Week 1- Mixing Tee

AIM

To simulate a steady state flow of hot air and cold air through a short and long mixing tees and compare the mixing effectiveness. The simulation is carried over different mesh sizes and models such as k-epsilon and k-omega and the results to get a conclusion.

OBJECTIVE

1. The main objective of this challenge is to set up steady-state simulations to compare the mixing effectiveness of long and short tee – junctions, when the hot inlet temperature is 36⁰C & the cold inlet is at 19⁰
2. To carry out the simulation for two cases,

Case – 1 :

• Short mixing tee with a hot inlet velocity of 3 m/s.
• Momentum ratio of 2, 4.
• Meshing sizes of 5,4,3,2,1mm

Case – 2 :

• Long mixing tee with a hot inlet velocity of 3 m/s.
• Momentum ratio of 2,
• Meshing sizes of 5,4,3,2,1mm
  3. Use the realizable k-ε and k–ω SST model for the cases.

INTRODUCTION

In this project simulation of a steady state flow of hot and cold air through a short and long mixing Tee will be carried out. The inlet hot and cold temperature are 36⁰C and 19⁰C. Realizable k-ε and k–ω SST model will be used for all the cases and a comparative study is done. Mesh independence study is obtained for various element mesh length from 5,4,3,2,1mm respectively. The outlet velocity and temperature of each cases is compared with the analytical values. Velocity and temperature at outlet are studied model wise as well as mesh length wise.

THEORY

Mixing Tee

Mixing of fluids at different temperatures and velocity is quite common in Industry. Fluids are transported through flow sections. Flow sections of circular cross sections are known as pipes. Most fluid especially liquids are transported in circular pipes. This is because, pipes with a circular cross section can withstand large pressure differences between the inside and outside without significant distortion. A typical piping system involves pipes of different diameters connected to each other by various fittings (T-Junction, Y-Junction) or elbow to ensure continuous transport of the fluid. Mixing Tee is also called T-Junction.

The desired temperature at the outlet is obtained in the mixing tee is by regulating the temperature and velocities of the hot inlet and outlet temperature.

Analytically the outlet temperature can be calculated using this mixing formula

K-Epsilon (k−ϵ) Model

The k-epsilon (k−ϵ) model for turbulence is the most common to simulate the mean flow characteristics for turbulent flow conditions. It belongs to the Reynolds-averaged Navier Stokes (RANS) family of turbulence models where all the effects of turbulence are modeled.

It is a two-equation model. That means that in addition to the conservation equations, it solves two transport equations (PDEs), which account for the history effects like convection and diffusion of turbulent energy. The two transported variables are turbulent kinetic energy (k), which determines the energy in turbulence, and turbulent dissipation rate (ϵ), which determines the rate of dissipation of turbulent kinetic energy.

The k−ϵ model is shown to be reliable for free-shear flows, such as the ones with relatively small pressure gradients, but might not be the best model for problems involving adverse pressure gradients, large separations, and complex flows with strong curvatures.

There exist different variations of the k-epsilon model such as Standard, Realizable, RNG, etc. each with certain modifications to perform better under certain conditions of the fluid flow.

K-Omega (k−ω)

The k-omega (k−ω) turbulence model is one of the most commonly used models to capture the effect of turbulent flow conditions. It belongs to the Reynolds-averaged Navier-Stokes (RANS) family of turbulence models where all the effects of turbulence are modeled.

It is a two-equation model. That means in addition to the conservation equations, it solves two transport equations (PDEs), which account for the history effects like convection and diffusion of turbulent energy. The two transported variables are turbulent kinetic energy (k), which determines the energy in turbulence, and specific turbulent dissipation rate (ω), which determines the rate of dissipation per unit turbulent kinetic energy. ω is also referred to as the scale of turbulence.

The standard k−ω model is a low Re model, i.e., it can be used for flows with low Reynolds number where the boundary layer is relatively thick and the viscous sublayer can be resolved.

Thus, the standard k−ω model is best used for near-wall treatment. Other advantages include a superior performance for complex boundary layer flows under adverse pressure gradients and separations (e.g., external aerodynamics and turbomachinery). On the contrary, this model has also shown to predict excessive and early separations.

There exist different variations of the k-omega model such as standard k-omega (discussed above), baseline k-omega, k-omega SST, etc., each with certain modifications to perform better under certain conditions of the fluid flow.

SST stands for shear stress transport. The SST formulation switches to a k−ϵ behavior in the free-stream, which avoids the k−ω problem of being sensitive to the inlet free-stream turbulence properties.

