Plasma properties along the stagnation streamline of blunt bodies moving at hypersonic speeds

Abstract The non-equilibrium flow pertinent to blunt-body hypersonic vehicles is modeled using a reduced form of the Euler equations, a non-equilibrium three-temperature plasma chemistry model, and a plasma-surface interaction model. The combined model is applied to rarefied air to compute the flow along the stagnation streamline of hypersonic vehicles flying at mid altitudes (40 km). Three flow regimes have been distinguished. For free-stream velocities below 2 km s −1 , the flow is practically uncoupled from the chemistry (‘frozen’ flow). At 3 km s −1 , a slowly evolving plasma appears in which the gas, electron, and vibrational temperatures equilibrate close the surface. At 6 km s −1 the three temperatures equilibrate immediately behind the bow shock due to a self-limiting process in which the chemical reactions in the plasma generate high-enthalpy species that lead to energy re-distribution. The O 2 molecules dissociate completely and the dissociation of N 2 reaches equilibrium balance. The Damköhler number (the ratio of the characteristic flow time to chemical reaction time) for collisional dissociation of N 2 is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>a</mml:mi> <mml:mo>&gt;&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> behind the bow shock (fast chemistry compared to flow time) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>a</mml:mi> <mml:mo>&lt;&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> along the stagnation streamline (slow chemistry compared to flow time). The excited states populations of N 2 increase exponentially with free-stream velocity, giving rise to radiation that can be used as a spectroscopic tool. The Zeldovich reaction <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>v</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> <mml:mo accent="false" stretchy="false">→</mml:mo> <mml:mrow> <mml:mtext>NO</mml:mtext> </mml:mrow> <mml:mo>+</mml:mo> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> depopulates the tail of the Vibrational Distribution Function of N 2 ( X ) molecules and Boltzmann equilibrium does not hold.