numerical study on abnormal heat flux augmentation in high

Numerical Study on Abnormal Heat Flux Augmentationin High Enthalpy Shock Tunnel (HIEST)*

Tomoaki ISHIHARA,1) Yousuke OGINO,1) Naofumi OHNISHI,1) and Hideyuki TANNO2)

1)Department of Aerospace Engineering, Tohoku University, Miyagi 980–8579, Japan2)Kakuda Space Center, Japan Aerospace Exploration Agency, Miyagi 981–1525, Japan

Unexpected heat flux augmentation in a free-piston high-enthalpy shock tunnel (HIEST) was numerically analyzed.Since a previous experimental study implied that the radiation heating from the shock layer caused the augmentation, athree-dimensional thermochemical non-equilibrium CFD code including radiation transport calculation in the shock layerwas developed. This calculation was conducted under the following models: 1) Radiation heating from the air species inthe shock layer was calculated by a solving radiative transport equation using tangent slab approximation; and 2) Radiationheating from impurities such as carbon soot and metal particulates, which could be included in the upstream test gas, wascalculated by assuming the shock layer as a grey body with averaged shock layer temperature for a trial calculation. Thecalculations were performed at the stagnation enthalpy and stagnation pressure from 7 to 21MJ/kg and 31 to 55MPa,respectively. For air species radiation, radiative heat flux was too small to contribute heat flux augmentation. On the otherhand, for grey body assumption, we could find that abnormal heat flux augmentation could be expected by "�T 4

ave for anengineering technique, where ¾ denotes the emissivity ¾ = 0.132 and T 4

ave was the average shock layer temperature.

Key Words: Hypersonic Flows, Shock Tunnel, Aerodynamic Heating, Radiation, Computational Fluid Dynamics

Nomenclature

B� : Plank function at a given wavelengthCs: mass fraction of species sc: speed of lightD: diameter of test modelH: total enthalpyh: Planck functionI� : radiant intensity at a given wavelengthk: Boltzmann constantM: Mach numbern: number densityq: heat fluxr: direction of radiation propagationR: radius of test model

Re: Reynolds numbers: coordinate along the wall-normal directionSt: Stanton numberTt: translational-rotational temperatureTv: vibrational-electronic temperature¾: emissivity

�� : absorption coefficient at a given wavelength: wavelength¤: angle between the direction of radiation propagation

and the wall normal directionμ: densityº: angle shown in Fig. 3·: Stefan-Boltzmann constant+: solid angle

Subscripts0: stagnated condition

1: free stream conditionave: averagecalc: calculatedconv: convectiveexp: experimentmax: maximumrad: radiatives: species

1. Introduction

In designing a thermal protection system for atmosphericentry vehicles, accurate prediction of aerodynamic heatingis crucially important. The High Enthalpy Shock Tunnel(JAXA-HIEST) at Kakuda Space Center aims to providethe required aerothermodynamics data on scale models ofvarious space vehicles in the hypersonic flow region. InFig. 1, the heat flux data along the centerline of the Apollocommand module (CM) 6.4% scale model measured inHIEST1) are compared with the convective heat flux profilesgiven by a thermochemical non-equilibrium computationalfluid dynamics (CFD) code.2) When the heat flux data isscaled by St � ffiffiffiffiffiffiffiffiffiffiffiffi

Re1D

pwhere Re1D is the Reynolds num-

ber based on the typical model dimension D, it is known thatthe convective heat flux should fall on a single curve for alaminar flow. Although the computed convective heat fluxprofiles fall on a single curve reasonably well, the experi-mental data obtained in HIEST show higher heat flux values.Moreover, one can find that the difference between the meas-ured heat flux and the corresponding heat flux given by CFDbecomes larger as the stagnation enthalpy of the test flow

© 2015 The Japan Society for Aeronautical and Space Sciences+Received 3 September 2014; final revision received 5 March 2015;accepted for publication 22 June 2015.

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becomes higher. We note that such an anomalously higherheat flux as discussed above seems to be observed commonlyin other high enthalpy shock tunnels.3–8) The effect of aug-mentation caused by the turbulence and surface catalysiswere examined. By assuming fully turbulent flow or thesuper catalytic wall, calculated convective heat flux canreach the experimental values. However, the distributioncould not be reproduced. The cause of such higher heat fluxhas not been clearly determined yet. In the HIEST experi-ments, such abnormal heat flux augmentation is larger thanthe one in other facilities. Therefore, the data in the HIESTexperiments is useful for examining abnormal heatflux aug-mentation.