The k−ω SST model provides a better prediction of flow separation than most RANS models and also accounts for its good behavior in adverse pressure gradients. It has the ability to account for the transport of the principal shear stress in adverse pressure gradient boundary layers. It is the most commonly used model in the industry given its high accuracy to expense ratio.

On the negative side, the SST model produces some large turbulence levels in regions with large normal strain, like stagnation regions and regions with strong acceleration. This effect is much less pronounced than with a normal k-epsilon model though.

SOLVING & MODELLING APPROACH

We have two mixing tees one is shorter than the other given in the challenge

Short Tee Long Tee

So the above challenge can be grouped based on the following conditions

1. Mixing Tee
2. Short Tee
3. Long Tee
4. Momentum Ratio
5. momentum ratio = 2
6. Momentum ratio = 4

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

Hot Inlet Velocity = 3m/s

3. Turbulence Model
4. k-epsilon
5. k-omega SST
6. Mesh Element Size
7. 5mm
8. 4mm
9. 3mm
10. 2mm
11. 1mm

Hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C.

Based on the above condition we categorise the total number of cases as show in the table below.

Total Cases

Analytical results to be obtained and compared with the obtained result. We are considering our working fluid as air, whose density (ρ) is 1.225 kg/m. We have the formula,

T_hot=36^oC

T_hot=36^oC

V_hot=3 m/s

T_cold=19^oC

V_cold=6m/s

A_hot=891.86mm²

A_cold=221.42mm²

ρ_air=1.225 kg/m

Mass Flow Rates,

m_hot=ρ⋅A⋅V_hot

=1.225×887.9154×3

m_hot=3263.0891 kg/s

m_cold=ρ⋅A⋅V_cold

=1.225×222.2797×3

m_cold=1633.7557 kg/s

Analytical Average Outlet Temperature,

T_mixture=

T_mixture=30.3282^oC

Likewise for all the cases T_{mixture values are calculated and computed} as given in the table below.

Analytical Outlet Temperature

Since there are many cases as shown above we will go for a tree approach in the workbench. Start with a geometry.

We can load the given model in the geometry. Since there are two mixing tees two separate geometry is used. In the geometry volume of the Mixing Tee that is to be analysed is extracted.

Then after the geometry we will go for meshing. Since we have 5 different mesh sizes, create 5 different mesh modules and connect with parent geometry as in the figure.

After the meshing fluent module are created to solve and simulate the mixing Tees. Since we have two turbulence model and two momentum ratios, total of 4 modules to be created under each meshing and to be connected accordingly as shown in the figure. All the parameters and boundary conditions are given inside the solution.

Once the solution are generated results module are added and connected to each model. Result module is used to get various results of the problem statement. Such as Contour plots, vector plot Graphical chart plots, Animations etc.,

These graphs, plots and section plane views are used in the better understanding of the results obtained for the given problem statement and are used for comparing the values to get the conclusions and findings.

PRE PROCESSING AND SOLVER SETTING

In our challenge we will create a flow simulation of cold and hot air through two mixing Tees for the previously mentioned cases in the table. In general I will be explaining only one case and posting the screenshots of the other cases.

Case 1

Short Tee – Mesh 5mm – K Epsilon – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Step 1 : Load the short tee in the geometry Space Claim. Since we are analysing the inside volume mixing, we extract the volume using extract function in the Space Claim. Only the volume is required for analysis and so the solid part is suppressed.

Once this process is done. We will close the space claim and open the mesh module.

Step 2 : Open the mesh module and under the mesh details give CFD Fluent as preference and Element size of 5mm. We can refine the mesh by giving sizing and other options. But since we are going to go for mesh independence study uniform meshing size is maintained through out the volume. Note the number of nodes and elements for the study.

After the meshing is done check for the quality criterion.Check whether the mesh quality is above 5%. Once this is done name the faces of the volume as Inlet Cold, Inlet Hot, Outlet & Wall.

Step 3 : After the meshing and face naming are done move on to Fluent Solver. In the fluent launcher select double precision, display mesh after reading and give the appropriate solver processors and GPUs.

In the ANSYS CFD we need to give all the conditions, parameters and models. To start with go to physics menu and click general settings. In that select Pressure based type solver, Absolute velocity formulation and steady state flow. Since we are handling with temperature check the energy box under Physics menu. Next we need to give the model. For this case K Epsilon realizable model is selected.

Next is the flow material selection. By default air is selected. Hence no need to change any values or selection. After that boundary conditions are to be assigned. For that click on zones- boundaries.

