Modeling Approach for Intumescing Charring Heatshield Materials Journal of Spacecraft and Rockets July 2006

P1: PIT/GUR P2: ILTAIAA [jsr] 15:27 29 June 2006 JulyAugust2006 #04-A12098(A)/Russell

JOURNAL OF SPACECRAFT AND ROCKETSVol. 43, No. 4, JulyAugust 2006

Modeling Approach for Intumescing CharringHeatshield Materials

Gerald W. RussellU.S. Army Aviation and Missile Research Development and Engineering Center, Redstone Arsenal, Alabama 35898

andForrest Strobel

ITT Industries Advanced Engineering Sciences, Huntsville, Alabama 35806

Intumescing heatshield materials have been shown to provide significant thermal protection for missile sys-tem environments. The design and use of these materials requires the analytic understanding of a considerablelevel of thermodynamic phenomena occurring on the surface as well as in-depth. These phenomena can includein-depth thermochemical decomposition, pyrolysis gas generation and mass transfer, thermophysical propertychange, thermochemical and mechanical ablation, intumescence or conduction path growth, and boundary-layermodification due to pyrolysis gas injection or surface reactions. The current state of the art for modeling thermo-chemically decomposing heatshield materials is enhanced through the addition of intumescent behavior effects tothe Aerotherm Charring Material Thermal Response and Ablation Program (CMA). State-of-the-art real-timeradiography methods along with embedded thermocouples were utilized in a radiant heating environment to obtainin-depth thermochemical decomposition, thermal response, and intumescence. The resulting intumescence modelwas applied and validated for a low-shear hypersonic high-altitude environment.

NomenclatureA = area, in.2 (cm2)Cp = specific heat, Btu/lbm F (kJ/kg K)E = activation energy, lbf ft/lbm (N m/kg)h = enthalpy, Btu/lbm (kJ/kg)h = weighted enthalpy, Btu/lbm (kJ/kg)k = thermal conductivity, Btu/ft h F (W/m K)L = node thickness in intumescence model, in. (cm)LFAC = intumescence term (function of char state and heat rate)m = mass, lbm (kg)m = mass flow rate, lbm/s (kg/s)n = Arrhenius decomposition reaction orderPF = preexponential factor, 1/sq = heating rate, Btu/ft2 s (W/cm2)R = gas constant, lbf ft/lbm R (K)s = surface erosion depth or position, in. (cm)s = surface erosion rate, in./s (m/s)T = temperature, F (C)x , y = spatial coordinate, in. (cm) = resin to fiber volume fraction = time, h = temperature varying density of material,

lbm/ft3 (kg/m3) = char state

Subscripts

c = charg = pyrolysis gases0, v = initial condition or virgin material

Received 17 December 2004; revision received 18 September 2005; ac-cepted for publication 24 September 2005. This material is declared a workof the U.S. Government and is not subject to copyright protection in theUnited States. Copies of this paper may be made for personal or internaluse, on condition that the copier pay the $10.00 per-copy fee to the CopyrightClearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; includethe code 0022-4650/06 $10.00 in correspondence with the CCC.

(Job title), (dept.), AMSRDAMRPSPI.(Job title), (dept.).

Introduction

D URING the past several years, a significant level of researchand development has been applied to optimization of missilesystems for performance enhancement. One of the primary methodsof enhancing performance is to reduce weight, thereby increasingvelocity and range. To address the weight reduction requirement,composite technology has been increasingly utilized in missile air-frame design. Although these composite structures afford a sig-nificant weight reduction, they are typically limited in operatingtemperature. As a result, a thermal protection system is requiredand must be designed in an optimal manner to maintain the weightreduction achieved through the use of the composite airframe.

One of the most widely accepted methods for analysis and de-sign of external thermal protection systems is the charring materialapproach,1 in which an attempt is made to model the thermody-namic phenomena occurring throughout the material and boundarylayer. This approach provides a relatively rigorous mathematicaltreatment of thermochemical decomposition and ablation, allow-ing for the identification of sensitivities to the various phenomena.This also provides a means of optimizing heatshield requirementsfor given geometries and aerothermal environments. Whereas thisapproach adds significantly to the analytic capability of modelingheatshield thermodynamic behavior, it still requires a level of em-piricism due to its current inability to model the effects of intumes-cence (swell or expansion) on in-depth thermal response. Recentstudies2 have led to the identification of intumescing heatshield ma-terials having significantly higher thermal performance than manyof the nondecomposing and ablating materials commonly used. Thephenomenon of intumescence increases conduction path length andinduces additional thermophysical property changes that contributeto the reduction of in-depth thermal penetration. Figure 1 provides aschematic of the nonintumescent model compared to the new intu-mescent model. Figure 1 shows the various regions within the heat-shield undergoing decomposition and expansion. As can be seen forthe nonintumescent model, the conduction path is fixed, whereas thenew intumescent model accounts for the effects of conduction pathgrowth.

The objective of this research is to further reduce the level ofempiricism through the development and experimental validationof mathematical relationships for intumescence and to incorporatethese relationships into the Aerotherm Charring Material Thermal

739


740 RUSSELL AND STROBEL

Fig. 1 Schematic of models for thermochemically decomposing heat-shields.

Fig. 2 Schematic of thermochemical decomposition phenomena.

Response and Ablation Program (CMA),3 providing a means ofmore accurately predicting heatshield requirements and enhancingsystem level optimization. The approach for accomplishing the re-search objectives were initiated with the development of mathemat-ical expressions for intumescence. These expressions were then in-corporated into the existing thermochemical decomposition modelCMA in a one-dimensional finite difference approach. Experimen-tal data were collected through the use of a high heat flux test facil-ity while aerodynamic shear effects were minimized. The test en-vironment provided a controlled thermal boundary condition andallowed for in-depth decomposition to be monitored as a func-tion of time and position through the use of real-time radiographyand embedded thermocouples. The resulting model was then ap-plied to low- and moderate-shear hypersonic convective thermalenvironments for which test data had been previously collected.These results provided an indication of the model accuracy in anactual freestream air environment for various levels of mechani-cal shear. The comparisons of predictions with test data for theconvective aerothermal environments allowed for the identifica-tion of sensitivities to mechanical shear and the necessity to fur-ther enhance the analytic approach through modeling mechanicalerosion.

DiscussionThermodynamic Phenomena Overview

A schematic of the physical processes that occur for missile heat-shield materials during exposure to aerothermal environments isshown in Fig. 2. It is quickly evident that a significant level of chem-ical reactions, mechanical interactions, and boundary-layer effectsare possible during the heating and corresponding outgassing of de-composing materials. The following is a discussion of each of theparameters specifically identified in Fig. 2.

