CFD analysis of a Mixing Tee efficiency using different Turbulent models in ANSYS FLUENT

ABSTRACT

The given problem is focused in analyzing the mixing effectiveness of hot and cold fluid in a tee shaped pipe. A numerical study using CFD approach is applied to predict the outlet temperature and velocity of the pipe at a steady state condition. The computational geometry is modeled using URANS based solver namely k-epsilon and k-omega model. With different momentum ratio, physical parameters like no of iterations, cell count, area weighted average, standard deviation of temperature at the outlet is predicted. Finally, with different grading of mesh size a grid independence test is conducted to justify the effectiveness of mixing fluids and to measure out the best model for the problem.

AIM: CFD analysis to study the mixing efficiency of a Tee joint using ANSYS Fluent using different turbulent model.

INTRODUCTION:

Mixing problems, such as the design and scale-up of a mixer and quantification of mixing, have been traditionally tackled by developing empirical design equations mainly due to the complexity of the fluid dynamics of mixing. Although this approach has proven to be satisfactory for many applications, it is rather limited because it neglects the complexity of flow in most mixing applications. Applications where pipeline mixing with tees is used include low viscosity mixing such as wastewater treatment and blending of some oils (injection of additives) and petrochemical products. Other applications include blending of fuel gas, and mixing of feed streams for catalytic reactors. A tee is formed by two pipe sections joined at a right angle to each other. One stream passes straight through the tee while the other enters perpendicularly at one side as shown in Fig 1. This flow arrangement is known as the side-tee. However other flow arrangements may be used, such as having the two opposing streams entering co-axially and leave through a pipe, which is perpendicular to the entering direction. This is known as the opposed-tee.

Fig. 1

Tee pipes are commonly used in piping systems and multi-channel network in various industries like electronic, petrochemical, nuclear plant etc. the mixing of hot fluid and cold fluid give rise to temperature fluctuation in the vicinity of mixing zone. The flow pattern of fluid gives necessary information such as area, where thermal zones are high. Using different momentum ratio, the efficiency of the model and its effectiveness is checked.

PROBLEM STATEMENT

To compare the mixing effectiveness of tee shaped pipe using k-epsilon and k-omega model at momentum ratio factor 2, 4. The inlet temperature and velocity conditions are given as 36degreeC at inlet x, 19degreeC at inlet y and 3m/s at inlet x.

OBJECTIVE

1. Run simulation for small tee and long tee geometry based upon RANS model
2. Compare cell count, no of iteration and outlet temperature between two tee pipes.
3. Perform grid independence study.
4. Thermal and velocity profile plot on cut plane and across the geometry.

SOLVING AND MODELLING APPROACH

The solving approach is represented as a workflow diagram are shown in the following steps:

1. Setup the geometry in Ansys workbench
2. Extract the fluid volume region.
3. Generate mesh for a correct sizing.
4. Set up post processing data and the required turbulence model.
5. Run the solver.
6. Check for convergence.
7. Post process the results

The flowchart for the above steps are shown below

TURBULENCE MODELLING

Most of the CFD problems are based on turbulence modelling, some popular turbulence model applied to the present problem is discussed below:

k-epsilon model- This is one of the most common CFD model used for turbulent flow modelling. This model basically utilises two transport variable properties, k, which is the turbulent kinetic energy and epsilon, which is the rate of dissipation of kinetic energy.

k-omega model- This is also one of the common URANS based solver used in turbulent flow problems. This model attempts to predict turbulence by solving two different partial differential equation, which is k(turbulent kinetic energy) and omega(specific rate pf dissipation of energy).

PREPROCESSING SETUP

1. GEOMETRY OF THE MODEL:

• The geometry of the mixing tee pipe is attached to the ANSYS space claim geometry using the step file format.
• Next, we extract the fluid volume region by selecting the edge command from the volume extraction tool at prepare physics section. The solid model is suppressed from the fluid model to create mesh at the region of interest.

2. MESH GENERATION:

• Fluid geometry is imported to the workbench, where mesh size of 10mm is defined around the entire body.
• Clicking on the statistics option, the no of elements and nodes are highlighted. The mesh metric shows the no of triangular, pyramidal, trapezoidal members required at a certain percentage to optimize the mesh model.
• Using named selection option define the inlet x, inlet y, outlet and wall.
• After clicking on mesh generation, click on update to update the mesh model.

3. SET UP OF PHYSICS SOLVER:

• The FLUENT solver setting is activated, where the console and the graphics pane appear.
• From General tab, we select the pressure-based solver having absolute velocity formation and within a steady state condition.
• The energy parameter is activated and then the viscous model is selected, which is k-epsilon Realizable or K-omega SST.
• Specify the material as air.
• Define the boundary condition for inlet x, inlet y, wall by specifying the inlet temperature and velocity.
• The monitor setting is specified to two parameter area weighted average and standard deviation.
• Initialize the solver with hybrid schemes.
• Set up the no of iterations. Click on calculate option.

POST-PROCESSING RESULTS

STEPS

1. After the computation ends check for graphical visualization for the interation convergence rate, area weighted temperature and standard deviation plot at the outlet section.
2. Go to POST CFD and activate the inlet, outlet and wall section to view the geometry.
3. Select planes along and across the geometry of pipe at different crosssection.
4. Highlight the planes with velocity and temperature variables.
5. Use line plot along and across the pipe and measyre the temperature and velocity variation in a chart.

