Mixing efficiency

MIXING T EFFICIENCY CALCULATION

1. PROBLEM STATEMENT- Set up a steady state simulation to compare the mixing effectiveness when hot & cold air is mixed at certain conditions Use K-omega SST model & K-epsilon model. Based on your judgement, use a suitable model for analysis.

1.1 GIVEN DATA

• HOT AIR INLET TEMPERATURE = 36-DEG C
• COLD AIR INLET TEMPERATURE = 19-DEG C
• HOT AIR INLET VELOCITY = 3 m/s
• HOT AIR INLET VELOCITY = 6 m/s & 12 m/s… 2 different cases
• MOMENTUM RATIO = 2 & 4

2. INTRODUCTION, AIM & APPLICATION

This project focus on mixing efficiency of two fluid at different inlet velocity & temperature condition. We will be monitoring outlet temperature due to change in inlet speed of cold air keeping all other parameter constant. We will also observe the effect of increasing the length of pipe keeping all other parameter constant.

The application of this project can be seen in many industrial applications like cooling a machine shop, HVAC system, air conditioning of room e.t.c.

3. GEOMETRY &MESHING DETAILS

3.1 MESHING

Fig below shows the meshing & another figure shows cut-section shows the cut section view of meshing. This type of meshing is known as 3-D meshing. The 3-D element created in cut section clearly shows the pyramidal element. If we consider for shorter length the total number of nodes is 21347 & total numberof elements is 105865.

Statistics for shorter & longer geometry has been compared in the following table.

Meshing data is taken after performing mesh independent study. Earlier meshing was done at 5mm element size & later on meshing was done by changing element size from 5 mm to 13.853 mm. Both cases give almost same monitoring parameter at monitoring point. So, 13.853 mm element size as a reference for further calculation has been taken.

GEOMETRY	SHORTER LENGTH GEOMETRY	LONGER LENGTH GEOMETRY
NUMBER OF NODES	21347	3495
NUMBER OF ELEMNTS	105865	15689
ELEMENT SIZE	2 mm	13.853 mm

From above table, the number of elements & nodes for a longer length geometry is quite lesser than a shorter length geometry. The reason behind this is the element size. The size of element for longer length of geometry is quite large as compared to shorter length of geometry.

3.2 MESHING QUALITY

Quality of mesh can be observed with the help of following histogram obtained from meshing quality details. This histogram tells the details of number of elements falls under certain size of element.

We can conclude that all the meshing element of shorter length geometry are having size greater than 0.3 m.

If we compare statistics for MESH MATRIX (element quality), the minimum & maximum size of element for longer length of geometry are 0.32226 & 0.99993 respectively. Same data for shorter length of geometry are 0.28002 & 1. All data are in mm.

4. SETUP & PHYSICS

Pressure based with absolute velocity formulation type solver was chosen for simulation. There is no role of gravity.

4.1 MODELS

The viscous model was chosen as k-omega SST model. Shear Stress Transport (SST) is a variant of standard k-w model. It combines the original Wilcox k-w model for use near wall & the standard k-e model away from the wall using a blending function. The eddy viscosity formulation is modified to account of transport effects of the principal turbulence shear stress.

SST IS RECOMMENDED FOR HIGH ACCURACY BOUNDARY LAYER SIMULATION.

The result for our particular simulation doesn’t differ a lot. Data has been compared in result section.

4.2 MATTERIAL

Air has been chosen as a flow material. All the standard properties of air have been imposed on this material.

5. BOUNDARY CONDITION

Boundary condition has been mentioned in problem statement in section (1.1). There are 4 different cases. Two cases are due to change in length of geometry & two cases are due to change in momentum ratio.

6. RESULT & DISSCUSION

6.1 CASE 1

This is the case where shorter length of geometry was considered with a momentum ratio of 2. The temperature of inlet hot air was 36 degree-centigrade with an incoming velocity of 3m/s. The temperature of cold air was 19 degree-centigrade with an incoming velocity of 6m/s.

Figure shows the residue plot. The simulation was run for 400-time step in order to confirm for convergence of simulation results. The simulation was converged after running it for 250 iteration. It can be observed from residue that the all parameters are repeating its value after 250 iteration up to 400 iterations.

