Aerosp. Sci. Technol.4 (2000) 347–361 2000 Éditions scientifiques et médicales Elsevier SAS. All rights reservedS1270-9638(00)00145-0/FLA

High-enthalpy hypersonic project at ONERA

Bruno Chanetz *, Thierry Pot, Reynald Bur, Véronique Joly, Serge Larigaldie, Michel Lefebvre,Claude Marmignon, Ajmal K. Mohamed, Jean Perraud, Daniel Pigache, Philippe Sagnier,

Jean-Luc Vérant, Johan William

ONERA, BP 72, 29 Avenue de la Division Leclerc, 92322 Châtillon cedex, France

Received 10 May 1999; revised 14 February 2000; accepted 31 March 2000

Abstract This article deals with the research performed in the framework of the internal ONERA HyperenthalpicHypersonic Project. This project involved fifteen researchers specialised in different domains, which arethe following: fundamental studies on shock/wave and shock/boundary layers interactions; study of thelaminar/turbulent transition; real gas effects and associated physical modelling; the development of non-intrusive optical diagnostic methods usable in cold and hot wind tunnels; flow rebuilding in a hot shot windtunnel such as F4; conception, realisation and validation of computational fluid dynamics (CFD) solvers. 2000 Éditions scientifiques et médicales Elsevier SAS

shock-boundary layer interaction / laminar-turbulent transition / non-intrusive optical diagnosticmethod

Résumé Projet Hypersonique Hyperenthalpique à ONERA.Cet article traite des recherches effectuées dans lecadre du Projet de Recherche Fédérateur ‘Hypersonique Hyperenthalpique’. Ce projet mobilise quinze cher-cheurs spécialisés dans les différents domaines étudiés qui sont : études fondamentales concernant les inter-actions onde de choc/couche limite et les interférences de chocs ; étude de la transition laminaire/turbulent ;effets de gaz réel et modélisations physiques associées ; développement de méthodes de diagnostic optiquenon intrusives utilisables en soufflerie hypersonique ; conception, réalisation et validation de codes de calcul. 2000 Éditions scientifiques et médicales Elsevier SAS

choc-couche limite / transition laminaire-turbulent / méthode de diagnostic optique non intrusive

1. Introduction – the Hyperenthalpic HypersonicProject at ONERA

Between 1960 and 1970 a lot of fruitful research wasundertaken at ONERA in the field of hypersonics. TheELECTRE mission was the most spectacular, since itinvolved a rocket fired from the test centre in the Landes.After having reached its maximum altitude at 130 kmfrom earth, the rocket was reoriented in the direction ofthe earth. The third stage was ignited, which accelerated

* Correspondence and reprints; E-mail: chanetz@onera.fr

the vehicle to the altitude of 60 km, where re-entryconditions were realised. A significant contribution to theplasma re-entry characterisation was brought by ONERAat this time.

Unfortunately during the following decade, the fall inhypersonic research brought this program to a stop andthe facilities devoted to the study of hypersonic flow wereunderused.

Hypersonic studies in France resumed at the end of the80s thanks to the Hermès Project. At this time, it was

348 B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361

decided to build new facilities to replace those that hadbeen dismantled or closed. Thus a laminar low densitywind tunnel, R5Ch, was put into operation at ONERA’sChalais-Meudon centre and the construction of a highenthalpy wind tunnel F4, at ONERA’s Le Fauga-Mauzaccentre (near Toulouse) was undertaken [5].

In 1992, when the decision was made to stop theHermès project, the R5Ch and F4 wind tunnels hadjust become operational. Furthermore ONERA had un-dertaken a special effort to develop novel non-intrusivediagnostics for high enthalpy hypersonic ground test-ing facilities. With the advent of modern computers andthe concomitant progress in numerical methods, it be-came possible to solve Navier–Stokes equations in non-equilibrium and with chemical effects. The end of Her-mès project could have marked the end of hypersonicstudies. Therefore it was decided to keep at ONERA amulti-disciplinary project devoted to hypersonic hyper-enthalpic studies, the aim being to continue the researchundertaken in the framework of Hermès project. Thisproject involved about fifteen researchers specialised indifferent domains, which are:

– fundamental studies on shock/shock and shock/boundary layer interactions;

– study of laminar /turbulent transition;– real gas effects and associated physical modelling;– development of non-intrusive optical diagnostic

methods usable in cold and hot wind tunnels;– flow rebuilding in hot shot wind tunnel such as F4;– conception, realisation and validation of Computa-

tional Fluid Dynamics (CFD) solvers.This last point is the ultimate goal of the project. Thevalidation of CFD codes requires well documented test-cases. The facilities mainly used for this action are thecold hypersonic R5Ch low density wind tunnel and thehigh enthalpy F4 wind tunnel. However the sole inspec-tion of the wall properties and some fragmentary visual-isations are not sufficient to elucidate the cause of dis-crepancies between experiments and calculations. There-fore the surface measurements are often complementedby flowfield measurements based on optical techniqueslike Electron Beam Fluorescence (EBF), Diode LaserAbsorption Spectroscopy (DLAS) and Coherent Anti-Stokes Raman Scattering (CARS).

2. Test-cases in cold hypersonics includingmeasurements by advanced optical diagnostics

2.1. Conditions of the experiments

The tests described in this section have been performedin the blow-down wind tunnel R5Ch located at theONERA Chalais-Meudon research centre near Paris.The facility is equipped with a contoured nozzle ofrevolution providing a uniform Mach 9.91 flow under thefollowing nominal conditions: stagnation pressurepst=2.5× 105 Pa and stagnation temperatureTst= 1050 K.

The duration of the run close to one minute is verycomfortable for the development of optical diagnostics.The R5Ch wind tunnel appears to be a privileged wayof developing the instrumentation associated with the F4high enthalpy wind tunnel.