In the previous numerical study,2) we calculated the con-vective heat flux profile with a Baldwin-Lomax algebraic tur-bulence model.9) We assumed fully turbulent flow to deter-mine whether or not turbulence could be the cause ofhigher heat flux. The computed heat flux increased onlyslightly in the shoulder region in the leeward side, whilethe experimental data indicated that the heat flux is increasedrather in the entire surface. Therefore, it was difficult to ex-plain the higher heat flux profile obtained in the experimentby the effect of turbulence.

In order to clarify the cause of higher heat flux, other aero-dynamic heating measurements on small hemispheres werecarried out in HIEST.10) The anomalously higher heat fluxwas insignificant for small models at the same stagnation en-thalpy for which the higher heat flux did appear for the Apol-lo CM test model. In addition aeroheating measurements on aflat plate were conducted with optical filters, which can

measure radiation and convective heat flux independently.11)

Figure 2 shows the time history of pressure and heat fluxat the stagnation point on the flat plate (shown in Fig. 7 inTanno et al.11)). One can find that the radiation heat flux isdelayed compared to the rising time of pressure and total heatflux, which was measured by thermocouples without opticalwindows. It indicates that the body surface received radiationafter developing the shock layer. However, the source of theradiation is yet unknown.

The objective of the present paper is to clarify the mecha-nisms of the radiative heating and obtain an engineeringtechnique to estimate the abnormal heat flux augmentationin HIEST. We focus on following two radiation heatings inthe shock layer as the source of such anomalously higherheat flux: 1) The radiation heating from air species, and 2)The radiation heating from impurities like soot and metalwhich can be included in the test gas under the high stagna-tion temperature condition. First, we calculate the radiationheat flux from air species in the shock layer to show whetheror not it can be the source of the enhanced heat flux. Then,we show some evidence that suggests radiation from impuri-ties involved in the test flow can explain the elevated heatflux. However, the chemical species and amount of impuri-ties are unknown. In this study, we assume the impuritiesas a grey gas for a trial calculation. In the following, numer-ical methods are described in Sec. 2, numerical conditionsare shown in Sec. 3, and obtained results and related discus-sions are given in Sec. 4. The conclusions are finally stated inSec. 5.

2. Numerical Methods

2.1. Flowfield calculationThe governing equations for the flow field calculation are

the three-dimensional Navier-Stokes equations accountingfor thermochemical non-equilibrium. We employ Park’stwo-temperature thermochemical model.12) Five neutral airspecies (O, N, NO, N2 and O2) with the following chemicalreactions are considered,

O2 þM $ Oþ OþM;

N2 þM $ Nþ NþM;

(a)

(b)

Fig. 1. Comparison of the calculated convective heat fluxes and the meas-ured data2); (a) AoA ¼ 0 deg., and (b) AoA ¼ 30 deg.

Fig. 2. Time history of surface pressure and heat flux at stagnation pointon the flat plate.11)

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NOþM $ Nþ OþM; ð1ÞN2 þ O $ NOþ N;

NOþ O $ O2 þ N;

where M stands for collision partners. The forward rate coef-ficients are given by Arrhenius form, and the backward ratecoefficients are determined by the equilibrium constant. Thedetails of forward reaction rates and equilibrium constant aregiven in Park.12) The translational-vibrational relaxation termis given by the Landau-Teller model with Park’s two modi-fications12); that is, introducing the limiting cross-section forthe relaxation time of Millikan and White, and the bridgingformula for the Landau-Teller equation. A preferential disso-ciation model is also included in the calculation.

The molecular viscosity for each chemical species is givenby Blottner’s model13) and the thermal conductivity byEucken’s relation.14) The transport properties for the gasmixture are obtained from Wilke’s semi-empirical mixingrule.15) The diffusion coefficients are assumed to be constantfor all air species with a constant Schmidt number of 0.5.

