Radiation and Roughness Effects on Nozzle Thermochemical Erosion in Solid Rocket Motors Alessandro Turchi * and Daniele Bianchi † University of Rome “La Sapienza,” 00184 Rome, Italy Piyush Thakre ‡ CD-adapco, Ltd., Melville, New York 11747 Francesco Nasuti § University of Rome “La Sapienza,” 00184 Rome, Italy and Vigor Yang ¶ Georgia Institute of Technology, Atlanta, Georgia 30332-0150 DOI: 10.2514/1.B34997 Surface roughness and radiation effects on the erosion behavior of a graphite nozzle are studied for both metallized and nonmetallized propellants. A validated numerical approach that relies on a full Navier–Stokes flow solver coupled with a thermochemical ablation model is used for the analysis. A modification of the Spalart–Allmaras turbulence model is implemented to account for surface roughness. Net radiative heat flux is considered in the surface energy balance at the nozzle interface. Two different simplified models are used to evaluate the integral emissivity of dispersed alumina particles. Individual and combined effects of roughness and radiation are analyzed. Surface roughness enhances the erosion rate for both metallized and nonmetallized propellants noticeably. The radiation influences the erosion rate of nonmetallized propellant more than the metallized one, mainly due to the different erosion regimes, kinetically controlled for the former and diffusion controlled for the latter. Nomenclature D ij = binary diffusion coefficient, m 2 ∕s D im = effective diffusion coefficient, m 2 ∕s e 0 = total specific energy, J∕kg h = enthalpy, J∕kg h eq = equivalent sand grain roughness, m j = diffusional mass flux, kg∕m 2 · s k = thermal conductivity, W∕m · K _ m = mass blowing rate per unit area, kg∕m 2 · s N s = number of species p = pressure, N∕m 2 _ q = heat flux, W∕m 2 _ s = erosion rate, m∕s T = temperature, K t = time, s u τ = friction velocity v = velocity component normal to surface, m∕s v = flow velocity vector, m∕s _ w = species source term, kg∕m 3 · s x = mole fraction y = mass fraction α = absorptivity ε = integral emissivity η = inward (from solid to gas) coordinate normal to surface μ = dynamic viscosity, kg∕m · s ν = kinematic viscosity, m 2 ∕s ρ = density, kg∕m 3 σ = Stefan–Boltzmann constant _ ω = species source term in control surface, kg∕m 2 · s Subscripts b = bulk value c = combustion chamber conditions g = gas phase i = species s = solid state w = gas properties at gas–solid interface 0 = initial condition Superscript  = wall units I. Introduction Ablative materials provide a reliable and relatively low-cost way to manage the extremely high heat fluxes that are normally encountered in a wide variety of aerospace applications. Reentry [1] and launch vehicles [2] provide some examples of the thermal protection system (TPS) application, in which ablation is used to mitigate harsh thermal and chemical conditions. The material response represents one of the key issues when working with ablative TPS. One of the applications of TPS in launch vehicles is in solid rocket motor nozzles. In the nozzles, ablative material consumption depends on numerous factors including propellant composition, engine oper- ating conditions, duration of firing, nozzle geometry and material properties, transport of reacting species, homogeneous reactions in the gas phase, and heterogeneous reactions at the nozzle surface. Specification of ablative material characteristics and thickness for Presented as Paper 2013-0186 at the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, 6–10 January 2013; received 21 March 2013; revision received 8 August 2013; accepted for publication 8 August 2013; published online 20 February 2014. Copyright © 2013 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-3876/ 14 and $10.00 in correspondence with the CCC. *Ph.D. Candidate, Dipartimento di Ingegneria Meccanica e Aerospaziale, Via Eudossiana 18; currently von Karman Institute for Fluid Dynamics, 1640 Rhode-Saint-Genèse, Belgium. Student Member AIAA. † Assistant Professor, Dipartimento di Ingegneria Meccanica e Aerospaziale, Via Eudossiana 18. Member AIAA. ‡ Senior Development Engineer. Senior Member AIAA. § Associate Professor, Dipartimento di Ingegneria Meccanica e Aerospaziale, Via Eudossiana 18. Associate Fellow AIAA. ¶ William R. T. Oakes Professor and Chair, School of Aerospace Engineering. Fellow AIAA. 314 JOURNAL OF PROPULSION AND POWER Vol. 30, No. 2, March–April 2014 Downloaded by GEORGIA INST OF TECHNOLOGY on March 26, 2014 | http://arc.aiaa.org | DOI: 10.2514/1.B34997