2.2. Study of the shock wave/boundary layerinteraction in low density flow: flowfieldmeasurements by X-ray detection

The model consists of a hollow cylinder/flare with asharp leading edge followed by a flare terminated bya cylindrical part (figure 1). The reference lengthL,comprising the distance between the leading edge andthe beginning of the flare, is equal to 0.1017 m, whichleads to a unit Reynolds numberReL = 18 375. Fig-ure 2shows a comparison between the experimental wallheat-flux distribution and the numerical results obtainedby two ONERA Navier–Stokes solvers, NASCA whichis a two-dimensional/axisymmetrical research solver andFLU3M, which has a three-dimensional industrial voca-tion. Both use a finite volume approach.

Figure 1. Hollow cylinder/flare test set up.

Figure 2. Hollow cylinder/flare – longitudinal evolution of theheat flux (Stanton number).

B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361 349

Figure 3.Hollow cylinder/flare – density profile atX/L= 0.76(by X-ray detection).

The heating rate comparisons given infigure 2 bythe Stanton number show a good overall agreement.The distributions are characteristic of those for laminarflows, with the heating rate showing an initial decreaseat the location separation (X/L = 0.76) and a rapidincrease along the flare. For this problem, the maximumheating rate occurs downstream of reattachment, whichtakes place just before the expansion onto the cylinderextension.

The density flowfield measurements have been per-formed by X-ray detection thanks to a cooperative activ-ity with the Institute of Thermophysics of Novosibirsk,Russia [6]. The technique uses an electron gun locatedon the top of the testing chamber. To limit the interferenceof radiation from the model material, it has been neces-sary to pass the electron beam through a tube of 2 mmas shown infigure 1. The interference is thus minimal,and measurements as close as about 1 mm to the modelsurface are feasible. The detector is made of a Soller col-limator, composed of two 80 mm-long plates separatedby 0.8 mm and a silicon detector. With an electron beamcurrent of 0.5 mA, integration time is 10s per point. Weuse two detectors, one measuring the reference densityin the free stream flow and another detector moving in-side the boundary layer.Figure 3 is related to the profilefor X/L= 0.76. At this station, the increase of density isdue to the shock generated by the sharp leading edge. Itis very satisfying to observe a good agreement betweenthe numerical results and experimental ones, as far as thedensity peak amplitude is concerned.

2.3. Fundamental study of shock/shock in lowdensity flow: flowfield measurements byDLCARS

This study has been undertaken in the framework of theProgram of REsearch for Advanced Hypersonic Propul-sion (PREPHA). The air intake situation is simulated herevery schematically by a shock generator which produces

Figure 4. Evolution of the temperature on the stagnation line infront of the cylinder.

a weak oblique shock and a cylinder located perpendicu-larly to the free stream flowfield direction [16].

The shock/shock interferences thus can produce lo-cally a spectacular heat flux and the pressure increases.Indeed the shocks produced by the compression rampsintersect the shock forming ahead of the cowl, whoseprofile is blunt so as to limit the heat flux. Here is pre-sented only the reference case without shock generator.The cylinder (diameterN = 16× 10−3 m, spanwise=100×10−3 m) is lying perpendicularly to the free streamin the testing chamber. The detached shock region in frontof the cylinder has been probed by Dual-Line CoherentAnti-Stokes Raman Scattering (DLCARS). In this tech-nique, the rotational temperature is deduced from the ra-tio of the intensities of the two Raman lines, assuming aBoltzman equilibrium between the rotational level man-ifold. Furthermore, the gas density is obtained from theabsolute intensity of one Raman line or both, after cal-ibrating the optical response at the spectral position ofeach Raman line. The laser beams are delivered from oneoptical bench equipped with a seeded Nd-YAG laser anda dye chain producing 12 ns long pulse duration at a rep-etition rate of 12.5 Hz. The beams are developed succes-sively in the test chamber of the R5Ch wind tunnel and ina reference cell, using the folded boxcar configuration.

In the test chamber, the CARS signals are generatedfrom the probe volume which is 40 mm long and 0.2 mmin diameter; the axis of the probe volume is perpendicularto the direction of the Mach 10 flow. So the spatialresolution is 0.2 mm in the direction of the strongestgradient. During a run, six positions separated 0.5 mmfrom each other are probed. For each position, 120 lasershots are averaged to increase the number of collectedphotoelectrons, so limiting the shot noise influence. Insuch conditions, the relative precision on temperatureand density is better than 7% and 10%, respectively.Figure 4shows the evolution of the rotation temperaturealong the stagnation line. Since in the R5Ch conditions,rotation equilibrium is recovered after a few collisions

350 B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361

Figure 5.Evolution of the density on the stagnation line in frontof the cylinder.

between molecules, the rotation temperature is equal tothe static temperature. The temperature jump due to theshock, particularly intense at large Mach numbers, isin good agreement with the numerical results obtainedwith ONERA-Homard2 solver, which is a finite volumetwo-dimensional Navier–Stokes solver. Density, deducedfrom the CARS probing along the stagnation line, ispresented infigure 5. The good agreement betweencalculation and experiment leads to two conclusions:

– the validity of the measurement technique;– the accuracy of the continuum approach used to

solve the conservation equation for mass momentumand energy (Navier–Stokes equations).

2.4. Velocity measurements across the boundarylayer in hypersonic flows using anelectron-beam-assisted glow discharge

This experiment has been performed on a flat platewith a sharp leading edge (a length of 400 mm, a spanof 200 mm). This plate was at zero incidence.

The main goal here is to perform – through a timeof flight principle [13] – accurate measurements of thevelocity profile in the boundary layer developing at thewall. A miniature pseudo-spark [12] type electron gunis used. The profile is fitted across the boundary layerfrom the surface of a grounded plane metallic model upto the point where the free stream is reached. In theseexperiments, an intense pulsed electron beam is emittedby a very small (20 mm× 30 mm) pulsed electron gunlocated inside the model. It penetrates within the flowfrom a 0.3 mm hole across the surface, and traces thepath of a high voltage glow discharge in some 10 ns. Thefilamentary discharge is instantaneously connected to ahigh voltage capacitor via a thin high voltage metallic rodplaced, parallel to the flow axis, 100 mm away from thegun exit. This maintains the gaseous filament very brightduring some microseconds.

