SIMULATION OF VARIOUS TURBULENCE MODELS IN A MIXING TEE

AIM:

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

Using the k-epsilon and k-omega SST model for the first case and based on judgment using the more suitable model for further cases.

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

Comparing the following values from the 2 cases.

1. Cell count
2. Average outlet temperature
3. Number of iterations for convergence

OBJECTIVES:

1. Velocity and temperature contour plots on the cut planes along and across the pipe.
2. Velocity and temperature line plots along and across the length of the pipe.
3. Performing Mesh independent study for any one case.
4. Discussing the effect of length and momentum ratio on results.

STEADY-STATE SIMULATIONS:

CASE 1: (SHORT MIXING TEE, Length=0.1932m)

MODEL BEFORE CLEANUP:

The actual model of the mixing tee, including the flow volume and the unnecessary geometry during flow simulation.

MODEL AFTER CLEANUP:

Using the volume extraction tool in ANSYS SpaceClaim, the fluid volume can be extracted from the mixing tee for turbulence simulation.

BOUNDARIES:

MESH:

A). SOLVER AND SETUP (Turbulent, k-epsilon):

The solver used is ANSYS Fluent (Double precision).

Type: Pressure-based

Velocity Formulation: Absolute

Time: Steady

Physics Model: Turbulent, k-epsilon with energy equation and standard wall functions.

Material Assigned to cell Zone(volume): Air (properties below)

Solution Initialization: Hybrid Initialization

Number of Iterations: 550

FOR MOMENTUM RATIO=2:

Boundary Conditions:

Inlet-hot-x: velocity magnitude (normal to boundary) =3 m/s

Temperature = 36^oC

Inlet-cold-y: velocity magnitude (normal to boundary) =6 m/s

Temperature = 19^oC

Outlet: Gauge Pressure (Pascal) = 0

Wall: Stationary wall

Shear Condition = No slip

Convergence Plot: Number of Iterations given to run = 550

Number of Iterations to converge = 450

Outlet Temperature (area weighted average plot) = 30.17^oC

Total enthalpy at outlet = 5250.0 j/kg

Temperature Variation along Length

Velocity Variation along Length

Temperature variation across outlet

Velocity Variation across outlet

CONTOUR PLOTS:

Temperature (X-Y Plane, Z=0m)

Temperature (Y-Z Plane, X=0m)

Temperature at OUTLET (Y-Z Plane, X=0.115m)

Velocity (X-Y Plane, Z=0m)

Velocity (Y-Z Plane, X=0m)

Velocity at OUTLET (Y-Z Plane, X=0.115m)

LINE PLOTS:

Temperature along length

Temperature along the diameter (X=0m)

Temperature along diameter at OUTLET

Velocity along length

Velocity along diameter (X=0m)

Velocity along diameter at OUTLET

FOR MOMENTUM RATIO=4:

Boundary Conditions:

Inlet-hot-x: velocity magnitude (normal to boundary) =3 m/s

Temperature = 36^oC

Inlet-cold-y: velocity magnitude (normal to boundary) =12 m/s

Temperature = 19^oC

Outlet: Gauge Pressure (Pascal) = 0

Wall: Stationary wall

Shear Condition = No slip

Convergence Plot: Number of Iterations given to run = 550

Number of Iterations to converge = 132

Outlet Temperature (area weighted average plot) = 27.50^oC

Total enthalpy at outlet = 2700.0 j/kg

Temperature Variation along length

Velocity variation along length

Temperature variation across outlet

Velocty variation across outlet

CONTOUR PLOTS:

Temperature (X-Y Plane, Z=0m)

Temperature (Y-Z Plane, X=0m)

Temperature at OUTLET (Y-Z Plane, X=0.115m)

Velocity (X-Y Plane, Z=0m)

Velocity (Y-Z Plane, X=0m)

Velocity at OUTLET (Y-Z Plane, X=0.115m)

LINE PLOTS:

Temperature along length

Temperature along the diameter (X=0m)

Temperature along diameter at OUTLET

Velocity along length

Velocity along diameter (X=0m)

Velocity along diameter at OUTLET

B). SOLVER AND SETUP (Turbulent, k-omega):

The solver used is ANSYS Fluent (Double precision).

Type: Pressure-based

Velocity Formulation: Absolute

Time: Steady

Physics Model: Turbulent, k-omega (SST Model) with energy equation and standard wall functions.

