Hybrid integral/quasi-steady solution of charring ablation

Abstract

Bhsapu r s S Approximate techniques for rapidly estimating ablation and charring of heat-shield materials in severe aerothennal/erosive environments are required for many practical situations. Pure heat balance integral (HBI) or quasi-steady-state (QSS) approaches, however, are less than satisfactory for predicting the response of materials that char, especially when surface heat flux and ablation rates an affected by the outgassing from indepth charring. This paper presents a new, hybrid expansion of the integral method that satisfactorily models charring ablator responG. Quasi-steady state techniques an used at cert&n steps to consmct the hybrid method. but the dependence on recession rate is eliminated so that the method applies even when the material undergoes non-quasi-steady response. As further contributions. this paper reviews thermal properties and modeling coefficients for carbon-phenolic. and it presents new curve-fit equations for carbon-phenolic ablation in air. A a B B ' gh gh0 Nomenclatun collision frequency, st blowing coefficient. Eq. (B20) activation temperam (E&, K mass transfer driving force ( n e e d ablation rate) B in the limit of no blowing specific heat, J/(g K) specific heat of virgin ablator, char ablator. and pyrolysis gases, respectively. J/(g K) activation energy. cal I mole exponential integral. Eq. (41) reacfion-rate transition factor, Eq. (830) heat transfer conductance. g/(cmZs) heat transfer mnductance in the absence of mass injection (Le.. no "blowing"), g/(cm%) enthalpy. J/g enthalpy of gawous m i x m on vapor side of wall J/ enthalpy of solid m a d a t the wall, Jig enthalpy of edge gas (air) at wall temperaom. J/g integral heat storage, Fq. (46). 11-2 k = mnductivity of ablator maurial. J/(cm s K) ril = mass flux, g/(cmk) n = reactionorder P = pressure,bar Q. = = universal gas constant, effective heat of ablation, JI 1.987 cal/(mole K) = heat flux, J/(cm2s) = Wlcm ! i 4 * Senior Scientist, Member AIAA 1 a P'i 0 7 h10w S&mlts ab cond cony CR C cw e a eq carbon yield surface recession, cm surface recession rate. c d s t e m p t u n . K time, s flow s p e d indepth distance from initial surface. cm indepth distance from current surface, cm thermal diffusivity of ablafor material. cm% initial volume fraction of resin initial mass fraction of resin heat of formation. J/g heat of pyrolysis per unit mass of gas produced. Jlg thermal penenation depth, cm effective char depth, cm emissivity virgin fraction, Eq. (A29) heat density, Eq. (27). J/cm3 density (of ablatar material unless subscripted by "e"). p/cm3 fractional density of species i, Eq. (AI) Stefan-Boltunann constant, 5.670 x 10-12 J/(cm2 sK4) time. s blowing correction, Eq. (820) ablation ftdy-chamd, or carbonanceous conduction COnVCCtiVC char residue cold wall at edge of boundary laya equitibrium erosion ew = edge gas composition at wall F --f = formation g = pyrolysis gas gw = value for pyrolysis gas at the wall underside i = speciesindex = pyrolysis gas 01 resin component index = mtconduction j nct R = naction-rate I = re...

Thermochemical Performance of a Lightweight Charring Carbon Fiber Reinforced Plastic

“…The emissivity of the char surface is set to 0.85. 19,22) The reference value for the thermal conductivity of a virgin material k vref is constructed from the measured value of the LATS materials with a density of approximately 300 kg/m 3 ( Fig. 2).…”

“…The specific heat of the pyrolysis gas c pg is set to a constant value of 1,674.6 J/(kg K). 22) The coefficients in the Arrhenius equation [Eq. (5)] are determined from the TGA data of the LATS ablator.…”

“…19,22) Okuyama et al confirmed that the rate-controlled oxidation and diffusion-controlled oxidation regions exist when CFRP is exposed to air or nitrogen under approximately 3,000 K. 23) In the diffusion-controlled oxidation region, Metzger et al expressed the total mass loss rate _ m m t in the diffusion-controlled oxidation region of the graphite as follows 20) …”

Study of the Effects of Heat Load, Ablator Density and Backup Structure upon the Thermal Protection Performance of Heat Shield Systems Consisting of Phenolic Carbon Ablators

“…[10][11][12][13][14][15][16] The in-depth governing equations for onedimensional charring ablator response are energy, mass continuity, and decomposition equations, and are expressed by…”

“…blowis the blowing correction factor, which means the ratio of heat transfer coefficient with and without ablation mass injection into the boundary layer from the ablator surface.he factor blowalso means the correction (reduction) factor of heat flux due to the mass injection into the boundary layer. 13,14) As for the back surface boundary condition, radiation heat exchange between the back surface and the back environment is assumed.…”