Mixing Tee challenge

Aim :

• For this challenge, we have created two versions of the mixing tee. One of them is longer than the other.our job is to set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36⁰C & the Cold inlet is at 19⁰C Use the k-epsilon and k-omega-SST model for the first case and based on your judgment use the more suitable model for further cases. Giving the reason for choosing a suitable model is compulsory. 

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)

• In a table, compare 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. Perform Mesh independent study for any one case.
4. Discuss the effect of length and momentum ratio on results. 

For each simulation, you need to show the convergence plot 

Reference Research paper:- https://www.sciencedirect.com/science/article/pii/S0029549309005676

[Note - It is just a reference research paper, those who do not have access to this paper can use any other research paper. Try to imitate the results from this paper, even if answers don't match]

Reference Formulas:-

Theory :

1.     Introduction to fluid :

• Fluid is a substance i.e. having the ability to flow or deform(angular) continuously under the action of shear force(no matter how much small the force).
• Generally liquids and gases falls in this category of fluids.
• Ex : water, air, petrol, steam, mercury etc.
• There are 3 ways we are studied on fluids
  1. Fluid statics – study of fluid at rest
  2. Fluid kinematics – study of fluid in motion without considering pressure forces
  3. Fluid dynamics – study of fluid in motion(i.e. with considering forces)

2.     Fundamentals of fluid mechanics :

• Newton’s law of viscosity (NLV):
  • A fluid shear stress is defined as the tangential deformation of a fluid element when a force is applied to it.
  • The law states that , this shear stress is directly proportional to the normal velocity gradient experienced by that fluid element.
  • Mathematically it is given as

`tau=mu(du/dy)`

Where

`tau`=shear stress (Pa or N/m²)

`mu`= dynamic viscosity or viscosity(N-S/m² or Pa-S)

 `du/dy`= velocity gradient (S^-1)

3.     Types of fluids :

• Ideal fluid – it is a fluid which shows non-viscous, incompressible and zero surface tension in nature.
• Real fluid – possesses viscosity
• Newtonian fluid - which obeys NLV(Ex: oil,water,air etc.)
• Non-newtonian fluid – which does not obey NLV (Ex : blood.paints etc.)
• Ideal plastic fluid – in which shear stress is more than the yield value and obeys NLV.( Ex: toothpaste ,gels etc)
• Compressible fluid – a fluid in which the density of a fluid changes with change in the pressure or volume called as compressible fluids.(Ex : air)
• Incompressible fluid - a fluid in which the density of a fluid doesnot change w.r.t. change in pressure and volume.(Ex : water)

4.      Introduction to mixing tee :

• Mixing tee is nothing but the there is a mixing of fluids in a T-joint.
• In this there are 2 inlets and 1 outlet. The 2 fluids with different properties are mixed in this joint and flows to the outside as a 1 fluid.
• The application of this model is in central air conditioning .

Procedure :

1.     Case-1: Short mixing tee with Momentum ratio=2 :

• Open the workbench

• Now drag the fluid flow(fluent) to the workspace

• Now right click on the geometry and import the short tee model

Now it has been imported.Now right click on geometry and click on edit with spaceclaim

Now wait to open spaceclaim

Now goto prepare and extract the volume

Now select the edges

Now click on green tick and here the volume has been extract

Now suppress the solid part for further physics.  for that right click on shell and then click on ‘supress for physics’

Now it has been suppress and shows symbol as not as highlited.now close this spaceclaim.

• Now right click on mesh and goto edit and wait for open

Now click on mesh

Now change the element size=5mm

Now right click on mesh-> generate mesh

And wait for mesh

Let select the faces and gives names to the faces

Now give name as ’Inlet-x’.to give this press short-cut key ‘N’ or right click on face and goto create name selection 

After clicking one popup opens

Now type the name and click on ok.

Similarly we are giving the names as ‘Inlet-y and outlet’

Now right click on mesh->update to update this data to fluent

After that close this mesh window.

• Now right click on setup->edit

 

A new popup opens

Now click on double precision and solver processes=4 then click on start and wait to open ansys fluent.

Just click on ok or close this window

Now goto units and find temperature and set unit as celcius

Close this tab.

Now double click on models

Now double click on energy and enable.this model is used for thermal energy calculations

Click on ok.

Now double click on viscous model

Now select k-epsilon->realizable->standard wall function->click on ok.

Now the model has been selected.now double click on materials

Here we are doing analysis by using air.so no need to change.it has been default selected.

Now goto cell zone and apply material

Now double click volume-volume to edit

Default air has been selected click on apply and close this tab.