The initial straight pattern of the discharge then closelyfollows the stream lines (one verifies that no distortionoccurs when the discharge is triggered within the same

Figure 6. View of the boundary layer by the electron beamfluorescence with a delay of 5µs.

Figure 7. Comparison between NS calculation and experimen-tal profiles.

gas at static pressure). At a precise delay time (5µs)after the electron gun actuation, a CCD camera is openedbriefly (250 ns) to image the position of the luminouscolumn convected by the flow (figure 6). The localvelocity of the stream versus the distance above the planeis simply deduced from the horizontal displacement of agiven point during the selected delay time.

The observation field extends 20 mm above the model.As a calibrated grid is used to determine the magnifica-tion of the optics, the global accuracy of this method canbe estimated to 50−100 m/s. For identical aerodynamicconditions, a measured velocity profile is compared (fig-ure 7) to the results of a numerical Navier–Stokes cal-culation (HOMARD2 solver). Even though the overallagreement is correct, there are however unexplained dif-ferences between experiment and calculation. This pointwill be elucidated in future work.

B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361 351

3. Study of laminar/turbulent transition in cold andhot hypersonics

3.1. Generalities

The laminar-turbulent transition in hypersonic bound-ary layers remains a key issue with respect to thermalexchange and protection. Linear stability theory, togetherwith theeN method, is routinely used for transition pre-diction at lower speeds. In hypersonic flow, high tempera-tures may cause molecular dissociation and chemical re-actions. Also, the simultaneous existence of several un-stable modes has to be accounted for.

3.2. Linear stability theory and transition prediction

Let x denote the streamwise direction, andy thenormal to the wall. The aim is to study the propagationof small, wave like perturbations (order 1), added to theboundary layer base flow (order 0). Linearity is assumed,and the base flow is supposed locally parallel: zero orderquantities do not depend onx. In spatial theory, theperturbation is written:

f ()= f̂ (y)exp(i(αrx + βrz−ωt)

)exp(−αix) (1)

with ω the frequency,αr, βr wavenumbers, andαi thelocal amplification rate (forcingβi = 0). This representsa wave, with wave-vector (αr, βr).Ψ is the angle betweenthe wave-vector and the external velocity. Determinationof these wavenumbers is the crucial part of any stabilitycalculation. In hypersonic flows, several unstable modesusually exist. For 2D base flow, the first mode is oblique,with Ψ ≈ 65◦. Multiple higher 2D modes (Mack modes)are then expected. The lowest of these is usually thedominant instability above Mach 4.

The relative amplitude of the wave is given by the lastexponential term in (1). TheN -factor is defined after thelocal amplification rate as

A

A0= exp(N)= exp

( x∫x0

−αi dx

), (2)

whereA andA0 are the amplitudes at locationsx andx0,respectively. In many cases, theN -factor provides usefulresults for transition correlation purposes, hence fortransition prediction. While transition in flight conditionswould correlate to aN -factor close to 10, experimentalstudies in most hypersonic facilities produce transitionN -factor in the range 1 to 6, above Mach 7. This resultsfrom the high level of perturbation in these facilities,mostly due to acoustic waves from the nozzle boundarylayer.

3.3. Three dimensional flows

An experimental study of transition on a cone with 2◦incidence was conducted in 1994 as part of an ESA Tech-nical Research Program. The ONERA-ENSAE Mach 7wind tunnel (M7) was used, allowing unit Reynolds num-bersRu of 25× 106 m−1. Extensive analysis of this ex-periment, using linear, local stability theory, was then per-formed as part of a doctoral work [10,14]. The aim isto correlate the experimental transition line with theN -factor computed on the 7◦ half-angle, 20 cm long, sharpcone. Prior to this work, base flow was computed by CFDNorway, using a laminar Navier–Stokes code. On thisconfiguration, the second mode calculated frequency isextremely high, about 106 Hz. Its contribution to transi-tion seems unrealistic. The transverse velocityW reachesabout 5%, at some altitude, of the external velocity. Thissmall W component has a dramatic effect on the firstmode of instability, as shown infigure 8.

Without incidence, the first mode wavevector direc-tions are±65◦. With incidence, the wavevector turns to−88◦ on the equatorial ray, loosing its symmetry. Ampli-fication rates significantly increase. Hence, the first modebecomes a ‘first/crossflow’ mode, a nice candidate fortransition correlation close to the equator. In the verti-cal plane of symmetry, bothW and crossflow instabilitydisappear. Consequently, there is no single mode that isresponsible for transition over the entire cone.

As shown in figure 9, transition is associated withthe first mode in the vertical plane of symmetry, andwith the crossflow mode near the equator. The numericaltransition line is quite comparable to the experimental

Figure 8. Effect of incidence on instability.

Figure 9. Experimental and numerical transition lines.

352 B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361

Figure 10.Experimental results at F4.

line, on the figure. It should be stressed that these twomodes, both oblique, are associated with quite differentvalues of transitionN -factors, about 1 for the first mode,and about 5 for crossflow.

3.4. High enthalpy effects

In a high enthalpy boundary layer, a very high tem-perature causes dissociation intoN chemically react-ing species. In case of chemical equilibrium, significantchanges in stability equations concern transport and dif-fusion coefficients. For non equilibrium, species massfraction perturbations need to be added to the set of un-knowns. The rank of the system to be solved rises from 8to 8+ 2(N − 1). Extension of linear stability theory hasbeen presented in [15]. Then, experimental work has beenconducted in the ONERA F4 high enthalpy wind tunnel,equipped with nozzle 3. The aim was to obtain a bound-ary layer transition on a 1 meter long flat plate, withoutand with chemical dissociation, in order to validate thecomputation. Wall flushed thermocouples, placed every20 mm, allow measurements of the wall heat fluxφ.A sudden rise of the functionφ

√Rx (constant in the lam-

inar region) marks the beginning of transition. Two setsof conditions have been considered: a low enthalpy one,with HiR = Hi/Rta = 30, Pi = 800× 105 Pa (Rta =78,721), andRu= 3×106 m−1, and a high enthalpy casewith HiR = 150,Pi = 400× 105 Pa,Ru= 5× 105 m−1

(for completeness, in the previous M7 case,HiR = 8,Pi = 80× 105 Pa,Ru= 25× 106 m−1).