Give all the boundary conditions such as pressure, velocity, temperature etc., to all the boundaries of the volume as required. Care should be taken while assigning the boundary type. In our case Inlet cold and hot initials values are to be assigned.

After the physics part is done move to the solution part. To generate any particular report such as area weighted average or standard deviation for temperature and velocity, click definitions-new and select the required one. In the popup window select the appropriate field variable, surfaces and other options.

Once the report definition part is completed click Initialize to initialize the boundary conditions. Hybrid method is selected before initialization. Click on Autosave to obtain a animation of the flow in the post results.

Then run the calculation for a given number of iterations till the convergence is obtained. Depending upon the number of elements and model selected the time required for convergence varies. In the CFD module itself we can compute, measure, plot, animate, etc., if needed.

Step 4 : After the solutions and calculations move to the result module to get different graphs, plots, contours, animations etc.,. Sectional views can be created if required.

RESULTS

SHORT TEE

Case 1

Short Tee – Mesh 5mm – K Epsilon – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 5mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 2

Short Tee – Mesh 5mm – K Epsilon – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 5mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 3

Short Tee – Mesh 5mm – K Omega – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 5mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 4

Short Tee – Mesh 5mm – K Omega – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 5mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 5

Short Tee – Mesh 4mm – K Epsilon – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 4mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 6

Short Tee – Mesh 4mm – K Epsilon – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 4mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 7

Short Tee – Mesh 4mm – K Omega – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 4mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 8

Short Tee – Mesh 4mm – K Omega – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 4mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 9

Short Tee – Mesh 3mm – K Epsilon – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 3mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 10

Short Tee – Mesh 3mm – K Epsilon – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 3mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 11

Short Tee – Mesh 3mm – K Omega – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 3mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 12

Short Tee – Mesh 3mm – K Omega – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 3mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 13

Short Tee – Mesh 2mm – K Epsilon – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 2mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 14

Short Tee – Mesh 2mm – K Epsilon – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 2mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 15

Short Tee – Mesh 2mm – K Omega – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 2mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 16

Short Tee – Mesh 2mm – K Omega – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 2mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 17

Short Tee – Mesh 1mm – K Epsilon – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 1mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 18

Short Tee – Mesh 1mm – K Epsilon – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 1mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 19

Short Tee – Mesh 1mm – K Omega – Momentum ratio 2

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 1mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

Case 20

Short Tee – Mesh 1mm – K Omega – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 1mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature Fig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

The entire result of the short Tee mixing simulation can be summarized as given in the table above. There are a total of 20 cases in short Tee. For each cases we have noted the nodes count, elements count, Analytical outlet temperature, average outlet temperature, average outlet velocity and Standard deviation of outlet temperature. We will discuss the result under two momentum ratio categories.

Momentum Ratio – 2

In momentum ratio 2 there are total of 10 cases. 5 each for the K epsilon and K omega models. Here we can calculate the analytical value of the outlet temperature which is equal to 30.3282^oC. We got a maximum average outlet temperature of 30.5507 ^oC for the K omega model with a mesh size of 1mm and a minimum average outlet temperature of 30.2393 ^oC for the K epsilon model with a mesh size of 4mm. The minimum and maximum average outlet velocity was obtained as 4.4945m/s and 4.5244 m/s for the K epsilon model with mesh size of 3mm and for the K omega model with mesh size of 1mm respectively. The standard deviation of outlet temperature was observed to be minimum 1.2438 for K-epsilon model with 5mm mesh size and maximum 2.4345 for K-omega model with 2mm mesh size. It was observed that there is no much difference between the analytical and simulation results.

Momentum Ratio – 4

In momentum ratio 4 there are total of 10 cases. 5 each for the K epsilon and K omega models. Here we can calculate the analytical value of the outlet temperature which is equal to 27.4942^oC. We got a maximum average outlet temperature of 27.6646 ^oC for the K omega model with a mesh size of 3mm and a minimum average outlet temperature of 27.5456 ^oC for the K epsilon model with a mesh size of 4mm. The minimum and maximum average outlet velocity was obtained as 6.0151m/s and 6.1175 m/s for the K epsilon model with mesh size of 3mm and for the K omega model with mesh size of 2mm respectively. The standard deviation of outlet temperature was observed to be minimum 1.0276 for K-epsilon model with 3mm mesh size and maximum 2.2012 for K-omega model with 1mm mesh size. It was observed that there is no much difference between the analytical and simulation results.

Effectiveness of Short Tee

Comparing the results of all the cases we can conclude that the minimum standard deviation gives the better mixing. Here Standard deviation of 1.0276 is the lowest of all. Hence K Epsilon model with momentum ratio of 4 and mesh size of 3 has better efficiency than the others. While comparing the temperature and velocity contour graphs, it was observed that long tee mixing is more efficient compared to the short tee.

