Proceedings of COBEM 2005 18th International Congress of Mechanical Engineering Copyright © 2005 by ABCM November 6-11, 2005, Ouro Preto, MG Mixed Convection Effects in Cavities with Oscillating Boundaries Monique Soriano Vital da Silva ♦ & José Carlos César Amorim Department of Mechanical and Materials Engineering Instituto Militar de Engenharia 22290-270 – Rio de Janeiro – RJ monique@lmt.coppe.ufrj.br, jcamorim@ime.eb.br Albino José Kalab Leiroz ♣ Department of Mechanical Engineering – POLI/COPPE Universidade Federal do Rio de Janeiro Caixa Postal 68503 - Rio de Janeiro – RJ – 21945-970 leiroz@ufrj.br Abstract: The transient evolution of the flow and temperature fields inside two-dimensional cavities with inwards oscillating wall is discussed in the present work. The existence of openings in the cavity wall is considered. The flow governing equations are solved using a Vorticity-Stream Function formulation. Appropriate stream-function boundary conditions are used to describe the openings along the upper wall and the oscillation wall movement. Vorticity values along the cavity solids boundaries and the openings are solved by an iterative solution method. Density variations are considered by the use of Boussinesq approximation. Initially, analytical transformations are used to obtain a stationary solution domain and to cluster points near the upper wall. The transformed governing equations are discretized using an implicit Finite-Difference scheme. The resultant algebraic system is solved by an iterative solution method with sub-relaxation and local error control. The parametric study is presented based on the Reynolds, Prandtl and Grashof numbers influence on the transient evolution of the flow and temperature fields inside the cavity. Obtained results are compared with pure forced convection data showing the influence of density variation on the evolution of flow and temperature fields. Keywords: Cavity Flow, Mixed Convection, Numerical Methods and Grid Generation. 1. Introduction Flows within cavities with moving boundaries are commonly used for studies of basic fluid mechanics phenomena. Different flow structures associated with boundary layers and recirculation zones can be found in a yet simple geometry. Besides fundamental studies, cavity flows are related with important industrial applications that include the cooling of electronic equipment and building thermal insulation. The studies of flow field in cavities with openings through which mass is exchanged with the surroundings is of particular interest for applications in alternative engines and compressors. Mixed convection in open cavities is numerically studied for different configurations considering vertical, horizontal and inclined external flows (Khanafer, 2002). A parametric study on the nondimensional parameters governing the phenomena, such as Reynolds and Grashof numbers and the cavity aspect ratio, is conducted. Results show that the flows associated with the opening can be used to thermally insulate the cavity from the surroundings. Low Grashof results indicate low mean Nusselt values for opening flow angle between 45 o and 90 o . The existence of a critical Reynolds number for which the opening flow becomes dominant over the natural convection effects is observed for the 90 o angle (Khanafer, 2002). The numerical study of the mixed convection effects during the hydrodynamic removal of contaminants in a cavity inside a duct uses the solution of the transient Navier-Stokes equations coupled with the energy conservation equation (Fang, 2002). The mixed convection effects on the temporal evolution of the flow field and on the contaminants removal from the cavity are discussed. Results indicate a strong dependence of the flow field structure and the removal efficiency on the Grashof number due to the interaction between the external duct flow and the buoyancy force generated by the heating source. Flow in deep cavities induced by moving boundaries and temperature gradients are also analyzed for a wide range of (Prasad, 1996). The nondimensional parameters are defined using the upper wall velocity, the vertical temperature difference and the cavity depth as characteristic values for velocity, temperature and length, respectively. Liquid crystals are used for flow visualization. Heat flux measurements along the lower walls are also performed. Results show that the flow pattern near the lower wall is unaffected by the cavity aspect ratio and imposed temperature gradient and that weak dependence of the heat transfer coefficient on the values (Prasad, 1996). 2 Gr / Re 2 Gr / Re ♦ Present Address: Department of Mechanical Engineering – COPPE, Universidade Federal do Rio de Janeiro. ♣ Author to whom correspondence should be addressed.