Turbulent Natural Convection In Differentially Heated Cavity

Problem Definition:

Turbulent natural convection with inlet and outlet through which air flows inside the square cavity is simulated and results are shown here for two grids. The geometry of the problem is given in Fig. 4.1. Standard κ − model is used. Non-dimensionalization of the governing equations is done including κ and equations. Two different cases are considered. One is with = 0.25m/s (Re = 3187) and other is with = 0.1m/s (Re = 1275). In both the cases, Raleigh number is Ra = .


Parameters used:





Figure 4.1: Geometry of Turbulent mixed convection




Case 1: From Fig. 4.2(b), it is observed that the upper part of cavity remains nearly isothermal due to the air flow from inlet whereas the rest of the cavity thermally stratified. A recirculation zone (Fig. 4.2(a)) appears just below the upper stream. Non-dimensional horizontal velocity and temperature distributions are shown in Fig. 4.3(a) and 4.3(b). It is observed that when the flow velocity increases, the isothermal region also increases.


Case 2: A weak recirculation region(Fig. 4.4(a)) is found compared to the case 1 due to the lower inlet velocity. The isothermal region(Fig. 4.4(b)) also decreases. From the Table 4.1, it can be seen that, heat transfer is enhanced by increasing the velocity. The Nusselt number along the cold wall increases, when the inlet velocity increases. This indicates that the heat transfer by forced convection is more effective than the free convection.





(a)



(b)

Figure 4.2: For Case - 1 (a) Stream lines (b) Temperature contour



(a)



(b)

Figure 4.3: (a) Non-dimensional horizontal velocity distribution (b) Non-dimensional Temperature distribution at x* = 0.5

Table 17.1: Average Nusselt number comparison





(a)



(b)

Figure 4.4: For Case - 2 (a) Stream lines (b) Temperature contour

[1] Perez-Sagarra C.D., Oliva A., Costa M., and Escanes F. (1995) ‘Numerical experiments in turbulent natural and mixed convection in internal flows’, inter-national Journal of Numerical Methods of Heat and Fluid Flow, vol. 5, pp.13–33