GuillaumeGrossirJuly1,2015 LongshotHypersonicWindTunnelFlowCharacterizationandBoundaryLayerStabilityInvestigations vonKarmanInstituteforFluidDynamics Universit´eLibredeBruxelles

Universit´

e Libre de Bruxelles

´

Ecole Polytechnique, Facult´

e des Sciences Appliqu´

ees

von Karman Institute for Fluid Dynamics

Aeronautics & Aerospace Department

Thesis presented in order to obtain the Degree of Doctor of Engineering Sciences

of the Universit´e Libre de Bruxelles

Longshot Hypersonic Wind Tunnel

Flow Characterization and

Boundary Layer Stability Investigations

Guillaume Grossir

July 1, 2015

Promoter: Prof. Herman Deconinck

Prof. G´

_{erard Degrez (ULB, President)}

Prof. Herman Deconinck (ULB, Promoter)

Prof. Olivier Chazot (VKI, Supervisor)

Prof. Alessandro Parente (ULB)

Prof. Herbert Olivier (RWTH Aachen, Germany)

M. Jean Perraud (ONERA Toulouse, France)

Contact information:

Guillaume Grossir

von Karman Institute for Fluid Dynamics Chauss´ee de Waterloo, 72

1640 Rhode-Saint-Gen`ese BELGIUM

`

A ma Maman.

“If we all worked on the assumption that what is

accepted as true really is true, then there would be

little hope for advance.”

Acknowledgments

Nearly five years have passed since I have written the first lines related to this work. To

all those who have contributed to make this time unique, enjoyable and unforgettable, I

wish to express here my most sincere acknowledgments.

My first words go to my initial supervisor, Prof. Patrick Rambaud, with whom

everything started. Thanks for always believing in me and pushing me to give my

very best. Your thoughtful guidance, support, and understanding have been very much

appreciated all the way from the request of my fellowship till my defense.

Thanks to Prof. Olivier Chazot, for your continuous encouragements and for the difficult

task of taking over this supervision during the last year and a half. Your support over the

last steps and suggestions to improve the present manuscript have also been very welcome!

I would also like to express my gratitude to my promoter, Prof. Herman Deconinck.

I am very thankful for your interest, assistance and the absolute support I have received

for each of the milestones of my work.

Thanks to all my jury members for your feedback and useful comments.

The door of Prof. Thierry Magin was always open to discuss the rebuilding of the flow

conditions and the physical mechanisms occurring through the Longshot nozzle. I have

deeply appreciated your interest and constructive ideas.

I have also had the chance to supervise several master students over these years. Alessio,

Bart, Bruno, Gabriele, Julien, Luis, Morgane, Zdenek... I have very much enjoyed your

fresh minds and our positive discussions. I am wishing you the best of success for your

future!

The linear stability theoretical results provided by Fabio Pinna have brought a lot more

significance to the results presented throughout this work. Thank you so much for your

expertise and your patience!

I equally appreciate your efforts Ross Wagnild (Sandia) for running PSE computations

on additional cases. Looking forward to meeting you!

Thank you Tamas for always being so enthusiastic about my experiments! I am indebted

to you for all your efforts to develop this flow visualization technique.

Best thanks are then due to Prof. Steve Vanlanduit and Alexandru Nila, from the

Vrije Universiteit Brussel, for the loan of their ILA High Speed PIV system and without

who only very few images of these beautiful flow disturbances would have been acquired.

Dear Khalil... no hard feelings for the Mach 14! Do not worry, I am not gonna work

on the sun surface, go on safely ;-) All the best!

Damien and Imre, thank you for setting up your optical diagnostics in the Longshot

for these few preliminary experiments. I am looking forward to seeing the next steps!

not disturbed too much our quiet working environment ;-) Thank you for your complete

understanding!

To Christelle and Evelyne, the best librarians I could have hoped for, always welcoming

and available to look for the reports I was requesting: many thanks for your time!

None of this work would have been performed without the support from VKI technicians,

either to operate the Longshot wind tunnel or to manufacture the different probes and

models I have used and to instrument them. Cheers to the Longshot team: Patrick and

Jerôme for carefully maintaining the Longshot, and Pascal for cautiously following the

checklists for its successful operation. Thank you Maurice, Sébastien, Willy and José in

the workshop; and Terrence and Walter for your nimble fingers.

Thank you Luigi and Jean-Jacques for your clear technical drawings and your expertise

which eased so much each of the technical problems I have faced.

Jerôme, my DC mate, you have shown me the path! Işıl, Bernd, you are next! I have

also very much enjoyed your HuGe Bels concerts! From the same year: Péter, Sophia,

Tyler, and also J.-B., thank you all for the very good time we have spent together.

Thank you Sébastien for all your valuable technical experience and for allowing me

to run your Longshot. Congratulations on being such a talented beer brewer and thanks

for sharing your products with us during these Wednesday late meetings. Batch #30 has

been my favorite!

Beside the VKI life, Gliding Weeks have been amazing opportunities to change my

mind, meet new people, enjoy new experiences, and have the best of fun during our

Fetnnapf evenings. Thank you Ringo, Till, Falke, Juan, and Thomas for teaching me some

of your skills! No wonder it was difficult to get back to work after each of these flights.

I am forever grateful to Cey for organizing these events so successfully!

Last but not least, I wish to thank my family who always stood by me, even from far.

Thanks Dad for welcoming me and Silvânia every time we needed to rest and free our

minds! Flo, my brother, thanks for your interest, your conscientious proof reading and for

your admirable skills to generate some of the images I have needed! And finally, many

many thanks to you, Sissi, for your love, patient listening, and unlimited understanding.

Merci !

Guillaume Grossir

July 1, 2015.

Abstract

The hypersonic laminar to turbulent transition problem above Mach 10 is addressed experimentally in the short duration VKI Longshot gun tunnel. Reentry conditions are partially duplicated in terms of Mach and Reynolds numbers. Pure nitrogen is used as a test gas with flow enthalpies sufficiently low to avoid its dissociation, thus approaching a perfect gas behavior. The stabilizing effects of Mach number and nosetip bluntness on the development of natural boundary layer disturbances are evaluated over a 7◦ _half-angle

conical geometry without angle of attack.

Emphasis is initially placed on the flow characterization of the Longshot wind tunnel where these experiments are performed. Free-stream static pressure diagnostics are implemented in order to complete existing stagna-tion point pressure and heat flux measurements on a hemispherical probe. An alternative method used to determine accurate free-stream flow condi-tions is then derived following a rigorous theoretical approach coupled to the VKI Mutation thermo-chemical library. Resulting sensitivities of free-stream quantities to the experimental inputs are determined and the cor-responding uncertainties are quantified and discussed. The benefits of this different approach are underlined, revealing the severe weaknesses of tradi-tional methods based on the measurement of reservoir conditions and the following assumptions of an isentropic and adiabatic flow through the nozzle. The operational map of the Longshot wind tunnel is redefined accordingly. The practical limits associated with the onset of nitrogen flow condensation under non-equilibrium conditions are also accounted for.