Freestream FlowThe freestream flow represents the resulting airflow over an air-

frame during flight. This term also represents the flow imparted overa test item during aerothermal experimentation.

Boundary LayerThe boundary layer is defined as the viscous region adjacent to

a surface exposed to aerodynamic flow. The analytic modeling ofboundary-layer flow is extensively discussed in Schlichting,4 and isused in this research effort.

Convective and Radiative Heat TransferThe convection heat transfer term corresponds to the thermal ef-

fects of aerodynamic flow over an airframe. The resulting viscousdissipation within the boundary layer results in a temperature riseat the wall surface. The net radiation term defines the external ra-diation energy exchange between the external reservoir, possibleshock-layer radiation, and the heatshield surface temperature. Forthe present research for missile applications, shock-layer radiationis negligible.

Chemical Diffusion/ReactionsThe chemical diffusion and reaction processes are a result of gas

generation from the thermochemically decomposing material beinginjected through the solid surface into the boundary layer. Additionalreactions can occur between the solid surface and boundary-layergas species such as the recombination of carbon or coking, withinthe char layer of a decomposing material. The reaction kinetics anddiffusion rates are highly dependent on the freestream and injectedgas components. For heatshields dominated by mechanical erosion,these rates are less important than for materials having a high levelof decomposition and gas injection.

DecompositionAs a heatshield material is exposed to a sufficient level of con-

vective or radiative heat transfer, the in-depth temperature increaseinduces relative levels of thermochemical decomposition. This de-composition results in pyrolysis gas generation and material densityreduction that can be partially quantified through the use of thermo-gravimetric analysis (TGA).5 Use of an inert medium while heatingthe sample eliminates the potential influence of reactions with airand represents the in-depth thermodynamic response of the decom-posing material where air is not present. A brief description of thespecific terms considered in the analytic heatshield model follows.

CharThe char term is defined by the fully decomposed or fully reacted

heatshield material region and is quantified during TGA where noappreciable density changes occur during additional temperaturerise. This region can vary significantly depending on the level ofthermochemical ablation and mechanical erosion. The char layer istypically of a black, carbonaceous nature. However, the char canalso be represented by a combination of a variety of nonreacting orcondensed species that collect on the surface.

PyrolysisThe pyrolysis region is defined as the layer at which the heated

material is undergoing thermodynamic reactions and is bounded bythe fully reacted char layer and the non-reacting virgin material.This is the region from which the pyrolysis gases are generated andpercolated through the char to the boundary layer. It is also con-sidered, for this research, the primary region where intumescenceoccurs and expansion of the conduction path moves the heated sur-face away from the substrate.

Blowing/Mass InjectionThe evolving gases due to decomposition are percolated up from

the pyrolyzing layers through the fully decomposed porous charlayer and injected into the boundary-layer. As a result of the massinjection, the boundary-layer thickness increases, providing a po-tential reduction in heat transfer from the boundary-layer edge tothe heated surface. Depending on the severity of the thermal envi-ronment, these gases can also react with air in the boundary layer.

Surface Recession/IntumescenceThe surface recession term is defined as the mechanical or ther-

mochemical removal of condensed species from the surface of theheatshield material. This phenomenon is highly dependent on thelevel of aerodynamic shear, heatshield char strength, enthalpy level,reactivity of boundary-layer gases, and surface material decompo-sition state. For high-speed aerodynamic heating and sufficiently


RUSSELL AND STROBEL 741

weak char layers, the mechanical shear removal typically domi-nates the ablation process and can greatly reduce the influence ofthermochemical ablation. The current CMA code requires the use ofa fail temperature to simulate mechanical erosion of char layers dueto aerodynamic shear forces. Although this approach can be used,it does not represent the true physics of mechanical erosion andmay be limited in applicability. The intumescence is a direct resultof the internal thermodynamic decomposition, causing a range ofexpansion levels of the pyrolyzing material. The specific differencein the existing nonintumescing model as compared to the proposedintumescing model is contained in the ability to model the effectintumescence or swelling has on conduction heat transfer into thedecomposing material. Figure 1 provided a schematic of this dif-ference. A variety of approaches such as thermal expansion6 andequivalent thermal properties7 have been investigated in an attemptto model this behavior with varied success. A new approach will bepresented for modeling intumescence relating the pyrolysis regionexpansion to the decomposition state and heating rate with the goalof more accurately capturing the thermodynamic phenomenon andrelative effects on conduction heat transfer.

Existing CMA Numerical ModelThermochemical Decomposition Model

The approach to providing a means of accurately predicting spe-cific behavior of decomposing heatshield materials has been of greatinterest to missile design engineers due to the excessive heat loadsof reentry and hypersonic flight. In the initial design stages withnew materials, only limited data and material understanding may beavailable until more extensive testing and evaluation is conducted.Initial design studies can be conducted with semi-empirical proce-dures such as the simplified heat of ablation model (SHOA).8 Thisdesign approach is adequate for conservative design as long as ex-periments can be conducted in thermal environments similar to thoseof flight. However, as design requirements are refined, optimizationplays a more significant role in missile design. This requires refine-ment of thermal protection system design to minimize weight whileproviding increased thermal protection. To obtain this analytical re-finement in design of thermal protection systems, more accuratemodels of the ablation phenomena are required. In response to theneed for a more accurate characterization of the ablation phenomenadesired for typical reentry vehicle thermal design, a significant steptoward providing a more theoretical model of heatshield thermo-dynamic behavior was developed by Moyer and Rindal,9 namely,the CMA. This program provides a means of modeling much of thesurface thermochemistry and in-depth material response phenom-ena, allowing for identification of specific contributors that providematerial insulative capability. However, a significant amount of ther-mophysical property data and material characterization are requiredbefore a thermal response model can be developed that utilizes thisprogram. A discussion of the pertinent derivations and resultingfinite difference expressions is provided in the following text.

