Week 1- Mixing Tee

GIVEN

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

Use the k-omega SST model for the cases

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.

Momentum ratio = velocity at cold inlet/velocity at hot inlet

Procedure

THE PURPOSE OF MIXING TEE IS USE TO MIX TWO TYPES OF FLUID OR THE SAME FLUID WITH DIFFERENT PROPERTIES. IN OUR CONDITION WE USE THE SAME FLUID (AIR) FOR MIXING AND DIFFERENT PROPERTIES ARE USED (VELOCITY AND TEMPERATURE). FROM THAT THE VELOCITY, TEMPERATURE AND MIXING EFFECTS ARE MONITORED AT THE OUTLET.

STEPS TO BE FOLLOWED

Step 1: Initially, start with importing the geometry to the Ansys workbench and extrude the internal volume of the given mixing tee for the internal flow analysis.

Step 2: From the extracted volume meshes the volume with mesh sizes 5mm,4mm, and 3mm mesh for the grid-independent study, after creating the mesh or before making the mesh name the surfaces as per the boundary condition, so that the fluent can recognize the boundary condition itself.

After generating the mesh, the number of nodes and elements is investigated using the statistics option. Then the mesh quality is checked by choosing the mesh matrices option in the quality section.

Step 3:In this step, the meshed geometric file has been imported to the fluent module and set the following conditions as follows in the fluent in solving the problem.

This procedure will be constant for the short tee and long tee with a momentum ratio

SOLVER TYPE	Pressure based
VELOCITY FORMULATION	Absolute
TIME	Steady
VISCOUS MODEL	K-omega SST model and enable energy equation to solve the energy equation
MATERIAL	Air
CELL ZONES	Fluid type: air
BOUNDARIES (depends on the momentum ratio)	Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature -`36 ^@c` Inlet_y (velocity inlet) Velocity magnitude 6m/s or 12 m/s Temperature –`19^@c` Outlet (pressure outlet) Gauge pressure – 0 pa Walls – stationary walls
Report definition	· Area weighted average of temperature at the outlet · The standard deviation of temperature

the hybrid scheme is used for the initialization

with the given formula and the literature review

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

Results for grid independent study

case1: 5 mm mesh

contour plots

streamline plot

case2: 4 mm mesh

contour plot

streamline plot

case3: 3 mm mesh

contour plot

streamline plot

solution discussion

MESH SIZE	NO. OF ELEMENTS	AVERAGE OUTLET TEMPERATURE	NO. OF ITERATIONS
5mm	14400	30.200	150
4mm	22167	30.310	115
3mm	39725	30.316	121

The mesh size of 3mm gives the best results compared to the other two cases. Decreasing the mesh size increases the accuracy of the results but it consumes more computational time so we need to take 3 mm as the final mesh

BY FOLLOWING THE SANE PROCEDURE WE NEED TO SOLVE SHORT TEE AND LONG TEE CONCERNING THE MOMENTUM RATIO AND FIX THE MESH (3MM) AS CONSTANT AND THE RESULTS ARE SHOWN BELLOW

FOR BOTH SHORT TEE AND LONG TEE AS SAME SOLVING CONDITIONS

SOLVER TYPE	Pressure based
VELOCITY FORMULATION	Absolute
TIME	Steady
VISCOUS MODEL	K-omega SST model and enable energy equation to solve the energy equation
MATERIAL	Air
CELL ZONES	Fluid type: air
BOUNDARIES (depends on the momentum ratio)	Inlet_x (velocity inlet) Velocity magnitude 3m/s Temperature -`36 ^@c` Inlet_y (velocity inlet) Velocity magnitude 6m/s or 12 m/s Temperature –`19^@c` Outlet (pressure outlet) Gauge pressure – 0 pa Walls – stationary walls
Report definition	· Area weighted average of temperature at the outlet · The standard deviation of temperature

results

1. short tee with a momentum ratio of 2

2. short tee with a momentum ratio of 4

3 long tee with a momentum ratio of 2

4 long tee with a momentum ratio of 4

contour plots

STREAMLINE

SOLUTION DISCUSSION

GEOMETRY	MOMENTUM RATIO	AVERAGE OUTLET TEMPERATURE [K]	NO. OF ITERATIONS	STANDARD DEVIATION
SHORT TEE	2	30.31	120	2.09
SHORT TEE	4	27.559	131	1.064
LONG TEE	2	30.41	100	1.011
LONG TEE	4	27.51	111	0.629

1 The average temperature of both short tee and long tee is comparatively the same so the is not much impact on the length of the pipe

2 The average temperature decreases with respect to the momentum ratio increases .

3 By comparing all these conditions short tee with momentum ratio is comparatively very efficient than others