Figure 10 shows typical low enthalpy results. Takenfrom a number of shots, curves are time averaged over 20to 60 ms of constant Reynolds. This clearly shows thevariation of transition, from 0.5 to 0.38 m asRu goesfrom 1.7 to 3× 106 m−1. This produces an increasingRXT function ofRu, characteristic of flat plate transition.Linear stability has been applied to the above case, forRu= 3×106 m−1, assuming a constant wall temperature

Figure 11.N -factor calculation, F4 flat plate.

of 300 K. Results, infigure 11, show the existence ofthree modes.

The second mode is the most unstable, at about105 Hz. Comparing to the experiment gives a secondmode transitionN -factor of 0.9, close to the first modetransition N -factor that was obtained in the M7 andin ONERA S4Ma ‘cold’ wind tunnels. High enthalpyexperiments in the same F4 wind tunnel showed noevidence of transition, even when 3D roughness elementsare placed on the plate. Extrapolation from low enthalpycase, assuming constantRXT , produces a transitionlocation atx = 2 m. This should even be taken as a lowestimate if one takes into account the increase inRXTwith increasing enthalpy, as noted by Candler [4].

3.5. Synthesis

It has been demonstrated in this work that first andcross-flow modes must be considered when dealing with3D flows. A second result is that the F4 wind tunneldoes not allow high enthalpy transition simulation in itspresent state. Unit Reynolds increase should be soughteither through an increase of reservoir pressure or/and anincrease of the throat section. In the mean time, futurestability analysis will be conducted on the nozzle’s wallboundary layers.

4. Coupled radiation calculations in shock wavesgenerated by bodies at high velocities in theatmosphere

4.1. Generalities

Shock waves capable of emitting ultraviolet radiationare created in front of bodies moving at high velocitiesin the atmosphere. Radiative heat fluxes are expected tobe of the order of convective ones at high velocities. Thegaseous mixture is highly dissociated, collisions between

B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361 353

atoms and electrons leading to the excitation of electroniclevels. A review of the available data for the physico-chemical processes has been realised and a new approachfor the calculation of the radiation totally coupled tothe aerodynamic phase has been developed. The Navier–Stokes code CELHYO is used and radiation is modelledwith an approach taking into account the various physicalcharacteristic times of the problem.

4.2. Basic assumptions

The CELHYO (Calculs d’Ecoulements LaminairesHY personiques Onera) code treats ideal mixtures of per-fect gases made of electrons and heavy species (see Sec-tion 6). The mixture usually consists of the species N2,O2, NO, NO+, N, N+ and O. Here the electronic excitedlevels of N are added and considered like specific chem-ical species. A two phase system of monodimensionalequations is considered [3]: an aerodynamic phase for theflow and a radiative phase for the radiative transfer:

– aerodynamic:

∂tρYα + ∂x(ρYαv− ρD∂xYα)

=PαColl︷ ︸︸ ︷

P 0Coll

α + Pe−Collα+PαPhoton, (3)

∂tρv+ ∂x(ρv2+ p+ pe

)− ∂x(υ∂xv)= 0, (4)

∂tρE + ∂x(ρE + p+ pe)v− ∂x(υv∂xv+ κ∂xT ) (5)

− ∂x(∑

α

ρDhα∂xYα

)+ ∂xqR(Iν)= 0,

∂t se + ∂xsev= (γe − 1)

(S0t−e + Set−e

)(Yeρ

γe−1)−1g′(

pe

Yeργe

),

se = ρg(

pe

Yeργe

); (6)

– radiative:

dIν(x)

dx= κν(x)

[Sν(x)− Iν(x)

], (7)

where Iν is the radiative intensity in the frequencyinterval betweenν andν + dν, Sν is the source function(classical definition in radiative transfer with Einsteincoefficients of emission and absorption) andκν is theabsorption coefficient. This last formula is adapted for themono-dimensional approach.

The first system represents the governing conserva-tion equations for a viscous flow. The continuity equa-tion (mass conservation) represents the species densityevolution including collisional and radiative processes.ρis the mixture density,Yα the mass fraction of species

α, v the velocity andD the diffusion coefficient.P 0coll

α

describes collisional processes involving heavy speciesandPe−coll

αdescribes electronic collisional processes [1,

2]. Pαphotondescribes radiative processes [1,2]. The othersequations represent momentum, total energy and electrongas entropy.p is the pressure andpe is the electron gaspressure.E is the total energy andse the electron gasentropy.υ andκ are respectively the viscosity and ther-mal conductivity of the mixture.g is a strictly increasingfunction.S0

t−e expresses the change in electronic energycaused by elastic collisions andSe−t−e the change frominelastic collisions. The coupling occurs in the energyconservation equation by the term∂xqR(Iν) determinedin the radiative phase. Discrete emission coming fromthe contribution of atomic lines is calculated assuminga Doppler profile. This Doppler profile seems sufficientlywell fitted at the high temperatures considered here andalso enables to define a ‘squared profile’ which allowsenergy conservation along the grid with a simpler form.For the continuum emission contribution (coming fromN+ recombination), the average energy photon approx-imation is used. The resolution necessitates an iterativeprocedure which provides a converged solution.

4.3. Applications

The method is applied to the flow on the stagnationstreamline in front of the Rosetta probe. The aim ofthe Rosetta probe was initially to bring to earth samplesfrom comet 46P/Wirtanen. The probe radius is 0.5 mand the re-entry altitude 63 km. The flight conditions forvelocity, pressure and temperature are 14.3 km/s, 15.5 Paet 240 K. The wall temperature is 1500 K and the wallis assumed totally reflecting. The results are presentedin the figures 12 (without radiation) and13 (with

Figure 12.Temperature of the flow in front of the Rosetta probe(without radiation, flight conditions 14.3 km/s, 15.5 Pa and 240K).