Lets goto the boundary

Now click on inlet-x

Now it is showing velocity-inlet . now double click on this to change/apply bc.

Select the velocity specification method as shown above and here the velocity magnitude is given as 3m/s so give the value and goto the thermal section

Now from inlet-x the hot fluid enter so here the temp given as=36 C so put this value and apply and then close

Now double click on inlet-y.here this also a velocity inlet type.

Now give velocity value.here velocity is given in terms of momentum ratio=2

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

From above formula by keeping the values we are getting

velocity at cold inlet=momentum ratio * velocity at hot inlet = 2 * 3=6 m/s

so put this and temp=19 C and then apply and close.

Now click on outlet

It showing pressure-outlet.now click on edit

There is no need to change so just apply and close this.and now we have done with bc.

Now goto solutions->report definitions because we want to findout temps at outlet after calculations

Now goto new to crate a new report and as shown below

For creating area avg temp.now select the following parameters and give name as shows below

Now click on ok.

Now we have defined avg-temp report. Similarly define std-deviation temp report

Now close this.now goto solution->initialization

Here we are selecting hybrid initialization method because here 2 inlets are present and if we want to initialize the solution from particular point then we will gofor standard initialization technique.now click on initialize.

Now goto run calculation

Now give the no.of iterations=200 and scroll down and click on calculate

Now wait for calculation to be done.

Now its done let see plots.an the message we got as solution has converged.from below plots we can understand the solution is converge on iteration 148.

1. Residual plot

From above graph we can see that the solution is converged at 148 iteration.

2. Area-avg-temp plot

From above graph we can see that the temp graph is almost convergerd from 40^th itr and we are getting avg temp at outlet=30.262 C

3. Standard deviation plot

From above graph we can see that std dev temp plot starts converge from 60^th iteration and std.dev temp=1.342 c.

Now lets  plots velocity and temp contours .now close this fluent.

• Goto the results

Now enabeled geometry

Now double click on wall volume

Now change the color and then click on apply

Now goto render and change the transparency

Now goto default legend view

Now goto appearance-> precision and select fixed

Now click on apply. Now goto locations and select plane

Now give the name and click on ok.

Now just click apply to create the plane

Now goto the color

Now select mode as variable

Select variable=temp and click on apply.

Now just goto render give transparency

Here the deformation is less at mixing point and also not a good one.from above temp contour we can say that mixing of fluid is not done properly at bottom.so the hot fluid flows and show high temp.

Now similarly we will plot a velocity contour for that just goto color and change the variable as velocity.

From above velocity contour we can see that inlet-y velocity is not that much in more amount.due to this at upper and lower boundary the velocity of fluid is zero due to Maxwell condition or no slip condition.

• Lets compare these contour plots by changing the model k-epsilon to k-omega and lets see is there any change in outlet temp value.now we are keeping mesh size as 5mm.now close the results and goto setup and change the models to k-omega,initialize the solution and run calculation.

From above graph we can say that the solution is not coverged at 200 itr.

 

From above graph we can seen the avg temp almost converge and avg temp=30.283

From above graph std dev temp graph almost same and std dev. Temp=1.474

Now lets plot a countours and see

Now by seeing both models counters and by comparing these we can say that there is not that much change in the contor plots .so we can use anyone in this case.

• Lets see counters by changing mesh size to finer and then compare all models.now just goto mesh and change the mesh size and run the calculation.
  • Mesh size=3mm and k-epsilon model :

Now repeat the all procedure and find out final countour plots and also final temp.

The solution has almost converged.

 

Here also avg temp=30.324

Std dev temp=1.474

Let see countour plots

Now by comparing to course mesh type this contours looks smoother and little bit deform.

• Mesh size=3mm and viscous-omega-sst model :

Similar to above just change the model and see the output values and contour graphs

The solution is converged at 174 itr

Here the avg temp at outlet=30.369

Std.dev temp=1.739.

Let see contours

 

Now lets do comparison between these two models and 4 cases for all contour plots and outlet temp.

Parameters	k-epsilon model		k-omega-sst model
	Course mesh	Fine mesh	Course mesh	Fine mesh
Average temp	30.262	30.324	30.283	30.369
Std dev temp	1.342	1.396	1.474	1.739
Temp countours
Velocity counters

From above table we can see that there is not that much change in temp values and not change in contour plots so we can choose any one.this model is independent on mesh size. As we decrease the mesh size or fine the mesh size the plots gets smoother and also independent on model type but gives good value for k-omega-sst model because it covers k-epsilon as well as k-omega model. Now for further cases we are considering k-omega-sst model and fine mesh type=3mm.