The give section below demostrates the post processing results.

SHORT TEE

Model: k-epsilon model

momentum ratio 2

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 200 iterations and also the average outlet temperature becomes 303k. The temperature and velocity shows fluctuation from 309to 302k and 3to 5.5m/s along and from 309to 291k and 0to 6m/s across.

momentum ratio 4

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 250 iterations and also the average outlet temperature becomes 300.5k. The temperature and velocity shows fluctuation from 309-to302kC and 3to 5m/s along and from 309to 291k and 0to 12m/s across.

Model: k-omega model

momentum ratio 2

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 200 iterations and also the average outlet temperature becomes303k. The temperature and velocity shows fluctuation from 309to 302k and 3to 4.1m/s along and from 309-to291k and 0to 6m/s across.

momentum ratio 4

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 260iterations and also the average outlet temperature becomes 300k. The temperature and velocity shows fluctuation from 309-to 302k and 3.5to 5m/s along and from 301-to 290k and 1.5to11m/s across.

LONG TEE

Model: k-epsilon model

momentum ratio 2

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 100 iterations and also the average outlet temperature becomes 303.5k. The temperature and velocity shows fluctuation from 309-to 303k and 3to 4.5m/s along and from 309to 291k and 0to 6m/s across.

momentum ratio 4

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 150 iterations and also the average outlet temperature becomes 300.5k The temperature and velocity shows fluctuation from 309to 302k and 3to 6.1m/s along and from 309to 291k and 0to 12m/s across.

Model: k-omega model

momentum ratio 2

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 100 iterations and also the average outlet temperature becomes 303.5k. The temperature and velocity shows fluctuation from 309to 302k and 3to 4.5m/s along and from 309to 292k and 0.5to 6m/s across.

momentum ratio 4

Convergence for iterations

area weighted temperature

standard deviation of temperature

Post processing results

Temperature along the length

Temperature across the length

Velocity along the length

Velocity across the length

Thermal plot along the length

Thermal plot across the length

Velocity plot along the length

Velocity plot across the length

The post processing results shows the variation of temperature and velocity along and across the length of pipe. The standard deviation reaches stability at 160 iterations and also the average outlet temperature becomes 301 k. The temperature and velocity shows fluctuation from 309 to 301.5kand 3to 6.1m/s along and from309to 290.5k and 0to 12m/s across.

Comparison between both the turbulent model for different geometry with analytical solution

K-EPSILON MODEL

GEOMETRY	MOMENTUM RATIO	CELL COUNT	AVERAGE OUTLET TEMPERATURE	ITERATION TO CONVERGE
Short tee	2	12798	26.5	130
Long tee	2	15593	29.5	90
Short tee	4	12798	28.5	100
Long tee	4	15593	28.8	60

K-OMEGA MODEL

GEOMETRY	MOMENTUM RATIO	CELL COUNT	AVERAGE OUTLET TEMPERATURE	ITERATION TO CONVERGE
Short tee	2	12798	28.5	120
Long tee	2	15593	29	200
Short tee	4	12798	18	100
Long tee	4	15593	27	150

ANALYTICAL SOLUTION

MOMENTUM RATIO 2

Mass of hot fluid`m_h=ρ.A.v_h=997*0.0009*3=2.69kg/s`

Mass of cold fluid`m_c=ρ.A.v_c=997*0.0002*6=1.35kg/s`

Temperature of mixture`T_mixture=(m_h*T_h+m_c*T_c)/( (m_c+m_h))=30.315^o c`

MOMENTUM RATIO 4

Mass of hot fluid`m_h=ρ.A.v_h=997*0.0009*3=2.69kg/s`

Mass of cold fluid`m_c=ρ.A.v_c=997*0.0002*6=2.3928kg/s`

Temperature of mixture`T_mixture=(m_h*T_h+m_c*T_c)/( (m_c+m_h))=27.46^o c`

On comparing the two viscous model from the analytical solution, it is seen that k-epsilon model gives the best predicted results. For momentum ratio 2, the numerical outlet temperature of long tee matches with analytical solution. Even for momentum ratio 4 it gives the same result. Considering these factors long tee is preferred due to its effectiveness in producing an accurate mixing outlet temperature. Also at high momentum ratio the effect of temperature and velocity distribution gets uniform.

GRID INDEPENDENCY TEST

MESH SIZE	NO OF ELEMENTS	NO OF NODES	NO OF ITERATIONS	AVERAGE OUTLET TEMPERATURE
5	16223	3474	260	28.5
3	59162	11554	100	29
1	1551673	273479	60	27.5

From the grid independency test it is seen that mesh size of 3mm gives the best predicted results and as close as compared to other mesh sizes. It is seen that on decreasing the mesh size the average outlet temperature also starts approaching towards the analytical results. Taking too finer mesh size shows deviation from the analytical solution.

CONCLUSION

1. The k-e model is seen to be effective in capturing the physics of thermal and flow behaviour starting from entry to the outlet.
2. The mesh grid independency test shows the effect of meshing parameter on the average outlet temperature distribution.
3. The long tee is suitable for better mixing of fluid effectiveness and numerical prediction of temperature and velocity variation.