Mixing efficiency
Mixing tee
AIM:-
To simulate the mixing in a mixing tee to determine the mixing efficiency of cold and hot fluid along the length of pipe. The velocity and temperature is measured to quantify the mixing. Two different cases were solved.
1.Short mixing tee with a hot inlet velocity of 3m/s. Momentum ratio of 2,4.
2.Long mixing tee with a hot inlet velocity of 3 m/s. Momentum ratio of 2,4.
INTRODUCTION:-
The design of mixing equipment to achieve the maximum effectiveness is always been done traditionally with design of prototype and by deriving design equations for mixing. Although when it come to complex geometry with complicated flow it seems to be limited
Mixing tee has been widely used in industry for many flow application like mixing of hot and cold fluid in air conditioning system, anesthetic machine ,breathing gas for scuba diving, shielding of welding gas blending of some oils, petrochemical industry and catalytic reactors. A side tee is formed by two pipe section joined at right angle to each other.one main stream pass straight to the tee and other enter at perpendicular to one side.
THEORY:-
Mixing is performed to allow heat or mass transfer to occur between one or more steam, components and phases. This operation is performed by interspreading two or more fluid in one space. Mixing is frequently employed to develop the desired product characterises. The performance of mixing is assessed by achieving degree of mixedness.
In a mixing tee application as hot fluid flow through a main stream it get intersect by another fluid flowing at different velocity this velocity difference cause zone of turbulence area where the mixing happens.
MODEDL PREPARATION:-
Flow in a pipeline is simulated by solving the mass and momentum conservation equation equation. The degree of mixing is investigated by solving the energy equation and by monitoring the temperature at various position along the flow .the general purpose three dimensional CFD package FLUENT is used to solve the governing equation.
A three dimensional mode is shown in figure1 .the model is first loaded in spaceclaim and then the fluid volume is extracted by using volume extract option as shown in Figure 2. Then its loaded influent and open for meshing we choose a tetrahedral mesh because it is fine and take less computation time without compromising the accuracy. The suitable mesh is choosen after doing grid dependency and it is shown in Figure 3. For getting accurate result at wall to determine heat transfer and velocity profile at wall for turbulence modelling we insert a 5 inflation layer. Then name the boundary as needed and update the mesh.
Figure 1, Mixing tee geometry
Figure 2,Extracted fluid volume
Figure 3, 3 mm Mesh size of mixing tee
SOLUTION PROCEDURE:-
Three dimensional model is loaded in fluent and double precision with series processer is selected.in FLUENT pressure based model is selected and energy equation is turn on to calculate heat transfer. Then turbulent flow we have chosen a k-e reliable with scalable wall function then in material select the air as fluid. Boundary conditions are defines. For inlet it be velocity inlet and for outlet it be pressure outlet of gauge pressure of 0 PA because we take outlet pressure as a atmospheric pressure. To measure the convergence criteria we choose to two monitor plot .First is the temperature at outlet and for studying the mixing effectiveness we choose Standard deviation of temperature at outlet as shown in figure 5 and 6. Initialised the solution with hybrid initialization and run for200 iteration.
POST PROCESSING:-
The numerical and experimental result of mixing are loaded in a CFD POST .numerical results are first tested for dependency on mesh size and turbulence model and then a detailed is presented.
CASE 1
For case 1 the hot fluid flow velocity at inlet is 3 m/s with a temperature of 36 C. and by using momentum ratio of 2.4 the inlet velocity of cold fluid is 7.2m/s and temperature of 19 C.A mesh size of 2 mm is used and the turbulence model is k-e model.
Figure 7,8, show the velocity and temperature contour in a plane along and across the length of pipe, the convergence plot is plotted in figure 4,which indicated that problem is smoothly converge.to analyse the result quantitatively the value of temperature verses location and velocity verses location along the pipe axis are plotted in figure 11 and 12 .
Figure 4,Convergence graph of short mixing tee
Figure 5, Temperature monitor point Figure 6,Standard Deviation monitor point
Figure 7, Velocity profile of Short mixing tee
Figure 8, Temperature profile of short mixing tee
Figure 9,Velocity profile along and across length Figure 10, Temperature profile along and across
Figure 11, Velocity graph along length Figure 12, Temperature graph along length
CASE 2
For case 2 the hot fluid flow velocity at inlet is 3 m/s with a temperature of 36 C. and by using momentum ratio of 2.4 the inlet velocity of cold fluid I 7.2 m/s and temperature of 19 C .the length of mixing tee is increased .Convergence plot is shown in figure 13 along with monitor point in figure 14 and 15.