In-Depth Energy Differential EquationsMathematically representing the terms shown in Fig. 2, the dif-

ferential equation defining the in-depth energy balance is

(h A)y =

y

(

k ATy

)

+ y

(mghg) (1)

The conservation of mass for a chemically decomposing material isdefined as

m

y

)

= A

)

y

(2)

where mass transfer is associated with the pyrolyzing constituentspercolating through the char, assuming no reaction with the char. Aspointed out by Rohsenow and Hartnett,1 the use of an Arrhenius-typefit has been found to model adequately the decomposition behav-ior of thermochemically decomposing materials. The expression is

written as

)

y

= PF exp(

ERT

)

0

(

c0

)n

(3)

The expression for density can be defined in terms of a variety ofreacting components combined to form the single material. TGAcharacterizes the weight loss and weight loss rate based on specificreactions occurring in the material while it is heated. The generalform of the expression is

=

i + (1 )

j (4)

where represents the volume or mass fraction of effective resin toeffective reinforcement and the subscripts i and j represent the var-ious reactions attributable to the resin and reinforcement densities,respectively. Early versions of CMA limited the decomposition pro-cess to three material constituents. However, more recent versionshave incorporated the ability to model more than three reactions thatcan occur for the highly decomposing materials of interest for thisresearch.

Boundary ConditionsThe boundary conditions defined for the surface energy balance

are shown in Fig. 3. The control volume is allowed to move withthe receding surface as ablation/erosion/intumescence occurs. Thismovement can be either a net recession or expansion. The energyfluxes entering the control volume include the convective heatingand energy due to chemical reactions. (This may be either a netpositive or negative value depending on the nature of the chemicalreactions.) The exiting energy terms represent the conduction andradiation.

Transformation of Partial Differential EquationsThe existing CMA mathematical model is a finite differencing

scheme that uses fixed node sizes. To account for surface removal,nodes are removed from the backside of the ablating material suchthat the nodal network is referenced to the receding surface. A trans-formation of the differential equations is performed from the globalor fixed coordinate system to a body or moving coordinate system.This approach also allows for conservation of energy and mass. Thedifference form of the energy equation reduces to the conservationof mass equation when temperature and enthalpy are uniform. Thesefinite difference equations are implicit in temperature. However, thedecomposition finite difference forms are explicit in temperature.The decomposition nodal network utilizes a refinement of the ther-mal nodal network (called nodelets) to provide better resolutionof decomposition gradients. The resolution is user defined and isbased on the required level of refinement to capture density gradi-ents through the decomposing material. The process utilized in thenumerical scheme first involves the calculation of the decomposi-tion gradients using the fixed nodal and nodelet thicknesses. Thenthe intumescence or nodal thicknesses are determined using the charstate and heating rate obtained during the decomposition calcula-tion. The thermal gradients are then calculated using the intumesced

Fig. 3 Surface boundary condition schematic.



nodal thicknesses. The resulting thermal gradients are used to definethe decomposition gradients for each successive temporal iteration.

The energy equation solution determines the in-depth temperaturegradient and is based on intumesced nodal thicknesses. The intu-mescent process results in an increased conduction path and thermalresistance. This node thickness increase is only accounted for in theenergy equation and not utilized in the decomposition gradient cal-culation. This is possible because the decomposition equation doesnot actually include a spatial dimension. The equations are cast interms of density, but they are actually manipulated in terms of mass.The basic in-depth energy balance, as shown in Eq. (1), is furthertransformed to the moving coordinate system and results in the finitedifference expression

CpT

)

x

= 1A

x

(

k ATx

)

+ (hg h)

)

y

+ SCp Tx

)

+ mA

hgx

)

(5)

h = 0h0 chc0 c (6)

The respective terms in Eq. (5) represents the sensible energy, netconduction, net chemical, and net convection occurring within thecharring material. The conduction term containing x defines thenodal thickness modified according to the level of intumescenceexperienced for each node through the thickness of the material.

These expressions represent the in-depth energy balance and sur-face boundary conditions for decomposing materials. The nodalthicknesses along the x coordinate are fixed in the existing CMAnumerical scheme. The modification discussed in the current re-search defines the provision for predicting transient nodal thicknessor intumescence along the x coordinate.

Modified CMA Numerical Model for IntumescenceThe intumescence phenomenon has been documented in a vari-

ety of analytic investigations of heatshield materials. In particular,when heatshields are used as internal insulators for rocket motors,a significant level of intumescence can occur, providing additionalinsulative value. Analytic modeling efforts have been performed inthe past on internal motor insulation materials, such as DC93-104,where intumescence was noted. However, due to limited measure-ment techniques, the intumescence phenomenon could not be ad-equately modeled. This phenomenon was again observed during aheatshield test and evaluation program8 in which the intumescencewas such that simplified modeling techniques could not readily beused to predict heatshield thickness requirements. As a result ofthese analytical and experimental findings, research was directed10to identify a method of modeling intumescent behavior of heat-shields along with validation efforts for specific environments.

The initially proposed analytic expression for modeling the intu-mescence as a function of char state is

L = fnc() (7)

where L is the node thickness (as related to the x coordinate systemin the numerical scheme) and is an expression quantifying charstate. It was observed that the amount of intumescence appearedto be char state dependent and also dependent on the rate at whichthe material was charred. Therefore, the following relationship wasadopted to model the thickness change of the material:

L

= L

(8)

The char state is a function of the virgin and fully charred materialdefined as

= (v )/(v c) (9)

where the subscripts v and c represent the virgin and fully charredconditions and is the instantaneous density. Differentiating thechar state with respect to time provides

= 1

v c

(10)

Combining terms results in the expression for intumescence

L

= 1v c

L

(11)

These expressions provide the basis for relating intumescence to achar state for the thermochemically decomposing material. The re-maining expression, L/, must be formulated to model the actualintumescence of the material. Until additional research and devel-opment is devoted to understanding, on a microscale, the materialproperties that cause growth, empirical data must be used. Thesedata must be collected during flight-similar hypersonic aerother-mal test and evaluation programs in which real-time radiography ofintumescence and decomposition, as well as pre- and posttest in-tumescence, are measured. Along with transient intumescence anddecomposition measurements, in-depth temperature measurementsmust be collected to verify in-depth thermal response and thermalproperties of the various decomposition states.

The L/ contributions to the intumescence relationship wereselected utilizing a variety of analytic and experimental means.Oven tests were performed to correlate material appearance withchar state. These oven tests also provided an indication of the on-set and termination of intumescence for the respective heating rate.Note that these oven tests were strictly qualitative due to the dif-ferences in thermal environments and chemistry as compared toflight. However, it was noticed that discoloration for the varioustemperatures seen in the oven samples were similar to what was seenin the WrightPatterson Air Force Base Laser Hardened MaterialsEvaluation Laboratory (LHMEL) tests with embedded thermocou-ples. Chemical analyses of the oven samples and LHMEL sampleswould provide more comparable quantitative data. The laser facilitytests provided the most useful data as a result of recording transientradiography. The radiography data provided material density as afunction of time and location within the test sample. This allowedfor validating both char surface position and internal layer posi-tion as a function of time. These results coupled with the densitymeasurements through the thickness as a function of time allowedfor accurate predictions of in-depth thermochemical decompositionand intumescence. The embedded thermocouples provided a meansof quantifying the thermal properties of the various char states. Be-cause the thermocouple locations, density gradients, and tempera-tures were known as a function of time it was possible to developa material model that could accurately predict in-depth response ofthe intumescing material.

