Conjugate Heat Transfer Simulation
SIMULATION OF FLOW THROUGH PIPE TO WHICH CONSTANT HEAT FLUX IS SUPPLIED
1.AIM OF THE PROJECT: -
The aim of the project to simulate the air flow through the circular pipe while the heat flux is provided to the pipe across the pipe. This project also demonstrates the influence of grid size on results.The project also aims to show the variation in results on varying SuperCycle Stage Interval.CONVERGE_Studio has been used for the simulation.
2. INTRODUCTION: -
Flow through pipe exposed to heat exchange is very common flow type in industries, laboratories etc. This helps in analysing the change in temperature of fluid or transferring heat to/from the pipe which further helps in efficiency of the process. Such simulation helps in obtaining fully thermally developed profile, Hydrodynamically fully developed flow, hydrodynamic entrance length, Thermal entrance length. The flow simulation also helps to setup the relationship between hydrodynamic entry and thermal entry length which depends on Prandtl number. The fully developed profile for Velocity and temperature are different from each other. The velocity and its velocity profile don’t change in the hydrodynamically fully developed region but Temperature and its profile change in the thermally fully developed region. While the dimensionless Temperature profile (equation 01) doesn’t change in the thermally fully developed region provided the flux remains constant at the surface. The local friction coefficient and the local heat convection coefficient remain constant throughout the hydrodynamically fully developed and thermal fully developed region respectively.
ꝺu (r, x)/ ꝺx =0 -> u =u(r) -> (Hydrodynamically fully developed flow) – (1)
ꝺ[(Ts(x)-T (r, x))/(Ts(x)- Tm(x))]/ ꝺx =0 -> (Thermally fully developed) – (2)
Figure 01: -Different regions showing velocity profile (Taken from Yunus_A_Cengel,Het and Mass transfer)
Figure 02: --Different regions showing Temperature profile (Taken from Yunus_A_Cengel,Het and Mass transfer)
Figure 03: - variation of friction factor and Heat coefficient factor for pr>1.
The flow can be turbulent and laminar depending upon the Reynolds Number. Both entrance lengths for the laminar flow are longer than that of the turbulent flow. The Comparative length of both the entrance length depends on the Prandtl number. If Pr=1, Then both the entrance lengths are almost equal like in case of air. If Pr>1 like in case of oil, the hydrodynamically entrance length is shorter than Thermal entrance length. There are two ways of heat transfer that are either by heat flux at the surface or the temperature (different from the fluid temperature) at the surface.In the current project, I have used air as fluid and the flow is turbulent. The constant heat flux is provided into the flow through the surface.
3.PROBLEM STATEMENT
An Aluminium pipe has inner diameter 0.03m and outer diameter 0.04m. Its length is 0.2m. Constant heat flux 10000w/m2 is provided to the air flowing inside the pipe. The heat flux is provided across the circular curved part of the pipe. The velocity of air at the inlet 10m/s. The corresponding Reynolds Number is 15,000 for air at 300k and 1atm. The flow is turbulent.
4. SETTING THE CASE USING CONVERGE STUDIO: -
STUDY 01:- To study the variation of results on varying SuperCycle Stage Interval for the given grid size (0.002m for all the three directions).The converging rate of temperature in solids are lesser than that of air. So, allocating same time to both will not allow to obtain the correct results.So, SuperCycle concept is used in which the simulation of fluid is stopped for particular repeatitive time interval in which only flow through the solids is allowed to converge.The SuperCycle stages are used :-
Case 01(A):- SuperCycle Stage interval =0.03
Case 01(B):- SuperCycle Stage interval =0.02
STUDY 02:- To study the dependence of flow parameters on mesh grid size and also try to obtain the Temperature and Velocity values the simulation is converging to.
Case 02(A):- Mesh size =0.002m
Case 02(B):- Mesh size =0.003m
4. RESULTS
STUDY 01:-
Case 01(A): - Both temperature and pressure graphs are symmetric about the axis of the pipe.The temperature is maximum at the boundary as heat is provided to the pipe at the curved surface area of the pipe while the velocity is maximum at the mid-point because it 0 at the boundaries (no Slip Condition).The maximum velocity is 12m/s. The maximum and minimum temperature are 585 K and 300 K respectively.
Figure 04 (A):- Velocity Profile
Figure 04 (B): - Velocity Graph
Figure 05 (A): - Temperature Profile
Figure 05 (B): - Temperature Graph
Case 01 (B): - Both temperature and pressure graphs are symmetric about the axis of the pipe.The temperature is maximum at the boundary as heat is provided to the pipe at the curved surface area of the pipe while the velocity is maximum at the mid-point because it 0 at the boundaries (no Slip Condition).The maximum velocity is 12m/s. The maximum and minimum temperature are 585 K and 300 K respectively.
Figure 06 (A): - Temperature Profile
Figure 06 (B): - Temperature Graph
Figure 07 (A): - Velocity Profile
Figure 07 (B): - Velocity Graph
Comparision between case 01 (A) and case (B): - As far as the final values of Temperature and Velocity are concerned final values are same for both the cases.
Figure 08 (A) :- Average Velocity at the outlet
Figure 08 (B) :- Average Temperature at the outlet
STUDY 02: -This study about the effect of mesh size on the results. As results of Case 02(A) depends on finer mesh ,so it shows more minute details at the walls in figure 09(B) and 09(D) than that of Case 02(B).Maximum temperature is larger (600 K) in case 02 than that for Case 02(A).The maximum velocity is lesser in case 02(B) than that of case 02 (A).
Case 02 (A): -
Figure 09 (A) Meshing
Figure 09 (B) Velocity profile
Figure 09 (C) Velocity Graph
Figure 09 (D) Temperature Profile
Figure 09 (E) Temperature Graph
STUDY 02: -
Figure 10 (A): -Meshing
Figure 10 (B): -Temperature Profile
Figure 10 (C): -Temperature Graph
Figure 10 (D): - Velocity Profile
Figure 10 (E): - Velocity Graph
Comparision of Case 02(A) and Case 02(B):- The time taken for case 02 (Case 02(B)) is lesser than that of case 01(Case 02(A)).The final approaching values are the same for both the case.
Figure 11 (A): - Temperature Comparision
Figure 11 (B): - Velocity Comparision
YPLUS: -The flow of air in the pipe is turbulent flow and K-epsilon model has been used for the turbulence modeling and the acceptable value of YPLUS is above 30 for K-epsilon model.
5 . CONCLUSIONS: - All the graphs and profiles for all the cases are not varying much.The coarser mesh grid even provides almost the same results by simulating longer time than the finer mesh grid. The shape of the velocity profile is downward faced parabola and the shape of temperature profile is upward parabola for the obvious reason i have mentioned.The maximum velocity seems to be 12m/s and the maximum temperature attained is approximately 585 K but the finest mesh has provided 600 K. For the average outlet temperature is 330 k and average outlet velocity is 12m/s. The YPLUS value near the boundary is above 30 (i.e. 38) is totally acceptable.The most important thing can be observed that time taken by the mesh size =0.002m is 0.3s while the corser mesh size=0.003m takes 0.5s to converge to the same results.
Animations: -