Shock Waves @ Marseille I

Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Tokyo

R. Brun L. Z. Dumitrescu (Eds.)

Shock Waves @ Marseille I

Hypersonics, Shock Tube & Shock Tunnel Flow

Proceedings of the 19th International Symposium on Shock Waves Held at Marseille, France, 26-30 July 1993

With 390 Figures

Springer

Professor Dr. Raymond Brun

Professor Dr. Lucien Z. Dumitrescu

Universite de Provence, Centre Saint-Jercme IUSTI-MHEQ, Case 321, F-13397 Marseille Cedex 20, France

ISBN-13: 978-3-642-78831-4 e-ISBN-13: 978-3-642-78829-1 DOl: 10.1007/978-3-642-78829-1

Set (Volumes I-IV):

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Preface

From the Prefaces written by the chairmen of the previous International Symposia on Shock Waves, it appears that records are broken at each meeting: of participants, of papers, etc. The 19th ISSW, held in Marseille in 1993 is not an exception to this rule: about 450 Abstracts were received by the Papers Committee, which firmly establishes this series of Symposia as the main international forum for discussing topics related to shock waves, and guarantees employment to future organizers.

The diversity of the topics treated is proof of the large number of scientific fields in which shock waves are involved. The same is true for applications, as they cover such traditional fields as aeronautics and astronautics, combustion, lasers, blast waves and detonations, but also a lot of other interesting industrial areas such as high-speed trains, car engines, surface cleaning or underwater explosions. Concern for the environment is also present with forest fires, volcanic eruptions and meteorite fall, not to forget the biological effects of shock waves on cancerous tissues, gallstones or the pulmonary system.

Among the fundamental topics, nonequilibrium hypersonic flow, as well as shock tube and shock tunnel flow continue to be extensively researched, and new diagnostic methods, especially optical, are being developed. In numerous papers, various CFD methods are also applied to these flows in complex configurations. Like in the past, physico-chemical processes and relaxation phenomena, shock wave kinematics: diffraction and refraction, shock-vortex and shock-boundary layer interactions, are well represented, as is the propagation of shock waves in condensed matter and various heterogeneous media.

Finally, after the examination of each paper by two experts from Western Europe, about 300 papers were retained and presented during the five days of the Symposium, 175 in oral sessions and 125 in poster sessions. There were 355 participants from 22 countries and, among them, many young scientists and graduate students, who benefited from the preferential fares reserved for them. Ten invited papers covered the major topics of the Symposium and two Memorial Lectures - the Paul Vieille and the Ernst Mach Lectures - respectively opened and closed the meeting: the Paul Vieille Lecture was given by Prof. K. Takayama and constituted a superb review of optical visualisation methods in shock wave research; the Ernst Mach Lecture was presented by Prof. L.Z. Dumitrescu, who described the successive and often difficult steps of his own involvement with shock waves during 40 years.

In view ofthe large number of papers and ofthe diversity of the topics, the present Proceedings of the 19th ISSW have been divided into four volumes, each of them devoted to a group of related topics, as follows:

• Vol. I: Hypersonics, Shock Tube and Shock Tunnel Flow • Vol. II: Physico-Chemical Processes and Nonequilibrium Flow • Vol. III: Shock Waves in Condensed Matter and Heterogeneous Media • Vol. IV: Shock Structure and Kinematics, Blast Waves and Detonations.

Each volume includes about 75 papers - contributed, invited and memorial- and an Introduc­tory Survey. The presence of the latter was suggested by the Publisher; well-known personalities have been asked, after the completion of the Symposium, to write the Surveys; they are Profs. J .L. Stollery (Vol. I), J. Kiefer (Vol. II), M. van Dongen (Vol. III) and L.F. Henderson (Vol. IV), to whom warm thanks are due.