354 B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361

Figure 13.Temperature of the flow in front of the Rosetta probe(with radiation).

radiation). The translational and electronic temperaturedistributions show the cooling and the decreasing of theshock stand off distance due to a lot of energy escapingthe flow. Temperature gradients are more important nearthe wall when radiation is taken into account, however,the maximaT and Te values are quite the same. Theshock stand-off distance when radiation is taken intoaccount is at a distance 18% less than the initial distancewithout radiation. This is due to the important energy lossby radiation which reaches 43 MW/m2.

5. F4 high-enthalpy nozzle flows rebuilding

5.1. Generalities

Several years experimental results obtained in theONERA F4 hot-shot wind tunnel were analysed to ad-dress two important problems for this type of wind tun-nel [18,19]; i.e., the determination of reservoir condi-tions and the thermochemical nature of the nozzle flow.Built in the early 1990s to simulate atmospheric re-entryof hypersonic vehicles, the F4 facility is today a uniquemeans to perform high enthalpy flows up to settling-chamber pressuresPi of 500 bar and reduced totalenthalpyHi/RT0 of 250 (20 MJ/kg). Unique in the senseof long duration run achieved up to 400 ms but withslowly decreasing total conditions with time less than 1%per millisecond. F4 is equipped with 4 different nozzles#1, #2, #3 and #4 withA/A∗ varying respectively from1850 to 32 000. Nozzle #2 with an area ratio of 4490, alength of 3.4 m and an exit diameter of 0.7 m was usedfor most of aerothermal tests.

The work performed in F4 facility to determine thereservoir enthalpy and the knowledge gained during thisinvestigation about the thermochemical nature of the noz-zle flow are hereafter described. We demonstrated theneed for numerical simulations with sophisticated physi-cal models, even for flows around simple geometries, tocorrectly describe the features of high enthalpy flow phe-nomena. Because of a large number of parameters con-tained in such gas flows, only a numerical and parametri-cal strategy allows the extreme limits of thermochemicaland fluid mechanical assumptions to be simulated beforedeeper investigations.

5.2. Reservoir enthalpy determination

Since total enthalpy in F4 cannot be deduced from anyclassical method adapted for arc jet facilities, a correla-tion was built over a dozen Navier–Stokes computationsof the stagnation-point heat fluxes assuming catalyticwall and thermochemical non equilibrium or perfectgas (in 1994, [18]). This relationship links heat-transferrates measured in the stagnation region of spherical cat-alytic reference probes, pitot pressures and total enthalpy(within±12% of uncertainty according to Navier–Stokescomputations scatter). This useful relationship is sys-tematically crosschecked with heating measurements andconfirmed with new stagnation Navier–Stokes points as-suming a wide spectrum of physical modellings.

Qstag

√RnosePstag[

Htot−HwallRT0

]1.0688= 23.787= constant, (8)

where all variables are in SI units.

5.3. Thermochemical nature of the flow in nozzle #2

5.3.1. Numerical tools

To determine the freestream flow properties, severaltype of measurements can be compared with theoreti-cal calculations, i.e., nozzle and wall-pressure distribu-tions, pitot pressure profile, freestream velocity, transla-tional temperature, and NO concentration. For this pur-pose, nozzle exit-flow charts have been constructed inwhich the thermochemical conditions at the nozzle exitare given in the a priori extreme limits of thermochemi-cal and fluid mechanical assumptions. These exit-airflowcharts exist for the nozzles #2, #3 and #4. This workhas been performed with the help of 1D numerical toolssuch as the TUYEQ and TURGE codes [17]. Moreover,2D viscous computations are systematically performedin thermochemical equilibrium or non equilibrium withthe help of a Parabolised Navier–Stokes code namedPANASCE [11]. This code allows sophisticated physi-cal models in 2D nozzle flow calculations with compu-tational time low enough for encouraging parametrical

B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361 355

studies. CELHYO code is also proposed for model flowsimulations in thermochemical non equilibrium whenNavier–Stokes assumptions are necessary (blunted regionor separation zones). A stagnation line method based on1D Navier–Stokes equations is also employed to rebuildthe non equilibrium shock layer of spherical probes andis implemented in the CELHYO code [8] as the 1D op-tion (CASL [3]). The CASL (Calculation Along the Stag-nation Line) method is able (and has been validated) tosimulate within less than a few percent discrepancy, theshock location, the distribution of thermodynamic vari-ables along the stagnation line and the heat transfer atthe stagnation point compared to a 2D Navier–Stokesequivalent calculation. Most of the investigated vibra-tional and chemical couplings are implemented in the for-mer method.

5.3.2. Measurements

The wall and Pitot pressures have been compared ini-tially to different flowcharts. Agreements were foundbest for turbulent-flow assumption at low-enthalpy andlaminar-flow assumption at high-enthalpy according topitot measurements. Furthermore, the measured wallpressures at the nozzle (#2) exit seemed to agree with anequilibrium assumption at high enthalpies. This pressurebehaviour observed through a one-dimensional analysisprompted us to investigate further using the more sophis-ticated 2D method described above. PNS computationsconfirmed analysis yielded by one-dimensional results.Whatever the materials chamber used (copper-tungstenconfiguration before 1996 and carbon-carbon configura-tion after 1996 to diminish metallic contamination), wallpressure measurement levels were only confirmed by anequilibrium modelling of physics, removing the role ofprobable copper or metal contaminants as catalysts forrecombination reactions since with the new carbon cham-ber, similar results in the flow were obtained with negli-gible parts of metals (only from the throat).