Temperature Vs Length Comparison

These are the comparison graphs of temperature. Each graph represent the change in temperature of outlet along the length of the model for different mesh sizes. For each mesh sizes we have plotted a graph with the comparison of 4 cases.

1. K-Epsilon MR2
2. K-Epsilon MR4
3. K-Omega MR2
4. K-Omega MR4

We can observe that the there is a sudden drop in the temperature in all the cases at a particular area. This region is the area where cold and hot air enters. At this point mixing has just began. After that the mixing progresses along the model giving a required temperature at output. It can be noticed that momentum ration 4 cases reaches the steady state at a length of 0.05m. From there is not much comparable change in the temperature implying that the mixing has been occurred effectively. But for momentum ratio 2 cases the mixing is occurring to the very outlet giving an undesired temperature. From the graph it can be noted that K Epsilon with momentum ration of 4 and mesh size of 3mm has the highest mixing effectiveness. Also plotted temperature Vs length for all the models which gives the same inference as above.

Velocity Vs Length Comparison

These are the comparison graphs of velocity. Each graph represent the change in velocity of outlet along the length of the model for different mesh sizes. For each mesh sizes we have plotted a graph with the comparison of 4 cases.

1. K-Epsilon MR2
2. K-Epsilon MR4
3. K-Omega MR2
4. K-Omega MR4

We can observe that the there is a sudden rise in the velocity in all the cases at a particular area. This region is the area where cold and hot air enters. At this point mixing has just began. After that the mixing progresses along the model giving a required velocity at output. It can be noticed that momentum ration 4 cases reache the steady state at a length of 0.05m. From there is not much comparable change in the velocity implying that the mixing has been occurred effectively. But for momentum ratio 2 cases the mixing is occurring to the very outlet giving an undesired velocity. From the graph it can be noted that K Epsilon with momentum ration of 4 and mesh size of 3mm has the highest mixing effectiveness. Also plotted temperature Vs length for all the models which gives the same inference as above.

By comparing all the results it is evident that the K-Epsilon model with momentum ratio of 4 and mesh size of 3mm gives as the better mixing. Hence I will chose this as my main model for the long tee. All the cases for long tee has been computed as short tee. But the optimum results are explained in the report.

LONG TEE

Short Tee – Mesh 2mm – K Epsilon – Momentum ratio 4

Inlet Hot Temperature – 36^oC

Inlet Cold Temperature – 19^oC

Inlet Hot Velocity – 3m/s

Fig 1 : 2mm Mesh

Fig 2 : Residual Plot

Fig 3 : Standard deviation of temperature F ig 4: Average Temperature

Fig 5 : XY plane temperature contour

Fig 6 : XY plane velocity contour

Fig 6 : XY plane velocity Vector

Fig 7 : Wall Temperature contour Fig 8: YZ plane velocity contour

Fig 9 : Wall Velocity contour Fig 10: YZ plane velocity contour

Fig 11 : Temperature Vs Length

Fig 12 : Velocity Vs Length

The entire result of the long Tee mixing simulation can be summarized as given in the table above. In the previous case we came to know that K epsilon model with momentum ration 4 has the highest effectiveness. In this long tee model case also minimum standard deviation is obtained K epsilon model with momentum ratio 4 and a mesh size of 2mm. But in short tee model optimum mesh size was 3mm.There are a total of 20 cases in short Tee. For each cases we have noted the nodes count, elements count, Analytical outlet temperature, average outlet temperature, average outlet velocity and Standard deviation of outlet temperature. We will discuss the result under two momentum ratio categories.

Momentum Ratio – 2

In momentum ratio 2 there are total of 10 cases. 5 each for the K epsilon and K omega models. Here we can calculate the analytical value of the outlet temperature which is equal to 30.3281^oC. We got a maximum average outlet temperature of 30.5816 ^oC for the K omega model with a mesh size of 1mm and a minimum average outlet temperature of 30.3047 ^oC for the K epsilon model with a mesh size of 5mm. The minimum and maximum average outlet velocity was obtained as 4.4901m/s and 4.5152 m/s for the K epsilon model with mesh size of 3mm and for the K omega model with mesh size of 1mm respectively. The standard deviation of outlet temperature was observed to be minimum 0.9530 for K-epsilon model with 5mm mesh size and maximum 2.0655 for K-omega model with 2mm mesh size. It was observed that there is no much difference between the analytical and simulation results.

