Kuz'min Boundary Value Problems for Transonic Flow

1. Auflage 2003
ISBN: 978-0-470-85295-8
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 316 Seiten, E-Book

Transonic flow occurs around moving objects as they approach andcross the sound barrier. Serious problems can occur at this point,such as shock-induced flow separation which can cause the aircraftto spin out of control. Another important practical problem is theachievement of higher aerodynamic performance of aircraft at cruiseconditions, which leads to considerable fuel savings. The successin application of numerical methods for simulation of transonicflow and aircraft design depends on developments in the underlyingmathematical theory.
This book presents a breakthrough in the solvability analysis ofboundary value problems, which makes it possible to establishconvergence of finite element approximations for shock-free flowand to provide a framework for putting the existing numericalmethods on a more sound basis. Also, physical aspects concernedwith patterns of formation and propagation of weak shock waves areanalysed. This contributes to the understanding of the extremesensitivity of transonic flow to perturbation of freestreamconditions. The developed theoretical knowledge base yieldspromising concepts of the airfoil design and active flow control byairfoil/wing shape modifications or suction/blowing through aperforated surface.
Boundary Value Problems for Transonic Flow
* Focuses on Computational Fluid Dynamics.
* Addresses practical problems, such as airfoil design and flowcontrol.
* Presents developments made in the last two decades.
In essence this is a much needed monograph for researchers andengineers in applied mathematics and numerical analysis applied toaerodynamics and for algorithm developers in Computational FluidDynamics in the aircraft industry. It gives design engineers theunderlying mathematical theory necessary for developing newconcepts for airfoil/wing design and flow control.

Autoren/Hrsg.

Kuz'min, Alexander G.

Inhaltsverzeichnis

1. Linear Partial Differential Equations of Mixed Type.
Solvability of a Basic Boundary-Value Problem.
Equation of the Elliptic-Hyperbolic Type.
Equation of the Hyperbolic-Elliptic Type.
Equation with a Local Hyperbolic Subdomain.
Other Developments.
The Tricomi Equation.
2. Flow That Accelerates from Subsonic to Supersonic Velocity in aChannel.
A Uniqueness Theorem.
Solvability of a Nonlinear Pertubation Problem.
The Full-Potential and the Chaplygin Euqations.
Finite-Element Solutions.
Unsteady Inviscid Flow.
Finite-Difference Schemes.
Acoustical Oscillations in Transonic Flow.
Nonisentropic Flow.
Flow with a Local Region of Deceleration.
3. Flow with a Local Supersonic Region.
Particular Smooth Solutions and Shockless Airfoils.
A Modification of the Frankl Problem.
Concepts of the Arising of Shock Waves.
Flow with a Local Supersonic Region over a Porous Boundary.
Flow that Decelerates from Supersonic to Subsonic Velocities.
FE and FE Treastment of Flow with Shock Waves.
Viscous Transonic Flow.
4. Numerical Simulation of Transonic Flow Patterns.
Formation of Shock Waves in the Local Supersonic Region.
Inrteraction of a Shock Wave with the Sonic Line.
Off-design Conditions and Flow Control.
Unsteady Transonic Flow.
Other Studies Concerned with a Flow Structure.
Nonunique Numerical Solutions.
Appendix A -
Boundary-Value Problem with a Damping Condition
References