As for the previous Symposia, no permanent body was in charge of the 19th ISSW. Therefore an organization had to be entirely set up and financial support to be found; this would not have been possible without the enthusiastic support and generous contribution from many. I am especially endebted to my colleagues and co-workers of the Executive Committee, as well to all

VI Preface

the graduate students of our Department; I wish to express special thanks to Prof. D. Zeitoun, the Papers Committee Co-Chairman, who had to "master" the flow ofthe papers, to Dr. L. Houas for having spent much effort and time on many points of the material organization, and to Mrs. M. Leboisne, the Symposium Secretary, for her efficiency and almost unlimited availability. Thanks are also due Prof. W. Beiglbock (Springer Verlag, Heidelberg) and his team, for their help in publishing, in excellent graphical conditions, these Proceedings

External cooperation has not been lacking either. The members of the International Advisory Committee have given numerous suggestions and advice for improvement. The members of the Papers Committee have examined in a short time the many abstracts submitted. The members of the Sponsoring Committee and the heads of the supporting organisations are at the origin of the decisive financial support for the Symposium; in particular, the participation of colleagues from Eastern Europe is due mainly to their generosity. It must also be underlined that that support represented about 65% of the total expense, only 35% coming from the participants' fees. The ladies of the Companions' Program Committee, helped also by Prof. A. Chauvin, must be especially thanked for the preparation and achievement of a pleasant program, which was followed by more than 80 companions.

Locally, I have received sympathetic and generous help from the Municipalities of Marseille and Cassis, as well as from the Regional Council of Provence-Alpes-Cote d'Azur and, of course, from the Universite de Provence. I am pleased to express my gratitude to M. P. Vigouroux, Mayor of Marseille, M. G. Rastoin, Mayor of Cassis, M. J-C.Gaudin, President of the Region and to Prof. V. Kaftandjian, President of the University, as well as to their numerous collaborators, who have offered their precious cooperation that has facilitated the task of the Executive Committee.

The 19th ISSW was held from July 25 to July 30, 1993 on the Saint Charles Campus of the Universite de Provence, Marseille. It followed the 18th, held in Sendai, Japan (Chairman, Prof. K. Takayama) and preceeds the 20th, which will be organized in Pasadena, USA (Chairman, Prof. H. Hornung).

In the end, the success of such a meeting is essentially due to the contribution of its partici­pants. In the present case, that contribution was important and multiple, and thus warmly felt by the Chairman and his team. I would like to wish all these participants further fruitful research in the field of shock waves, and new meetings at future Symposia.

Marseille, June 1994 Raymond BRUN Chairman, 19th ISSW

19th ISSW - Committees and Supporting Organisations

Host Organisation

Departement Milieux Hors d'Equilibre Institut Universitaire des Sciences Thermiques Industrielles, URA CNRS 1168 Universite de Provence, Marseille, France

International Advisory Committee

T. Akamatsu (Japan) F. Higashino (Japan) F. Obermeier T. Bazhenova (Russia) Z. Han (China) C. Park G. Ben-Dor (Israel) R. Hanson (USA) N. Reddy D. Bershader (USA) L. Henderson (Australia) H. Reichenbach A. Borisov (Russia) A. Hertzberg (USA) P. Roth R. Brun (France) R. Hillier (UK) D. Russell F. Demmig (Germany) H. Honma (Japan) J. Sandeman J. Dewey (Canada) H. Hornung (USA) S. Sharma L.Z. Dumitrescu (Romania) O.Igra (Israel) B. Skews R. East (UK) V. Kedrinskii (Russia) R. Stalker R. Emrich (USA) Y. Kim (USA) J. Stollery N. Fomin (Bielorussia) A. Lifshitz (Israel) B. Sturtevant B. Forestier (France) H. Matsui (Japan) K. Takayama W. Gardiner (USA) B. Milton (Australia) M. VanDongen I.I. Glass (Canada) H. Mirels (USA) Z. Walenta J. Gottlieb (Canada) M. Miyajima (Japan) R.Yu H. Gronig (Germany) R. Nicholls (Canada)

Executive Committee

R. Brun (Chairman) M.Imbert K. Koffi M. Autric M. Leboisne (Secretary) L. Labracherie M. Billiotte G. Leboisne M. Llorca Y. Burtschell G. Meolans F. Lordet A. Canova J. Moutouh F. Mazoue A. Chauvin D. Zeitoun M. Marti L.Z. Dumitrescu D. Benghrib E. Schall Y. Fienga P. Delmer A. Touat B. Forestier M.-P. Dumitrescu J. Vuillon L. Houas S. Granjeaud

(Germany) (USA) (India) (Germany) (Germany) (USA) (Australia) (USA) (South Africa) (Australia) (UK) (USA) (Japan) (Netherlands) (Poland) (China)

