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TECHNICAL PAPERS: Forced Convection

Numerical Simulation of Reciprocating Flow Forced Convection in Two-Dimensional Channels

[+] Author and Article Information
Cuneyt Sert, Ali Beskok

Mechanical Engineering Department, Texas A&M University, College Station, TX 77840-3123

J. Heat Transfer 125(3), 403-412 (May 20, 2003) (10 pages) doi:10.1115/1.1565092 History: Received January 14, 2002; Revised December 04, 2002; Online May 20, 2003
Copyright © 2003 by ASME
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Figures

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The geometry and thermal boundary conditions used in this study. On the top surface, uniform heat flux of q=1 is specified at 5≤x≤15. For 4≤x≤5 and 16≥x≥15, the heat flux varies from zero to unity sinusoidally. Zero wall temperature is specified for x≤4 and x≥16. Bottom wall is insulated, while side surfaces are periodic (cyclic/repeating).
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Schematic view of a hypothetical problem that consists of a channel with repeating heated and constant temperature boundaries
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Analytical solution of the velocity profiles at various times during a cycle for (a) α=1, and (b) α=10 flow. Index i represents time within a period of the pressure pulse (t=i−1/8 τ).
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Top: Half of the actual mesh used in the simulations. Quadrature points for a 9th -order expansion are also shown for selected elements. A finer mesh is used at the Neumann/Dirichlet boundary interface on the top wall (4<x<4.5) to resolve large temperature variations. Bottom: A portion of the spectral element mesh showing only cross-channel discretization with different expansion orders (N). Thick lines show the elements, while thin lines show the collocation points. Progressively increasing the element order (N) by keeping the total number of elements fixed is known as p-type refinement.
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Space and time accuracy for α=10 flow. (a) Variation of L error as a function of the expansion order N (obtained using Δt=10−5). Exponential decay of the discretization error indicates spectral convergence. (b) Variation of L error as a function of the time step (obtained using 12th order elements). Shows second-order time accuracy.
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Instantaneous temperature contours for cases 2, 4, 6, and 8. Index i represents time within half a period of the pressure pulse (t=(i−1)τ/8). The flow and thermal conditions are presented in Table 1.
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Instantaneous temperature and velocity profiles at axial locations of x=5 (solid-lines) and x=10 (dashed-lines). Index i represents time within a period of the pressure pulse (t=(i−1)τ/8). Simulation parameters are presented in Table 1.
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Instantaneous top-wall temperatures. Index i represents time within half a period of the pressure pulse (t=(i−1)τ/8). Simulation parameters are presented in Table 1.
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Time-averaged wall-temperature (solid lines) and time-averaged bulk temperature (dashed-lines) variations for reciprocating flows. Wall temperature (dashed-dotted lines) and bulk temperature (dashed-dotted-dotted lines) variations for unidirectional steady flows are also shown. Simulation parameters are presented in Table 1.
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Axial distribution of time-averaged Nusselt number for (a) reciprocating, (b) unidirectional steady flows. Simulation parameters are presented in Table 1.

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