It was discovered through experimental validation that the intu-mescence model, for the particular material of interest, was alsohighly dependent on heating rate. As a result, the L/ term wasdetermined as a function of both decomposition state and heatingrate to provide an approximate method of quantifying intumescence.The correlation for heating rate dependency was developed from thevarious aerothermal tests and imposed as a multiplier of the non-intumescing thickness. The resulting relationship to define the charstate and heating rate dependent intumescence is shown in Eq. (12):

L

LFAC() LFAC(q) L inital (12)

for 100C/min q 20,000C/min, where LFAC is the intumes-cence term as a function of the char state and heating rate. Thisexpression represents the use of multipliers for char state and heat-ing rate effects on the initial node thickness for each time step.These multipliers are characteristic of material properties and, be-cause they incorporate both decomposition state and heating rate,they should be applicable to a variety of aerothermal environments.



The laser test facility was utilized to isolate and quantify these in-tumescence properties for the analytic model. The resulting overallintumescence as defined in Eq. (12) is used in the in-depth energybalance to define conduction path length and in-depth heat transfer.

The data collected during the LHMEL tests provided the regionsof intumescence as a function of char state and heating rate usedto establish the L/ empirical model. The resulting multipliersgenerated and validated for the laser thermal testing were also usedfor predicting intumescence and in-depth thermal response for theNASA Hot Gas Test Facility2 high-altitude hypersonic aerothermaltesting. Predictions were in excellent agreement with posttest mea-sured decomposition and intumescence data, as well as embeddedthermocouple data for the lower shear conditions.

Intumescent Material DescriptionOverview

The material investigated for this research, Firex RX2390(Ref. 11) was selected due to its highly intumescent behavior andexceptional thermal performance recently identified for missile ap-plications. During heating the material experiences large levels ofintumescence and, through decomposition, reradiation, and con-duction path growth, minimizes the support structure temperaturerise. The material is an inexpensive, sprayable, or trowelable fiber-reinforced epoxy. It functions as an intumescent (char swells) underlow to moderate shear in high-temperature environments. At higher-shear conditions the char layer can be removed, and the thermalperformance of the material is somewhat degraded. For the presentstudy, the focus is on environments for which shear removal of thechar layer does not occur.

Thermal PropertiesInitial temperature-dependent thermal properties for RX2390

were determined by Perry et al. (see Ref. 12). During this programthermal properties were experimentally determined by VirginiaPolytechnic Institute and State University (VPI) to verify the mate-rial properties provided by the vendor. Vendor data reported the roomtemperature conductivity and specific heat to be 0.19 Btu/ft h F(0.33 W/m2 K) and 0.36 Btu/lbm F (1500 kJ/kg K), respec-tively. However, the VPI measurements yielded different virgin ma-terial properties than the vendor supplied data, 0.135 Btu/ft h F(0.23 W/m2 K) and 0.47 Btu/lbm F (1959 kJ/kg K) for thermalconductivity and specific heat, respectively. As a result, for pre-liminary predictions conducted before the intumescent model de-velopment, the VPI data were used. The VPI thermal propertiesprovided reasonable agreement for the hypersonic aerothermal re-sponse data collected in several ground-test programs. When theindependently measured virgin properties were used, the elevatedtemperature properties were backed out from only a backside tem-perature response, leaving uncertainty in the specific properties forthe char, pyrolysis, and virgin materials. Additionally, due to thehighly decomposing behavior of RX2390 at temperatures above200F (93.5C), the temperature range of the data is limited.

When the laser thermal test results with embedded thermocou-ples and real-time radiography were used, it was possible to backout the necessary combination of thermal conductivity and spe-cific heat, shown in Figs. 4 and 5, respectively, while incorporatingthe thermochemical decomposition and intumescence or conductionpath growth. This represents a more rigorous approach for devel-oping thermal properties of decomposing materials. This was ac-complished through the use of transient density measurements andintumescence to validate the thermochemical decomposition predic-tions and ensure that more realistic conduction effects are isolatedas opposed to assuming gross effective thermal properties to includedecomposition. It was also determined that the independently mea-sured thermal property data were suspect for the virgin material. Asa result, vendor supplied virgin thermal properties were assumedfor the intumescent model development. A comparison of the previ-ously assumed properties obtained using laboratory thermal prop-erty data and convective aerothermal test data with only a backsidetemperature response is shown in Figs. 4 and 5. The fundamentalimportance of including the effects of intumescence can be seen on

conduction heat transfer. As shown in Fig. 4, thermal conductivityfor the various decomposition states can significantly affect the ap-plicability of heatshield analytic design models when not accountingfor the relative intumescence behavior in low-shear aerothermal en-vironments. The current approach in CMA is to utilize a weightingfactor between fully charred and virgin states. A more appropriatemethod would be to attempt to understand the thermal propertiesfor each phase of the decomposition process: virgin, pyrolysis, andfully charred. Note that the properties that have been determined arenot necessarily the actual thermophysical material properties. Theyare simply the property values that yielded the best correlation of thethermal response data, given the modeling procedures and assump-tions that have been made. This correlation was achieved throughnumerous iterations on thermal response for the three thermocouplelocations within the material. The model was iterated until the tran-sient density gradients, intumescence, thermal properties (thermalconductivity and specific heat), and corresponding in-depth thermalresponses were accurately predicted through the material.

Elemental CompositionThe elemental composition was determined for use in the ther-

mochemical decomposition model defining the virgin material, char,and pyrolysis gases. The organic composition shown in Table 1 rep-resents the pyrolysis gases passing through the char and mixingwith the boundary-layer gases. The inorganic composition shownin Table 2 represents the fully charred material that remains after de-composition is complete. Percent weight of each element of organic

Table 1 Organic elemental composition

Element wt%

Moisture 7.89Carbon 52.3Hydrogen 5.66Nitrogen



Table 2 Inorganic elemental composition

Element wt%

LOIa 54.51Silica 30.37Sodium 52.15Sulfur 9.22Aluminum 8.26aLoss on ignition (organic constituents).