The DLAS technique (since 1994) can provide thefreestream velocity within±5%, the translational tem-perature within±30% and the NO concentration within±30%. These data are obtained through the analysis ofthe absorption spectra of an infrared laser beam crossingthe test section. Both velocity and translational tempera-ture can be used to determine the reservoir enthalpy bymaking some assumptions about the flow thermochemi-cal state:

Hi DLAS = CpTDLAS+ V 2DLAS/2

with an equilibrium value forCp= Cp(TDLAS).Compared to the former copper chamber results, the

disagreement on the velocity with the carbon arc chamberis seen to be smaller, though it is still present at thebeginning of the run. Recently, with the carbon arcchamber further improved, DLAS and spherical-probefreestream velocity results were successfully compared

Figure 14. Free stream velocities from DLAS, pseudosparkelectron gun and computations (from sphere stagnation heattransfer and stagnation pressure assuming equilibrium andlaminar nozzle boundary layer).

(seefigure 14) with EBF technique (Pseudo-spark) forwhich only one datum can be obtained during the rundue to the limiting intensified camera (one picture every4 seconds). Although the principle of the method remainssimple, the recurrent effect of the plasma column in theflow could induce a local radiation pressure allowing anacceleration illustrated by a slight higher velocity than theDLAS data. However, too few EBF time-of-flight data areavailable to conclude.

5.3.3. Analysis of computations/measurements

The computations performed with up-to-date but clas-sical thermochemical non equilibrium modelling (Parkair set of reactions, Millikan & White for vibrationalkinetics,. . .) lead to the conclusion that, at high enthalpy,the core flow thermodynamics seem to be close to equi-librium values and the nozzle boundary layer is in tran-sitional regime (according to growing of the boundarylayer thickness expressed by Pitot measurements). Theseaxisymmetric results are the same as those obtained fromthe one-dimensional calculations used during the Hyper-boloid calibration campaign in 1993. However, the tran-sitional behaviour assumed in the calculations for theboundary-layer flow (transition from the throat to theexit) may not necessarily be the true behaviour of theflow, pitot pressure profiles are consistent with the as-sumed behaviour as it could be for unit Reynolds numberfar below 106 (at the exit usually 104 to 105). Confirma-tion of the close-to-equilibrium state observed systemat-ically in the wall pressure distributions for nozzle #2 isgiven by the freestream translational temperature mea-surements with the DLAS technique. The thermochem-ical assumption that is the closest to DLAS data infig-ure 15 is undoubtedly that the equilibrium flow, also iftaking into account the uncertainties. The first 20 mil-liseconds after the departure of the plug are systemati-cally considered as unstable (Pstag/Ptotal versus time ex-

356 B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361

Figure 15. Nozzle #2 DLAS NO translational temperature(±30% accuracy) distribution compared to frozen and equilib-rium ones deduced from charts (turbulent nozzle flow) accord-ing to the spherical probe (15 mm diameter for the sake of sim-plification).

presses the stability of the flow) for the run and the testanalysis starts after this point.

The DLAS technique gives translational temperaturesthat are even larger than the equilibrium temperature.This is a general trend for carbon-chamber runs. Theclose-to-equilibrium behaviour of the flow cannot becompletely simulated with a classical air Mollier diagramwhich gives zero NO concentration at the test sectionexit whereas the DLAS technique estimates about 2%.This value is closer to those obtained with frozen ornon equilibrium assumptions (6%) but still lower bya factor 3. So, as a matter of fact, the F4 nozzle#2 flow behaves like a close-to-equilibrium flow withregards to wall static pressure and DLAS translationaltemperature measurements, but the presence of 2% ofNO concentration indicates that the classical equilibriummodelling does not represent adequately the chemistrythat acts in the nozzle flow.

5.3.4. Thermochemical modelling

Let us summarise the available information about thenozzle-flow thermochemistry.

(1) The nozzle wall-pressure distribution is close tothat given by equilibrium model at high enthalpy (twicethe value of non equilibrium ones) [18,19].

(2) The Electre sphere-cone pressure distributionsindicate also that the freestream Mach number is closeto equilibrium and then the pressure and the translationaltemperature to equilibrium, too. Note that the pressureand translational temperature must vary similarly becauseof mass-flow conservation and the equation of state [20].

(3) The DLAS technique give translational tempera-ture values close to equilibrium values and even larger.

(4) The DLAS technique gives NO concentration muchcloser to frozen-non equilibrium than equilibrium values.

(5) It is difficult to draw conclusions about DLASand pseudo-spark technique (EBF) for obtaining fromfreestream velocity a thermochemical trend of the flowbecause of the low sensitivity of this parameter to thethermochemistry with regard to the uncertainties.

(6) All these observations are fully repeatable, regard-less of the arc-chamber option (copper-tungsten or carbonconfiguration).

(7) It has not been discussed here, but the compar-isons of Navier–Stokes shock layers with schlieren im-ages tend to demonstrate that the flows around modelsare driven by conventional non equilibrium kinetics. Theapparent relaxation to equilibrium of the nozzle #2 flowthat could be indicated by the wall static pressure andtranslational temperature behaviours is in contradictionto conventional assumptions about high enthalpy flowin large-area-ratio nozzles, i.e., the freezing of the ther-mochemistry beyond the throat. Experimental results forhigh enthalpy nozzles at conditions close to the presentones are not abundant in the literature, and conclusionsnot possible based when only the pitot or enthalpy mea-surements are available. Atomic recombination rates ap-parently are speeded up in the F4 nozzle #2, and mea-surements obtained in the vicinity of the exit test sectionlead to a difference with those expected. The process thataccelerates atomic recombination is far from being un-derstood and even further from being controlled. The re-combination rate modelling that contains the vibrationaleffect increases both static pressure and translational tem-perature close to the equilibrium values measured (theclassical approach only involves the translational temper-ature). Such an approach corresponds to an atomic re-combination with a high level of vibration for the result-ing molecule. This effect has been introduced in one andtwo-dimensional codes defined above, applying either thePark model for the chemistry-vibrational coupling as fol-lows:

