Prescribed Wall-Heat-Flux Control of Blockage and Impulse in a Rarefied Micro-Nozzle

TL;DR

This study investigates how prescribed wall heat flux influences flow control in a rarefied micro-nozzle using DSMC simulations, revealing effects on temperature stratification, flow blockage, and specific impulse enhancement.

Contribution

It provides a detailed analysis of thermal effects on micro-nozzle flow control, highlighting the coupled wall-bulk thermal response and low-dimensional heat-flux response characteristics.

Findings

Heating causes strong wall-bulk temperature stratification.

Cooling leads to sign changes in local temperature differences, causing singular responses.

Heating increases specific impulse despite reducing mass flow rate.

Abstract

Prescribed wall heat flux provides an active route for controlling rarefied micro-nozzle flows, but its effect is governed by the coupled wall--bulk thermal response rather than by the imposed flux alone. This work uses direct simulation Monte Carlo (DSMC) simulations to study nitrogen flow in a converging--diverging micro-nozzle with cooling, adiabatic, and heating applied on the diverging wall. The imposed heat flux is scaled by the inlet kinetic-energy flux, $E=0.5\rho_i U_i^3$, giving $Q_w/E$ from $-10.5\%$ to $97.3\%$; this range spans moderate cooling, weak-to-intermediate heating, and a near-unity thermal-forcing regime. Wall and mass-flux-weighted bulk temperature profiles, film-temperature-based Nusselt and local-viscosity Brinkman-type diagnostics, gradient-length Knudsen indicators, mass-flux thickness, thrust decomposition, and proper orthogonal decomposition (POD) of signed numerical schlieren are analyzed. The results show that heating creates strong wall--bulk stratification: the wall temperature exceeds five times the inlet value, while the bulk temperature responds more gradually. Cooling cases contain locations where $T_w-T_b$ changes sign, making the local Nusselt-type response singular; the raw singular behavior is retained for diagnosis and a validity mask is used only for comparative plotting. Heating contracts the effective mass-carrying core, increasing aerodynamic blockage and reducing mass flow rate. However, strong heating increases the specific impulse from $156$ s to $201$ s because thermal and pressure-thrust augmentation outweigh the mass-flow penalty. The internal compression feature evolves into a finite viscous--thermal compression zone, and its heat-flux-parametric response remains low-dimensional, with the first two POD modes capturing more than $97\%$ of the fluctuation energy.