Material Assigned to cell Zone(volume): Air (properties below)

Solution Initialization: Hybrid Initialization

Number of Iterations: 550

FOR MOMENTUM RATIO=2:

Boundary Conditions:

Inlet-hot-x: velocity magnitude (normal to boundary) =3 m/s

Temperature = 36^oC

Inlet-cold-y: velocity magnitude (normal to boundary) =6 m/s

Temperature = 19^oC

Outlet: Gauge Pressure (Pascal) = 0

Wall: Stationary wall

Shear Condition = No slip

Convergence Plot: Number of iterations given to run = 550

Number of Iterations to converge = 197

Outlet Temperature (area weighted average plot) = 30.25^oC

Total enthalpy at outlet = 5270.0 j/kg

Temperatue variation along length

Velocty variation along length

Temperature variation across outlet

Velocity variation across outlet

CONTOUR PLOTS:

Temperature (X-Y Plane, Z=0m)

Temperature (Y-Z Plane, X=0m)

Temperature at OUTLET (Y-Z Plane, X=0.115m)

Velocity (X-Y Plane, Z=0m)

Velocity (Y-Z Plane, X=0m)

Velocity at OUTLET (Y-Z Plane, X=0.115m)

LINE PLOTS:

Temperature along length

Temperature along the diameter (X=0m)

Temperature along diameter at OUTLET

Velocity along length

Velocity along diameter (X=0m)

Velocity along diameter at OUTLET

FOR MOMENTUM RATIO=4:

Boundary Conditions:

Inlet-hot-x: velocity magnitude (normal to boundary) =3 m/s

Temperature = 36^oC

Inlet-cold-y: velocity magnitude (normal to boundary) =12 m/s

Temperature = 19^oC

Outlet: Gauge Pressure (Pascal) = 0

Wall: Stationary wall

Shear Condition = No slip

Convergence Plot: Number of iterations given to run = 550

Number of Iterations to converge = 203

Outlet Temperature (area weighted average plot) = 27.50^oC

Total enthalpy at outlet = 2700.0 j/kg

Temperature variation along length

Velocity variation along length

Temperature variation across outlet

Velocity variation across outlet

CONTOUR PLOTS:

Temperature (X-Y Plane, Z=0m)

Temperature (Y-Z Plane, X=0m)

Temperature at OUTLET (Y-Z Plane, X=0.115m)

Velocity (X-Y Plane, Z=0m)

Velocity (Y-Z Plane, X=0m)

Velocity at OUTLET (Y-Z Plane, X=0.115m)

LINE PLOTS:

Temperature along length

Temperature along the diameter (X=0m)

Temperature along diameter at OUTLET

Velocity along length

Velocity along diameter (X=0m)

Velocity along diameter at OUTLET

INFERENCE:

Comparing the above results with hand calculations:

ρ = 1.225 kg/m³

A_Hot = 0.0009 m²

A_Cold = 0.0002 m²

V_Hot = 3 m/s

T_Hot = 36^oC = 309.15 K

T_Cold = 19^oC = 292.15 K

For Momentum ratio = 2,

From simulation, T_Mixture = 30.17^oC (at outlet for k-epsilon) and 30.25^oC (at outlet for k-omega)

V_Cold = 6m/s

T_Mixture =`(0.0033075×36+0.00147×19)/(0.0033075+0.00147)`= 30.76^oC (approximately closer to k-omega)

For Momentum ratio = 4,

From simulation, T_Mixture = 27.50^oC (at outlet for k-epsilon and for k-omega)

V_Cold = 12m/s

T_Mixture = `(0.0033075×36+0.00249×19)/(0.0033075+0.00249)`= 28^oC (approximately close to the simulation value)

C_P = 1006.43 j/kg-K

For Momentum ratio = 2,

From simulation, h_Mixture = 5250 j/kg (at outlet for k-epsilon) and 5270 j/kg (at outlet for k-omega)

V_Cold = 6m/s

T_Mixture = 30.76^oC (approximately closer to k-omega)

△ T_Mixture = 36 – 30.76 = 5.24

h_Mixture = 106.43 x 5.24 = 5273.699 j/kg (closer to k-omega)

We can conclude that the simulation model is correct and that the k-omega model has the least error in result.

Based on Momentum Ratio:

From the above turbulence simulations having a higher momentum ratio (4) i.e, a higher inlet-cold-y velocity (12m/s) giver a more efficient mixing, with the contour plots sowing that the temperature at the outlet is more or less constant along the y and z direction.

Moreover, the simulations with momentum ratio 2 or the inlet-cold-velocity 6m/s shows that the mixing is not efficient. While the mixture of cold and hot air reaches the outlet there is a considerable deviation of temperature along the y direction. Hotter air seems to be more prevalent towards the bottom end of outlet (31.72^oC), when the area average temperature was close to 30.25^oC. For the case of momentum ratio of 4 the temperature across the outlet along y and z direction displayed the least deviation from the area average temperature at the outlet of 27.50^oC.

