Thin-airfoil aerodynamics in a rarefied gas wind tunnel: A theoretical study

We study the steady aerodynamic field and loadings about a thin flat plate placed in a wind tunnel under non-continuum conditions. Considering a two-dimensional straight tunnel configuration, the flow is driven by either density or temperature differences between the inlet and outlet tunnel reservoirs, producing a pressure gradient across the channel. Focusing on highly rarefied conditions, we derive a semi-analytic description for the gas flow field in the free-molecular limit for diffuse- and specular-wall configurations. The solution is valid at arbitrary differences between the inlet and outlet reservoirs as well as plate angles of attack α. The results are compared with direct simulation Monte Carlo calculations, indicating that the free-molecular description is valid through O(1) plate-size-based Knudsen numbers. The aerodynamic lift and drag forces are evaluated and their variations with α, reservoir conditions, and tunnel size are analyzed. At a fixed pressure ratio between the outlet and inlet reservoirs, the density-driven flow generates higher aerodynamic loads compared with its counterpart temperature-driven configuration, in line with the associated larger mass flow rate in the former. The results are discussed in light of the existing rarefied-gas description of the free-stream (non-confined) problem.