momentum ratio 4 the average outlet fluid temperature is 300k. From these we can say that there will be a drop in temperature if momentum ratio increases.
• In order to obtain better mixing the velocity of cold air is important. By increasing the cold fluid velocity the outlet temperature gets reduced.

NO. OF ITERATIONS:

The longer Tee takes more time to converge than short Tee.

CONCLUSION:

• Higher the momentum ratio, higher will be the mixing efficiency of Tee joint.
• Increasing the length of the pipe doesn’t serve the purpose of mixing efficiently. So, it is efficient to use short pipe.