• Now lets create the line plots along the length of the pipe.for that goto the results

Now goto the location and create a line

Then click on ok

Select cut from outline and click on apply

Now it has been created.to increase the thickness goto render

Now increase the line width as required and click on apply.

Now its done.now goto the charts to plot a graph

Give name as temp line chart and then click on ok.

Now give title as we want

Then goto data series

Now goto location and select line-1 and then click on apply.

Now change series name as ‘ST with MR=2’ and then goto x-axis

Now change the variable to x and uncheck the used data for axis labels to give name as ‘length of pipe(m)’

Now goto the y-axis and change the variable to temperature

Now its done.so the final temp line plot as

Here the sudden drop is due to cold fluid is entering at that location and after that there is a rise in temp is due to mixing of fluids taks place and temp of fluid started to stable by exchanging the heat .similarly we are creating the velocity line plot

Here the sudden rise is due to the high velocity fluid enters to the pipe at this length of pipe and as move forward the mixing of fluids with different velocity and gets try to balance as length of pipe increases.

Now its all done.

• Now lets calculate avg outlet temp for this case.this can be calculated by using following formula

Here m_hot and m_cold are the mass flow rate and can be obtained directly ansys fluent model For that goto calculators->function calculator -> select variable-> mass flowrate->select location->inlet-x->click on calculate

From here mhot=   0.00329553 [kg s^-1]

Similarly mcold at inlet-y location= 0.00163376 [kg s^-1]

Area Average of Temperature on inlet x

Thot=   309.15 [K]

Area Average of Temperature on inlet y

Tcold=  292.15 [K]

Now put these values in above eq. and calculate

Tmix(th)= = 303.59 k

And numerically , Area Average of Temperature on outlet

 Tmix= 303.519 [K].

Now by comparing these both are approx equal.

Now we will move for next case.

• Just export the data from chart to sheet formate to compare with other cases. for that goto chart which we have created.

Now click on export

Now give proper name select location where you want and click on save.now lets goto case-2.

2.     Case-2: Short mixing tee with Momentum ratio=4 :

• Now crate and new project fluent flow

Now connect these 2 cases. for that just drag the mesh from case-1 and transfer to setup in case-2

• Now open the setup.

Now goto models and enabeled energy model and visous-omega-sst model

Now check material and cell zone condition

Now apply the boundary conditions.

Now goto the inlet-x and apply velocity=3m/s and temp=36c

Now click on apply and close. Then goto inlet-y

Here temp=19c and MR=4=Vc/Vh

So, Vc=4*Vh=4*3=12m/s

Now click on apply and close.now goto the outlet

No need to change so just close.then goto solutions->report definition->new-> and create two reports as area-avg-temp and std-dev-temp.

Now close this and goto solution->initialization->hybrid initialization->initialize

Now goto run calculation and give no.of iteration=200 and hit calculate and wait until calculation done

Now calculation done.lets see plots.

From this graph we can say that the solution is convergrd at 129 iteration.

The avg temp is almost constant from 50 iteration and this give value as 27.05 C for this case.

From above graph we can say that std dev temp is almost constant and gives value as 1.452 C

• Lets goto the results to plot temp and velocity contour plots along the cut plane and line plots across the length of pipe in similar procedure.

Now plot the temp and velocity contour plots on plane by creating plane in similar way as mentioned in case-1 

Now here  high velocity cold fluid is mixes with low velocity hot fluid. Due to this we can see sudden temp drop at joint and compare to 1^st case the temp contour is more deviated.and in forward direction the fluid mixes very good.

Due to high velocity fluid mixed with low velocity fluid there is sudden change in velocity.and as we see after the t-location in pipe there is a blue contour shows low velocity is due to sudden entering of high velocity fluid some turbulane created. Lets plot line plot across the length of pipe.

As seen from temp line plot across the length of pipe there is sudden drop in temp due to a cold fluid enters in pipe after that due to mixing of fluid the temp of fluid increasing as move forward by exchanging the heat between fluids.

From above graph we can say that sudden increase in velocity at around 0.05m length of pipe is due to high velocity fluid enters in pipe at this location.and afterward as length of pipe increases 1^st velocity of fluid drops and then started gradually increases by exchanging the momentum with wach other.

• Let plot comparision plot for short tee

For that goto temp chart

Now goto data series

Then click on new

Give the name and open data points which we have stored sheet and then click on apply

Now its done.Now do similar for velocity also

• Lets calculate theoretically outlet temp by using above mention formula

Tmix=mhot*thot+mc*tc/mtotal

By putting values we are getting

Tmix=300.23 (K)

And by software we are getting as

Area Average of Temperature on outlet
  Tmix=300.72 [K]

By comparing these values our result is validated.