Fig. 6 TGA at 50C/min.

and inorganic composition are required to determine the compo-sition of the pyrolysis gases. Given the composition, the pyrolysisgas enthalpy is determined, assuming thermochemical equilibrium,with the ACE81 computer code.13

TGAIn addition to the characteristic thermal property measurements,

thermodynamic decomposition (mass loss) as a function of temper-ature rise rate or heating rate was measured. These measurementsare known as TGA and represent the outgassing that occurs when thetemperature of a material exceeds reaction temperatures of the com-ponents. This information is used to define decomposition kineticswhere specific coefficients are developed to model the intumescentheatshield material decomposition response.

Figure 6 provides the peak heating rate TGA data taken fromtests conducted at two heating rates. Note that there are essentiallyfour reactions that must be specifically modeled to ensure an accu-rate characterization of the internal decomposition. The peak reac-tion rate of 0.17%/F for RX2390 occurs at approximately 600F(316C) with fairly substantial reactions occurring at even lowertemperatures. The current Arrhenius model used for this researchaccounts for four reactions all occurring below 1500F (816C).A fifth reaction appears to be occurring above 2000F (1094C),but this is likely the result of small leaks within the TGA apparatuswherein the material sample is exposed to oxygen within the air. Be-cause the thermal responses of interest for the missile applicationsinvestigated remained below 1500F (816C), it was determinedthat the current four reaction model was sufficient.

Intumescence Material Model Development and ValidationOverview

The two test facilities used to evaluate material performance ex-perimentally represent a broad range of aerothermal environmentswith the intent of quantifying a variety of material behavior param-eters. The test facilities utilized include the LHMEL for in-depthmaterial thermodynamic response and the NASA Hot Gas Test Fa-cility (HGTF) was for a realistic hypersonic convective environmentresponse. These test facilities have capabilities to either reproduceor simulate some specific flight environment or effect. Importancehas been placed on identifying the appropriate experimental facilityand method to obtain the physical response necessary to separateand quantify phenomena of interest.

Laser Test Facility and Intumescence Model DevelopmentThe LHMEL is located in Dayton, Ohio, and maintains two car-

bon dioxide laser systems. LHMEL-1 is a 15-kW continuous waveelectric discharge coaxial laser (EDCL) and the LHMEL-2 is a150-kW continuous wave EDCL. The LHMEL-1 was used for thisresearch effort. The laser beam is delivered and reflected to thetarget sample through the use of mirrors. The sample is attached tothe holding fixture where the real-time radiography x-ray head is lo-cated. An exhaust system is in place to help evacuate pyrolysis gasesduring testing. This test facility provided a means of quantifying thetransient intumescence and accompanying material decompositiondecoupled from mechanical erosion due to shear. Through the useof these measurements and corresponding in-depth thermocoupledata, the numerical model of the heatshield in-depth thermochemi-cal behavior was developed and validated.

Test SetupThe test samples were attached to the holding fixture as shown

in Fig. 7. This rectangular sample is 1.5 2.5 in. The laser beamwas split and adjusted to impart the desired heat load on the sample.The radiography head was located above the sample looking down.The thermocouple plug (evident in Fig. 7) was located in the centerof the sample. The thermocouple plug configuration is shown inFig. 8 and involves the use of 36-gauge thermocouple wire andbeads located at three different depths within the material. Thisprovides for an in-line thermal response of the material as a functionof time. The fixed x-ray reference plane was selected to be the0.05-in. thermocouple bead location based on predicted thermalresponse and expansion and provided the in-depth density changeand intumescence. Measurements are taken throughout the thicknessof the sample but are centered about this reference plane becausemost of the response is expected to occur in this area.

Thermal EnvironmentTwo heat fluxes were imparted to the samples representing Mach

4 and 5 type environments. These heat fluxes were imparted using22 Btu/ft2 s (25 W/cm2) and 66 Btu/ft2 s (75 W/cm2), respectively,to induce the desired material thermal response. A 2-in.-diam beamwidth was used that minimized two-dimensional conduction effectsat the sample edges.

Fig. 7 Assembled sample configuration.

Fig. 8 Thermocouple plug configuration.



Posttest ResultsTypical pre- and posttest photos of an RX2390 material sample

are provided in Figs. 9 and 10. An example of the resulting real-timeradiography used for defining transient density is provided in Fig. 11.Figure 11 shows the pre- and posttest positions of the relative heat-shield sample surface. Along with the radiography photographs, theLHMEL test facility digitized the transient densities as a functionof position within the material. When the density through the thick-ness is qualitatively defined as a function of time and this responseis correlated to the embedded thermocouple response, the densityas a function of temperature and heat rate can be obtained. Figure12 provides an example of the pre- and posttest density gradientsthrough the material. The resulting weight and depth measurementsare provided in Table 3. The weight measurement was obtained tovalidate the analytic model decomposition predictions of mass lossand in-depth decomposition. The pre- and posttest thickness mea-surements provide the total intumescence or swell, which can beused in conjunction with the real-time radiography to validate theintumescence model. The lower heating rate, test 1, resulted in ap-proximately one-half of the total mass loss that the higher heating

Fig. 9 Posttest material response.

Fig. 10 Sectioned view of material sample posttest.

Fig. 11 Example of real-time radiography.

Table 3 Pre- and posttest measurements

Test 1 Test 2Measurement Pretest Posttest Change Pretest Posttest Change

Weight, g 107.7 106.1 1.6 108.4 105.3 3.2Thickness, in. 0.4 0.53 0.13 0.4 0.56 0.16

Fig. 12 Density gradient through sample.

Fig. 13 Intumescence model functions.

rate test 2 experienced. However, the total intumescence was verysimilar for each test.

The baseline intumescence model was developed using the tran-sient data collected on the two thermal tests conducted at LHMEL.Because two heating conditions were utilized and the material ex-periences a range of heating conditions in-depth, the heating ratedependency of intumescence could be determined. The model de-velopment was initiated by using the baseline intumescence modeldepending solely on decomposition state and comparing in-depththermal responses at each of the thermocouple stations. The in-tumescence function was modified until the transient positions ofheated surface, the 0.05-in. (0.13-cm) thermocouple bead, and in-depth heat-affected region (decomposition and virgin material in-terface) were matched. Matching rates, rather than final positions,provided an added fidelity to the analytic model. Once these intu-mescence trajectories were matched, the surface temperature andin-depth thermocouple response were correlated through modifica-tion of temperature-dependent properties. After a best match wasselected for the relative thermal properties, the same analytic modelwas used to predict heatshield behavior in a realistic convective hy-personic high-altitude environment for which significant test datahad been previously collected. Application to a convective environ-ment quantified the usefulness of the model as well as the use of theLHMEL test facility to develop intumescence material properties.The analytic model was then used to predict thermal response fora supersonic sea-level (high-shear) convective environment to eval-uate applicability for high-shear conditions. The results of thesepredictions provided indications of accuracy, applicability, and nec-essary model refinements for future research.