Kf =Kf(Ta),

Ta= T qTv(1−q),

Kb=Kf(Ta)/Keq(T ),

or Brun & Belouaggadia, Treanor-Marrone and Fordmodels. These models are called the Vibrational-Disso-ciation-Recombination models (VDR) [18]. Further in-vestigations demonstrated the necessary use of fast chem-ical air reactions rates (Park or Shatalov rather than Gar-diner) and V-T relaxation time (Millikan & White re-vised by Park instead of classic Millikan & White) withregard to fast processes occurring in expanded nozzleflows (compared to compression flows). Moreover, V-Vexchanges were observed negligible (1%) for an increaseof the translational temperature for such flows [21]. Thedescription of energy exchange during the nozzle expan-sion (from the throat to the exit) indicates that the only en-ergy reservoir available, allowing a transfer to the trans-lational mode to reach measured values, is the chemi-

B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361 357

Figure 16. Computational distributions of modal energiesalong the F4 nozzle #2 considering classical nonequilibriummodelling.

Figure 17.Computational distributions of modal energies alongthe F4 nozzle #2 considering the fast atomic recombinationmodelling.

cal heat of formation of oxygen (atomic nitrogen con-centration remains insufficient). When classical modelsof non equilibrium are assumed, the atomic oxygen con-centration freezes from the vicinity of the throat, allow-ing no energy transfer to the translational mode. In con-trast, when a VDR model is used, the atomic oxygendistribution decreases monotonically, providing throughthe expansion sufficient energy in terms of heat releaseto the translation and kinetic modes. This effect beginsto be efficient for translation when the velocity gradientdoes not remain important (seefigures 16and17). Para-metric studies performed with the codes demonstratedthat:

(1) the effect of fast atomic recombination rates partic-ularly for atomic oxygen occurs all along the nozzle butis only visible whenA/A∗ > 2000 (where the discrep-ancy cannot be included into experimental or numericaluncertainties);

(2) the effect of fast atomic recombination is sensitiveto the shape of the nozzle geometry, i.e., contourednozzle will induce more effect than conical nozzle at anequivalent distance from the throat.

Recent measurements and computations performed inthe F4 nozzle #3 indicated that the discrepancy be-tween experimental data (static pressure distributions)and non equilibrium calculations are much lower thanthose obtained for nozzle #2. The explanation is thatthe nozzle #3 expands about 3 times less than nozzle#2, i.e.,A/A∗ = 1800 confirming 1). Further computa-tions were conducted concerning other high enthalpy fa-cilities with comparable F4 reservoir conditions (HEG,TCM2,. . .) for which some measurements were available(LIF, DLAS and wall pressures). Since these high en-thalpy facilities haveA/A∗ < 2000 (this point is shifteddownstream for conical nozzle), both non equilibriumand fast atomic recombination models gave values closeto the measurements.

5.4. Synthesis of F4 flows rebuilding

The analysis of experimental results obtained in the F4wind tunnel has contributed to the addressing of prob-lems of prime importance for this type of wind tunneland for high-enthalpy testing in general, i.e., the determi-nation of the reservoir enthalpy and the thermochemicalnature of the nozzle flow in the test section. The analysisof several types of experimental results (nozzle wall pres-sure, DLAS translational temperature, and NO concen-tration) yields the undoubted conclusion that freestreamdata such as translational temperature and pressure areclose to equilibrium at high-enthalpy conditions. As faras measurements (static pressure and translational tem-perature) are provided in the nozzle region whereA/A∗remains lower than 2000, deviation due to fast oxygen re-combination processes is included within the experimen-tal uncertainty margins and so being also simulated bythe classical non equilibrium modelling (this is the casefor HEG [21]). But for larger ratios the physics will nolonger be reproduced due to a significant deviation as weobserved in the F4 nozzle #2 withA/A∗ ∼ 4500. Thereis room for interpreting and modelling the fast atomicrecombination processes in highly expanded nozzles athigh total enthalpy and pressure conditions. New diag-nostics based on the LDAS technique with the molecu-lar oxygen will allow to confirm or deny this hypothesiswithin next 2 years.

358 B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361

6. Presentation of the CELHYO solver andapplications

6.1. Motivation

Modern design of hypersonic vehicles relies heavilyon numerical simulation for a number of typical re-entryflight regimes. The physical phenomena present withinthe corresponding flow fields are highly complex and realgas effects need to be taken into account in the simu-lation. Since it is impossible to simulate experimentallyall the aerothermodynamic conditions encountered dur-ing a re-entry trajectory, numerical simulation is moreand more used to evaluate the flight feasibilities, as wellas to indicate heatloads and the possibilities of integra-tion of propulsion systems. The freestream conditions inflight can differ substantially from the freestream condi-tions generated in high enthalpy and shock tube facili-ties. It may occur that in the experiment the degree ofnon equilibrium of the flow is higher than for flight con-ditions. This will largely influence the excitation of in-ternal energy modes or dissociation. This is one of thereasons why the extrapolation of wind tunnel or high en-thalpy facility data to flight conditions is a difficult task,which cannot be undertaken without CFD. For a betterunderstanding of the complex phenomena that charac-terise hyperenthalpic flows, ONERA first developed thetwo-dimensional code CELHYO [8].

This Navier–Stokes solver is devoted to the numeri-cal simulation of hypersonic viscous flows in chemicaland thermal non equilibrium, such as high enthalpy at-mospheric re-entry or nozzle flows. Turbulence effectscan be modelled by means of a standard algebraic modelof Baldwin-Lomax (two layer algebraic eddy viscositymodel). In addition to its simplicity, the justification forthe use of such a model is that it yields reasonable re-sults across a wide range of Mach number. This code iscontinuously enriched with new physical modellings andnumerical schemes. For example, ionisation and radiationcan be taken into account [7]. If a two-dimensional codeis essential for a deeper insight into the phenomena con-cerned, three-dimensional calculations need to be madeon realistic geometries in the phase of design of the re-entry vehicle. Due to the improvement of computer ca-pabilities, it has now become possible to calculate suchcomplex geometries. A 3D code has recently been devel-oped. It allows the prediction of viscous laminar flowsin chemical non equilibrium. This solver essentially usesthe modelling and the numerical schemes available in the2D code. The code is highly modular both in aerothermo-dynamic and numerical modelling.

