Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity

SUMMARYFor convection-dominated flows, classical second-order methods are notoriouslyoscillatory and often unstable. For this reason, many computational-fluid-dynam-icists have adopted various forms of (inherently stable) first-order upwinding overthe past few decades. Although it is now well known that first-order convectionschemes suffer from serious inaccuracies attributable to artificial viscosity ornumerical diffusion under high-convection conditions, these methods continue toenjoy widespread popularity for numerical heat-transfer calculations, apparentlydue to a perceived lack of viable high-accuracy alternatives. But alternatives areavailable. For example, nonoscillatory methods used in gasdynamics, includingcurrently_opular "TVD" schemes, can be easily adapted to multidimensional incom-pressible 1low and convective transport. This, in itself, would be a major advance fornumerical convective heat transfer, for example. But, as this report shows, second-order TVD schemes form only a small, overly restrictive, subclass of a much moreuniversal, and extremely simple, nonoscillatory flux-limiting strategy which can beapplied to convection schemes of arbitrarily high-order accuracy, while requiringonly a simple tridiagonal ADI line-solver, as used in the majority of general-purposeiterative codes for incompressible flow and numerical heat transfer. The new uni-versal limiter and associated solution procedures form the so-called ULTRA-SHARPalternative for high-resolution nonoscillatory multidimensional steady-state high-speed convective modelling.INTROI) UCTIONFor many years the state of the art in high-speed convective modelling, espe-cially in the field of numerical heat and mass transfer, has been dominated by first-order upwinding, often in the guise of the "Hybrid" scheme of Spalding [1] or, morerecently, the related "Power-Law Differencing Scheme" (PLDS) of Patankar [2].This situation has clearly evolved from an attempt to remedy the infamous problemsof unphysical oscillations and instabilities associated with "classical" central-differ-ence methods under high-convection conditions, using practical grids. The Hybridscheme avoids oscillatory behaviour by switching from second-order central to first-order upwinding for convection (and omitting modelled physical diffusion) whereverthe local component grid Peclet (or Reynolds) number exceeds a value of 2. PLDSand the exponential differencing scheme (EDS) on which it is based [3] involve amore subtle blending strategy, but both are also equivalent to first-order upwindingfor convection (with physical diffusion totally suppressed) for component grid PecletWork funded by Space Act Agreement C-99066-G.

ULTRA-SHARP Nonoscillatory Convection Schemes for High-Speed Steady Multidimensional Flow

Accurate three-dimensional lid-driven cavity flow

Stabilized finite element method for incompressible flows with high Reynolds number

The steady flow in rectangular cavities is investigated both numerically and experimentally. The flow is driven by moving two facing walls tangentially in opposite directions. It is found that the basic two-dimensional flow is not always unique. For low Reynolds numbers it consists of two separate co-rotating vortices adjacent to the moving walls. If the difference in the sidewall Reynolds numbers is large this flow becomes unstable to a stationary three-dimensional mode with a long wavelength. When the aspect ratio is larger than two and both Reynolds numbers are large, but comparable in magnitude, a second two-dimensional flow exists. It takes the form of a single vortex occupying the whole cavity. This flow is the preferred state in the present experiment. It becomes unstable to a three-dimensional mode that subdivides the basic streched vortex flow into rectangular convective cells. The instability is supercritical when both sidewall Reynolds numbers are the same. When they differ the instability is subcritical. From an energy analysis and from the salient features of the three-dimensional flow it is concluded that the mechanism of destabilization is identical to the destabilization mechanism operative in the elliptical instability of highly strained vortices.

Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures

A facility has been constructed to study shear-driven, recirculating flow, namely, a three-dimensional lid-driven cavity flow. In the extant case, the cavity depth-to-width aspect ratio is 1:1, while the span-to-width aspect ratio is 3:1. A description of the circulation cell structure obtained by flow visualization is given for two Reynolds numbers with and without temperature-induced density stratification. The experimental results are compared to simulations by two different numerical codes, one employing finite differences and one employing finite elements. The numerical codes reproduce the overall behavior observed in the experiments, but fail to simulate observed longitudinal vortices. There are some significant differences also between the numerical results, highlighting the effects of using the HYBRID (upwind/central) differencing scheme in one code.

Three-dimensional lid-driven cavity flow: experiment and simulation

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Three-dimensional lid-driven cavity flow: experiment and simulation