The numerical method is based on the cell-centered finitevolume scheme. The convective numerical flux is calculatedusing the SLAU scheme.16,17) The viscous flux is evaluatedby a central difference scheme. We employ the MUSCL ap-proach18) to attain second-order spatial accuracy. In the timeintegration, the LU-SGS implicit method19) is employed. Thediagonal point implicit method is utilized in order to improvestability in the integration of the source terms.20)

2.2. Radiation calculationThe radiative transfer equation is solved by tangent-slab

approximation.14) In a one-dimensional local-thermodynam-ic-equilibrium medium, the radiative transfer equation is giv-en by

l@I�

@s¼ �� ðB� � I� Þ; ð2Þ

where l ¼ cos ’. The coordinate system is shown in Fig. 3.Radiation intensities at each cell boundary are obtained bysolving Eq. (2) along only the cells that are normal to thewall surface in the tangent-slab approximation. The Planckfunction, B� , is a function of temperature T and is given by

B� ¼ 2hc2

�5

expð�hc=k�T Þ1� expð�hc=k�T Þ: ð3Þ

The spectral radiation heat flux q� is obtained by integratingover the solid angle,

q� ¼Z4�

I� ld� ¼Z 2�

0

Z �

0

I� l sin ’d’d� ¼ 2�

Z 1

�1

I� ldl:

ð4ÞThe total radiation heat flux qrad is then given by

qrad ¼Z�

q�d�: ð5Þ

The flowfield calculation and radiative transport calcula-tion are uncoupled. The radiative heat flux is calculated fromthe solution of steady-state flowfield.2.2.1. Radiation from air species in shock layer

For calculating air test gas radiation, the absorption coef-ficient �� shown in Eq. (2) is expressed as a sum of those forindividual species in the form of

�� ¼X

sns��f; ð6Þ

where s indicates radiation-contributing chemical speciessuch as O, N, NO, O2 and N2. The wavelength region from750 to 15,000Å is considered with the local thermodynamicequilibrium assumption. The wavelength points are 10,000.The number density of each species ns is obtained by thesteady-state flowfield. The cross-section values ��s are pre-pared in advance curve-fitted formulae as follows,

��s ¼ expAs

�1

zþ As

�2 þ As�3 lnðzÞ þ As

�4zþ As�5z

2

!; ð7Þ

where z ¼ 10;000=Tv. The five parameters As�1{5 are calcu-

lated using a multi-band model.21)

2.2.2. Radiation from particulatesIn these calculations, radiative heat flux is computed

by utilizing tangent slab approximation employed in theevaluation of radiation from air species in the shock layer.However, the chemical species of impurities in test flowand the amount of impurities are unknown, and therefore,we cannot determine the radiation intensity from impurities.In the HIEST experiments, strong emission is observed afterdeveloping the shock layer. So we assume the impurities as agrey body at the average shock layer temperature. The aver-age temperature is determined along the wall-normal direc-tion in between the end of the relaxation region behind theshock wave and the edge of the boundary layer. The Planckfunction B� multiplied by the emissivity ¾ is set as a boun-dary condition of Eq. (3). The emissivity ¾ is determined atthe stagnation point in order to reproduce the experimentalheat flux. The details are discussed in Sec. 4.2.

3. Numerical Conditions

3.1. Upstream and wall boundary conditionsTable 1 summarizes the upstream conditions for the flow

field calculation over the Apollo CM test model1) and smallprobes.10) These values were determined using a JAXA in-house code.22)

For the wall boundary conditions, an isothermal and fully-catalytic wall are assumed for all cases. Figure 4 shows theFig. 3. Coordinate system for tangent-slab approximation.


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dependence of the surface catalysis on the convective heatflux at Shot No. 1783 where the stagnation enthalpy is high-est, and the surface catalysis is likely to affect the convectiveheat flux in all cases in Table 1. One can find that the differ-ence is ignorable. The dependence of the wall temperature onconvective heat flux is also investigated. Figure 5 shows theheat flux at the wall temperatures of 300, 500 and 700 K. Thedifferences are negligibly small. Since the wall temperaturebecomes about 500K in the experiment, the wall temperatureis set to be 500K.3.2. Test models and computational grids

Three different test models, namely the Apollo CM modeland two probe models of different size, referred to asD50R100 and D20R10, are employed in the heat flux meas-urements conducted in HIEST.1,10) Figure 6(a) shows theApollo CM 6.4% scaled test model, which has a diameterof 250mm and a nose radius of 300mm, and is the largestamong the models. On the other hand, small probe model

D50R100 shown in Fig. 6(b) has a diameter of 50mm anda nose radius of 100mm. Though not shown, small probemodel D20R10 has a similar shape with a diameter of20mm and a nose radius of 10mm.