Boundary layer transition experiments are then performed in this environ-ment with free-stream Mach numbers ranging between 10–12. Instruenviron-menta- Instrumenta-tion along the 800 mm long conical model includes flush-mounted thermo-couples and fast-response pressure sensors. Transition locations on sharp cones compare favorably with engineering correlations. A strong stabilizing effect of nosetip bluntness is reported and no transition reversal regime is observed for ReRN, ∞≤120 000. Wavelet analysis of wall pressure traces

Contents

Nomenclature xv

1. Introduction 1

1.1. Hypersonic framework, milestones . . . 1

1.2. Hypersonic challenges . . . 3

1.3. Boundary layer transition phenomenon . . . 5

1.3.1. Definition . . . 5

1.3.2. Consequences . . . 6

1.3.3. Need for transition predictions . . . 7

1.4. Thesis objectives and structure . . . 9

1.4.1. Objectives . . . 9

1.4.2. Structure . . . 10

I.

The Longshot wind tunnel

and its measurement techniques

11

2.1.1. Purposes . . . 13

2.1.2. Duplication parameters . . . 14

2.1.3. Different types of hypersonic wind tunnels . . . 15

2.2. Historical note on the development of the Longshot tunnel . . 23

2.3. General characteristics of the Longshot wind tunnel . . . 24

2.3.1. Main elements . . . 24

2.3.2. Wave diagram . . . 26

2.3.3. Test gas . . . 29

2.3.4. Initial conditions . . . 29

2.4. The contoured nozzle . . . 30

2.4.1. Overview of the design method used . . . 30

2.4.2. Nozzle contour analysis . . . 31

2.4.3. Critical review of the method used . . . 32

2.4.4. Influence of stagnation conditions on the nozzle contour 35 2.5. Numerical modeling . . . 36

2.5.1. Compression cycle . . . 36

2.5.2. Nozzle flow . . . 36

3. Measurement techniques 39

3.1. Stagnation probe . . . 39

3.1.1. Purpose . . . 39

3.1.2. Design and instrumentation . . . 39

3.2. Stagnation pressure rake . . . 40

3.2.1. Purpose . . . 40

3.2.2. Design and instrumentation . . . 41

3.3. Free-stream static pressure probe . . . 43

3.3.1. Purpose . . . 43

3.3.2. Review of hypersonic static pressure measurements . . 44

3.3.3. Designs for the Longshot wind tunnel . . . 46

3.3.4. Instrumentation . . . 48

3.3.5. Calibration . . . 48

3.3.6. Numerical simulations . . . 49

3.3.7. Experimental investigations . . . 57

3.4. Summary . . . 62

II. Hypersonic nozzle flow characterization

63

4.2. Previous method used for the Longshot . . . 66

4.3. Other free-stream rebuilding procedures in the literature . . . 68

4.4. Improved method for the Longshot wind tunnel . . . 69

4.4.1. Overview and flowchart . . . 69

4.4.2. Measurements required . . . 71

4.4.3. Assumptions . . . 72

4.4.4. Detailed procedure . . . 73

4.4.5. Validation . . . 80

4.4.6. Possible extensions of the method . . . 81

4.5. Summary . . . 82

5. Longshot flow characterization 83 5.1. Nozzle flow and boundary layers . . . 83

5.1.1. Numerical prediction . . . 83

5.1.2. Measurements along the nozzle . . . 87

5.2. Free-stream disturbance levels . . . 93

5.2.1. Origins and characteristics . . . 93

5.2.2. Estimations in the Longshot wind tunnel . . . 94

5.3. Determination of free-stream flow properties . . . 96

5.3.1. Comparison of “nozzle” and “free-stream” methods . . 96

5.3.2. Further proofs for a lower free-stream Mach number . 104 5.3.3. Origins of the lower free-stream Mach number . . . 106

Contents xi

5.4. Update of the Longshot operational map . . . 114

5.5. Summary . . . 114

6. Flow condensation 117 6.1. Review of flow condensation in high-speed wind tunnels . . . 117

6.1.1. Historical note . . . 117

6.1.2. Condensation mechanisms . . . 119

6.1.3. Parameters influencing the onset of condensation, su-percooling effects . . . 120

6.1.4. Consequences of condensation on flow quantities . . . 120

6.1.5. Detection methods . . . 121

6.1.6. Literature results . . . 122

6.2. Investigations in the Longshot . . . 128

6.2.1. Past attempts . . . 128

6.2.2. Standard operating condition . . . 130

6.2.3. Increasing/decreasing stagnation temperature . . . 132

6.2.4. Discussion, comparisons with literature results . . . . 136

6.2.5. A mechanism explaining the lower Mach number? . . 139

6.3. Summary . . . 140

III. Hypersonic boundary layer transition investigation

143

7.2. Linear stability theory and eN _{method . . . 147}

7.2.1. Formulation . . . 147

7.2.2. Results for incompressible flows . . . 149

7.2.3. Results for compressible flows . . . 151

7.2.4. Other types of instabilities . . . 155

7.2.5. eN _{method . . . 156}

7.3. Measurement techniques for transition studies . . . 157

7.3.1. Transition location . . . 157

7.3.2. Instabilities . . . 158

7.4. Influencing parameters . . . 159

7.4.1. Mach number . . . 160

7.4.2. Free-stream turbulence . . . 161

7.4.3. Wall to total temperature ratio . . . 163

7.4.4. Nose bluntness and entropy layer effects . . . 163

7.4.5. Pressure gradient . . . 169

7.4.6. Free-stream unit Reynolds number . . . 170

7.5. Second mode instabilities characteristics . . . 172

7.6. Engineering predictions methods . . . 176

7.6.1. A word of caution . . . 176

7.7. Review of transition experiments at large hypersonic Mach numbers . . . 179 7.8. Summary . . . 181 8. Conical model 183 8.1. Model choice . . . 183 8.2. Design . . . 183 8.3. Instrumentation . . . 185 8.3.1. Layout . . . 185 8.3.2. Coaxial thermocouples . . . 185

8.3.3. Piezoresistive pressure sensors . . . 189

8.3.4. Piezoelectric pressure sensors . . . 190

8.4. Test section installation . . . 192

8.5. Summary . . . 192

9. Experimental transition results 195 9.1. Flow topology . . . 195

9.1.1. Flow establishment time and quasi-steady analysis . . 195

9.1.2. Wall pressure distribution . . . 196

9.1.3. Derivation of free-stream Mach number . . . 198

9.1.4. Entropy layer swallowing distance . . . 200

9.1.5. Boundary layer thickness . . . 200

9.2. Wall heat fluxes . . . 201

9.2.1. Transition location and nosetip bluntness effects . . . 201

9.2.2. Comparison with Pate’s correlation . . . 208

9.3. Disturbances measured at the wall . . . 210

9.3.1. Wavelet analysis . . . 210

9.3.2. Spectra analysis and comparisons with LST results . . 216

9.3.3. Group velocities . . . 226

9.3.4. Standard deviation and higher-order moments . . . . 227

9.3.5. Wavelengths . . . 229

9.3.6. Lateral extension . . . 231

9.4. Flow visualization . . . 232

9.4.1. Illustration of the transition process . . . 233

9.4.2. Group velocities . . . 236

9.4.3. Location of disturbances across the boundary layer . . 238

9.5. Comparison between different measurement techniques . . . . 243

9.6. Summary . . . 247

Contents xiii

10.2. Synthesis . . . 256

10.2.1. Hypersonic ground testing and flow characterization . 256 10.2.2. Hypersonic boundary layer transition investigation . . 259