The average outlet (area-weightage) temperature was found to be 30.3957 degree-centigrade with a standard deviation of 2.4831 degree-centigrade. All the result has been compared in a single table under conclusion section. Above residue has been plotted for k-w SST model.

We can also do the same calculation with k-epsilon model instead k-omega SST model. The result was compared for both cases of viscous model for case 1. There was not much difference between output temperature. There was a difference in residue plot only.

Residue plot for k-epsilon model has been plotted below. The simulation was run for 500-time steps. The convergence has been observed after a time step of 230 iterations. The residue kept repeating its value after converging.

The average outlet (area-weightage) temperature was found to be 30.304 degree-centigrade with a standard deviation of 2.270 degree-centigrade. All the result has been compared in a single table under conclusion section.

6.1.1 PLOTS

The following plots shows the contours of temperature on a plane which was generated in between of the geometry.

The following plots shows the contours of velocity on a plane which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (across length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (across length) which was generated in between of the geometry.

Figure below shows the temperature contour at outlet of short tee at momentum ratio of 2.

Figure below shows the velocity contour at outlet of short tee at momentum ratio of 2.

6.2 CASE 2

This is the case where shorter length of geometry was considered with a momentum ratio of 4. The temperature of inlet hot air was 36 degree-centigrade with an incoming velocity of 3m/s. The temperature of cold air was 19 degree-centigrade with an incoming velocity of 12m/s.

Fig.below shows the residue plot. The simulation was run for 280-time step in order to confirm for convergence of simulation results. The simulation was converged after running it for 225 iteration. It can be observed from residue that the all parameters are repeating its value after 225 iteration up to280 iterations.

The average outlet (area-weightage) temperature was found to be 27.607 degree-centigrade with a standard deviation of 1.342 degree-centigrade. All the result has been compared in a single table under conclusion section.

6.2.1 PLOTS

The following plots shows the contours of temperature on a plane which was generated in between of the geometry.

The following plots shows the contours of velocity on a plane which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (across length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (across length) which was generated in between of the geometry.

Figure below shows the temperature contour at outlet of short tee at momentum ratio of 4.

Figure below shows the velocity contour at outlet of short tee at momentum ratio of 4.

6.3 CASE 3

This is the case where longer length of geometry was considered with a momentum ratio of 2. The temperature of inlet hot air was 36 degree-centigrade with an incoming velocity of 3m/s. The temperature of cold air was 19 degree-centigrade with an incoming velocity of 6m/s.

Figure above shows the residue plot. The simulation was run for 500-time step in order to confirm for convergence of simulation results. The simulation was converged after running it for 350 iteration. It can be observed from residue that the all parameters are repeating its value after 350 iteration up to 500 iterations.

The average outlet (area-weightage) temperature was found to be 30.5284 degree-centigrade with a standard deviation of 1.6843 degree-centigrade. All the result has been compared in a single table under conclusion section.

6.3.1 PLOTS

The following plots shows the contours of temperature on a plane which was generated in between of the geometry.

The following plots shows the contours of velocity on a plane which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (across length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (across length) which was generated in between of the geometry.

Figure below shows the temperature contour at outlet of long tee at momentum ratio of 2.

Figure below shows the velocity contour at outlet of long tee at momentum ratio of 2.

6.4 CASE 4

This is the case where longer length of geometry was considered with a momentum ratio of 4. The temperature of inlet hot air was 36 degree-centigrade with an incoming velocity of 3m/s. The temperature of cold air was 19 degree-centigrade with an incoming velocity of 12m/s.

Figure below shows the residue plot. The simulation was run for 350-time step in order to confirm for convergence of simulation results. The simulation was converged after running it for 160 iteration. It can be observed from residue that the all parameters are repeating its value after 160 iteration up to350 iterations. The viscous model is k-omega SST model

The average outlet (area-weightage) temperature was found to be 27.4733 degree-centigrade with a standard deviation of 0.6468 degree-centigrade. All the result has been compared in a single table under conclusion section.

6.4.1 PLOTS

The following plots shows the contours of temperature on a plane which was generated in between of the geometry.

The following plots shows the contours of velocity on a plane which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (along length) which was generated in between of the geometry.

The following plots shows the contours of temperature on a line (across length) which was generated in between of the geometry.

The following plots shows the contours of velocity on a line (across length) which was generated in between of the geometry.

Figure below shows the temperature contour at outlet of long tee at momentum ratio of 4.