The resulting char state and heating rate dependency factorsare provided in Fig. 13. These relationships represent the best fit



combination for matching the LHMEL test conditions. However,through additional refinement and more accurate measurement ofthermal properties for the various pyrolysis regions, these fits may beimproved. Note that whereas these curves are considered a baseline,they do provide insight to the relative influence and trends associatedwith the intumescence phenomena. For example, when the char statefactor is considered, it is evident that the majority of intumescenceoccurs in the initially pyrolysizing region where decomposition isbelow 32% weight loss. Therefore, the higher charred region ex-periences less intumescence. However, intumescence behavior ishighly dependent on material formulation and flow chemistry. Theuse of different materials may lead to different intumescence prop-erties. The lower intumescence of the charred region was againobserved during the hypersonic convective thermal testing where itwas seen that an insignificant level of additional swell was expe-rienced between 200 and 300 s of testing. The additional 100 s ofheating caused additional decomposition of the more fully charredregions but little additional intumescence. The addition of the heat-ing rate factor was a result of realizing that with the use of only charstate to quantify intumescence, a reasonable match of intumescenceand in-depth thermal response could not be obtained for the widerange of thermal environments. An iterative process was used to ob-tain reasonable agreement with each LHMEL test condition. It wasobserved that below heating rates of approximately 72180F/min(40100C/min), very little intumescence occurred. When the tran-sient radiography from tests 1 and 2 were used, the thermocouplestation at 0.05 in. (0.13 cm) began moving when the heating ratereached and exceeded 180F/min (100C/min). The correspond-ing heating rate at the 0.05-in. (0.13-cm) station coupled with thetransient radiography provided a means of determining the relativeheating rate and temperature at which the thermocouple motion ini-tiated. By adjustment of this heating rate dependency, the resultingintumescence factors shown in Fig. 13 were determined and providea reasonable match for both laser thermal tests as well as the hyper-sonic convective thermal tests of test 3. It is possible that the heatingrate dependency is a result of higher pyrolysis gas generation ratesand limited gas transfer causing the localized material to puff upand initiate expansion, after which intumescence is reduced and isless dependent on heating rate. These concepts will be investigatedin future research to expand the model applicability to a wider rangeof convective aerothermal and radiative environments.

The predicted transient intumescence as compared to data col-lected from the transient radiography is provided in Fig. 14. Identi-fied in Fig. 14 are the surface position, in-depth decomposition, andthe 0.05-in. (0.13-cm) thermocouple position as a function of time.This provides a comparison of the predicted and measured surfaceposition and thermocouple position due to intumescence. The datawere collected from video of x-ray data. Good agreement is obtainedfor the surface motion using the proposed intumescence properties.Some variation in data exists due to unevenness in the intumescedsurface. A reasonable match was obtained for the in-depth decompo-sition, qualitatively assuming the ability to distinguish a 5% densityloss in the radiography. The analytic model appears to overpredictthe initial decomposition rate moving in-depth. This could be a resultof uncertainties in thermal properties or inaccuracies in identifyingthe decomposition front from the radiography.

Fig. 14 Intumescence behavior predictions vs data.

Fig. 15 Test 1, overall thermocouple response predictions vs data.


The 0.05-in. (0.13-cm) thermocouple motion shows very goodagreement, suggesting that not only total growth but also expansionrate is being modeled with reasonable accuracy. The initiation ofthermocouple motion was noticeable for each of the tests at approx-imately 1720 s with a measured temperature of 250260F (121127C). This response was identified for both the radiative heatingenvironment imparted using the LHMEL test facility as well as thehypersonic convective environment imparted by the NASA HGTF.The thermocouple response appears to be disrupted at this time andtemperature. This response provides an indication of intumescenceand decomposition below the thermocouple.

Figure 15 provides a comparison of predicted temperatures withmeasured test data for the lower heating rate laser test, test 1, inwhich a heating rate of 22 Btu/ft2 s (25 W/cm2) was imparted tothe sample surface. Good agreement was obtained for surface tem-perature between the model predictions and optical pyrometer mea-surements with peaks of approximately 2000F (1093C). As can beseen in Fig. 15, a very good match was obtained for in-depth thermalresponse throughout the test until the thermocouple measurementand prediction intersect at approximately 34 s. However, because ofmovement of the thermocouple bead, quality of the measurementis degraded for times greater than 17 s. This effect becomes moresignificant later.

Note that a series of trades were performed during the thermalresponse predictions to define sensitivities to node size in the finitedifference mesh resolution. Previous methods suggested node thick-nesses on the order of 0.0100.005 in. (0.0250.013 cm) sufficientlycaptured the thermal gradient through the decomposing heatshieldmaterial. As a result of incorporating the intumescence model, itwas determined that mesh resolution of 0.0020.0005 in. (0.0050.0013 cm) was required to define the thermal gradients accuratelythrough the char and pyrolyzing regions. With additional statisticallysignificant testing, better definition of thermodynamic response andcorresponding sensitivities to mesh and material properties can bedeveloped.

Figure 16 provides the in-depth thermocouple response predic-tions for the higher heating laser test, test 2, as compared to data. Al-though not shown in Fig. 16, the surface temperature measurement



Table 4 Mass loss comparison of predictions and measurements

Test 1 Test 2Measurement Data Prediction Difference, % Data Prediction Difference, %

Posttest weight, g 1.60 1.21 32 3.2 1.40 220Modified model weight, g 1.60 1.4 13 3.2 2.6 19

Fig. 17 Sectioned view of in-depth decomposition.

and predictions were in good agreement with peaks of approxi-mately 2700F (1482C). As can be seen, at approximately 17 s, themeasured thermal response drops and recovers its increasing slope.As a result, the 0.05-in. (0.13-cm) thermocouple response does nottruly represent the 0.05-in. (0.13-cm) layer within the decomposingmaterial. Therefore, the temperature at this location is not accuratelymeasured and prediction should be higher than the data throughoutthe remainder of the test. Because significant intumescence did notoccur at the 0.15-in. (0.38-cm) and 0.25-in. (0.64-cm) thermocou-ple positions, the thermal response measurements are smooth. Forthe assumed pyrolyzing region thermal properties and intumescencefactors, a reasonable match is obtained for these thermocouple mea-surements. With additional iteration of thermal properties, a bettermatch could be obtained throughout the test. However, the primarygoal of this effort is to develop analytic models to account for intu-mescence. Future efforts will be directed toward better quantifyingin-depth thermal properties as a function of decomposition and tem-perature. The ability to model intumescence also provides a meansof more accurately decoupling and quantifying thermal propertiesof an intumescing material.

