Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles

Abstract

Electron transpiration cooling (ETC) is a recently proposed approach to manage the high heating loads experienced at the sharp leading edges of hypersonic vehicles. Computational fluid dynamics (CFD) can be used to investigate the feasibility of ETC in a hypersonic environment. A modeling approach is presented for ETC, which includes developing the boundary conditions for electron emission from the surface, accounting for the space-charge limit effects of the near-wall plasma sheath. The space-charge limit models are assessed using 1D direct-kinetic plasma sheath simulations, taking into account the thermionically emitted electrons from the surface. The simulations agree well with the space-charge limit theory proposed by Takamura et al. for emitted electrons with a finite temperature, especially at low values of wall bias, which validates the use of the theoretical model for the hypersonic CFD code. The CFD code with the analytical sheath models is then used for a test case typical of a leading edge radius in a hypersonic flight environment. The CFD results show that ETC can lower the surface temperature of sharp leading edges of hypersonic vehicles, especially at higher velocities, due to the increase in ionized species enabling higher electron heat extraction from the surface. The CFD results also show that space-charge limit effects can limit the ETC reduction of surface temperatures, in comparison to thermionic emission assuming no effects of the electric field within the sheath.

Effect of total emitted electron velocity distribution function on the plasma sheath near a floating wall

“…In this study, only the classic sheath and critical SCL sheath, 6,[18][19][20][21][22][23][24][25][26] i.e. φ monotonically decreases along x direction, is considered.…”

“…6 They found that sheath potential drop decreases with increment of Γ, and thereby heat flux at wall increases; when Γ reaches a critical value Γ c,SCL = 1 8.3(m e /m i ) 0.5 , the sheath goes into space-charge limited (SCL) regime, with wall potential relative to sheath edge φ w = 1.02T e /e and wall electric field equals zero, where m e and m i are the masses of electron and ion respectively, T e is plasma electron temperature and e is the unit charge. Some other kinetic sheath models combined with PIC or Vlasov kinetic simulation also found that strong electron emission causes sheath structure transition from classic sheath to SCL sheath; [20][21][22][23][24] while the sheath was predicted to transit to an inverse Debye layer structure with a fixed ion flux through the sheath region, 25 and a more entirely inverse sheath structure with no ion through the sheath region; 26 and if ion collisions are included, these collisions cause ions get trapped in virtual cathode and force a transition to the inverse sheath. 27 The effect of emitted electron temperature (EET) on potential of critical SCL sheath was specially investigated in recent several years by Sheehan et.al with kinetic theory analysis, particle-in-cell simulation and experiment measurement.…”

Thermal Protection System and Thermal Management for Combined-Cycle Engine: Review and Prospects

“…The experiment confirmed the sweat cooling system to be a potential solution to high wall temperature and mechanical load of ramjets. For sharp components in hypersonic propulsion systems, Hanquist proposed a new potential cooling method, electric transpiration cooling (ETC), and conducted a series of studies on modeling and computational fluid dynamics (CFD) calculations [48][49][50][51]. However, since the ETC sweat cooling material is still being researched and developed in the current stage, most studies on ETC cooling mainly focus on analyzing the cooling principle and optimizing the calculation model.…”

Исследование Эффекта Электронного Охлаждения. Обзор Современного Состояния Работ

“…B работе [36] дается более полная теория физических процессов, существенных для понимания эффекта ЭО. Цель этой работы состояла в исследовании влияния физических процессов в плазменном слое на эффективность ЭО.…”