Computation of hypersonic flows with finite catalytic walls

Miller, James H.; Tennehill, John C.; Wadawadigi, Ganesh; Edwards, Thomas A.; Lawrence, Scott L.

doi:10.2514/3.691

Cited by 11 publications

(5 citation statements)

References 27 publications

(15 reference statements)

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“…The species diffusion fluxes along the x direction are based on Pick's law of diffusion, (4) This expression is an approximation because Pick's law holds rigorously only for a binary mixture; however, it can be applied reasonably well also in this case because the differences between the molecular weights of the species considered are not large. 6 The conductive, chemical, and vibrational parts of the total heat flux along the x direction are defined by…”

Section: -I Wdv + F -Nds = I Gdvmentioning

confidence: 99%

Heat flux on partially catalytic surfaces in hypersonic flows

Serpico

Monti

Savino

1998

Journal of Spacecraft and Rockets

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The combined effects of the chemical nonequilibrium and the surface catalysis on the stagnation-point heat flux of a blunt body are investigated by Navier-Stokes calculations on a spherical model under Scirocco Plasma Wind Tunnel conditions. The freestream properties in the test section are found by means of a preliminary nonequilibrium, full Navier-Stokes computation of the nozzle flow expansion. All available numerical heat flux results are correlated as a function of a dimensionless parameter, including the simultaneous effects of the finite-gas and the surface-phase reactions. The proposed parameter, which takes into account simultaneously the nonequilibrium effects in the bulk and surface phases, correlates well with the numerical results over a blunt-body stagnation region. The final correlation formula for the stagnation heat flux can be used to correlate experimental results on different materials with known catalytic coefficients or, conversely, to determine the surface catalytic efficiency of different thermal protection materials. Nomenclature a = speed of sound, m/s c p = specific heat per unit mass at constant pressure, J/kg • K D = diffusion coefficient, m 2 /s D a = homogeneous Damkohler number; Eq. (28) D as = heterogeneous Damkohler number; Eq. (31) E = total energy, J E v = vibrational energy source term, J/s e = specific total energy per unit volume, J/m 3 h = enthalpy per unit mass, J/kg hf" = heat envolved in the formation of component i, J/kg k = Boltzmann constant (1.38022 x 10~2 3 ), J/K k h>r = backward reaction-rate coefficient for reaction r k er = equilibrium constant for reaction r kf >r = forward reaction-rate coefficient for reaction r k w = catalytic reaction-rate constant, m/s M = molecular weight, kg/kg • mole n = normal to the wall coordinate p = pressure, Pa q = stagnation-point heat flux, W/m 2 qm = mole fraction Re = Reynolds number Rt = gas constant of component i r h = body radius Sc = Schmidt number T = absolute temperature, K u = x component of velocity, m/s v = y component of velocity, m/s x = jc-axis component Y = mass fraction y = v-axis component y = recombination coefficient X = thermal conductivity, J/m • s p = density, kg/m 3 r = heat flux correlation parameter a) = catalytic recombination rate, kg/m 2 • s a = atomic species c = conductive term d = diffusive term eq = equilibrium / = frozen few = fully catalytic wall / = i th component of mixture N = atomic nitrogen new = noncatalytic wall ns = number of chemical species nvs = number of vibrational species O = atomic oxygen p = partial derivative with respect to pressure t = partial derivative with respect to time v = vibrational term u; = wall x,y,z = Cartesian components p = partial derivate with respect to density 0 = stagnation conditions 02 = stagnation-point conditions oo = freestream value Superscripts p = reaction order for catalytic reaction + = nondimensional quantities

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Section: -I Wdv + F -Nds = I Gdvmentioning

confidence: 99%

Heat flux on partially catalytic surfaces in hypersonic flows

Serpico

Monti

Savino

1998

Journal of Spacecraft and Rockets

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“…From a microscopic simulation front, Rutigliano et al [28] only calculated the E-R reaction mechanism via DFT investigation, so the data they obtained are lower and the trend is different from other conclusions. Consequently, the thermal protection system (TPS) needs to use high design margins to protect the inner structure due to the uncertainty of the recombination coefficient and the lack of mechanistic understanding [17], especially the microscopic phenomena at the gas-solid interface [29]. In this regard, molecular dynamics simulation can provide a promising solution to advance the catalytic reaction mechanism at the microscale [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis of the Catalysis Recombination Mechanism on Nanoscale Silica Surfaces