VIII Committees and Supporting Organisations

Papers Committee

R. Brun (Chairman) D.Zeitoun(Co-Chairman) Marseille (France) R. Abgrall Nice (France) M. Autric Marseille (France) R. Borghi Rouen (France) E. Brocher Marseille (France) J. Brossard Bourges (France) M. Champion Poitiers (France) P. Chapron Courtry France) R. Cheret Paris (France) F. Demmig Hannover Germany) D. Desbordes Poitiers (France) A. Desideri Nice France) L. Deveseaux Chatillon (France) L.Z. Dumitrescu Bucharest (Romania) G. Dupre Orleans (France) J.-P. Dussauge Marseille (France) A. Dyment Lille (France) R.A. East Southhampton (UK) G. Eitelber Gottingen Germany) B. Fontaine Marseille (France) B. Forestier Marseille (France) R. Gatignol Paris (France) H. Gronig Aachen (Germany) J.-F. Haas Vaujours (France) R. Hillier London (UK) L. Houas Marseille (France)

Companions' Program Committee

J. Brun M.-N. Canova A. Chauvin M. Chauvin

M. Houas D. Musso M. Zeitoun

M.Imbert Marseille (France) J .C. Lengrand Meudon (France) A. Lerat Paris (France) J .-C. Loraud Marseille (France) J.P. Martin Paris (France) J.G. Meolans Marseille (France) A. Merlen (Lille (France) R. Monaco Genoa (Italy) K.W. Naumann Saint Louis (France,Germany) F. Obermeier Gottingen (Germany) C. Paillard Orleans (France) R. Perrin Paris (France) D. Poll Manchester (UK) F. Prat Lyon (France) P. Roth Stuttgart (Germany) F. Seiler Saint Louis (France,Germany) M. Sentis Marseille (France) G. Smeets Saint Louis (France,Germany) M. Sommerfeld Erlangen (Germany) J. Stollery Cranfield (UK) B. Stouffiet Paris (France) T. Srulijes Saint Louis (France,Germany) M. VanDongen Eindhoven (Netherlands) P. Vervisch Rouen (France) J. Warnatz Stuttgart (Germany) J. Wendt Brussels (Belgium)

Committees and Supporting Organisations

Supporting Organisations

• Aerospatiale • American Physical Society • Banque Populaire Proven«ale et Corse • Centre National de la Recherche Scientifique • Centre d'Etudes de Limeil-Valenton • Centre d'Etudes de Vaujours • Centre d'Etudes Scientifiques et Techniques d'Aquitaine • Commissariat it I'Energie Atomique • Commission of European Communities • European Office of Aerospace Research & Development • European Space Agency • Institut Fran«ais du Petrole • International Science Foundation • Ministere des Affaires Etrangeres • Ministere de la Defense • Ministere de l'Education Nationale • Ministere de la Recherche et de I'Espace • Societe de Mathematiques Appliquees et Industrielles

• Conseil General des Bouches du Rhone • Region Provence, Alpes, Cote d'Azur • Universite de Provence • Ville de Marseille • Ville de Cassis

Endorsing Orgnisations

• Institut National de Recherche en Informatique et Automatique • Institut National de la Sante et de la Recherche Medicale • Societe Fran«aise de Physique

Sponsoring Committee

D. Besnard R. Cheret B. Sitt

(CELV) (CEA-DAM) (CEV)

G. Duffa (CESTA) H. Hollanders (Aerospatiale)

J. Muylaert (ESA) J. Periaux (SMAI)

IX

Contents - Volume 1*

Survey Paper

Volume I: Hypersonics, Shock Thbe and Shock Thnnel Flow - An Introductory Survey John L. Stollery .............................. 3

Plenary Lectures

A Life with Shock Waves (Ernst Mach Memorial Lecture) Lucien Z. Dumitrescu . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Computational Analysis on Generic Forms in European Hypersonic Facilities: Standard Model Electre and Hyperboloid-Flare J. Muylaert, L.M.G. Walpot and G. Durand . . . . . . . . . . . . . . . . . . .. 19

Shock Thbe Investigations of Combustion Phenomena in Supersonic Flows G. Smeets ........................... .

