Evaluation of Finite-Rate Surface Chemistry Models for Simulation of the Stardust Reentry Capsule

2015

Modern space vehicles designed for planetary exploration use ablative materials to protect the payload against the high heating environment experienced during reentry. To properly model and predict the aerothermal environment of the vehicle, it is imperative to account for the gases produced by ablation processes. The present study aims to examine the effects of the blowing of ablation gas in the outer flow field. Using six points on the Stardust entry trajectory at the beginning of the continuum regime, from 81 to 69 km, the various components of the heat flux are compared to air-only solutions. Although an additional component of the heat flux is introduced by mass diffusion, this additional term is mainly balanced by the fact that the translational-rotational component of the heat flux, the main contributor, is greatly reduced. Although a displacement of the shock is observed, it is believed that the most prominent effects are caused by a modification of the chemical composition of the boundary layer, which reduces the gas-phase thermal conductivity. NomenclatureB 0 = nondimensional ablation rate C = vector of source terms D = mass diffusion coefficient, m 2 ∕s E = energy, J∕m 3 e = energy, J∕kg F = inviscid flux matrix F d = diffusive flux matrix h = species enthalpy vector, J∕kg I = identity matrix J = directional species diffusion, kg∕m 2 · s Kn = Knudsen number k = thermal conductivity, W∕m · K _ m 0 0 = mass flow rate, kg∕m 2 · s p = pressure, Pa Q = vector of conserved variables q = heat flux, W∕m 2 T = temperature, K U, v = velocity, m∕s _ w = mass source term, kg∕m 3 · s _ w v = vibrational energy relaxation source term, J∕m 3 · s Y = mass fraction, kg∕kg η = distance normal to the wall, m ρ = mass density, kg∕m 3 τ = viscous tensor, Pa Subscripts c = char g = gas blown nc = next to the wall s = species t = time tr = translational-rotational ve = vibrational-electron-electronic w = wall ∞ = freestream

Section: Lemans: Unstructured Three-dimensional Navier-stokes Somentioning

confidence: 99%

Modeling of Heat Transfer Attenuation by Ablative Gases During the Stardust Reentry

Martin

2015

“…It can be used to investigate the effects of surface catalysis as well as surface participating reactions. The FRSC model developed by Marschall and MacLean [36] and MacLean et al [37] was implemented in LeMANS by Alkandry et al [38]. The model can simulate the chemical reactions between the hypersonic gas and surface of the vehicle during planetary entry.…”

Section: Finite Rate Surface-chemistry Modelmentioning

confidence: 99%

“…The finite rate surface-chemistry (FRSC) model is a general gassurface interaction model [36][37][38]. It can be used to investigate the effects of surface catalysis as well as surface participating reactions.…”

Section: Finite Rate Surface-chemistry Modelmentioning

confidence: 99%

Numerical Analysis of Surface Chemistry in High-Enthalpy Flows

Anna

2015

The effects of surface-chemistry processes of a graphite sample exposed to a subsonic high-enthalpy nitrogen flow are investigated using a coupled computational fluid-dynamics/surface-chemistry model. The results obtained are assessed for the accuracy of the model using experimental data from tests conducted in a 30 kW inductively coupled plasma torch facility at the University of Vermont. Significant discrepancies are observed between the computational and experimental results. Therefore, a study is performed to determine sensitivities of flow and surface parameters to variations in testing input conditions, as well as physical modeling parameters. Measurements of the absolute number density are required to draw firm conclusions about the surface-chemistry models, as well as the surface reactions involved.Nomenclature C k = concentration of gas species k, mol∕m 3 D k = diffusion coefficient of species k, m 2 ∕s E ad = energy barrier for adsorption, J∕mol E ER = energy barrier for Eley-Rideal recombination, J∕mol h = species enthalpy, J∕kg K = total number of species K g = total numbers of gas species K nb = number of species in bulk phase nb K ns;na = number of species in active site set na on surface phase ns k B = Boltzmann constant k fi , k bi = forward and backward reaction rates for reaction i M k = molar weight of species k, kg∕mol _ m b = mass blowing rate due to surface reactions, kg∕m 2 ∕s N = total number of phases N nb = number of bulk species N g , N s , N b = number of gas, surface, and bulk phases N ns;a = number of active site sets in surface phase ns N R = number of surface reactions P = pressure, Pa q = total heat flux, W∕m 2 q conv = convective heat flux, W∕m 2 q diff = diffusive heat flux, W∕m 2 R u = universal gas constant, J∕mol∕K r i;ns = reaction flux of reaction i on surface phase ns, mol∕m 2 ∕s S, S 0 = sticking coefficient T = translational-rotational temperature, K ν ki = net stoichiometric coefficient for species k in reaction i ν s = sum of the stoichiometric coefficients of all surface reactants ν k = thermal speed of gas-phase species k, m∕s ν 0 ki = reactant stoichiometric coefficient for species k in reaction i ν 0 0 ki = product stoichiometric coefficient for species k in reaction i _ w k = production rate of species k in all reactions, mol∕m 2 ∕s _ w ki = production rate of species k in reaction i, mol∕m 2 ∕s, Y = mass fraction Γ k = impingement flux of gas species k, m 2 ∕s γ = reaction efficiency θ ns;k = fraction of active sites occupied by species k on surface phase ns ρ = density, kg∕m 3 σ = Stefan-Boltzmann constant, W∕m 2 ∕K −4 Φ ns = active site density on surface phase ns, mol∕m 2 Φ ns;k = concentration of species k on surface phase ns, mol∕m 2 χ k = mole fraction of species k χ nb;k = mole fraction of bulk species k in bulk phase nb Subscripts b = bulk phase e = empty site g = gas phase na = number of active sites nb = number of bulk phases ns = number of surface phases s = surface phase tr = translational-rotational energy mode ve = vibrational-electronic energy mode...

