Simulation of flow through a mixing tee
In the current project, we will simulate flow through a mixing tee using ANSYS for the following three different configurations:
(i) Short mixing tee with hot stream entering at `25^oC` and 3m/s and cold stream entering at `10^oC` and 6m/s.
(ii) Long mixing tee with hot stream entering at `25^oC` and 3m/s and cold stream entering at `10^oC` and 6m/s.
(iii) Short mixing tee with hot stream entering at `25^oC` and 3m/s and cold stream entering at `10^oC` and 12m/s.
The goal of the project is to determine which (if any) of the above three configurations result in the best mixing at the exit. To estimate the quality of mixing, the standard deviation of temperature at the exit plane is compared for all three configurations. The one with the smallest value of standard deviation yields the best mixing.
Case 1: Short mixing tee with hot stream entering at `25^oC` and 3m/s and cold stream entering at `10^oC` and 6m/s.
1. Physical description:
The above figure shows the geometry of the mixing tee alongwith the dimensions. The hot stream enters through the 3.39cm diameter inlet whereas the cold fluid enters through the 1.7cm diameter inlet. The length of tube is 19.24cm.
2. Numerical description:
For performing computations, the domain is discretised with 14247 tetrahedral cells of element size=0.005m. The governing equations are solved using steady state pressure-based solver with absolute formulation of velocity, in the Fluent module. The turbulence is modeled using the realizable `k-\epsilon`model. The working fluid for the simulation is air with the following properties:
The following boundary conditions are employed:
(a) Hot stream inlet:
(b) Cold stream inlet:
(c) Wall:
(d) Outlet:
The solution is initialized using a hybrid initialization with 10 iterations.
3. Results:
(i) Residual plot:
The above plot shows variation of residuals with iterations. It can be concluded that after 250 iterations steady state is achieved since the residual values start repeating.
(ii) Area averaged temperature at the outlet:
The above figure displays the iteration-history of the area-averaged temperature at the outlet. Based on the plot the steady state value of temperature at the outlet is `19.93^oC`.
(iii) Standard deviation of temperature at the outlet:
The above plot shows the iteration-history of standard deviation in temperature profile at the outlet. At steady state the standard deviation is equal to 1.26.
(iv) Area-averaged velocity at the outlet:
The above plot shows the iteration-history of area-averaged velocity at the outlet. At steady state the area-averaged velocity magnitude is nearly 4.5m/s.
(v) Steady state velocity contours:
The above plot displays the steady state velocity contours (after 400 iterations).
(vi) Steady state temperature contours:
The above plot shows the steady state temperature contours (after 400 iterations). From the plot it can be seen that at the outlet the temperature is not homogenous.
Case 2: Long mixing tee with hot stream entering at `25^oC` and 3m/s and cold stream entering at `10^oC` and 6m/s.
1. Physical description:
The above figure shows the geometry of the mixing tee alongwith the dimensions. The hot stream enters through the 3.39cm diameter inlet whereas the cold fluid enters through the 1.7cm diameter inlet. The length of tube is 26.83cm.
2. Numerical description:
For performing computations, the domain is discretised with 17698 tetrahedral cells of element size=0.005m. The governing equations are solved using steady state pressure-based solver with absolute formulation of velocity, in the Fluent module. The turbulence is modeled using the realizable `k-\epsilon`model. The working fluid for the simulation is air with the following properties:
The following boundary conditions are employed:
(a) Hot stream inlet:
(b) Cold stream inlet:
(c) Wall:
(d) Outlet:
The solution is initialized using a hybrid initialization with 10 iterations.
3. Results:
(i) Residual plot:
The above plot shows variation of residuals with iterations. It can be concluded that after 250 iterations steady state is achieved since the residual values start repeating.
(ii) Area averaged temperature at the outlet:
The above figure displays the iteration-history of the area-averaged temperature at the outlet. Based on the plot the steady state value of temperature at the outlet is `19.97^oC`.
(iii) Standard deviation of temperature at the outlet:
The above plot shows the iteration-history of standard deviation in temperature profile at the outlet. At steady state the standard deviation is equal to 0.96.
(iv) Area-averaged velocity at the outlet:
The above plot shows the iteration-history of area-averaged velocity at the outlet. At steady state the area-averaged velocity magnitude is equal to 4.5m/s.
(v) Steady state velocity contours:
The above plot displays the steady state velocity contours (after 400 iterations).
(vi) Steady state temperature contours:
The above plot shows the steady state temperature contours (after 400 iterations). From the plot it can be seen that at the outlet the temperature is quite homogenous.
Case 3: Short mixing tee with hot stream entering at `25^oC` and 3m/s and cold stream entering at `10^oC` and 12m/s.