Part 1: Hypersonic Flow and Aerospace Studies

Interference and Transient Effects on Compression Ramp Flows at Hypersonic Mach Numbers

29

A.J .D. Smith and R.A. East . . . . . . . . . . . . . . . . . . . . . . . . . 41

Effects of Leading-Edge Bluntness on Control Flap Effectiveness at Hypersonic Speeds D. Kumar and J.L. Stollery ......................... 47

Measuring the Effect of Nose Bluntness on Drag of a Cone in a Hypervelocity Shock Thnnel Facility L.M. Porter, A. Paull and D.J. Mee ............... .

Navier-Stokes Simulation and Measurement of Cone Drag at Moo = 7.9 C. Jessen, H. Gronig, M. Watanabe and K. Takayama . . . .

The Boundary Layer on a Sharp Cone in High-Enthalpy Flow P. Germain and H. Hornung ....... .

Shock Wave Interactions in Hypervelocity Flow

53

57

63

S.R. Sanderson and B. Sturtevant . . . . . . . . . . . . . . . . . . . . . . . 69 Experimental Investigation of Shock-on-Shock Interactions in the High-Enthalpy Shock Tunnel Gottingen (HEG) S. Kortz, T.J. McIntyre and G. Eitelberg ..................... 75

Oblique Shock Interactions with Mach Number Distributions D.R. Buttsworth and R.G. Morgan .......... . 81

Shock Wave/Boundary Layer Interaction in High-Enthalpy Compression Corner Flow S.G. Mallinson, S.L. Gai and N.R. Mudford . . . . . . . . . . . . . . . 87

Strength of Characteristics at a Curved Shock Wave Sannu Molder 93

* The Contents of the other volumes are given at the end of the book.

XII Contents - Volume I

Blunt Body Flow - The Transonic Region Sannu Molder Shock Thbe Application to the Study of Compressible Thrbulent Boundary Layer With Mass Injection

101

J .-Y. Liaw and D. Bershader . . . . . . . . . . . . . . . . . . . . . . . . . 105 Interaction of Thermal Protection Materials with the High-Enthalpy Flow of the Arc-Heated Wind Thnnel LBK A. Giilhan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 An Attractor-Driven Approximation for Thrbulent Burst Dynamics in a Supersonic Free Shear Layer J.A. Johnson III, L.E. Johnson, and J. Zhang .................. 117

Effect of Nozzle Configurations on Unsymmetrical Supersonic Flows Y. Watanabe, S. Matsuo and F. Higashino .......... .

Radiative Heat Transfer from a Shock Layer Generated Around a Projectile Launched in a Ballistic Range Kimiya Komurasaki, Jiro Kasahara, Shujiro Yano and Toshi Fujiwara ..

Aerodynamic Heating in Three-Dimensional Bow Shock Wave/Thrbulent Boundary Layer Interaction Region Syozo Maekawa, Shigeru Aso, Shigehide Nakao, Kazuo Arashi, Kenji Tomioka and Hiroyuki Yamao

Parabolic Viscous Shock Layer Theory for 3D Hypersonic Gas Flow S.V. Peigin ........................ .

Viscous Hypersonic Flow over a Body Flying Through a Thermal in the Atmosphere

123

127

133

139

I.F. Muzafarov, V.U. Nabiev, S.V. Utyuzhnikov and N.K. Yamaleev . . . . . . . . 145

Part 2: Combustion and Ram Accelerators

Hydrogen Mixing and Combustion in a High-Enthalpy Hypersonic Stream R.T. Casey and R.J. Stalker . . . . . . . . . . . . . . . . . . . .

Transverse Jet Mixing and Combustion Experiments in the Hypersonic Shock Thnnel T5 at GALCIT J. Belanger and H. Hornung

Three-Dimensional Mixing Flow Field in Supersonic Flow Induced by Injected Sec­ondary Flow Through a Traverse Circular Nozzle Shigeru Aso, Shozo Maekawa, Michiaki Tan-Nou, Satosh Okuyama, Yasunori Ando

151

157

and Yoshiyuki Yamane .......................... 163

Limitations of the Ram Accelerator M. Brouillette, D.L. Frost, F. Zhang, R.S. Chue, J.H.S. Lee, P. Thibault and C. Yee 171

Stability Studies of Detonation Driven Projectiles F. Zhang, D.L. Frost, R.S. Chue, J.H.S. Lee, P. Thibault and C. Yee

Bow Shock Wave Heating and Ablation of a Sharp-Nosed Projectile Flying Inside a Ram Accelerator F. Seiler and K.W. Naumann .......... .