From the velocity plots its clear that when the velocity of inlet-cold-y increased to 12m/s from 3m/s the velocity distribution across the outlet became uniform along the interior of the flow. In the flow with 3m/s inlet-cold-y velocity there seems to be an even larger variation in the y and z direction. Moreover, the simulations showed that due to the viscous force along the wall the fluid velocity closer to the wall is almost 0 and the fluid velocity at the wall is 0.

Based on Turbulence Model (K-epsilon and K-omega):

It can be observed that the number of iterations to converge varied between these two models.

K-epsilon: Momentum Ratio = 2, Convergence at 450^th iteration, convergence by pattern

Momentum Ratio = 4, Convergence at 132^th iteration

K-omega: Momentum Ratio = 2, Convergence at 197^th iteration

Momentum Ratio = 4, Convergence at 203^rd iteration

Selection of model depends on the specific problem; no turbulence model is suited for every case. Fine tuning is required. SST model used good mesh at boundary and with wall treated usually works in most cases.

The major feature of k-epsilon is its “wall sensitivity”. This is due to the fact that the formulation simply cannot be integrated all the way to a solid boundary. Instead, either the law of the wall must be employed to provide velocity “boundary conditions” away from solid boundaries. To circumvent some of the standard drawbacks is to use the Realizable k-ε Turbulence Model.

However, k-epsilon model predicts well far from the boundaries (wall) and k- omega model predicts well near wall. SST model in K-omega which is a combination of these. SST variant combines two models into one model where we use the k-ω model in the inner portion of the boundary-layer then smoothly switch to the k-ε model when we move away from the wall, and into the free stream area.

For further cases, k-omega model will be used due these advantages

CASE 2: (LONG MIXING TEE, Length=0.2673m)

MODEL BEFORE CLEANUP:

The actual model of the mixing tee, including the flow volume and the unnecessary geometry during flow simulation.

MODEL AFTER CLEANUP:

Using the volume extraction tool in ANSYS SpaceClaim, the fluid volume can be extracted from the mixing tee for turbulence simulation.

BOUNDARIES:

MESH:

SOLVER AND SETUP (Turbulent, k-omega):

The solver used is ANSYS Fluent (Double precision).

Type: Pressure-based

Velocity Formulation: Absolute

Time: Steady

Physics Model: Turbulent, k-omega (SST Model) with energy equation and standard wall functions.

Material Assigned to cell Zone(volume): Air (properties below)

Solution Initialization: Hybrid Initialization

Number of Iterations: 550

FOR MOMENTUM RATIO=2:

Boundary Conditions:

Inlet-hot-x: velocity magnitude (normal to boundary) =3 m/s

Temperature = 36^oC

Inlet-cold-y: velocity magnitude (normal to boundary) =6 m/s

Temperature = 19^oC

Outlet: Gauge Pressure (Pascal) = 0

Wall: Stationary wall

Shear Condition = No slip

Convergence Plot: Number of iterations given to run = 550

Number of Iterations to converge = 210

Outlet Temperature (area weighted average plot) = 30.35^oC

Total enthalpy at outlet = 5375.0 j/kg

Temperature variation along length

Velocity variation along length

Temperature variation across outlet

Velocity variation across outlet

CONTOUR PLOTS:

Temperature (X-Y Plane, Z=0m)

Temperature (Y-Z Plane, X=0m)

Temperature at OUTLET (Y-Z Plane, X=0.190995m)

Velocity (X-Y Plane, Z=0m)

Velocity (Y-Z Plane, X=0m)

Velocity at OUTLET (Y-Z Plane, X=0.190995m)

LINE PLOTS:

Temperature along length

Temperature along the diameter (X=0m)

Temperature along diameter at OUTLET

Velocity along length

Velocity along diameter (X=0m)

Velocity along diameter at OUTLET

FOR MOMENTUM RATIO=4:

Boundary Conditions:

Inlet-hot-x: velocity magnitude (normal to boundary) =3 m/s

Temperature = 36^oC

Inlet-cold-y: velocity magnitude (normal to boundary) =12 m/s

Temperature = 19^oC

Outlet: Gauge Pressure (Pascal) = 0

Wall: Stationary wall

Shear Condition = No slip

Convergence Plot: Number of iterations given to run = 550

Number of Iterations to converge = 133

Outlet Temperature (area weighted average plot) = 27.50^oC

Total enthalpy at outlet = 2500.0 j/kg

Temperature variation along length

Velocity variation across length

Temperature variation aross outlet

Velocity variation across outlet

CONTOUR PLOTS:

Temperature (X-Y Plane, Z=0m)

