The matrix of cubes is placed on one of the walls of a two-dimensional channel as sketched in the figure. The flow is fully developed at the measurement section, which enables periodic boundary conditions to be applied. First and second moment velocity data, measured by a two-component LDA system, is available, together with measurements of local convective heat transfer from a cube.
The matrix consists of a total of 25x10 cubes in the streamwise and spanwise directions respectively. The flow measurements are performed around the 18th row from the inlet, at mid-height of the channel. For this location, a fully developed and symmetric state is achieved and the influence from the outlet is eliminated.
The x and y axes are taken in the streamwise and wall-normal directions respectively, and the z axis denotes the spanwise direction. The coordinate system originates from the channel wall at the centre of the windward face of the cube, as shown in the figure. Relevant experimental parameters are:
| Dimension of the cube: | H=15mm |
| Channel height: | h=3.4H (51mm) |
| Pitch of the cubes: | S=4H (both streamwise and spanwise directions) |
| Reynolds number of incoming flow: | Ubh/ =1.3x104 |
| Bulk velocity: | Ub=3.86m/s |
| Average mass flow rate in a sub-channel: | 6.85x10-3 kg/s |
| Fluid density: | 1.16kg/m3 (air at 20oC) |
A two-component back-scatter LDA system was used to measure the velocity components. The optical probe was primarily set perpendicular to the channel wall, ie. parallel to the y-axis, which enabled the simultaneous measurement of u and w components. A specially designed measurement cube with a mirror placed diagonally inside it allowed the velocity component in the y direction to be measured in a restricted area around the cube.
The convective heat transfer distribution from an individual cube was measured in the fully developed region. A cube made of copper, covered with an epoxy layer of thickness 1.5mm, was heated by means of an electric heater. The thermal conductivity of the epoxy substrate was 0.24W/mK, and that of the plastic (phenolic) base plate on which the cube was mounted was 0.33W/mK. The temperature of the copper core was kept constant at 75oC and the surface temperature distribution over the five surfaces of the cube exposed to air flow were measured by infrared and liquid crystal thermography.
Measurements of temperature profiles using a thin wire probe are currently being undertaken, and data should be available shortly before the workshop.
The fully developed flow in a sub-channel unit (see figure) is considered. The dimensions of the sub-channel are 4H x 3.4H x 2H in the x, y, z directions respectively. The computations should be performed employing periodic boundary conditions in the streamwise direction, which avoids any ambiguity due to the inlet boundary specification. Symmetry conditions can be applied in the spanwise direction.
Note that the sub-channel unit shown in the figure is merely an example for the choice of the computational domain. While the origin of the Cartesian coordinate should be defined as in the figure, the location of the boundary planes may be chosen arbitrarily in a computationally convenient way.
For the heat transfer, it should be noted that only one cube in the array is heated. It is therefore suggested that the flow field should be computed first, using periodic boundary conditions. The temperature field can then be computed as a passive scalar, with the entry cross-section taken sufficiently upstream of the stagnation region recirculation to avoid any upstream effect on the inlet flow of the heated cube. For the thermal boundary conditions, it is suggested that participants solve the complete conjugate problem including heat conduction through the epoxy layer and base plate, applying a constant temperature to the copper cube core.
We plan to compare the profiles of mean velocity components and temperature, as well as the second moments, at selected locations in the channel, and heat-transfer coefficients around the cube. For details consult the read-me file contained in the database.
Velocity field data:
case6_2.tar.gz (for gunzip)
case6_2.tar.Z (for uncompress)
Meinders, E.R., Van der Meer, T., Hanjalic, K., Lasance, C.J.M. 1997 "Application of infrared thermography to the evaluation of local convective heat transfer on arrays of cubical protrusions" Int J. Heat Fluid Flow, 18, 152-159.
Meinders, E.R., Van der Meer, T.H., Hanjalic, K. 1998 "Local convective heat transfer from an array of wall-mounted cubes" Int. J. Heat Mass Transfer, 41, 335-346.
Meinders, E.R., Hanjalic, K., Obi, S. 1997 "Experimental investigation into the flow structure in and the local convective heat transfer of a spatially-periodic matrix flow" Submitted for publication.