Lets go for next case.

3.     Case-3: Long mixing tee with Momentum ratio=2 :

• Create a new project

• now right click on geometry and import the geometry

Now browse the long tee model and import

After this rightclick on geometry and click on edit with spaceclaim

Now extract the volume

Suppress the solid model for further process

after this close spaceclaim and open mesh.

• Double click on mesh

Then goto mesh and give element size=3 mm and wait for mesh

Follow the same procedure as in case -1 and give names

Lets give names as inlet-x,inlet-y and outlet.after that right click on mesh and click on update and then close mesh.

• Goto setup

Follow same procedure.setup the models

Apply boundary conditions

Select inlet-x and give V=3m/s and T=36 C

Then click on apply and open inlet-y

Here v=6m/s(because  MR=2),T=19 C

Apply and close.then open outlet

Don’t change anything just close.now goto solutions -> report definition-> create 2 new reports as avg temp and std.dev temp at outlet.

Now initialize solution and run the calculation and wait for calculation complete.

now calculation done.let see residual,area avg temp,std.dev plots

By looking this the solution has converged at 327 iteration.

 

From above graph we are getting avg temp at outlet=30.39 C

From above graph we are getting std.dev temp at outlet= 1.17 C

• Lets plot temp and velocity contour plots on cut planes and along and across the the pipe.For that goto results and plot by similar procedure.

From above temp contour we can say that the cold fluid not mix properly with hot fluid at bottom position due to this at bottom the temp of fluid remains high.

Due to sudden enters of high velocity fluid there is littlebit turbulence created and velocity decreases slightly at after mixing location. 

Lets draw a temp and velocity line plots across the length of pipe for this case.

Here there is sudden drop in temp is due to at that location of pipe there is cold fluid enters in pipe and afterwards there is gradual increase in temp is due to mixing of fluids and exchange of heat between two fluids.

Here there is sudden increase in velocity is due to sudden enters the cold fluid at that location and afterwards velocity drop and gradually increases due to mixing of fluids take place and also momentum transfer between two fluids.

• Lets calculate outlet temp theoretical by using formula

Mass Flow on inlet x =  0.00329 [kg s^-1]

Mass Flow on inlet y =  0.00163 [kg s^-1]

Mass Flow on outlet = 0.00492 [kg s^-1]

Area Average of Temperature on inlet x =  309.15 [K]

Area Average of Temperature on inlet y = 292.15 [K]

by putting these values we are getting

Tmix=303.52 K

And by software

Area Average of Temperature on outlet =  303.547 [K]

so it almost equal so our result is validated.

Now we will move for next case.

4.     Case-4: Long mixing tee with Momentum ratio=4 :

• Open the new project

Now connect case-3 and case-4 by dragging mesh to setup as shown below

• Now open setup

Now apply models

Now apply boundary conditions

Now goto inlet-x and give v=3m/s and T=36 C

Now click on apply and then open inlet-y

here the MR=4

So Vc=4*Vh=4*3=12 m/s

And T= 19 C.apply these boundary conditions

Then open outlet

here nothing has to change so close this.

• then goto solutions->report definition-> create 2 reports as avg temp and std.dev.temp

Now goto initialization -> hybrid initialize -> initialize to initialize solution.

After that goto run calculation and give no. of iteration =200 and wait for calculation tobe  done.

Lets see plots

From this graph we can see that the solution has been converged at 156 iterations.

From above graph we can see that area avg temp get converged= 27.52 C

From above graph std dev temp= 0.412 C.

• now lets plot temp and velocity contour plots by same procedure.for that close fluent and goto results

From above graph we can see that there is a diffusion of temp contour of cold fluid and by seeing this the mixing of fluid is very well .

By seeing this velocity contour there is more diffusion of high velocity and less turbulence after T-joint.

Lets plot temp and velocity line plots

 

There is sudden drop of temp is due to cold fluid enters in a pipe at this section and afterward there is a gradually increase in temp is due to mixing of fluids and exchanging the between them.

There is sudden rise in velocity is due to high velocity fluid enters in pipe at this location.and after that mixing of fluid takes place due to this the momentum transfer takes place between fluids.

