Three Dimensional Flow Of Ideal Gas Past Smooth Bodies | K. I. Babenko, G. P. Voskresenskiy, A. N. Lyubimov, V. V. Rusanov

The book is devoted to an urgent problem of modern gasdynamics--the com­ putation of the flow field near a smooth body situated in an arbitrary manner with respect to the incident airflow. The book presents the results of in­ vestigations performed over a period of several years by a group of authors associated with the development and practical application of the method of finite differences to the solution of three-dimensional problems of gasdynamics by electronic digital computer.

The first chapter presents in detail the method of the three-dimensional flow around tapered bodies in a supersonic flow. A series of sections in the first chapter presents the theoretical investigation of the system of finite difference equations carried out in the general form, taking into account the application of the method to other problems of mechanics and mathematical physics.

The second chapter presents the results of calculations for the nonaxi- symmetric flow around several bodies of revolution with and without account of chemical reaction in the flow.

The third chapter contains tables for the nonaxisymmetric flow of circular cones in a wide range of Mach numbers, half cone angles, and angles of attack. The tables present exhaustive information concerning the gasflow and are con­ venient for practical applications.

The book is designed for scientific workers and engineers concerned with mathematical computations and computer programing, the aerodynamic design of flight craft and theoretical gasdynamics. The book may also be of use to teachers and students of upper classes in universities specializing in these fields.

Foreword  v

 Chapter I. Method of Computing Three-Dimensional Flows 1

 1. Formulation of the Problem 1

 2. Difference Scheme for Computing Three-Dimensional Flow 8

 3. Correctness of Boundary Value Problems for Difference  Equations 15

 4. Stability of the Sweep 23

 5 Stability of Difference Systems 30 

 6. Application to Equations of Gasdynamics 37 

 7. Calculation of Conic Flows 46 

 8. Computation of Thermodynamic Functions of Air Taking into Account Equilibrium Chemical Reactions 55 

 

 Chapter II. Results of Calculations 6l 

 

 9. Flow Past Circular Cones 6l 

 a. The Shape of Shock Waves 62

 b. Dependence of Gasdynamic Functions on Values of Coordinate 64

 c. Variation in Gasdynamic Functions with the Coordinate & 67

 d. Variation in Gasdynamic Functions with the Mach Number M^ 67

 e. Variation in Gasdynamic Functions with the Half Cone Angle fyr 67

 f. Variation in the Gasdynamic Functions with the Angle of Attack 72

 10. Examples of Flows Wear Smooth Bodies 72 

 11. Remarks on the Kopal Tables 97

  

Chapter III. Description of Tables for Flow Around Circular Cones 100 

12. Construction ofTables 100 13. Accuracy of the Tables 103

 References 106 

 Tables of Axisymmetric Flow Around Cones 109 

 Tables of Three-Dimensional Flow Around Cones 122

 Mco = 2 122 

 Mco = 3 158 

 Moo = 5 226 

 Moo = 7 314

 Appendix 1. Tables of Gasdynamic Functions Obtained by Interpolation 388 

 Moo = k 388 

 Moo = 6 452

 Appendix 2. Tables of Aerodynamics Coefficients 516