Contraction design for small low-speed wind tunnels

TLDR

An iterative design procedure was developed that first computes the potential flow field and pressure distributions of a contraction using a 3‑D panel method, then feeds these into 2‑D boundary‑layer codes to predict wall boundary‑layer behavior, and the resulting fifth‑order polynomial wall shape was selected for a new mixing‑layer wind tunnel. The study shows that for small, low‑speed contractions a laminar boundary layer originating at the contraction entry and remaining laminar throughout the passage is justified, as predicted momentum‑thickness values at the exit agree with measurements within 10 % and are generally lower.

Abstract

An iterative design procedure was developed for two- or three-dimensional contractions installed on small, low-speed wind tunnels. The procedure consists of first computing the potential flow field and hence the pressure distributions along the walls of a contraction of given size and shape using a three-dimensional numerical panel method. The pressure or velocity distributions are then fed into two-dimensional boundary layer codes to predict the behavior of the boundary layers along the walls. For small, low-speed contractions it is shown that the assumption of a laminar boundary layer originating from stagnation conditions at the contraction entry and remaining laminar throughout passage through the successful designs if justified. This hypothesis was confirmed by comparing the predicted boundary layer data at the contraction exit with measured data in existing wind tunnels. The measured boundary layer momentum thicknesses at the exit of four existing contractions, two of which were 3-D, were found to lie within 10 percent of the predicted values, with the predicted values generally lower. From the contraction wall shapes investigated, the one based on a fifth-order polynomial was selected for installation on a newly designed mixing layer wind tunnel.