• lets find out avg temp theoretically by using same formula

Mass Flow on inlet x =  0.00329553 [kg s^-1]

Mass Flow on inlet y =  0.00326751 [kg s^-1]

Mass Flow on outlet =0.00656304 [kg s^-1]

Area Average of Temperature on inlet x =309.15 [K]

Area Average of Temperature on inlet y =292.15 [K]

Tmix = mh * Th + mc * Tc/(mh + mc)= 300.23 K

And by numerically or by software

Area Average of Temperature on outlet =300.67 [K]

by comparing these ywo values our result is validated.

That conclude all . lets see results and conclude it.

Results :

1. Velocity and temperature contour plots on the cut planes along and across the pipe :
   1. Case-1 :short mixing tee with momentum ratio=2 :

Here at bottom of the pipe the mixing is not done properly due to this the hot air remains and temp is high.

due to mixing of fluid after t-section turbulence was created and velocity decreases near to T-section.

b. Case-2 : short mixing tee with momentum ratio=4 :

Compared to previous case we can see that as velocity of cold fluid is 2times the previous case due to this the mixing of fluids is done properly and temp distribution is more efficient to previous case.here at upper surface there is not a good mixing of fluid taks place so it shows high temp.

As we can see that in above contour as velocity is 2 times to the previous case there is more turbulence created near to the inlet-y and velocity deformation is more.

Case -3 : long mixing tee with momentum ratio=2 :

 As we see in this temp contour there is not properly mixing done at bottom. But compared to sort tee  the temp distribution is looks good.

As we seen in above velocity contour there is more deviation of cold fluid compared to previous two cases and there is less turbulence near to cold fluid inlet section.

d. Case-4 : long mixing tee with momentum ratio = 4:

Here due to high velocity the cold fluid is mixes with hot fluid very quickly and temp distribution takes properly but at upper side there is not a good mixing of fluid so heat transfer between fluids is not proper. again at upeer surface near to inlet-y there is not a good mixing of fluid takes place.so som hot fluid traces shows.

At boundary there is very low velocity but due to high velocity of cold fluid the deformation is more and gets steady state very quickly.

2. Velocity and temperature line plots along and across the length of the pipe :
   1. Case-1 :short mixing tee with momentum ratio=2 :

b. Case-2 : short mixing tee with momentum ratio=4 :

C. Case -3 : long mixing tee with momentum ratio=2 :

D. Case-4 : long mixing tee with momentum ratio = 4:

3. Comparison of plots of cases :

1. Comparison of temp and velocity line plots for Short tee

In this case as MR increases temp curve also gets stepper. after inlet-y section the temp gradually increses.at the center of pipe the temp gets little bit uniform/constant.

As MR increases the steepness of curve at inlet increases.

b. Comparison of temp and velocity line plots for long tee

 

In this case as MR increases the outlet temp decreases.after ceratain length of pipe the temp decreases for LT with MR=4.

 

c. Comparison of temp and velocity line plots for MR=2 :

as length of pipe increases there is no change in temp line plot for same MR. the plots gets coincide.

d. Comparison between temp and velocity line plots for MR=4 :

 

4. Numerically comparision of outlet temp

Sr no	Cases	Avg Outlet temp(K)			Cell count	No.of Iteration for convergence of solution
		Theoretically		Numerically
1	ST with MR=2	303.52	303.59		39725	174
2	ST with MR=4	300.23	300.72		39725	129
3	LT with MR=2	303.52	303.55		56670	327
4	LT with MR=4	300.23	300.67		56670	156

5. Mesh independent study

Parameters	k-epsilon model		k-omega-sst model
	Course mesh	Fine mesh	Course mesh	Fine mesh
Average temp	30.262	30.324	30.283	30.369
Std dev temp	1.342	1.396	1.474	1.739
Temp contours
Velocity counters

Conclusion :

1. From result1 i.e. from temp and velocity contours we can conclude that as velocity increases the deformation of temp and velocity is more and there is good mixing of fluids and heat transfer.
2. From result 2 i.e.from temp line plot and velocity line plot we can conclude that at inlet section of cold fluid there is a sudden drop in temp and afterwards as flow moves along a length of pipe temp gradually increases and mixing of fluid takes place and temp reaches steady state. As MR increases the curve becomes more steeper.Now talking about velocity line plot as high speed velocity fluid enters into the pipe there is sudden increase then falls at that cross-section in velocity and as mixture moves forward along the length of pipe the mixing of fluid takes place and there is a gradually increase in velocity and reaches the steady state .
3. From result-3 we can say that for same MR as we increase the length of pipe there is no difference in temp and velocity line plots across the length of pipe.
4. From result-4, we can say that our results are validated with theoretical results.
5. From result -5 , we can say that final results are independent on mesh size.as we give fine mesh size the computational and analysis time increases.