10.3. Recommendations and perspectives . . . 262

10.4. Outlook . . . 266

Appendices

267

A.2. Over a model . . . 273

A.2.1. Overview of wave and diffusion mechanisms . . . 273

A.2.2. Establishment of transitional boundary layers . . . 275

A.2.3. Longshot conical model . . . 275

A.3. Summary . . . 280

B. Other test gases in the Longshot 283 B.1. Carbon dioxide . . . 283

B.2. Air . . . 284

C. Nitrogen thermal non-equilibrium 285 C.1. Modes of molecular energy . . . 285

C.2. Equilibrium/frozen flows . . . 286

C.3. Nozzle flow expansions . . . 286

C.4. Influence on free-stream processing method . . . 287

D. Numerical computations 291 D.1. Longshot contoured nozzle . . . 291

D.1.1. Meshes . . . 291

D.1.2. Solver . . . 291

D.1.3. Boundary conditions . . . 292

D.2. Static pressure probes . . . 293

D.2.1. Meshes . . . 293 D.2.2. Solver . . . 294 D.2.3. Boundary conditions . . . 294 D.3. 7◦ _{half-angle cone . . . 295} D.3.1. Meshes . . . 295 D.3.2. Solver . . . 297 D.3.3. Boundary conditions . . . 297

D.3.4. LST (and PSE) computations . . . 297

E. Free-stream rebuilding methods in the literature 301 E.1. Low enthalpy . . . 301

F. The Fay-Riddell equation 307

F.1. General expression and assumptions . . . 307

F.2. Velocity gradient at the stagnation point . . . 308

F.3. Simplification of the Fay-Riddell equation for the Longshot wind tunnel . . . 312

F.4. Corrections for radial conduction effects . . . 312

F.5. Other equations estimating the stagnation point heat flux . . 313

G. Nitrogen flow properties 315 G.1. Dynamic viscosity . . . 315

H. Uncertainties on free-stream properties 317 H.1. Overview . . . 317

H.2. Sensitivity analysis . . . 318

H.3. Uncertainties . . . 319

H.3.1. Input uncertainties . . . 319

H.3.2. Final uncertainties . . . 321

I. LIF-based Schlieren technique 329 I.1. General purpose . . . 329

I.2. Review of light refraction based techniques . . . 329

I.3. LIF-based Schlieren . . . 331

I.3.1. Concept . . . 331

I.3.2. Experimental setup . . . 332

I.4. Summary . . . 334

J. Transition experiments test matrix 337

Nomenclature

Non-dimensional numbers

CF ₁ τw 2ρ∞u2∞

Skin friction coefficient. In Pate’s correlation (eq. 7.12), this coefficient is written CFII and

evaluated from the method detailed in van Driest (1956). Cp pγw− p∞ 2p∞M2∞ Pressure coefficient C_pmax pt2− p∞ γ 2p∞M2∞

Pressure coefficient at stagnation point G τ ue

L Dimensionless flow establishment time, eq. A.3

Kn λ L Knudsen number Le α D Lewis number M u a Mach number M M −c

a Relative Mach number, eq. 7.7

Pr µcp

k Prandtl number

ReL, ∞

ρ∞u∞L

µ∞ Reynolds number based on the reference length L_{and free-stream flow properties. Alternative}

ref-erence lengths are D, RN, s, x, θ or a unitary

length of 1 m. Boundary layer edge flow proper-ties, indicated by the subscript e, can also be used instead of free-stream flow properties.

St ˙qw

ρu(haw− hw) Stanton number. Depending on the definition_{chosen, reference flow quantities ρ and u can be}

considered in the free-stream or at the edge of the boundary layer. V _pM∞ Rex, ∞ √ C Viscous parameter χ M 3 ∞ p_Re x, ∞ √

Roman symbols

a m/s Speed of sound, eq. 4.42 A m2 Cross section area A − Wave amplitude

A₀ − Wave amplitude while crossing the neutral curve c − Non-dimensional phase velocity

c J/(kg·K) Specific heat

cp J/(kg·K) Specific heat at constant pressure cv J/(kg·K) Specific heat at constant volume

¯c − Normalizing parameter (Pate’s correlation, eq. 7.12)

C − Chapman-Rubesin constant C in Circumference of the test section

C₁ in Circumference of a reference test section (= 48 in) D mm Probe diameter

D m2/s Mass diffusivity

DN Derivative matrix of the nth order e J/kg Specific internal energy, eq. 4.8 eel J/kg Specific electronic energy, eq. 4.7 erot J/kg Specific rotational energy, eq. 4.5 etr J/kg Specific translational energy, eq. 4.4 evib J/kg Specific vibrational energy, eq. 4.6 E J/kg Specific total energy, eq. 4.9

f Hz Frequency

f₁ Hz Fundamental frequency

f₂ Hz Frequency of the second harmonic Fs Hz Sampling frequency

g Wavelet expression, eq. 9.7 h J/kg Specific enthalpy, eq. 4.28

hel J/kg Specific electronic enthalpy, eq. 4.27 hrot J/kg Specific rotational enthalpy, eq. 4.25 htr J/kg Specific translational enthalpy, eq. 4.24 hvib J/kg Specific vibrational enthalpy, eq. 4.26

= − Imaginary part

J Jacobian matrices, eqs. 4.21, 4.33 and 4.39 k − Inverse of the shock density ratio, k = ρ1

ρ2

Nomenclature xvii

k W/(m·K) Thermal conductivity

kB J/K Boltzmann constant, kB = 1.3806488 · 10−23J/K K − Constant, eq. 9.4

l m Length of the last characteristic of a contoured nozzle L mm Probe length

L m Reference length

m kg Mass

M kg/mol Molar mass

n Mode number

n − Amplification factor, eq. 7.8 n 1/m3 Number density, eq. 4.2 n Iteration index

N Number of points used in the Gauss-Chebyshev-Lobatto

law, eq. D.2

N − Number of species

N − N-factor, maximum of the amplification factors n over

all frequencies

NA 1/mol Avogadro constant, NA= 6.02214129 · 1023mol−1

p Pa Pressure

pc Pa Conical surface pressure ps Pa Saturation vapor pressure pt2 Pa Stagnation point pressure

pv Pa Vapor pressure

˙P s−1 _{Nozzle expansion rate, eqs. 6.2 and 6.3}

q∞ Pa Free-stream dynamic pressure

˙qc W/m2 Conical wall heat flux, eq. 8.4

˙qw W/m2 Stagnation point heat flux Q Generalized flow variable r − Recovery factor

r m Radial distance from the nozzle axis

r J/(kg·K) Specific gas constant, r = 296.80898 for nitrogen

< − Real part

R Residual matrices, eqs. 4.22, 4.34 and 4.40

R J/(K·mol) Universal gas constant, R = 8.3144621 J/(K·mol)