“…The viscous stresses are modeled assuming a Newtonian fluid and Stokes' hypothesis, and the heat fluxes are modeled according to Fourier's law for each temperature. A finite-rate surface chemistry module originally developed by Marschall and MacLean [9] and MacLean et al [10] has been implemented in LeMANS as a boundary condition to model the interaction between the hypersonic gas flow and the vehicle surface [11]. This module allows for the specification of several different surface reaction processes, including adsorption/ desorption, Eley-Rideal recombination, and oxidation/nitridation.…”

Section: Governing Equationsmentioning

confidence: 99%

Comparison of Transport Properties Models for Flowfield Simulations of Ablative Heat Shields

Alkandry

Martin

2014

Self Cite

The goal of this study is to evaluate the effects of different models for calculating the mixture transport properties on flowfield predictions of ablative heat shields. The Stardust sample return capsule at four different trajectory conditions is used as a representative environment for Earth entry. In the first part of the study, the results predicted using Wilke's missing rule, with species viscosities calculated using Blottner's curve fits and species thermal conductivities determined using Eucken's relation, are compared to the results obtained using Gupta's mixing rule with collision cross-section data. The heat transfer to the vehicle predicted using the Wilke/Blottner/Eucken model is found to be larger than the value obtained using the Gupta/collision cross-section model by as much as 60%. The Wilke/Blottner/Eucken model also produces a larger mass blowing rate due to the oxidation of bulk carbon by as much as 25% compared to the Gupta/collision cross-section model. In the second part of the study, the effects of the mass diffusion model are assessed using the Fick's, modified Fick's, self-consistent effective binary diffusion, and Stefan-Maxwell models. The results show that the flowfield properties calculated using the modified Fick's, self-consistent effective binary diffusion, and Stefan-Maxwell models are in good agreement. However, the Fick's model produces a larger heat transfer and mass blowing rate compared to the other diffusion models by as much as 20%. Nomenclature C p = specific heat at constant pressure, J∕K∕kg C v = specific heat at constant volume, J∕K∕kg D s = diffusion coefficient of species s, m 2 ∕s D s;r = binary diffusion coefficient of species s and r, m 2 ∕s J s = mass diffusion flux of species s, kg∕m 2 ∕s k B = Boltzmann constant, 1.38 × 10 −23 kg · m 2 ∕s 2 ∕K M = average molar weight of the gas-phase mixture, kg∕mol M s = molar weight of species s, kg∕mol m s = mass of species s, kg NS= number of gas-phase species N av = Avogadro's number, 6.022 × 10 23 mol −1 p = pressure, Pa p s = partial pressure of species s, Pa R = universal gas constant, 8.314 J∕mol∕K T tr = translational/rotational temperature, K T ve = vibrational/electronic/electron temperature, K X s = mole fraction of species s Y s = mass fraction of species s γ s = molar concentration of species s, mol∕kg Δ s;r = collision terms between species s and r, m · s κ = coefficient of thermal conductivity of the gas-phase mixture, W∕m∕K κ s = coefficient of thermal conductivity of species s, W∕m∕K μ = coefficient of viscosity of the gas-phase mixture, Pa · s μ s = coefficient of viscosity of species s, Pa · s ρ = density, kg∕m 3 ρ s = partial density of species s, kg∕m 3