Figure 16 and 17 ,shows the velocity and temperature contour . in figure 20,shows the comparison of Long and short mixing tee with its paremeters.it is clearly observe that the outlet temperature remains nearly same for this two case only there is change in Mixing efficiency the long tee has standard deviation of temperature of 0.28 its shows good quality mixing than short mixing tee which have Standard deviation of 0.69.
Figure 13, Convergence graph for long mixing tee
Figure 14,Standard deviation at outlet temperature Figure 15,Outlet temperature monitor point
Figure 16, Long mixing tee velocity contour
Figure 17, Long mixing tee temperature contour
Figure 18, Velocity graph along length Figure 19,Temperature graph along length
Figure 20, Temperature contour of Short and long mixing tee
Long and short mixing tee table
SN.NO Mixing tee type Iteration to converge Average outlet temperature Standard deviation at outlet
1 Long 63 29.7 C 0.28
2 Short 66 29.91 C 0.69
Dependency of solution on the grid size:-
The mesh size often has an impact on the accuracy of the solution. The size has to be small enough in order to properly resolve the fields that are solved for. To quantitatively compare the result with three different sizes ,mesh sizes of 5, 3, 2 mm. the number of nodes used are tabulated .
The effect of mesh size are tested by comparing a plot of the temperature verses location along the centreline of main pipe. Figure 21, shows such a comparison of the three mesh size with turbulence model k-e model. It is clear that the solution shows a significant change when the mesh size is reduced from 5 to 3 mm. the solution also changes when the mesh size change from 3 to 2 mm but the difference is not very significant. The number of cell for mesh size 2 mm is very high hence used long computational time. However because the solution is still converge with accuracy. Therefore the mesh size of 3 mm was used for all of the main runs.
Figure 21,Mesh independency
Mesh report
SN.NO Mesh size Nodes Iteration to Convergence Average outlet temperature Standard deviation at outlet
1 5 mm 8863 60 28.18 C 0.88
2 3 mm 21198 66 29.91 C 0.69
3 2 mm 49220 73 29.8 C 0.62
Turbulence Modelling:-
In this study, simulation is carried out using the k-e model and the k-w SST mode. Figure 22, shows a comparison of the numerical result for a base case with these two models of turbulence. In case of K -e model we choose reliable and scalable wall function because in reliable it predict more accurately the spreading rate of jet and recirculation. Scalable wall function take care of Y Plus value of 11.41 even it is low than it automatically account it for equal to 11.41. It shows that , for a outlet temperature both predict nearly same value but for standard deviation It shows differently. When we look at the region near the inlet of cold flow the significant difference in noted the K-w SST model shows a better estimation of the temperature profile near the intersection point. It produce large turbulence levels in region with normal strain like region with strong acceleration .this effect is less pronounced in K-e model. Here we concentrate on net outlet temperature and the mixedness so don’t have to bother about jet mixing at vicinity of intersection so we choose K- e model for reliability.
The computational time required when using the K-W SST mode is high it take 293 iteration to achieve converge solution but for K-E model it converge at 66 Iterations. The velocity and temperature graph is shown in Figure 23 and 24 along the length of pipe.
Figure 22, Turbulence mode temperature contour on left K epsilon model and om right K omega SST model
Figure 23,Velocity graph Figure 24,Temperature graph
CONCLUSION:-
Mixing of cold and hot fluid in mixing tee was numerically investigated. The average outlet temperature for long and short mixing tee is observed and result is plotted in figure. The K-E model and K-W SST model are used to turbulence modelling and each have its own improvement. The result for both case shows that he average outlet temperature for both long and short is approx. 29.8 C. but there is a significant deviation in mixing efficiency the long mixing tee have a standard deviation of 0.28 but for short mixing tee have standard deviation of 0.69. so long have better mixing because of the mixing length. The outlet temperature I depend upon the inlet cold fluid velocity as the velocity increase it shows a significant improvement in outlet temperature.