Temperature (Y-Z Plane, X=0m)

Temperature at OUTLET (Y-Z Plane, X=0.190995m)

Velocity (X-Y Plane, Z=0m)

Velocity (Y-Z Plane, X=0m)

Velocity at OUTLET (Y-Z Plane, X=0.190995m)

LINE PLOTS:

Temperature along length

Temperature along the diameter (X=0m)

Temperature along diameter at OUTLET

Velocity along length

Velocity along diameter (X=0m)

Velocity along diameter at OUTLET

INFERENCE:

Comparing the above results with hand calculations:

ρ = 1.225 kg/m³

A_Hot = 0.0009 m²

A_Cold = 0.0002 m²

V_Hot = 3 m/s

T_Hot = 36^oC = 309.15 K

T_Cold = 19^oC = 292.15 K

For Momentum ratio = 2,

From simulation, T_Mixture = 30.35^oC (at outlet for k-omega)

V_Cold = 6m/s

T_Mixture =`(0.0033075×36+0.00147×19)/(0.0033075+0.00147)`= 30.76^oC (approximately closer to k-omega)

For Momentum ratio = 4,

From simulation, T_Mixture = 27.50^oC (at outlet for k-omega)

V_Cold = 12m/s

T_Mixture = `(0.0033075×36+0.00249×19)/(0.0033075+0.00249)`= 28^oC (approximately close to the simulation value)

C_P = 1006.43 j/kg-K

For Momentum ratio = 2,

From simulation, h_Mixture = 5375 j/kg (at outlet for k-omega)

V_Cold = 6m/s

T_Mixture = 30.76^oC (approximately closer to k-omega)

△ T_Mixture = 36 – 30.76 = 5.24

h_Mixture = 106.43 x 5.24 = 5273.699 j/kg (closer to k-omega, simulation value)

FINAL OBSERVATIONS:

CASES	Turbulence Model	Momentum Ratio	Cell Count	Average Outlet Temperature	Number of iterations to Converge
CASE 1: Short Mixing Tee	k-epsilon (Realizable)	2	12583	30.17oC	450
		4	12583	27.50oC	132
	k-omega (SST)	2	12583	30.25oC	197
		4	12583	27.50oC	203
CASE 2: Long Mixing Tee	k-omega (SST)	2	15368	30.35oC	210
		4	15368	27.50oC	133

MESH INDEPENDENT STUDY OF LONG MIXING TEE & MOMENTUM RATIO 4

Previous Mesh:

New Mesh (Refined Mesh):

FOR MOMENTUM RATIO=4:

Boundary Conditions:

Inlet-hot-x: velocity magnitude (normal to boundary) =3 m/s

Temperature = 36^oC

Inlet-cold-y: velocity magnitude (normal to boundary) =12 m/s

Temperature = 19^oC

Outlet: Gauge Pressure (Pascal) = 0

Wall: Stationary wall

Shear Condition = No slip

Convergence Plot: Number of iterations given to run = 550

Number of Iterations to converge = 268

Outlet Temperature (area weighted average plot) = 27.50^oC

Total enthalpy at outlet = 2550.0 j/kg

Temperature variation along length

Velocity variation along length

Temperature variation across outlet

Velocity variation across outlet

CONTOUR PLOTS:

Temperature (X-Y Plane, Z=0m)

Temperature (Y-Z Plane, X=0m)

Temperature at OUTLET (Y-Z Plane, X=0.190995m)

Velocity (X-Y Plane, Z=0m)

Velocity (Y-Z Plane, X=0m)

Velocity at OUTLET (Y-Z Plane, X=0.190995m)

LINE PLOTS:

Temperature along length

Temperature along the diameter (X=0m)

Temperature along diameter at OUTLET

Velocity along length

Velocity along diameter (X=0m)

Velocity along diameter at OUTLET

INFERENCE:

From the above contour plots and line plots it is clear that, having a refined mesh gives a more accurate description of temperature and velocity variation along and across the mixing tee. Even the area averaged value of temperature and enthalpy experienced changes that made their values closer to the hand calculated values. Also, it took more number of iterartions in the new mesh for the governng equations to converge.

CONCLUSION:

Based on the simulations conducted it is evident that mixing of hot and cold air depends on both the length of the pipe (mixing tee) and the momentum ratio (velocity of input cold air). As the length increases the proportion or efficiency of mixing also increases. This can be seen through the comparison of hand calculations done above. As the length of the pipe increased the outlet temperature became closer to the ideal mixture temperature (T_Mixture).

The same can be said about the momentum ratio. As the inlet-cold-y velocity was increased the average outlet temperature became close to the ideal mixture temperature (T_Mixture).