A typical example of the computational grid for the ApolloCM model at an angle of attack (AoA) of 30 deg is shown inFig. 7. It is a structured mesh having 51 points in the normaldirection from the surface toward the outer boundary, 51points along the surface, and 65 points in the circumferentialdirection. The minimum grid spacing at the wall surface sat-isfies the cell Reynolds number of Recell ¼ 1. Several meshsurfaces are clustered and aligned parallel to the shock waveusing the solution adaptive technique which is critically im-portant particularly when a structured mesh is employed in

Table 1. Upstream conditions for the Apollo CM test model and small probes computed by JAXA in-house code.22)

Shot Test H0 Tt1 Tv1 �1 M1 CO1 CN1 CNO1 CO21 CN21No. model [MJ/kg] [K] [K] [kg/m3]

1781 Apollo 6.849 662.4 679.2 0.01978 6.721 2.45 � 10¹3 4.33 � 10¹12 5.94 � 10¹2 2.01 � 10¹1 7.37 � 10¹1

1782 Apollo 17.275 1861.1 1864.9 0.01686 5.945 7.77 � 10¹2 5.31 � 10¹7 4.78 � 10¹2 1.31 � 10¹1 7.54 � 10¹1

1783 Apollo 21.537 2158.9 2163.1 0.01216 5.890 1.41 � 10¹1 5.61 � 10¹7 3.39 � 10¹2 7.46 � 10¹2 7.51 � 10¹1

1784 Apollo 19.554 2035.2 2038.2 0.01457 5.909 1.09 � 10¹11 2.04 � 10¹6 4.10 � 10¹2 1.02 � 10¹1 7.48 � 10¹1

1785 Apollo 21.059 2143.0 2146.8 0.01315 5.885 1.31 � 10¹1 4.51 � 10¹6 3.60 � 10¹2 8.33 � 10¹2 7.50 � 10¹1

1787 Apollo 8.094 841.7 849.5 0.02643 6.496 3.82 � 10¹3 4.48 � 10¹12 6.03 � 10¹2 1.99 � 10¹1 7.37 � 10¹1

1791 Apollo 6.759 649.7 668.1 0.01919 6.739 2.40 � 10¹3 4.40 � 10¹12 5.93 � 10¹2 2.01 � 10¹1 7.37 � 10¹1

1886 Apollo 13.471 1455.9 1461.8 0.01633 6.108 4.14 � 10¹2 4.20 � 10¹8 5.57 � 10¹2 1.63 � 10¹1 7.40 � 10¹1

1889 D20R10 8.596 908.7 915.8 0.02717 6.440 4.79 � 10¹3 5.82 � 10¹12 6.05 � 10¹2 1.98 � 10¹1 7.37 � 10¹1

1891 D50R100 Apollo 8.318 869.9 877.3 0.02702 6.479 4.14 � 10¹3 4.74 � 10¹12 6.04 � 10¹2 1.99 � 10¹1 7.37 � 10¹1

1893 D50R100 Apollo 20.048 1946.4 1952.3 0.01050 6.013 1.30 � 10¹1 3.30 � 10¹6 3.65 � 10¹2 8.32 � 10¹2 7.50 � 10¹1

(a) (b)

Fig. 6. Test models employed in the HIEST experiments; (a) Apollo CM6.4% scaled model, and (b) D50R100 probe model.

Fig. 4. Dependence of surface catalysis on convective heat flux.

Fig. 5. Dependence of wall temperature on convective heat flux.

Fig. 7. Solution adaptive grids for the Apollo CM test model at an AoA of30 deg.


322©2015 JSASS

the evaluation of heat flux profiles.23) Figure 8 shows thecomputed convective heat flux using solution adaptive meshand no adaptive mesh at Shot No. 1791. For the no adaptivemesh, the grids are not clustered or aligned parallel to theshock wave. One can find that the heat flux distribution bythe no adaptive mesh oscillates near the stagnation region.However, numerical errors appeared at x ¼ y ¼ z ¼ 0m.This is due to the singularity of the grid. Since this error doesnot effect heat flux in the other region, treatment for this erroris out of the scope of this study.

4. Results and Discussion

4.1. Radiation from air species in shock layerFigure 9 shows the radiation heat flux profiles from air

species in the shock layer for Shot Nos. 1781 and 1783, withassociated convective heat flux profiles. Although radiation

heat flux becomes larger in the higher enthalpy condition,it is negligibly small compared to the corresponding convec-tive heat flux. It should be noted that tangent slab approxima-tion generally gives a higher radiation heat flux incident onthe surface of blunt bodies. Nevertheless, the computed radi-ation heat flux is far smaller than that of convective heat flux.This concludes that radiation from air species in the shocklayer cannot explain the augmented heat flux observed inHIEST.4.2. Abnormal heat flux augmentation and radiation