6.2. Numerical methods

The code CELHYO solves the Navier–Stokes equa-tions accounting for the physical modelling on curvilin-ear structured meshes using a fully implicit finite volume

method. The 3D code handles multi-block grids, madeof several structured, possibly overlapping domains. Theviscous part is discretised according to a central differ-encing procedure, while a quasi-second order accurateupwind scheme yields an approximation for the inviscidoperator. Upstreaming is achieved using an approach forupwind bias referred to as the Hybrid Upwind Splitting[9]. A wide variety of upwind schemes are also avail-able (van Leer, Roe,. . .) as well as limiters (van Albada,Minmod,. . .). Second order accuracy is achieved using aMUSCL approach written in primitive variables. The im-plicit operator is made up of a linearisation of both the in-viscid and viscous fluxes plus all the source term jacobianmatrices. Concerning the inviscid contribution, only theunderlying van Leer pair of split fluxes is accounted forto increase the overall robustness. No approximate fac-torisation is performed and a GMRES iterative procedurepreconditioned by an incomplete factorisation is used tosolve the resulting linear problem.

6.3. Application to 2D calculation on a blunt conemodel

In the frame of the Working Group 18 in the formerAGARD, a blunt cone model was designed to be testedin various high and low enthalpy wind tunnels. The back-ground of the blunt cone task corresponds to an evalu-ation of high enthalpy ground test facilities capabilitiesto provide benchmark data needed to develop and vali-date predictive methods in wake flows. Due to increasingmissions planned to planetary entries (such as Mars), ef-fects of wake flow on the payload located in the afterbodyregion is of great interest for prediction to avoid any dam-age to scientific material. Numerical rebuilding was per-formed in F4 conditions according to the matching pointof 400 bar and 10 MJ/kg chosen for tested high enthalpyfacilities.

The computational domain has been divided into twoparts. The meshes of the two domains respectively in-clude 80× 100 and 80× 120 points. The results areachieved with a decrease of ten orders of magnitude ofthe maximal residues.Figure 18 compares a schlierenphotograph at 30 milliseconds after the beginning of therun and the corresponding computation in thermochem-ical non equilibrium with the ONERA code CELHYO.Major features of the wake flow are visible. Infigure 19,comparison is made between numerical and experimentalresults concerning the forebody heating distribution. Nu-merical and experimental results are in good agreement,except in the shoulder zone. A good evaluation of suchan expansion region would need a higher resolution.

6.4. Application to a 3D calculation on the HALISmodel

The numerical simulation of flow on the HALIS modelat 40◦ angle of attack has been performed using a 6

B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361 359

Figure 18. Comparison between a schlieren photograph at 30ms after the beginning of the run with calculation.

Figure 19.Heat flux comparison between numerical and exper-imental.

block grid topology with 56 700 points (figure 20). Thefree-stream conditions on the re-entry vehicle correspondto F4 wind tunnel conditions. This tunnel was equippedwith nozzle #2 and the stagnation conditions were givenby a reduced total enthalpy equal to 165 and a reservoirpressure of 300 bar. The resulting free stream conditionsare:M4 = 9.7, V4 = 4930 m/s,P4 = 130 Pa andT4 =795 K. The wall is assumed to be non catalytic andits temperature is fixed to 300 K. At the present time,tridimensional calculations can only be performed withthe assumption of vibrational energy in equilibrium withthe translational mode.

The inviscid fluxes are evaluated by means of the HUSscheme. The result corresponds to a steady state obtained

Figure 20.Grid used for a 3D calculation on the HALIS model.

Figure 21. Iso pressure contours around the HALIS model.

after about ten thousand time-steps with a decrease offive orders of magnitude of the maximal residues. Themaximal value of the CFL number is 40 (global time-step). Figure 21 shows the pressure contours on thesurface of the re-entry body, in the symmetry plane andat three cross sections. NO mass fraction contours in thesymmetry plane are presented infigure 22. It indicatesthe degree of non equilibrium on the winward and theleeward sides. These results are preliminary results. Now,other calculations have to be performed and comparedto experimental results and other calculations in theliterature.

360 B. Chanetz et al. / Aerosp. Sci. Technol. 4 (2000) 347–361

Figure 22.NO mass fraction contours in the symmetry plane ofthe HALIS model.

7. Conclusion

This paper has presented some major results obtainedin the framework of the hypersonic research project. Welldocumented test-cases have been performed in cold hy-personics (R5Ch), including different aspects of the re-search in fundamental aerodynamics, in measurementtechniques and in CFD validation. The laminar/turbulenttransition has been carefully studied in cold and hot hy-personics, thanks to the linear stability theory. Among therealisations, one notes a physical modelling for re-entrycalculation which takes into account the effect of the ra-diation of the shock layer with a totally coupled approachwith aerodynamics. This method applied to Rosetta probehas led to very interesting results. Furthermore consider-able work has been performed for computation flow re-building in F4. It concerned particularly the fast recom-bination processes for high enthalpy strongly expandedflow for which new models of recombination vibrationcoupling have been investigated. At last, numerical re-sults have been obtained with the CELHYO solver, bothin axisymmetric and in 3D-version.

Thus, the hyperenthalpic hypersonic project has con-tributed to the development of knowledge in differ-ent domains involved in the study of atmospheric re-entry problems: fundamental research, instrumentationand flow rebuilding in high enthalpy facilities, physi-cal modelling and calculations. Thanks to the work per-formed at ONERA these last years – although there wereno contracts emanating from technological programs –,a good level has been reached as far as hyperenthalpicflows are concerned. The situation is very convenientsince a Franco-American ‘Mars Sample Return program’is activated from January 1999. Future works are goingto be undertaken in the framework of this program.

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