Wetted-Area Minimum and Inlet-Outlet Reciprocity in Optimal Manifolds of Rarefied Gas Flows

Abstract

While flow optimization has been extensively studied in the continuum regime, its extension to rarefied gas flows remains less explored. Here, based on the Boltzmann model equation, an adjoint topology optimization method is employed to design two-dimensional single inlet multi outlet manifolds, aiming to maximize the total mass flow rate while maintaining outflow uniformity. Two key findings are revealed. (1) analogous to the Knudsen minimum in mass flow rate in the transition regime, a wetted-area minimum is identified, but in the slip flow regime. This phenomenon arises from the competition between flow bend loss and surface friction loss, with the latter being affected by velocity slip at the solid surface. (2) the inlet outlet reciprocity emerges in the free molecular flow regime, where the optimal design becomes invariant to inlet outlet orientation and pressure ratio. Additional insights are gained regarding the channel curvature, compressibility effects, and the constraint of outflow uniformity. These findings elucidate the mechanisms governing rarefied gas transport and offer design guidance for manifolds operating in vacuum environments.