RN mm Nosetip radius s Wavelet scale, eq. 9.8 s J/(kg·K) Specific entropy

s mm Distance along the surface of the cone, from a

theoreti-cally sharp nosetip

sB mm Transition onset location, along the surface (local

mini-mum wall heat flux)

sE mm End of the transition region, along the surface (local

maximum wall heat flux)

ssw mm Entropy layer swallowing distance, along the surface S K Constant used in Sutherland’s equation, eq. D.1 SR − Saturation ratio, eq. 6.1

t s Time

T K Temperature

Tc K Non-equilibrium condensation temperature Ti K Initial temperature

Tr K Recovery temperature

Tr−t K Rotational-translational temperature Ts K Saturation temperature

Tvib K Vibrational temperature u m/s Streamwise velocity

U Matrix of unknowns, eqs. 4.20, 4.32 and 4.38 v m/s Normal velocity

x − Molar fraction, eq. 4.1

x mm Streamwise Cartesian coordinate x₀ mm Location of the first unstable wave

xB mm Transition onset location, along x (local minimum wall

heat flux)

xE mm End of the transition region, along x (local maximum

wall heat flux)

xLE m Leading edge location with respect to the throat location y − Mass fraction

y mm Normal to the wall Cartesian coordinate y₀ mm Point through the boundary layer at which _uu

e = 1−

1 Me

ya mm Location through the boundary layer where M

2

= 1

ys mm Location of the generalized inflection point through the

Nomenclature xix

y+ − Non-dimensional wall distance z mm Spanwise Cartesian coordinate

Greek symbols

α − Non-dimensional flow establishment time, α = 1/G,

eq. A.2

α − Non-dimensional streamwise wave number α ◦ Angle of attack

α m2/s Thermal diffusivity, α = _ρck

p

β − Non-dimensional spanwise wave number β ◦ Sideslip angle

γ − Specific heat ratio γ₁ Skewness (γ₁= µ3

σ3) γ₂ Kurtosis (γ₂= µ4

σ4 −3) γb Bandwidth of a wavelet γc Center frequency of a wavelet δ m Boundary layer thickness

δ∗ _{m Boundary layer displacement thickness}

∆ m Shock stand-off distance ¯

∆ − Dimensionless shock stand-off distance

 Infinitesimal quantity θ ◦ Flow deviation angle

θ m Boundary layer momentum thickness θc ◦ Cone half-angle

θv K Characteristic vibrational temperature, (θv = 3 392.7 K

for nitrogen)

λ m Disturbance wavelength λ m Mean free path

µ Pa·s Dynamic viscosity µ₃ Third central moment µ₄ Fourth central moment µt Pa·s Turbulent viscosity ν m2/s Kinematic viscosity ξ − Defined by eq. A.1

σ Standard deviation τ − Slenderness ratio

τ s Variable of integration, eq. 8.3

τ s Time required for the flow to be regarded as established τc 1/s Rate of chemical reactions

τf s Flow characteristic time τw Pa Wall shear stress

φ ◦ Roll angle

χ Either viscosity or thermal conductivity in Sutherland’s

equation, eq. D.1

χ Related logarithmic supersaturation, Fig. 6.5a

ψ ◦ Wave angle

ω − Non-dimensional frequency

ω ◦ Maximum deflection angle of the contoured nozzle wall

Subscripts

0 stagnation condition in the reservoir 1 condition before a normal shock 2 condition after a normal shock ∞ refers to free-stream flow properties inc incompressible

lam laminar turb turbulent

c at condensation onset

e at the edge of the boundary layer el electronic

eq under equilibrium chemical composition f r under frozen chemical composition i gas species

i imaginary part rot rotational

s at constant entropy

s stagnation condition outside the boundary layer

along the stagnation point streamline

T at constant temperature

Nomenclature xxi tr translational vib vibrational w at the wall

Superscripts

Acronyms

AEDC Arnold Engineering Development Complex ALTP Atomic-Layer ThermoPiles

ARD Atmospheric Reentry Demonstrator Cars Coherent Anti-Stokes Raman Spectroscopy CCD Charge-Coupled Device

CMOS Complementary Metal-Oxide-Semiconductor

Coolfluid Computational Object-Oriented Libraries for Fluid Dy-namics

DLR Deutsches Zentrum f¨ur Luft- und Raumfahrt DNS Direct Numerical Simulation

Expert EXPErimental Reentry Testbed FFT Fast Fourier Transform

FLDI Focused Laser Differential Interferometry

HEG High Enthalpy shock tunnel in G¨ottingen (at DLR) Hiest High Enthalpy Shock Tunnel (at Jaxa)

HTV-2 Hypersonic Technology Vehicle 2 IXV Intermediate eXperimental Vehicle Jaxa Japan Aerospace Exploration Agency LaRC Langley Research Center (Nasa) Lif Laser Induced Fluorescence LST Linear Stability Theory

Nasa National Aeronautics and Space Administration Nasp National Aero-Space Plane

Pant PAssive Nosetip Technology PDF Probability Density Function PIV Particle Image Velocimetry Plif Planar Laser Induced Fluorescence PSE Parabolized Stability Equations

RWTH Rheinisch-Westf¨alische Technische Hochschule Aachen SIV Structure Image Velocimetry

TDLAS Tunable Diode Laser Absorption Spectroscopy TS Tollmien-Schlichting

TZM Titanium-Zirconium-Molybdenum alloy

Chapter 1.

Introduction

1.1. Hypersonic framework, milestones

German scientists, in the early 1940’s, have been the first ones to put in prac-tice the high-speed flow theory developed earlier in that century. Following the successful operation of their supersonic wind tunnels up to Mach 4.4 in Peenemuende1_{, they have carried out there, on 17 April 1944, the first}

exper-iments at Mach 8.82_{. This was a first step towards the continuous operation}

of a Mach 10 wind tunnel being built near Kochel, Bavaria (Wegener, 1996; Eckardt, 2015). This research during World War II was primarily driven by the need to develop ballistic missiles such as the V1s and V2s (Fig. 1.1a), the latter reaching top speeds on the order of Mach 5 (Heppenheimer, 2007). German researchers however did not distinguish this higher Mach number flow regime from the supersonic one, and therefore did not describe it with a new name. It is only after the war, that Hsue-Shen Tsien, a former doctoral student of Theodore von K´arm´an working at the California Institute of Tech-nology, coined the term hypersonic3_{(Tsien, 1946), which is now commonly}

used to designate Mach numbers larger than 5.

The Cold War which followed was driven by the competition between the two blocks to be able to fly faster and higher than the other. This included the development of aircraft and Inter Continental Ballistic Missiles based on the knowledge and technologies gathered from German scientists. Out of these military projects would also be developed the space programs such as Mercury for U.S. and equivalent ones for the U.S.S.R.

It took some years before hypersonic manned flight could come at hand. On April 12, 1961, at Baikonur (Russia), was fired a multistage rocket car-rying the Vostok 3KA spaceship (Fig. 1.1b) in which the Flight Major Yuri Gagarin had taken place. After orbiting once the Earth it returned safely back to the ground at an initial Mach number greater than 25. A giant step had been taken and the first manned hypersonic flight was achieved4_.

Less than a month later, on the 5th_{of May, the American Alan B. Shepard}

1_{North-east of the actual Germany, on the Baltic Sea coast.}

2_{This was achieved for 15 seconds in a 0.4 × 0.4 m wind tunnel under the technical}

direction of Wernher von Braun and the aerodynamicist Siegfried Erdmann.

3_{From Greek hyper (over) and Latin sonus (sound).}

4_{Strictly speaking, the hypersonic flight conditions achieved were rather a consequence}

(a) Bumper program (V2 rocket + second

stage WAC Corporal) (b) Vostok 3KA spaceship

(c) X-15 (d) Apollo

(e) Space Shuttle (f) X-30 NASP project

1.2. Hypersonic challenges 3

became the second man in space during a suborbital flight and also reentered the Earth atmosphere at hypersonic velocities. 1961 was also the year of the first hypersonic flights using the experimental plane X-15 (Fig. 1.1c) which reached Mach 5.27 on the 23rd _{June piloted by the Major Robert White.}

This vehicle equipped with a rocket engine reached Mach 6.04 on the 9th

November 1961 and Mach 6.70 later in 1967. Out of the 199 flights of the three X-15 vehicles, 111 can be considered as hypersonic, having a Mach number greater than 5 (Jenkins, 2000), and few of them reached the K´arm´an line: the official space border with altitudes greater than 100 km. During the cumulated 87 minutes spent in hypersonic flight, this aircraft collected valuable data benefiting to numerous following projects aimed to reenter through the atmosphere.

