Natural Turbulent Convection in a Heated Box

Shortcuts to Pictures (longer descriptions are at bottom of page):
velocity profiles along y-planes | velocity profile at horizontal midline
complete temperature contour | temperature profile at vertical midline
selected rotational streamlines | close-up of vertical hot wall


In this test case, I have used Phoenics to model the flow in an entirely enclosed rectangular box, with adiabatic top, bottom, front, and back, but with a hot wall to the left and a colder wall to the right. The model set-up was chosen to be as close as possible to that described in a paper by Q. Chen of MIT, so as to verify the results by comparison with Chen's. (In his paper, Chen compares his own results, also obtained with Phoenics, to earlier experimental data). Many characteristics of the resultant flow in such a set-up are functions of the Rayleigh number, discussed below.

This experiment is an important building block in our effort to model flow in the Farnsworth House. We believe that the Rayleigh number in the house when the heat is on may be roughly comparable to the quantity found below, and thus it is of central importance to develop skill in using Phoenics for accurate modeling under these conditions. It should be noted that the Farnsworth House is inherently more complex than the hot box, because the heat source in the house is on the bottom rather than along one of the vertical walls. When the heat flows in and out of the walls only, the rotational direction of the convective forces is clearly defined: up the hot wall, down the cold wall. When the floor is hot and the cieling (and walls) are cold, then the flow may be initially unstable.

Physically, the box is 2.5m high (y-axis) and 0.5m wide (x-axis). The z-axis is considered a symmetry plane and the problem is modeled two-dimensionally. The left (x=0) wall is at +22.9 deg C and the right (x=0.5) wall is at -22.9 deg C. All other surfaces are assumed adiabatic. The walls are smooth, and friction is modeled with a log-law approximation. Note: any figures with x >> y are vertical pictures viewed on their side; they should be rotated 90 degrees clockwise to correct.