Figure below shows the velocity contour at outlet of long tee at momentum ratio of 4.

7. MESH INDEPENDENT STUDY

7.1 MONITER POINT & MONITERING PARAMETER

Here in order to perform mesh independent study we will consider case 4. Here model of longer length with momentum ratio of 4 is given. The inlet velocity of hot air is 3 m/s & cold air is 12 m/s. The inlet temperature of hot air is 36 degree centigrade & cold air is 19 degree centigrade.

The outlet face has been considered as a monitor point. The area weightage average temperature will be monitoring parameter for this observation.

7.2 MESHING DETAILS

We have to show that temperature at monitor point doesn’t depend on meshing of geometry.

The details for initial meshing & final meshing of geometry has been compared in table below

MESHING STAGE	INITIAL MESHING	FINAL MESHING
NUMBER OF NODES	40287	3495
NUMBER OF ELEMNTS	18173	15689
ELEMENT SIZE	5 mm	13.853 mm

Element size was increased from 5mm to 13.853mm. The number of nodes decreased from 40287 to 3495. There was also decreased in number of elements from 18173 to 15689.

If we compare above 3-d meshing element view with the meshing size of 13.85 mm element , we will find these elements are much smaller than those which are present in size of 13.85 mm element. Figure below present the element size of 13.85mm & figure above shows the element size of 5mm.

7.3 RESIDUE COMPARISION

Here residue plots for both type of meshing has been shown.Figure below shows for element size 5 mm & fig shown in section 6.4(residue) for element size 13.85 mm.

Here convergence of solution can be seen after 250 iteration. The values keep repeating after 250 iteration of calculation.

The following plot shows average area weightage temperature value at outlet. Figure below shows Temperature at outlet at element size of 5 mm

Figure below shows Temperature at outlet at element size of 13.85 mm

The monitoring parameter doesn’t depend on meshing element size at monitoring point. This statement can be concluded from above 2 plot

7.4 RESULT COMPARISON FOR MESH INDEPENDENT STUDY

Figure shown below is the outlet temperature at mesh element size of 13.85 mm.

Figure shown below is the outlet temperature at mesh element size of 5 mm.

Above two outputs don’t differ a lot and are within tolerance limit. Area weightage average temperature in both cases differ by only 0.0209 degree centigrade. This difference is almost negligible.

Hence it can be concluded from section 6 that, mesh independent study has been studied successfully & verified within tolerance limit.

We can use mesh element size 13.85 mm instead of 5mm for faster calculation because output are within acceptable limits.

8. CONCLUSION

8.1 COMPARAISION OF OUTLET TEMPERATURE OF ALL CASES

Following table contains data of temperature at outlet

PARAMETER	INLET VELOCITY IN m/s_HOT AIR	INLET VELOCITY IN m/s_HOT AIR	GEOMETRY TYPE	TEMPERATURE AT OUTLET IN CENTIGRADE	STANDERD DEVIATION OF TEMPERATURE
CASE-1	3	6	SHORT TEE	30.528	2.483
CASE-2	3	12	SHORT TEE	27.607	1.342
CASE-3	3	6	LONG TEE	30.395	1.684
CASE-4	3	12	LONG TEE	27.473	0.646

If we compare case 1 & case 3 then observing the outlet temperature, we can say that increasing the length of geometry doesn’t alter the outlet temperature in any significant amount.

If we compare case 1 & 2 then there is a significant difference in outlet temperature. As we increase the velocity of inlet cold air the outlet air temperature decreases by approximately 3 degree centigrade. This method is more fruitful wrt increasing the length of geometry.

If we compare case 1 & case 4, result is very similar to wrt case 2. Here we are successfully able to decrease the temperature by 3.055 degree centigrade. In case 2 we successfully decreased the outlet temperature by 2.921. We are getting only an insignificant decrease in temperature in case 4 wrt case 2 (0.134 degree centigrade).

8.2 MESH INDEPENDENT STUDY

Section 7 has been dedicated for this purpose. Section 7.3 compares the monitaring parameter in both type of meshing & it is found that temperature are within acceptable limit.

8.3 k-w SST model v/s k-e model

From section 4.1 & 6.1 it can be concluded that k-w SST IS RECOMMENDED FOR HIGH ACCURACY BOUNDARY LAYER SIMULATION.