The American space program with Mercury, Gemini and Apollo (Fig. 1.1d) encountered hypersonic flow conditions during numerous flights between 1959-1963, 1962-1966 and 1966-1972 respectively, peaking with the Mach 36 reached during the lunar returns (first reached during the Apollo 4 mission, without crew, on the 9th _{November 1967).}

More economical ways of reaching space and deliver payloads into orbit were then considered in the 1970’s leading to the development of the reusable Space Shuttle (Fig. 1.1e). Flying first in 1981, it has been retired in July 2011 after only 135 missions whereas initial plans had hoped for two weeks turn around. The complexity of the multidisciplinary design approach required to meet with hypersonic flight requirements had limited the cheap access to space and shortened its operational life.

Numerous hypersonic projects have been initiated over the years (NASP X-30 in Fig. 1.1f, Hermes, X-43A, Orion...), but only few have reached their completion because of the difficulties faced. While the access to space is now being opened to private companies, the challenges faced are not lessened, especially the ones associated to the reentry through the atmosphere at high velocities.

1.2. Hypersonic challenges

The reasons for distinguishing hypersonic flows from supersonic ones are the occurrence of harsh and often critical phenomena. As described by Bertin and Cummings (2003, 2006), designers of the early hypersonic vehicles were sometimes unaware of these differences and faced the “unknown unknowns” which have been responsible for critical failures or nearly critical damages.

barrier” in an analogy to the “sound barrier” experienced earlier. All hy-personic vehicles therefore require some kind of thermal protection system. Allen and Eggers (1953) demonstrated few years later that blunt geometries should be preferred in order to survive the atmosphere entry. This contrasts with the slender ones commonly used in the supersonic regime where the minimization of the drag coefficient prevails over the heat transfer.

Few years later in 1967, while flying the X-15 with a dummy ramjet engine fixed below the experimental vehicle, shock-shock interactions burned some probes off and significantly damaged the ventral fin of the aircraft by generating local heating rates an order of magnitude larger than the unperturbed values (Heppenheimer, 2007).

Hypersonic flows are also associated with the onset of chemical reactions around the vehicles. The Space Shuttle experienced it during its first reen-try, in 1981, and the magnitude of these high-temperature effects was much larger than anticipated leading to a pitching moment different from expecta-tions. Although, this could be corrected by deflecting the body flaps of the Shuttle, it was close to the limits of their operational capabilities (Arrington and Jones, 1983).

Even though these phenomena have been identified since then, their ac-curate prediction is still subject to large uncertainties and all hypersonic vehicles have therefore critical weaknesses. The crew loss of the Columbia Space Shuttle serves to remind us that hypersonic flight represents a serious technological and economical challenge which is still far from being routinely achieved.

The majority of hypersonic vehicles falls into four different categories (Hirschel, 2005): winged reentry vehicles, hypersonic cruise vehicles, ascent and reentry vehicles and aeroassisted orbit transfer vehicles. Each of them corresponds to different trajectories as they leave or enter the atmosphere, as illustrated in Fig. 1.2.

A recurring issue for each of these vehicles is the accurate prediction of the wall heat transfer rates and skin friction. Both quantities are severely influenced by viscous effects near the walls and by the nature of the bound-ary layers along these surfaces (either laminar, transitional or turbulent as will be discussed shortly). This is critical to reentry vehicles (whose thermal protection system is only designed to accommodate a limited heat flux dur-ing their reentry), as well as to ascent and cruise vehicles (for which larger drag prevents from reaching their correct orbit or reduces their operational ranges, in addition to the thermal issues).

1.3. Boundary layer transition phenomenon 5

Figure 1.2.: Major classes of hypersonic vehicles and some characteristic aerothermodynamic phenomena (Hirschel, 2005)

turn hypersonic projects into successful vehicles.

1.3. Boundary layer transition phenomenon

1.3.1. Definition

The concept of a boundary layer in a viscous flow originates in 1904 when Prandtl published his famous paper (Prandtl, 1904). Two types of viscous flows are usually distinguished: the laminar ones and the turbulent ones. Laminar flows have a regular and ordered motion of the flow elements: the streamlines are smoothly arranged on top of each other. On the contrary, turbulent flows are characterized by a disordered motion of the fluid ele-ments: streamlines are sinuous and irregular.

δ Laminar flow region Transitional flow region Turbulent flow region Inviscid flow region

Viscous flow region

x (xtr)B

(xtr)E

u∞

Figure 1.3.: Schematic illustration of a laminar, transitional, and turbulent boundary layer (Pate, 1978)

Reshotko (1969) describes the boundary layer transition process as fol-lows:

One may view the transition of the boundary layer to a turbulent state as the nonlinear response of a very complicated oscillator—the lami-nar boundary layer—to a random forcing function whose spectrum is assumed to be of infinitesimal amplitude as compared to the appropri-ate laminar flow quantities.

The mechanisms responsible for boundary layer transition will be discussed later. Sufficient is to say at this stage that a laminar boundary layer can be excited by its surrounding environment and that some naturally selected disturbances will grow large enough until destabilization is achieved.

1.3.2. Consequences

At subsonic speeds, turbulent boundary layers are mainly associated with an increase of the skin friction. This results in larger drag and justifies the various techniques employed (either passive or active) to delay the onset of transition and maintain the performances of the vehicles and reduce their fuel consumption. In some instances, turbulent boundary layers are actually beneficial since they minimize flow separation and improve control effective-ness. They are then tripped artificially and forced to become turbulent. This is a lot easier to achieve than to maintain a laminar boundary layer.

1.3. Boundary layer transition phenomenon 7

facing large uncertainties with respect to the behavior of the material itself (Panerai, 2012) so that providing them with the correct boundary conditions with respect to the state of the boundary layer is important too5_.

Beside, boundary layer transition influences the extension of flow separa-tion along control surfaces (hence the control effectiveness of the vehicle), modifies the stability of the vehicle (Martellucci and Neff, 1971), increases the surface pressure fluctuations which may lead to structural fatigue (Pate, 1980). Among others, it also influences the performance of integrated en-gines and their operability.

1.3.3. Need for transition predictions

Significant efforts have been dedicated over the years to predict the tran-sition location. Shortly before the end of the U.S. National Aero-Space Program (NASP), Shea (1992) summarized the needs for such estimations:

It is essential to understand the boundary layer behavior at hypersonic speeds in order to insure thermal survival of the airplane structure as designed, as well as to accurately predict the propulsion system perfor-mance and airplane drag. Excessive conservatism in boundary layer predictions will lead to an overweight design incapable of achieving [single stage to orbit], while excessive optimism will lead to an air-plane unable to survive in the hypersonic flight environment.

Still, transition phenomena in hypersonic flows are limitedly understood due to the complex process involved. Multiple possible instabilities and receptivity mechanisms, which depend on a large number of flow, surface and environment parameters, have prevented from obtaining a general tool to predict the transitional Reynolds number.

Numerical simulations are of little help since their transition models ini-tially need detailed experimental database, which are difficult to obtain both in wind tunnels and in flight, and would then likely be applicable to a nar-row range of free-stream conditions for a single geometry. On the other hand, Direct Numerical Simulations (DNS) bring a lot more insight into the physics involved with the transition mechanisms but the proper initial excitation of the boundary layer in this case remains a difficult task.

