On the boundary layer near a porous wall.
Differential and boundary layer equations for free convection flow along vertical hot wall, investigating existence question
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Differential and boundary layer equations for free convection flow along vertical hot wall, investigating existence question
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Wind tunnels can now simulate flows over airfoils at high Reynolds numbers and high subsonic speeds. Methods to correct for (or reduce) test section wall interference at these test conditions must be validated. The National Aeronautics Establishment (NAE) of Canada and NASA have a cooperative agreement to study this area. The NAE designed, built, and tested a CAST-10 airfoil model in its conventional Two-Dimensional High Reynolds Number Facility. The results were corrected using classical correction techniques. NASA then tested the same model in its 0.3-meter Transonic Cryogenic Tunnel with the adaptive wall test section. The adaptive wall test section reduced the wall interference to what was expected to be an acceptable level. The corrected NAE results are compared with the uncorrected NASA results. The NAE results are also compared with NASA results after residual corrections for top and bottom wall interference. Finally, a comparison of both sets of results corrected for interference from all four walls is presented.
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Exact solution of the laminar-boundary-layer equations for wedge-type flow with constant property values are presented for transpiration-cooled surfaces with variable wall temperatures. The difference between wall and stream temperature is assumed proportional to a power of the distance from the leading edge. Solutions are given for a Prandtl number of 0.7 and ranges of pressure-gradient, cooling-air-flow, and wall-temperature-gradient parameters. Boundary-layer profiles, dimensionless boundary-layer thicknesses, and convective heat-transfer coefficients are given in both tabular and graphical form. Corresponding results for constant wall temperature and for impermeable surfaces are included for comparison purposes.
Fluid from a reservior at constant pressure and temperature is forced through a porous wall of uniform thickness. The boundary through which the fluid exits has specified variations in pressure and temperature along it in one direction so that the flow and heat transfer are two-dimensional. The local fluid and matrix temperatures are assumed to be equal and therefore a single energy equation governs the temperature distribution within the wall. The solution is obtained by transforming this energy equation into potential plane coordinates, which results in a separable equation. A technique yielding an integral equation is used to adapt the general solution so that it satisfies the variable-pressure boundary condition. Analytical expressions are given for the normal exit velocity and heat flux along the exit boundary. Illustrative examples are carried out which indicate to what extent the solution is locally one-dimensional.
The feasibility of controlling the flow actively through the walls of a transonic, porous wall wind tunnel in order to minimize wall interference effects on a test model is demonstrated. The method is based upon measuring the components of the disturbance velocity at discrete points along an imaginary surface in the flow field within the tunnel. A mathematical formulation of the flow field exterior to the surface including the boundary condition for unconfined flow, i.e., that all disturbance vanish at infinite, is used to determine if these measured velocity components are consistent with that boundary condition. If they are not, the theory provides a better approximation to the velocity component for unconfined flow, and the flow through the tunnel walls is readjusted iteratively until the measured quantities are consistent with unconfined flow. A brief review of theoretical methods is followed by a description of the Calspan self correcting wind tunnel design and operation, calibration with and without active wall control. Typical results obtained by approximating a conventional porous wall wind tunnel for an 0012 airfoil show that active wall control largely reproduces the correct shock wave position, eliminates wall interference of lift and drag, and reduces the interference effects on pitching moment to 10%.