Table 4 contains the predicted mass loss results as compared tothe measured values. The initial predictions do not include observedtwo-dimensional effects due to conduction and increased decompo-sition outside the laser beam diameter. The second set of predic-tions was used to attempt to account for this effect and, as expected,brought predictions and data within reasonable accuracy. Note thatthe TGA model was developed for a maximum temperature of ap-proximately 1500F (816C). For the higher heating rate where sur-face temperatures approached or exceeded 2700F (1482C), sur-face reactions may have occurred and resulted in additional materialremoval.

Hypersonic Convective Intumescence Predictions and DataThe resulting predicted thermal response and intumescence

agreement obtained for the two laser heating tests led to the ap-plication of the analytic model and corresponding intumescenceproperties to the hypersonic convective heating test environment.The Mach 6 and 8 environments of interest were represented byconstant cold wall heat flux values of 6 and 8.5 Btu/ft2 s (6.8and 9.6 W/cm2), respectively. The total temperatures delivered bythe test facility were 2300F (1260C) for the Mach 6 conditionand 3000F (1649C) for the Mach 8 condition. For the Mach 6test case, the surface temperature response reached approximately950F (510C), with the average backside thermal response reaching160F (71C). The resulting in-depth thermochemical decomposi-tion is shown in Fig. 17 for the Mach 6 test condition. Note that

Table 5 Ablation measurements for Mach 6 testa

Measurement Material, in.

Pretest thickness 0.3Char depth 0.13Pyrolysis depth 0.09Virgin material depth 0.2Posttest thickness 0.42SHOA total ablation 0.1aAverage intumescence is 120%.


a significant level of internal decomposition occurred during thetest. The material maintained a relatively strong char. Table 5 pro-vides a summary of decomposition as measured after the test. Thevalue of total ablation for the test sample was 0.10 in. (0.25 cm) (asdefined by the SHOA procedure). This highly decomposing mate-rial provided significant thermal performance in the form of limit-ing backside temperature rise when compared to low-density, lowthermal conductivity materials. Note that where volume constraintsare more important than weight constraints, intumescing materialperformance should be investigated. When weight constraints areequal or more severe than volume constraints, decomposing mate-rials become less attractive. However, simply assuming the need forlow-density low thermal conductivity materials can greatly restrictthe potential identification of superior heatshield materials.

The predicted thermal response and intumescence agreement ob-tained for the two laser heating tests led to the application of theanalytic model and corresponding intumescence properties to thehypersonic convective heating test environment. The resulting pre-dictions as compared to data are provided in Figs. 18 and 19. As canbe seen in Fig. 18, the surface temperature prediction matches rea-sonably well for the initial 50 s. However, the curves deviate slightly,suggesting the need for additional understanding of the char statedensity and thermal properties. Good agreement is obtained for thein-depth thermal response matching both magnitude and slope. Thiswas one of the primary goals of developing the intumescence model.The necessity of better predicting the heat transfer and resulting ther-mal response slope was evident when applying the analytic model tolonger heating times seen in actual flight conditions. Original modelpredictions gave significantly different slopes for the test time andwould actually predict excessively higher thermal response and re-sulting excessive heatshield requirements for continued heating. Thesame thermocouple event (discontinuity at approximately 60 s) canbe seen as in the laser tests at a similar decomposition state and



Fig. 19 Test 3, in-depth thermocouple response predictions vs data.

Fig. 20 Test 3 earlier and new model prediction comparisons.

temperature. When in-depth heating rate predictions and measuredthermal response are used, an indication of motion and onset of de-composition was obtained. Similar to the lower heating rate laser testanalytic results, the predicted 0.05-in. (0.13-cm) thermal responseintersects the measurement and suggests that after the intumescenceregion is initiated and the thermocouple bead detaches from the sur-rounding material, the quality of the thermal response is question-able. Figure 19 shows the same results with the scale changed tobetter illustrate the comparison of the predicted and measured re-sponse. Figure 20 provides a comparison with the previous modelpredictions (using the standard CMA properties identified earlierin Figs. 4 and 5) and shows the improvement obtained by model-ing intumescence. The in-depth thermocouple responses are shownalong with the previous and new model predictions. As can be seen,the previous model predictions gave thermal response slopes signif-icantly different than test data. This model, using the standard CMAmethod, was the best fit that could be obtained (with only backsidetemperature data) and suggested the need for the more detailed in-tumescent modeling capability. The test data indicated a decreasingslope or plateau and gradual increase in temperature at the 0.25-in.(0.64-cm) thermocouple position. The previous model predicted arelatively constant temperature rise rate, suggesting an underpredic-tion for early test times and an overprediction for longer test times.(Note that the model had been developed to best match results at theend of the 300-s test.) The impact of the slope can be expressed asa function of predicted thermal protection requirements for flight-test times longer than those experimentally induced. A significantincrease in thermal protection and corresponding weight would berequired, adversely affecting system performance. However, the newmodel predictions clearly demonstrate a better match with the tran-sient thermal response of the in-depth thermocouples. By more ac-curate prediction of the transient thermal response, the model appli-cability is extended to actual flight environments, providing accuratethermal response and heatshield predictions for a range of aerother-mal environments, flight times, and geometric configurations.

SummaryIn summary, the objective of this research was to initiate the first

step of incorporating the effects of intumescence on the in-depth en-ergy balance as defined in the CMA. Previous methods to accountfor this effect on heat transfer in decomposing materials includedeffective thermal properties and an attempt to correlate a classicalthermal expansion model. These approaches were limited becausethey did not attempt to model the phenomena actually occurringbut instead attempted to lump unmodeled phenomenon into a singleterm. Some of the phenomena that must be specifically modeledinclude pyrolysis gas generation, intumescence, temperature- anddensity-dependent thermal properties, and decomposition energies.The addition of modeling intumescence provided a previously un-available capability to account for material expansion during ther-mochemical decomposition and its relative effect on in-depth con-duction. For external thermal protection systems exposed to extremethermal environments, a significant level of thermal performance canbe attributed to the conduction path growth and resulting reductionin heat transfer to temperature critical substructures. The intumes-cence model was initially derived through the use of high-enthalpyaerothermal environments with minimal aerodynamic shear contri-bution. These conditions induced sufficient intumescence to identifyspecifically the relative effects on in-depth heat transfer through theuse of embedded thermocouples. Real-time radiography providedthe method of validating in-depth intumescence as a function of de-composition state. Coupling the embedded thermocouple data withintumescence provided for the heating rate dependency. The analyticapproach included a mathematical model coupled to a material prop-erty table of intumescence as a function of char state and heating rate.The resulting model was then successfully applied to a low-shearhypersonic aerothermal environment in which significant thermaland intumescence data was previously obtained. Intumescence andin-depth thermal response predictions showed good agreement withmeasured data and further validated the models application to ahypersonic convective aerothermal environment.