from impurities in shock layerThe augmentations of heat flux at various stagnation

enthalpy conditions and test models are plotted in Fig. 10(a)and (b) in terms of the average vibrational temperature andmaximum vibrational temperature, respectively. Figure 11shows the translational temperature and vibrational tempera-ture profiles along the stagnation stream line at ShotNos. 1781 and 1783. To define the average temperature,we take into account the vibrational temperature in the shocklayer except the low-temperature region near the wall sur-face. The location of the maximum vibrational temperatureis immediately behind the shock wave. The augmentationsof heat flux, and the average temperature and maximumvibrational temperature are summarized in Table 2. For thelower enthalpy conditions such as Shot No. 1781 shown inFig. 11(a), the maximum vibrational temperature is higherthan the average temperature. On the other hand, for higherenthalpy conditions such as Shot No. 1783 shown in

(a)

(b)

Fig. 9. Radiation heat flux from air species with convective heat flux;(a) Shot No. 1781 (H0 ¼ 6:849MJ/kg), and (b) Shot No. 1783 (H0 ¼21:537MJ/kg).

(a)

(b)

Fig. 10. The abnormal heat flux augmentation at the stagnation point ofseveral blunt bodies with a fitted curve of the Stefan-Boltzmann law;(a) the emissivity ¾ is 0.132 when the data is reduced by the averagetemperature Tave, and (b) the emissivity ¾ is 0.118 when the data isreduced by the maximum vibrational temperature Tvmax.

Fig. 8. Heat flux distribution using solution adaptive grid and no adaptivegrid.


323©2015 JSASS

Fig. 11(b), the maximum vibrational temperature is compa-rable to the average temperature. The impurities that areheated due to the high temperature in the shock layer canemit radiation at the temperature of the heated impurities.We assume that the temperature of impurities equilibratewith the average vibrational temperature or the maximum vi-brational temperature. The relation between the augmenta-tion of heat flux and these temperatures is investigated. Usingthe average temperature Tave, augmentation is fairly well fittedby "�T 4

ave where · denotes the Stefan-Boltzmann constant. InFig. 10(a), the emissivity is determined as " ¼ 0:132.

Using this fitted emissivity, the sum of the convective andradiation heat fluxes, referred to as the total heat flux, is com-

Table 2. Heat fluxes at the stagnation point and the related quantities.

Shot Test H0 qexp qcalc qexp=qcalcqexp � qcalc Tave Tvmax

No. model [MJ/kg] [MW/m2] [MW/m2] [MW/m2] [K] [K]

1781 Apollo CM 6.849 3.74 2.17 1.72 1.57 3958.6 4688.11782 Apollo CM 17.275 22.47 8.98 2.50 13.49 6654.1 6678.01783 Apollo CM 21.537 27.32 10.86 2.52 16.46 7057.4 7090.11784 Apollo CM 19.554 37.45 15.79 2.37 21.66 7133.9 7164.41785 Apollo CM 21.059 36.63 14.79 2.48 21.85 7273.0 7321.01787 Apollo CM 8.094 8.40 5.12 1.64 3.28 4466.8 5102.61791 Apollo CM 6.759 4.67 2.92 1.60 1.75 4024.4 4590.51886 Apollo CM 13.471 15.23 5.97 2.55 9.26 6001.8 6206.11891 Apollo CM 8.318 6.33 3.54 1.79 2.79 4428.4 5228.01893 Apollo CM 20.048 28.33 9.33 3.02 18.89 6844.6 6870.01889 D20R10 8.596 23.62 20.36 1.16 3.26 4804.5 5397.11891 D50R100 8.318 9.92 6.95 1.43 2.97 4558.7 5300.41893 D50R100 20.048 31.22 17.30 1.80 13.92 6821.5 6870.0

(a)

(b)

Fig. 11. Translational temperature and vibrational temperature profilesalong the stagnation streamline; (a) Shot No. 1781 (H0 ¼ 6:849MJ/kg),and (b) Shot No. 1783 (H0 ¼ 21:537MJ/kg).

(a)

(b)

(c)

Fig. 12. Convective heat flux profiles, total heat flux profiles and corre-sponding experimental heat flux data are plotted for the Apollo CM testmodel at an AoA of 0 deg. The emissivity is " ¼ 0:132; (a) ShotNo. 1781 (H0 ¼ 6:849MJ/kg), (b) Shot No. 1782 (H0 ¼ 17:275MJ/kg), and (c) Shot No. 1783 (H0 ¼ 21:537MJ/kg).