Experimentally, when simple correlations are used with for instance the transition Reynolds number as a function of the local Mach number, as in Fig. 1.4a, the large scatter of the data defeats any attempt to find a predic-tive rule. Large variations are still observed in Fig. 1.4b while the dataset was restricted to conical geometries. Even for a single vehicle such as the Space Shuttle, transition has been experienced for free-stream Mach num-bers varying between 6.6 and 17.9 (Bouslog et al., 1991). Major difficulties

5_{The thermal protection system may ablate as well, thence influencing the boundary}

in correlating transition results stem from the fact that a large number of pa-rameters play a role: in Fig. 1.4b, the nosetip bluntness should for instance be accounted for, whereas for the Space Shuttle roughness induced transi-tion along the complex tile-based thermal protectransi-tion system can dominate the phenomenon (Heppenheimer, 2007; Camarda, 2014).

107 106 105 0 1 2 3 4 5 6 7 Me Rex, tr Open symbols Closed symbols Half-open symbols 10° < αw< 45° 46° < αw < 59° 60° < αw < 70° Sharp delta wings

Blunt delta wings

Lifting-body configurations Free-flight data

Sharp cone Slightly blunt cone Blunt cone Sharp pyramid Blunt pyramid Apollo Space shuttle configurations

(a) On various geometries (Beckwith and Bertram, 1972) 108 107 106 0 2 4 6 8 10 12 14 16 Me Rex, tr

wind tunnel data correlation: 568 points (not shown)

flight data: 77 points mean Re/ft ×10-6 23.5 8.5 3.4 1.3

(b) On cones in wind tunnels and in flight (Beckwith, 1975)

Figure 1.4.: Correlation of transition Reynolds number as a function of the local Mach number

The flight of the X-43A (Fig. 1.5a) in 2004 demonstrated performances of scramjet engines near Mach 10 (McClinton, 2006). For the cruise and ascent vehicles which could benefit from this technology, natural boundary layer transition is also critical because of the influence on the inlet flow properties for the engine. Rocket boosted gliders, such as the recent attempts with the HTV-2 waverider (Fig. 1.5b) which plan to fly beyond Mach 10, experience similar transition issues, which are critical to the determination of their trajectories.

1.4. Thesis objectives and structure 9

(a) X-43A scramjet (b) HTV-2 waverider

Figure 1.5.: Recent vehicles reaching Mach 10 for which boundary layer tran-sition is critical

1.4. Thesis objectives and structure

1.4.1. Objectives

The present work aims to perform boundary layer transition studies in the largest hypersonic facility of the von Karman Institute for Fluid Dynamics: the VKI Longshot wind tunnel. Reshotko (2007b) reminded the scientific community about some guidelines to be followed whenever performing such investigations. In line with these remarks, the objectives for the present work are actually twofold.

At first, the hypersonic environment in which these experiments should be performed must be characterized precisely. This implies to have a rather good understanding of the wind tunnel itself in order to take advantage of its full potential. Beside, the hypersonic flow characterization should be improved. Two decades after the last major upgrade of the Longshot wind tunnel, this is an excellent opportunity to benefit from new technologies, to implement new diagnostic techniques and to revisit the different method-ologies used earlier. As such, this key objective is relatively independent of any particular experimental study and is summarized as follows:

→ How well do we know our hypersonic wind tunnels

and can we improve the quality and relevance of experimental results gathered in there?

to turbulent transition should also be characterized and visualized using different measurement techniques. This is precisely the second objective of this doctoral work:

→ Based on the enhanced characterization of the Longshot wind tunnel,

can we perform boundary layer transition studies at large Mach numbers and refine our knowledge of the phenomenon?

1.4.2. Structure

The present doctoral thesis is structured as follows:

• Part I frames the von Karman Institute (VKI) Longshot wind tunnel among other hypersonic facilities and details its specificities, empha-sizing on the characteristics of the Mach 14 existing contoured nozzle (chapter 2). It is then introducing different probes which will be used for flow characterization (chapter 3).

In short, this part describes the different “tools” which will be used throughout the present work.

• Part II is entirely devoted to the flow characterization of the Longshot wind tunnel. Chapter 4 introduces a theoretical method used to re-build free-stream flow properties more accurately. This method is put in practice in chapter 5 and uncovers lower free-stream Mach num-bers than expected, ranging between 10 and 12. It also points out the inabilities of most methods used in other hypersonic wind tunnels to detect non-isentropic flow expansions. Investigations are carried out to determine the origins of these discrepancies. The threshold of flow condensation is reported in chapter 6 and additional investigations are then suggested.

This roughly corresponds to a “user guide”, albeit still incomplete, on the use of the Longshot wind tunnel, even for applications not related to transition studies, and may also apply to other hypersonic facilities. • Part III is laid out on the material reported in earlier chapters and is dedicated to the study of the boundary layer transition. A review of the relevant state of the art to the present study is presented in chap-ter 7. The conical geometry selected for transition investigations is then described together with its instrumentation in chapter 8. Bound-ary layer transition measurements are finally reported in chapter 9 including the influence of nosetip bluntness. Different measurement techniques are compared and discussed.

Part I.

Chapter 2.

The Longshot wind tunnel

The Longshot hypersonic wind tunnel will be used throughout this work to duplicate some of the phenomena occurring on reentry vehicles. This chapter aims to provide a wide and solid framework for this facility. It starts by distinguishing the Longshot gun tunnel from other devices such as shock tubes, free-piston shock tunnels or hot-shots, among many others. The Longshot wind tunnel is then described in details with particular attention being paid to the existing contoured nozzle since this will be the subject of numerous discussions in the following chapters. Current numerical modeling capabilities for the Longshot wind tunnel are finally reviewed.

2.1. Wind tunnel testing background

2.1.1. Purposes

Wind tunnel testing has been extensively used for the analysis of air flow past solid models. Experiments have ranged from low subsonic velocities during the 19th_{century and up to the supersonic and hypersonic flow regimes}

starting from the Second World War.

Many purposes exist for wind tunnel testing, among which the under-standing of the flow topology, the creation of a database, parametric studies using different configurations, the comparison of measurements with theory or the validation of numerical models. Wind tunnels are therefore impor-tant facilities which offer ground possibilities for the reproduction of flight conditions which can be both complex and expensive to obtain in situ. As such, experimental research represents one of the three pillars to the study of fluid dynamics together with theoretical and numerical activities. One should be well-aware of the abilities and limitations of each of them so that they can complement each other.

2.1.2. Duplication parameters

Discussions of the relevant fluid flow properties to be duplicated for experi-mental studies in wind tunnels are given by Lukasiewicz (1973); Bertin and Cummings (2006); Hornung (2010).

Typically, the Reynolds number ReL, ∞ = ρ∞_µu_∞∞L emerges from

dimen-sional analysis as a similarity parameter for the correct representation of viscous effects (where L is a reference dimension). The effects of compress-ibility are well represented by respecting the flow Mach number, defined as M∞=u_a∞_∞. Hypersonic flights take place at high altitude where rarefaction

effects may occur. In such cases, the Knudsen number (Kn = λ

L where λ

is the mean free path and L is a characteristic body length) may be a sim-ilarity parameter too (and is automatically satisfied if both Reynolds and Mach numbers are duplicated).