Following is a list of recommended future research that wouldadd significantly to the analytic modeling capability of heatshielddesign. The current modifications to CMA of intumescence couldbe used as the foundation for adding these capabilities.

1) Mechanical shear: It is recommended that the ability to modelmechanical shear removal of material as a function of char state andchar strength be incorporated into the CMA modeling approach.This additional phenomenon would complete the current goal toenhance the CMA code and accommodate much of the heatshielddesign and optimization requirements for current supersonic andhypersonic thermal protection systems.

2) Intumescence model refinement: Additional research is rec-ommended to refine the intumescence model. These efforts shouldbe devoted to refining the understanding of intumescence and vali-dating the analytic approach for a wide range of aerothermal envi-ronments. These environments should include commercial buildinginsulation designs where a significant benefit in optimization couldbe realized. The LHMEL test facility should be utilized for a statis-tically significant number of test samples to better quantify in-depthdecomposition, intumescence, and thermal response.

3) Test facility measurement capabilities, real-time radiogra-phy: It is also recommended that research be devoted to developreal-time radiography measurement capability that can readily beadapted for use at any aerothermal test facility. This capability cou-pled to the use of embedded thermocouples significantly increasesthe understanding of material response and can greatly reduce theoverdesign methodology and increase system performance throughoptimization.

4) Test facility measurement capabilities, pyrolysis gas injectionrates and species: Methods of quantifying pyrolysis gas injectionrates and mechanical erosion rates should be developed and incor-porated into aerothermal test facilities. These results could be usedto validate the transient thermochemical decomposition and corre-sponding mass loss predictions for various heatshield materials. Ofadditional interest is the ability to measure the individual mass in-jection species and injection rates within the boundary-layer flow,



as well as the resulting boundary-layer thickness increase. Thesemeasurements would greatly enhance the analytic model validationand increase the model application.

5) Transient skin friction and hot wall effects: Coupled to themeasurements and analytic model enhancements just suggested isthe ability to measure skin friction on intumescing and ablatingheatshields under aerodynamic heating conditions. Although thiswas specifically addressed during the NASA HGTF aerothermal testprogram, this capability should be developed for higher-shear and-enthalpy test facilities such as the U.S. Naval Air Warfare CenterT-Range, U.S. Air Force Holloman High Speed Test Track, ArnoldEngineering Development Center, as well as other aerothermal testfacilities. This ability would provide the transient hot wall effectsand external heatshield influence on the aerodynamic drag modelscommonly developed in cold flow wind tunnels.

AcknowledgmentsThis research was sponsored by the U.S. Army Aviation and Mis-

sile Research Development and Engineering Center, Redstone Ar-senal, Alabama. The authors express gratitude to Shi T. Wu, Dis-tinguished Professor at the University of Alabama in Huntsville,for his guidance in completion of the research and documentationefforts, and to Warren Jaul from the U.S. Naval Air Warfare Centerand Joseph Raymond of ITT Industries for their significant contri-butions to the completion of the test and evaluation program thatprovided the necessary data to support model development.

References1Rohsenhow, W. M., and Hartnett, J. P., Handbook of Heat Transfer,

McGrawHill, New York, 1973, Secs. 16-34 and 16-39.2Russell, G. W., Rembert, M., Strobel, F. A., and Jaul, W. K., Devel-

opment of High Performance Thermal Protection Systems for HypersonicMissiles, Proceedings, RLV/SOV Airframe Technology Review, NASA Lan-

gley Research Center, Hampton, VA, 2002, p. 4.14.3Aerotherm Charring Material Thermal Response and Ablation Program

(CMA87S), Acurex Rept. UM 87-13/ATD, Aerotherm Div., Acurex Corp.,Mountain View, CA, Nov. 1987.

4Schlichting, H., Boundary Layer Theory, McGrawHill, New York,1979, p. 24.

5Doyle, C. D., Kinetic Analysis of Thermogravimetric Data, Journal ofApplied Polymer Science, Vol. 5, No. 15, 1961, pp. 285292.

6Koo, J. H., Thermal Characteristics Comparison of Two Fire ResistantMaterials, Journal of Fire Sciences, Vol. 15, No. 3, 1997, pp. 203221.

7Shih, Y. C., Cheung, F. B., and Koo, J. H., Theoretical Modeling ofIntumescent Fire-Retardant Materials, Journal of Fire Sciences, Vol. 16,No. 1, 1998, pp. 4671.

8Reynolds, R. A., Russell, G. W., and Nourse, R. W., Ablation Perfor-mance Characterization of Thermal Protection Materials Using a Mach 4.4Sled Test, AIAA Paper 92-3055, June 1992.

9Moyer, C. B., and Rindal, R. A., An Analysis of the Coupled ChemicallyReacting Boundary Layer and Charring Ablator, Part IIFinite DifferenceSolution for the In-Depth Response of Charring Materials Considering Sur-face and Energy Balances, Aerotherm Rept. 66-7, Pt. 2, Vidya Div., ITEKCorp., Palo Alto, CA, Nov. 1968; also NASA CR-1061, Nov. 1968.

10Russell, G. W., Analytic Modeling and Experimental Validation ofIntumescent Behavior of Charring Heatshield Materials, Ph.D. Disserta-tion, Dept. of Mechanical and Aerospace Engineering, Univ. of Alabama,Huntsville, AL, June 2002, p. 45.

11Reynolds, R. A., Nourse, R. N., and Russell, G. W., Aerothermal Ab-lation Behavior of Selected Candidate External Insulation Materials, AIAAPaper 92-3056, 1992.

12Russell, G. W., Evaluation of Decomposition Kinetic Coefficients fora Fiber-Reinforced Intumescent Epoxy, AIAA Paper 93-1856, June 1993.

13Aerotherm Chemical Equilibrium Computer Program (ACE81),

Acurex Rept. UM 81-11/ATD, Aerotherm Div., Acurex Corp., MountainView, CA, Aug. 1981.

T. LinAssociate Editor

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