1. Physical description:
The above figure shows the geometry of the mixing tee alongwith the dimensions. The hot stream enters through the 3.39cm diameter inlet whereas the cold fluid enters through the 1.7cm diameter inlet. The length of tube is 19.24cm.
2. Numerical description:
For performing computations, the domain is discretised with 14247 tetrahedral cells of element size=0.005m. The governing equations are solved using steady state pressure-based solver with absolute formulation of velocity, in the Fluent module. The turbulence is modeled using the realizable `k-\epsilon`model. The working fluid for the simulation is air with the following properties:
The following boundary conditions are employed:
(a) Hot stream inlet:
(b) Cold stream inlet:
(c) Wall:
(d) Outlet:
The solution is initialized using a hybrid initialization with 10 iterations.
3. Results:
(i) Residual plot:
The above plot shows variation of residuals with iterations. It can be concluded that after 150 iterations steady state is achieved since the residual values start repeating.
(ii) Area averaged temperature at the outlet:
The above figure displays the iteration-history of the area-averaged temperature at the outlet. Based on the plot the steady state value of temperature at the outlet is `17.54^oC`.
(iii) Standard deviation of temperature at the outlet:
The above plot shows the iteration-history of standard deviation in temperature profile at the outlet. At steady state the standard deviation is equal to 1.21.
(iv) Area-averaged velocity at the outlet:
The above plot shows the iteration-history of area-averaged velocity at the outlet. At steady state the area-averaged velocity magnitude is equal to 6.03m/s.
(v) Steady state velocity contours:
The above plot displays the steady state velocity contours (after 400 iterations).
(vi) Steady state temperature contours:
The above plot shows the steady state temperature contours (after 400 iterations). From the plot it can be seen that at the outlet the temperature is not homogenous.
Comparison of results:
(i) Steady state area-averaged temperature at the outlet
The above plot compares the iteration-histories of area-averaged temperature at the outlet for the three cases. The following observations can be made from the plot:
(a) For cases 1 and 2, the values of area-averaged steady state temperature at the outlet are nearly same.
(b) The area-averaged steady state temperature at the outlet for case 3 is lower as compared to the other two cases.
Discussion: Energy balance across the mixing tee, at steady state, gives the final temperature as the average of hot and cold stream inlet temperatures, weighed by their respective mass flow rates. This estimation remains independent of the geometry. Since in both case 1 and 2, the mass flow rates remain the same for hot and cold streams, the final temperature is expected to be same. However the mass flow rate of cold stream in case 3 is twice its value for cases 1 and 2. Hence the average (final mixing temperature) will be shifted more towards the inlet temperature of cold stream.
(ii) Area averaged steady state velocity at the outlet
The following observations can be made based on the above plot:
(a) The outlet velocities for cases 1 and 2 are nearly same.
(b) The outlet velocity for case 3 is higher as compared to the other two cases.
Discussion: Mass balance across the mixing tee, at steady state for an incompressible fluid, dictates that the final velocity of the mixture is average of the inlet velocities for hot and cold streams, weighed by area of cross-section. Hence the final velocities for cases 1 and 2 are expected to be same, since the inlet velocities of the two streams and their cross-section areas remain the same for the two cases. However in case 3, since the inlet velocity of cold stream is increased, the weighed average and hence the final velocity is expected to increase.
(iii) Standard deviation of steady state temperature distribution at the outlet
The above plot shows the iteration-histories of standard deviation of steady state temperature distribution at the outlet, for the three cases. The following observations can be made based on the above plot:
(a) Even though the final temperature in cases 1 and 2 are the same, their standard deviations are quite different. Case 1 is the worst configuration so far as the mixing effectiveness is concerned whereas case 2 is the best.
(b) The increase in mixing effectiveness due increase in primary tube length is much more as compared to that due to increase in inlet velocity.
(c) The length of the primary tube is the dominant parameter controlling the mixing effectiveness.
Summary:
The table shown below lists the cell count, average outlet temperature, standard deviation of outlet temperature distribution, number of iterations to convergence for the three cases.
Conclusion:
The following conclusions can be drawn from the study:
(a) Mixing effectiveness depends on the contact time which in turn depends on the length of the primary tube. The greater the length, the more is the allowed contact time for mixing which in turn results in better mixing. This is clearly represented by the standard deviation values for the three cases.
(b) The final temperature of the mixed stream depends upon the inlet temperatures and the mass flow rates of the hot and cold streams. Hence if the mass flow rate of a particular stream is increased (say by increasing its inlet velocity), the final temperature after mixing will shift towards the inlet temperature of the stream (whose mass flow rate has been increased).
(c) The final temperature is controlled by the mass flow rates (inlet velocities) of the two streams but the mixing effectiveness depends on the length of the primary tube.