Extrapolation of critical Rayleigh values using static nodal integral methods

Conference · Fri Jan 01 04:00:00 EST 1988 · Transactions of the American Nuclear Society; (USA)

OSTI ID:5678298

Wilson, G L; Rydin, R A

The Benard problem is the study of the convective motion of a fluid in a rectangular cavity that is uniformly heated form below. Flow bifurcation in the cavity is a function of the Rayleigh number (Ra). The time-dependent nodal integral method (TDNIM) has been reported previously; its development leads to a set of 11 equations per node. The static nodal integral method (SNIM) was derived from the TDNIM by forcing the dependent variable at adjacent time steps (one of the velocity components or temperature) to take on the node integral average value. The paper summarizes the SNIM calculation of Ra for mesh sizes ranging from 4 x 4 to 24 x 24. The numerical calculation of Ra is within plus or minus one-half unit. The relative errors are calculated based on the obtained extrapolated value of Ra{sub best}* = 2584. The paper also summarizes three-point schemes used with increasingly finer mesh combinations. This approach avoids the contamination of the results with a coarse mesh; however, the calculation on n is very sensitive to small changes in the numerical values obtained for Ra*. In this approach, the extrapolated values quickly converge to Ra*{sub e} between 2583 and 2584 with n {approx}2.0 as desired, and give a best value of Ra*{sub best} = 2584.

• OSTI ID: 5678298
• Report Number(s): CONF-880601--
• Conference Information: Journal Name: Transactions of the American Nuclear Society; (USA) Journal Volume: 56
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
CONVECTION
CRITICAL FLOW
ENERGY TRANSFER
EXTRAPOLATION
FINITE ELEMENT METHOD
FLUID FLOW
FLUID MECHANICS
HEAT TRANSFER
HYDRAULICS
MASS TRANSFER
MECHANICS
NUMERICAL SOLUTION
SENSITIVITY