Cui

Sun

et al. 2022

Nanomaterials

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A deep understanding of surface catalysis recombination characteristics is significant for accurately predicting the aeroheating between hypersonic non-equilibrium flow and thermal protection materials, while a de-coupling sensitivity analysis of various influential factors is still lacking. A gas–solid interface (GSI) model with a hyperthermal flux boundary was established to investigate the surface catalysis recombination mechanisms on nanoscale silica surfaces. Using the reactive molecular dynamics (RMD) simulation method, the effects of solid surface temperature, gas incident angle, and translational energy on the silica surface catalysis recombination were qualified under hyperthermal atomic oxygen (AO), atomic nitrogen (AN), and various AN/AO gas mixtures’ influence. It can be found that, though the Eley–Rideal (E–R) recombination mechanism plays a dominant role over the Langmuir–Hinshelwood (L–H) mechanism for all the sensitivity analyses, a non-linear increasing pattern of AO recombination coefficient γO2 with the increase in incident angle θin and translational energy Ek is observed. Compared with the surface catalysis under hyperthermal AO impact, the AN surface adsorption fraction shows an inverse trend with the increase in surface temperature, which suggests the potential inadequacy of the traditional proportional relationship assumptions between the surface adsorption concentration and the surface catalysis recombination coefficient for other species’ impact instead of AOs. For the incoming bi-component AO/AN gas mixtures, the corresponding surface catalysis coefficient is not the simple superposition of the effects of individual gases but is affected by both the intramolecular bond energies (e.g., O2, N2) and intermolecular energies (e.g., Si/N, Si/O).

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“…The catalytic recombination rate coefficient is defined as the fraction of the total number of atoms impinging on a unit surface area that recombine per unit time (see e.g. Goulard 1958or Miller et al 1995 and, therefore, has a range of 0 to 1. The upper limit refers to a fully catalytic material where the surface reactions occur instantaneously, and the lower limit to a non-catalytic wall with no surface reactions.…”

Section: Introductionmentioning

confidence: 99%

“…Stewart, Rakich &Lanfranco 1983 andScott 1985 and references contained therein). Some more recent studies considered the effects of catalytic walls on a shock/boundary layer interaction (Grumet et al 1991), catalytic effects on a model of Martian atmospheric entry (Chen & Chandler 1993), and hypersonic flow past a sharp cone with finite catalytic walls (Miller et al 1995).…”

Section: Introductionmentioning

confidence: 99%

High-speed flow with discontinuous surface catalysis

2000

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In a reacting gas flow both gas-phase chemical activity and surface catalysis can increase the rate of heat transfer from the gas to a solid surface. In particular, when there is a discontinuous change in the catalytic properties of the surface, there can be a very large increase in the local heat transfer rate. In this study numerical simulations have been performed for the laminar high-speed flow of a high-temperature, non-equilibrium reacting gas mixture over a flat plate. The surface of the plate is partly catalytic, with the leading region non-catalytic, and a discontinuous change in the catalytic properties of the surface at the catalytic junction. The surface is assumed to be isothermal, and cold relative to the free stream. The gas is assumed to be a mixture of molecular and atomic forms of a diatomic gas in an inert gas forming a thermal bath, giving a three-species mixture with dissociation and recombination of the reactive species. The calculations are performed for a gas with atomic and molecular oxygen in an argon bath, but a full range of gas-phase chemical and surface catalytic effects is considered. Kinetic schemes with frozen gas-phase chemistry, and partial or full recombination of atomic oxygen in the boundary layer are investigated. The catalytic nature of the surface material is given by a catalytic recombination rate coefficient, which varies from zero (non-catalytic) to one (fully catalytic), and the effects on the flow and the surface heat transfer of materials which are non-, partially, or fully catalytic are considered. A self-similar thin-layer analytical model of the change in the gas composition downstream of the catalytic junction is developed. For physically realistic (O(10 −2 )) values of the catalytic recombination rate coefficient, the predictions from this model of the surface values of the atomic oxygen mass fraction and the catalytic surface heat transfer rate are excellent when the only change in the composition of the gas comes from the surface catalysis, and reasonable when there is partial recombination of the gas in the boundary layer due to the gas-phase chemistry. In contrast, when the surface is fully catalytic, the streamwise diffusion terms play a significant role, and the model is not valid. These results should apply to other situations with an attached boundary layer with recombination reactions. A comparison is made between the calculated and experimental measurements of the heat transfer rate at the catalytic junction. With a kinetic scheme which allows partial recombination in the boundary layer, good agreement is found between the experimental and predicted values for surface materials which are essentially non-catalytic. For a catalytic material (platinum), the experimental and numerical heat transfer rates are matched to estimate the value of the catalytic recombination rate coefficient. The values obtained show a considerable amount of scatter, but are consistent with those found in the literature.

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Computation of hypersonic flows with finite catalytic walls

Cited by 11 publications

References 27 publications

Heat flux on partially catalytic surfaces in hypersonic flows

Heat flux on partially catalytic surfaces in hypersonic flows

Sensitivity Analysis of the Catalysis Recombination Mechanism on Nanoscale Silica Surfaces

High-speed flow with discontinuous surface catalysis

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