324©2015 JSASS

pared with the measured heat flux profiles obtained inHIEST. In Fig. 12, the computed convective and total heatfluxes are plotted for the Apollo CM model with an AoAof 0 deg using the corresponding experimental data. Onecan find that the computed total heat flux profiles agree fairlywell with the experimental data over the entire surface. Sim-ilarly, in Fig. 13, the convective, total and the correspondingexperimental data are plotted for an AoA of 30 deg. Reason-able agreements are also obtained with the same emissivity.Therefore, this indicates that the augmentation of heat fluxcan be estimated using 0.132�T 4

ave.The ratio of measured and calculated heat flux qexp=qcalc is

shown in Fig. 14 (summarized in Table 2). The abnormalheat flux augmentation was not remarkable for small probemodels. However, when heat flux augmentation is definedas q � qexp � qcalc at the stagnation point, it is nearly iden-tical as the stagnation enthalpies are close. For example, thesurplus heat fluxes in Shot No. 1891 for the Apollo CMmodel and D50R100 probe model are 2.79MW/m2 and2.97MW/m2, respectively, even though the computed shockstand-off distance for the Apollo CMmodel (=26mm) is sig-nificantly larger than that for D50R100 probe model(=7mm). Furthermore, the surplus heat flux in Shot No.1889 for the D20R10 probe model is 3.26MW/m2, whichis close to that in Shot No. 1891 for the Apollo CM modeland D50R100, while the stagnation enthalpy in both Shotsis also close. The shock stand-off distance in Shot No.1891 for the Apollo CM test model (=26mm) is 26 timeslarger than that in Shot No. 1889 for D20R10 (=1mm). Asimilar trend can be observed for the Apollo CM model inShot No. 1783, the Apollo CM model in Shot No. 1893and D50R100 probe model in Shot No. 1893, where the sur-plus heat fluxes are 16.46MW/m2 18.89MW/m2 and13.92MW/m2, respectively. The surplus heat fluxes for theApollo CM model are only 1.18–1.36 times larger than thosefor theD50R100 probe model. The above results suggest thatthe augmentation depends only on stagnation enthalpy. Be-cause the convective heat flux becomes substantially higherfor small nose radii, the resulting ratio of qexp=qcalc becomesalmost unity for small probe models. These results also indi-cate the reason why the abnormal heat flux augmentation be-comes remarkable in HIEST. In HIEST, a larger test modelcan be used and the qexp=qcalc ratio becomes smaller.

For such situations, one can point out that the amount of

(a)

(b)

(c)

(d)

Fig. 13. Convective heat flux profiles, total heat flux profiles and corre-sponding experimental heat flux data are plotted for the Apollo CM testmodel at an AoA of 30 deg. The emissivity is " ¼ 0:132; (a) ShotNo. 1791 (H0 ¼ 6:759MJ/kg), (b) Shot No. 1787 (H0 ¼ 8:094MJ/kg), (c) Shot No. 1784 (H0 ¼ 19:554MJ/kg), and (d) Shot No. 1785(H0 ¼ 21:059MJ/kg).

Fig. 14. Ratio of the measured heat flux in HIEST experiment and the con-vective heat flux obtained by CFD at the stagnation point.


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heat flux augmentation should depend on the thickness of theshock layer, model size and stagnation enthalpy. It is thepresent scenario that the shock layer is optically thick dueto impurities, and the radiation from impurities that exist inthe relatively high temperature region near the edge of theboundary layer reaches the wall surface. The reason whythe fitted emissivity (" ¼ 0:132) becomes smaller than ablack body (" ¼ 1:0) may be that the specific wavelength re-gion is only optically thick. In order to identify the source ofradiation, spectroscopy analysis in the shock layer is needed.

5. Conclusion

The abnormal heat flux augmentation observed in HIESTwas numerically analyzed. The analysis revealed the follow-ing. (1) Radiation from air species was too small to contrib-ute to heat flux augmentation. (2) The engineering techniqueto estimate the abnormal heat flux augmentation was ob-tained, though the test campaign for spectroscopy in theshock layer is required to clearly determine the source ofthe radiation. The abnormal heat flux augmentation couldbe estimated using 0:132�T 4

ave and the computed total heatflux profiles agreed fairly well with the experimental data.

Acknowledgments

The study is partly supported by Grant-in-Aid for Japan Societyfor the Promotion of Science Fellows, JSPS 2013 04485.

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N. TsuboiAssociate Editor


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