The wall to free-stream temperature ratio Tw

T∞ is another similarity

param-eter which influences both skin friction coefficient and heat transfer (Stanton number). Additional parameters may be used to correlate specific investiga-tions. For instance, the viscous effects influencing the wall pressure distribu-tion can be correlated to the viscous interacdistribu-tion parameter χ = _√M3∞

Rex, ∞

√

C

(where C is the Chapman-Rubesin linear viscosity law constant). Quite sim-ilarly, the viscous parameter V = √M∞

Rex, ∞

√

C correlates the skin friction

and heat transfer. For inviscid flows, the hypersonic similarity parameter M∞τis another example used for slender bodies (τ is the slenderness ratio).

Hypersonic flights are associated with high-temperature effects with the partial dissociation and ionization of the medium, and chemical reactions of the different species. This complicates further the wind tunnel duplication requirements since the time derivative of the flow properties must be taken into account for a correct representation of thermal and chemical effects.

A rigorous duplication of flight conditions with the inclusion of the high-temperature effects would require the same flow velocity, the same vehicle dimensions and the same flow environment (Ferri, 1964). The power re-quirements to duplicate such a mass flow depend on the size of the test section and on the test duration. For instance, for a 1 m2 _{test section, a}

flow velocity of 7 km/s and a flow density about 0.01 kg/m3_{, about 2 GW}

are necessary (Hornung, 2010). This tremendous amount of power clearly cannot be sustained for long times. Very often, scaled models are therefore used in test sections of relatively small dimensions, the test time is reduced1_,

and only few of the similarity parameters are duplicated simultaneously. Fortunately, partial duplications can be sufficient to address specific prob-lems. Numerous hypersonic flows studies concern for instance the critical stagnation point area, in which case the flow Mach number is not so

impor-1_{On the other hand, this short test time is beneficial to test models themselves since they}

2.1. Wind tunnel testing background 15

tant in comparison to the achievement of the correct flow enthalpy and flow pressure. On the other hand, aerodynamic studies require the viscous and compressible effects to be duplicated in which case, the Reynolds and Mach numbers are of greater interest.

This has lead to the development of different classes of wind tunnels in order to reproduce the various similarity parameters. The trajectories fol-lowed by ballistic or lifting bodies during their reentry are extending over very wide ranges of flow conditions (Fig. 1.2) so that a single wind tunnel cannot be used for the duplication of the whole trajectory, even for a unique vehicle.

2.1.3. Different types of hypersonic wind tunnels

Overview: A wide variety of solutions exist to provide a source of gas

at sufficiently large pressure and temperature to use it as a working fluid for a hypersonic wind tunnel. Excellent reviews of the different types of hypersonic wind tunnels together with a historical perspective are given by Lukasiewicz (1973); Tropea et al. (2007). Additional details can be found in Ferri (1964); Pope and Goin (1965); Baals and Corliss (1981); Wendt (1984); Anderson and Matthews (1993); Maus (1993a); Lu and Marren (2002) and a detailed analysis of the limiting parameters of hypersonic facilities is given by Smith (1993).

The conventional design of closed-circuit supersonic wind tunnels can hardly be extended to reach larger flow enthalpies/velocities. In order to reach the lower range of hypersonic Mach numbers, numerous wind tunnels use instead the blowdown principle: the test gas is stored in a reservoir at high pressure and high temperature and subsequently released through a nozzle for a test duration of few seconds up to few minutes depending on the amount of gas initially stored and the test conditions2_.

For Mach numbers larger than 6 or so, the blowdown technique is again rarely applicable3 _{and other ways to achieve hypersonic flows have been}

sought, leading to the impulse-type of wind tunnels. Typically, kinetic, thermal, electrical or chemical energy is stored over a long period of time with a low input power and rapidly released.

Hereafter, shock heated facilities are distinguished from electrical dis-charge and compression heated ones (to which the Longshot belongs). An overview of these different impulse facilities is given in order to better dis-tinguish the Longshot hypersonic wind tunnel from others and in order to

2_{A similar technique, but cheaper to operate, is the Ludwieg tube where the nozzle is}

pressurized with the reservoir prior to a test. A diaphragm located downstream of the test section is ruptured to initiate the nozzle flow. For such wind tunnels, the test time is usually limited to few hundreds of milliseconds of constant test conditions.

3_{There exists few exceptions such as the AEDC tunnel 9 (up to Mach 14), the Sandia}

better understand its specific advantages and drawbacks.

Shock heated facilities: The first short duration hypersonic wind tunnels

were high-performance shock tubes in the 40’s. They are simple devices illustrated in Fig. 2.1 with a long tube split into a driver and driven tube by a diaphragm and respectively filled with high and low pressures gases.

The rupture of the diaphragm leads to the propagation of a shock wave within the driven tube while an expansion wave propagates upstream in the driver tube (both can be represented using x − t diagrams as in the top of Fig. 2.1). The high-speed flow set in motion by the shock can be used for high-speed testing.

Although the theoretical limit of the shock Mach number is about 6 using specific gases, the practical limit of shock tubes using air is only about Mach 3 (Lukasiewicz, 1973; Lu and Wilson, 1994). For this reason, they have been essentially used to study the stagnation point region of blunt hypersonic vehicles, because the flow in that region is quite independent of the free-stream Mach number for M∞ >2. The main drawback of shock

tubes is their very short test duration on the order of few milliseconds in the best cases.

time expansion waves contac t surfaceflow shock wave

stagnant flow region

maximum test time

reflect ed shock

Diaphragm

Driver tube Driven tube

distance

Figure 2.1.: Layout of a shock tube and corresponding x − t diagram A shock tube is closed at its end but modifications can be done to over-come the Mach number limitation. The end of the shock tube can for instance be replaced by a divergent section, that is the principle of the

straight-through shock tunnel or non-reflected shock tunnels used

2.1. Wind tunnel testing background 17

Alternatively, a convergent divergent nozzle can be fitted to the end of a shock tube. The primary shock wave which is reflected at the end of the driven tube generates large enthalpy stagnation conditions which can be used to generate hypersonic flows. This is the principle of reflected shock

tunnels. The expansion of the gas up to large Mach numbers is done at

the expense of lower Reynolds numbers when compared to the simple shock tube. Flow duration in such facilities is extended with respect to shock tubes but usually remains shorter than few tens of millisecond when used in a tailored condition (Schultz and Jones, 1973) and decreases with the use of large enthalpies.

Performances of these facilities can be improved by the following tech-niques, each of them aiming at increasing the speed of sound ratio between the driven and driver sections and increasing the driver gas pressure:

• Heated light molecular weight driver gas (hydrogen or helium) in-creases the speed of sound ratio between the driven and driver sections and allows for larger stagnation enthalpies. Among the typical wind tunnels of such type are the TH2, at Aachen, the LENS-I/-II shock tunnels, at CUBRC, and the recent world-largest shock tunnel built in China: JF-12.

