A weakly ionized hypersonic flow solver for the simulation of reentry flow is firstly developed at the University of Kentucky. This code is the fluid dynamics module of known as Kentucky Aerothermodynamics and Thermal Response System (KATS). The solver uses a second-order finite volume approach to solve the laminar Navier– Stokes equations, species mass conservation and energy balance equations for flow in chemical and thermal non-equilibrium state, and a fully implicit first-order backward Euler method for the time integration. The hypersonic flow solver is then extended to account for very low Mach number flow using the preconditioning and switch of the convective flux scheme to AUSM family. Additionally, a multi-species preconditioner is developed. The following part of this work involves the coupling of a free flow and a porous medium flow. A new set of equation system for both free flows and porous media flows is constructed, which includes a Darcy–Brinkmann equation for momentum, mass conservation, and energy balance equation. The volume-average technique is used to evaluate the physical properties in the governing equations. Instead of imposing interface boundary conditions, this work aims to couple the free/porous problem through flux balance, therefore, flow behaviors at the interface are satisfied implicitly.

<p>A specific class of small-scale plasmas (column diameters in a sub-mm to mm range) at rarefied pressures (under 10 Torr) enclosed in glass tubes hold significant interest currently in the scope  of  tunable  plasma  devices.  Specifically,  applications  of  these  plasmas  include  plasma antennas and plasma photonic crystals. Reliable diagnostics are necessary for the development and implementation of these technologies as conventional tools are inadequate in such small-scale plasmas.</p> <p>Coherent microwave scattering in the Thomson regime (TMS) was recently demonstrated for diagnostics of electron number density in miniature free-standing laser-induced plasmas in air under  10  Torr  with  plasma  column  diameters  <  0.5  mm.  However,  measurements  by  TMS diagnostics have never been applied for small-scale plasma objects enclosed within glass tubes. Additionally, TMS measurements were never independently confirmed with a previously verified experimental technique. This work aims to validate results of TMS measurements for small-scale plasma  objects  enclosed  within  glass  tubes  using  the  previously  established  and  well-known hairpin resonator probe. A DC discharge plasma column of fairly large diameter (about 1.5 cm) is used in the experiments to ensure reliable non-intrusive measurements by the hairpin resonator probe.</p> <p>The experiments were conducted in a DC discharge tube with a diameter of 1.5 cm and a length of 7 cm. TMS diagnostics yielded electron number densities of about 5.9×10¹⁰cm^-3, 2.8 ×10¹⁰cm^-3and  1.8 ×10¹⁰cm^-3at  pressures  of  0.2,  0.5  and  2.5  Torr,  respectively.  The corresponding  densities  measured  with  the  hairpin  resonator  probe  were  4.8×10¹⁰cm^-3,  3.8 ×10¹⁰cm^-3 and 2.6 ×10¹⁰cm^-3. Discrepancies between the two techniques were within 30% and can be attributed mainly to inaccuracies in the sheath thickness estimation required the hairpin resonator probe results.</p>

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