In-Thbe Photography of Ram Accelerator Projectiles C. Knowlen, A.J. Higgins, A.P. Bruckner and A. Hertzberg.

177

183

189

Contents - Volume I XIII

Part 3: Shock Tube Technology and Diagnostic Techniques

Hypervelocity Aerodynamics in a Superorbital Expansion Tube A.J. Neely and R.G. Morgan . . . . . . . . . . . . . . .

Influence of Secondary Diaphragm on Flow Quality in Expansion Tubes G.T. Roberts, R.G. Morgan and R.J. Stalker ........ .

Noise Reduction in Argon Driven Expansion Tubes A. Paull .................. . On the Principle, Design, and Performance of an Expansion-Shock Tube for Nucleation Studies K.N.H. Looijmans, J.F.H. Willems and M.E.H. van Dongen .......... .

High-Frequency Generation of High-Pressure Pulses Using a Diaphragmless Shock Tube Koji Teshima .............................. .

A New Diaphragmless Shock Tube Facility for Interface Instability and Mach Reflection Studies YongW. Kim

Analysis of Calibration Results in the High-Enthalpy F4 Hot-Shot Wind Tunnel

197

203

209

215

221

227

Ph. Sagnier and G. Fran"ois . . . . . . . . . . . . . . . . . . . . . . . 233

The Taylored Nozzle: A Method for Reducing the Convective Heat Transfer to Nozzle Throats by Gasdynamic Shielding A. Hertzberg, K. Takayama, J. Hinkey and S. Itaka . . . . . . . . . . . . . . .. 239

Dealing with Pressure Oscillations in Stalker Tubes M.-P. Dumitrescu, R. Brun, M. Billiotte, J .M. Bertoni, Y. Burtschell, A. Canova, L.Z. Dumitrescu, L. Houas, L. Labracherie and D. Zeitoun . . . . . . . . . . 247

Comparison of the Flow in the High-Enthalpy Shock Tunnel in Gottingen with Nu-merical Simulations T.J. McIntyre, J.R. Maus, M.L. Laster and G. Eitelberg ...... . 251

A Numerical and Experimental Study of the Free Piston Shock Tunnel Katsuhiro Itoh, Kouichiro Tani, Hideyuki Tanno, Masahiro Takahashi, Hiroshi Miyajima, Takahisa Asano, Akihiro Sasoh and Kazuyoshi Takayama . . . . . . . .. 257

Use of Argon-Helium Driver-Gas Mixtures in the T4 Shock Tunnel P.A. Jacobs, R.G. Morgan, R.J. Stalker and D.J. Mee ..... .

A Velocity Interferometric Study of the Performance of a Gas Gun T. Matsumura, H. Ohuchi, N. Narayanswami, A. Sasoh and K. Takayama

Balances for the Measurement of Multiple Components of Force in Flows of a Millisec­ond Duration D.J. Mee, W.J. Daniel, S.L. Tuttle and J.M. Simmons

Further Developments of the ISL Millisecond Aerodynamic Force Measurement Tech­

nique K.W. Naumann, H. Ende, G. Mathieu and A. George .....

Six-Component Force Measurement in the Aachen Shock Tunnel C. Jessen and H. Gronig . . . . . . . . . . . . . . . . . .

263

269

275

281

287

XIV Contents - Volume I

Driver Gas Detection by Quadrupole Mass Spectrometry in Shock Tunnels J .C. Slade, K.C. Crane and R.J. Stalker . . . . . . . . . . . . . . .

Skin Friction Measurements and Reynolds Analogy in a Hypersonic Boundary Layer

293

G.M. Kelly, J.M. Simmons and A. Paull . . . . . . . . . . . . . . . . . . . . 299

Optical Studies of the Flow Start-up in Convergent-Divergent Nozzles Klaus-Otto Opalka . . . . .. ............. .