Momentum Ratio – 4

In momentum ratio 4 there are total of 10 cases. 5 each for the K epsilon and K omega models. Here we can calculate the analytical value of the outlet temperature which is equal to 27.4942^oC. We got a maximum average outlet temperature of 27.6098 ^oC for the K omega model with a mesh size of 1mm and a minimum average outlet temperature of 27.4846 ^oC for the K epsilon model with a mesh size of 1mm. The minimum and maximum average outlet velocity was obtained as 5.9950m/s and 6.0647 m/s for the K epsilon model with mesh size of 3mm and for the K omega model with mesh size of 1mm respectively. The standard deviation of outlet temperature was observed to be minimum 0.5483 for K-epsilon model with 2mm mesh size and maximum 1.0826 for K-omega model with 1mm mesh size. It was observed that there is no much difference between the analytical and simulation results.

Effectiveness of Short Tee

Comparing the results of all the cases we can conclude that the minimum standard deviation gives the better mixing. Here Standard deviation of 0.5483 is the lowest of all. Hence K Epsilon model with momentum ratio of 4 and mesh size of 2 has better efficiency than the others. While comparing the temperature and velocity contour graphs, it was observed that long tee mixing is more efficient compared to the short tee.

Temperature Vs Length Comparison

These are the comparison graphs of temperature. Each graph represent the change in temperature of outlet along the length of the model for different mesh sizes. For each mesh sizes we have plotted a graph with the comparison of 4 cases.

1. K-Epsilon MR2
2. K-Epsilon MR4
3. K-Omega MR2
4. K-Omega MR4

We can observe that the there is a sudden drop in the temperature in all the cases at a particular area. This region is the area where cold and hot air enters. At this point mixing has just began. After that the mixing progresses along the model giving a required temperature at output. It can be noticed that momentum ration 4 cases reaches the steady state at a length of 0.05m. From there is not much comparable change in the temperature implying that the mixing has been occurred effectively. But for momentum ratio 2 cases the mixing is occurring to the very outlet giving an undesired temperature. From the graph it can be noted that K Epsilon with momentum ration of 4 and mesh size of 2mm has the highest mixing effectiveness. Also plotted temperature Vs length for all the models which gives the same inference as above.

Velocity Vs Length Comparison

These are the comparison graphs of velocity. Each graph represent the change in velocity of outlet along the length of the model for different mesh sizes. For each mesh sizes we have plotted a graph with the comparison of 4 cases.

1. K-Epsilon MR2
2. K-Epsilon MR4
3. K-Omega MR2
4. K-Omega MR4

We can observe that the there is a sudden rise in the velocity in all the cases at a particular area. This region is the area where cold and hot air enters. At this point mixing has just began. After that the mixing progresses along the model giving a required velocity at output. It can be noticed that momentum ration 4 cases reach the steady state at a length of 0.05m. From there is not much comparable change in the velocity implying that the mixing has been occurred effectively. But for momentum ratio 2 cases the mixing is occurring to the very outlet giving an undesired velocity. From the graph it can be noted that K Epsilon with momentum ration of 4 and mesh size of 2mm has the highest mixing effectiveness. Also plotted temperature Vs length for all the models which gives the same inference as above.

Mesh Independence Study

Mesh independence study is the study of the effect of the mesh element size in the final result. Here our desired result is average outlet temperature. So temperature is plotted against number of mesh elements. Elements for the below given table values.

The above table shows the different cases of short and long mixing tees. Number of nodes and elements was noted while meshing .Analytical temperature and average output temperature were also tabulated for each cases. From the table we can say that as the mesh element size is decreased the more accurate the simulated value towards the analytical value.

For example I have plotted two cases as shown in the above figure. When element size is decreased, accurate results are obtained. For the above flow conditions, calculated value for the outlet temperature is 30.3282°C. But for our mesh size = 5mm, the outlet temperature is 30.2798°C. So when the mesh size is decreased, obviously the better results are obtained. But computational time is higher. So one must be careful in choosing the type of element, mesh size for a particular problem to obtain better results.

CONCLUSION

• It was observed that the mixing efficiency is higher for Long Tee compared to the short Tee. The outlet temperature of Long Tee was found to be around 27.5^oC which is very near to the analytical temperature calculated. The minimum standard deviation for short Tee was observed for K-epsilon MR4 with mesh size of 3mm and for long tee it was observed for K-Epsilon MR4 with 2mm mesh size.
• As the mesh size decreases the number of elements increases resulting in more accurate result towards the analytical values. But computational time for solving the problem increases drastically. Hence one should take it important in selecting the type of element and its size.