• Free-pistonshock tunnels were developed by Stalker (1967) and rely on the principle of an adiabatic compression to reach large pressures in the driver gas. As illustrated in Fig. 2.2, a piston is initially located upstream of the driver section and is set in motion within the driver section by high-pressure air. While moving, the piston compresses the driver gas to large pressure and temperature. Benefits are similar to those obtained previously by heating the light molecular weight driver gases while the equivalent operating cost is brought down. The com-pression can either be isentropic (Schultz and Jones (1973), with light subsonic pistons) or adiabatic (Lu and Wilson (1994), with heavier and faster pistons) and the piston is reusable. The remaining pro-cess is identical to that of a reflected shock tunnel. Facilities such as T3, T4 (at the University of Queensland), T5 (at Caltech) or the Eu-ropean HEG (at DLR G¨ottingen) are all examples of free-piston shock tunnels, using piston weighing between 90 and 650 kg. HIEST (in Japan) is currently the largest one, achieving test gas stagnation en-thalpies up to 25 MJ/kg. The extremely high enen-thalpies which are generated do not allow for long operation times (typically few mil-liseconds), especially when the gas is stagnated upstream of the nozzle when operating in a reflected mode. Note that the Longshot wind tun-nel, which will be described below, does not belong to this free-piston family of hypersonic wind tunnels although it also involves a piston. • An alternative to the free-piston method is the detonation method,

air reservoir

compression tube pistondiaphragm

p ρ

V _{interface shock wave}

shock tube nozzle

diaphragm station end of shock tube x nozzle starting process primary sho

ck wave interfa ce refle cte_{d sho} ck piston trajectory τ influence of pressure decay transmitted along this characteristic t τ0 y

Figure 2.2.: Layout of a free-piston wind tunnel and corresponding x − t diagram, redrawn from Stalker (1967)

The costly hydrogen or helium driver gas is replaced by a section where the high pressure and temperature of the driver gas is initially obtained by the ignition of a reactive mixture (either at the upstream or downstream ends of the detonation section, leading to two slightly different operational modes, Tropea et al., 2007). This method leads to larger total enthalpies than commonly achieved with a shock tunnel. It also extends the test duration and lowers the operative costs. The previously mentioned TH2 shock tunnel (at Aachen) can also operate following this mode (Fig. 2.3) with a test time of few milliseconds.

Damping section Detonation section Diaphragm Shock Detonation Tim e Shock Length Refl. shock Contact surface Diaphragms Low-pressure

section Nozzle Vessel Test section 1

4 7

Figure 2.3.: Layout of an upstream detonation tunnel and corresponding

2.1. Wind tunnel testing background 19

• Another solution for the improvement of the driver performances is used by electric-arc tunnels. A large amount of electrical energy, stored in inductors or capacitors beforehand, is rapidly released into the driver gas. The NASA EAST wind tunnel is an example of such tunnel, generating shock speeds approaching 50 km/s and allowing studies relative to Jovian system entries (Grinstead et al., 2010). Another modification of shock tubes leads to the acceleration tubes family. These are still composed of driver and driven sections to which is added an acceleration tube, each one being isolated from the others by suited diaphragms (Fig. 2.4). The driven section contains the test gas while the acceleration tube is initially filled with a light gas at very low pressure. This uses an unsteady expansion through a constant diameter tube instead of a nozzle to accelerate the flow. This process is more efficient to convert the thermal energy into a kinetic energy than what is done through a nozzle.

Length Primary diaphragm Secondary diaphragm Time Unsteady expansion

Reflected expansion wave Unsteady

expansion Test time Contact surface Secondary shock Primary shock Contact surface

Driver Shock tube Acceleration tube _sectionTest

Figure 2.4.: Layout of an acceleration tube and corresponding x−t diagram (Tropea et al., 2007)

The main advantage of acceleration tubes is that, as for non-reflected shock tunnels, there is no stagnation region prior to the expansion and the flow remains in equilibrium conditions in the free-stream. This is therefore well suited for use with reactive flows. The test gas is processed only by a single shock so that the entropy rise is limited. This leads to larger stag-nation pressures and larger Reynolds number for the test gas. The most severe drawback of such wind tunnels is the very short test time, an order of magnitude smaller than for the reflected shock tunnels.

per-formances can be achieved by improving the driver gas perper-formances using the techniques mentioned earlier as with a free-piston (e.g. the X2 and X3 at the University of Queensland, Australia), or a detonation driver (e.g. the HYPULSE wind tunnel at GASL).

Electrical discharge facilities: There exists a class of wind tunnels slightly

apart from the shock tube principle but still able to generate relatively large enthalpy flows for hundreds of milliseconds. They are named

hot-shot tunnels4. The test gas is initially confined in a reservoir at moderate

stagnation conditions and heated up further using an electrical arc discharge (Fig. 2.5), similarly to the principle used for the electric-arc wind tunnels described earlier. Once the correct flow conditions are reached, the flow is expanded through a nozzle to high velocities. Due to the fixed size of the initial chamber, the stagnation conditions may evolve with time.

test section high-pressure test gas arc chamber diaphragm electrodes check valve

Figure 2.5.: Layout of a hot-shot wind tunnel, adapted from Ferri (1964) The main advantage of such wind tunnels is that the high Mach number flow at high enthalpy can be maintained for longer times with respect to the previous techniques described (on the order of 100 ms). Severe drawbacks are relative to the poor flow quality due to the erosion of the electrodes used to produce the arc in the reservoir. The French F4 (at ONERA), Russian IT-302 M (at ITAM) and the U.S. tunnel-F (at AEDC, now dismantled) are various examples of hot-shots tunnels.

Compression heated facilities: A third category of hypersonic wind

tun-nels encompasses the ones relying on a compression of the test gas by a piston. Unlike what is achieved in the free-piston wind tunnels, this pis-ton is used to compress the driven gas directly. It is actually the interface between the driver and driven gases which prevents their diffusion or com-bustion (Fig. 2.6).

As for a simple shock tunnel, there is a pressure difference between the driver and the driven tube. This is what drives the piston through the

4_{Hot-shot tunnels should not be confused with arc-jet wind tunnels which operate along}

2.1. Wind tunnel testing background 21

driver tube piston nozzle

diaphragm

driven tube

Figure 2.6.: Layout of a gun tunnel

driven tube to do work on the test gas. The process is analog to the one of a bullet within a rifle (whose extremities would be closed) which led to the

gun tunnelsdenomination. Among this category, heavy pistons should be

distinguished from lighter ones since they influence the compression process. As discussed by Bray (1961), heavy pistons typically lead to slow isentropic compressions whereas adiabatic ones can be achieved with very light pistons (hence, approaching a shock tube behavior).

• Heavy pistons have velocities below the speed of sound. Very large reservoir pressures can be achieved for relatively long periods with such pistons. The longest test times can be achieved with the heaviest ones, but this introduces significant recoil of the wind tunnel. East and Pennelegion (1962) have shown that by adjusting carefully the initial barrel pressure and the mass of the piston, the reservoir pressure can be maintained nearly constant during a run. An example of wind tunnel operating along this principle is the gun tunnel number 2 of the Imperial College (UK). The drawback of the isentropic compression is the relatively low stagnation temperatures which are reached. This is detrimental to large Mach numbers operation (due to possible flow condensation) even though it contributes to increase the free-stream Reynolds number (in combination with the large pressures obtained). • Light pistonsoffer the possibility to convert more efficiently the energy of the piston into thermal energy in the test gas. The compression is then divided into two main phases. The first one follows the release of the piston which accelerates progressively to supersonic velocities. The preceding shock wave stores energy into the test gas (both thermal and kinetic) while additional energy is stored into the kinetic energy of the piston. Once the shock wave ahead the piston reaches the end of the driven tube, it is reflected back towards the piston and brings the flow to rest, the kinetic energy of the gas being converted into thermal energy5_{. The second phase starts when the reflected}

shock waves rebounds against the front face of the piston, which is still moving forward supersonically. This is accelerating again the stagnant driven gas to the piston velocity and results in another shock wave traveling forward. The piston velocity then starts to decrease due to the higher frontal pressure but the shock wave reflection process is

5_{Until this point, the stagnation conditions are similar to the ones which would be}