Two Electric Discharge Methods for Visualizing Three-Dimensional Shock Shapes Around Hypersonic Vehicles Masatomi Nishio . . . . . . . . . . . . . . . . . . . . . . .

Dual-Laser PLIF Imaging Techniques for Shock Tube Studies of Mixing and Combustion

305

311

B.K. McMillin, J .M. Seitzman, J .L. Palmer and R.K. Hanson .......... 315

An Examination of the Aachen Shock Tunnel TH2 Gas Flows Using the HEG PUF Apparatus W.H. Beck, M. Scheer and M. Vetter

Part 4: Numerical Computations

Comparison of Numerical Methods 1: DSMC Simulations and N-S Predictions on Bluff Bodies

321

Martin Gilmore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Application of Multiblock Codes for Computational Aerothermodynamics of Hyper-sonic Vehicles Penelope Leyland, Franc,;oise Perrel and Jan B. Vos . . . . . . . . . . . . . . . 335

Numerical Analysis of Shock/Shock and Shock/Body Interactions for 3D Configura-tions G. Hartmann and S. Menne Hypersonic Shock-Wave/Boundary Layer Interactions with an Implicit Navier-Stokes Solver

341

penelope Leyland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 347

Visualisation of Shock Waves in Hypersonic CFD Solutions H.-G. Pagendarm, B. Seitz and S.l. Choudhry ..... .

Shock Wave Interactions in Hypersonic Flow S.L.B. Yeung and l.M. Hall ...... .

Numerical Simulation of Transient Bluff Body Flows J.F. Milthorpe . . . . . . . . . . . . . . . . .

An Efficient Unstructured Euler Solver for Transient Shocked Flows A.A. Fursenko, D.M. Sharov, E.V. Timofeev and P.A. Voinovich

CTH: A Software Family for Multi-Dimensional Shock Physics Analysis E.S. Hertel, Jr., R.L. Bell, M.G. Elrick, A.V. Farnsworth, G.l. Kerley, J .M. McGlaun, S.V. Petney, S.A. Silling, P.A. Taylor and L. Yarrington

353

359

365

371

377

Contents - Volume I XV

Computation of Viscous Shock/Shock Interactions with an Upwind LU Implicit Scheme D. Darracq and M. Gazaix ................. .

Numerical Calculations in Support of Complex Shock Interactions Charles E. Needham, Shuichi Hikida and Lynn W. Kennedy

Numerical Simulation of Shock Induced Unsteady Aerodynamic Heating with a Highly Dense Mesh System Kenichi Ohyama, Shigeru Aso and Masanori Hayashi

A Comparison Study of Two Finite-Element Schemes for Computation of Shock Waves

383

389

395

Hong Luo, Joseph D. Baum and Rainald Lohner . . . . . . . . . . . . . . .. 401

Adaptive Mesh Refinement Computation of Compressible Flow N. Uchiyama, O. Inoue

Shock-Capturing Schemes with Entropy Corrections and Dynamically Adaptive Unstructured Meshes Roland Richter and Penelope Leyland . . . . . . . . . . . . .

Computing Complex Shocked Flows Through the Euler Equations

407

413

A.M. Landsberg, J.P. Boris, T.R. Young and R.J. Scott . . . . . . . . . . . .. 421

A Third-Order ENO Scheme on Unstructured Meshes. Application to Shock Wave Calculations Remi Abgrall .

Numerical Simulation of Compressible Viscous Flows C. Miigler, B. Meltz, M. Vandenboomgaerde, S. Gauthier, S. Aubert, L. Hallo, P. Ferrand and M. Buffat ...................... .

Time-Dependent Simulation of Reflected-Shock/Boundary Layer Interaction in Shock Tubes G.J. Wilson, S.P. Sharma and W.D. Gillespie ......... -... .

Numerical Simulation of Viscous Flow in a Super-Orbital Expansion Tube N. Akman and R.G. Morgan ................... .

Analysis of the Flow Perturbations in a Shock Tube Due to the Curvature of the Diaphragm V. Daru and J.P. Damion

One-Dimensional Simulation of Free-Piston Shock Tunnel/Expansion Tubes M. Mitsuda, T. Oda, T. Kurosaka, S. Wakuri and T. Arai ....... .

Author Index Contents - Volumes II, III, IV

427

433

439

445

451

457

463 471