Explicit Exact and Third-Order-Accurate Pressure-Deflection Solutions for Oblique Shock and Expansion Waves
نویسنده
چکیده
This paper presents explicit analytical solutions of the pressure coefficient and the pressure ratio across the oblique shock and expansion waves in function of the flow deflection angle. These new explicit pressure-deflection solutions can be efficiently used in solving applied aerodynamic problems in supersonic flows, such as the aerodynamics of airfoils and wings in supersonic-hypersonic flows and the shock and expansion waves interactions, and can be also used to increase the computational efficiency of the numerical methods based on the Riemann problem solution requiring the pressure-deflection solution of the oblique shock and expansion waves, such as the Godunov method.
منابع مشابه
Aspects of planar, oblique and interacting shock waves in an ideal dissociating gas
We develop a compact dimensionless framework for the analysis of canonical thermo-chemical nonequilibrium flow fields involving normal, oblique and interacting shock waves. Discontinuous solutions of the conservation equations are coupled with thermodynamic and kinetic models for an ideal dissociating gas. Convenient forms are provided for the variation of the relevant dimensionless parameters ...
متن کاملExact Solution for Multidimensional Compressible Reactive Flow for Verifying Numerical Algorithms
A new exact solution of an oblique detonation is developed for the supersonic irrotational flow of an inviscid calorically perfect ideal gas, which undergoes a one-step, irreversible, exothermic, zero activation energy reaction as it passes through a straight shock over a curved wedge. The solution gives expressions for the velocity, pressure, density, temperature, and position as parametric fu...
متن کاملNonstandard explicit third-order Runge-Kutta method with positivity property
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...
متن کاملTransonic and Supersonic Overtaking of a Projectile Preceding a Shock Wave
In this paper, two-dimensional and axisymmetric, time dependent transonic and supersonic flows over a projectile overtaking a moving shock wave are considered. The flow is simulated numerically by solving full time averaged Navier-Stokes equations. The equations are linearized by Newton approach. The roe’s flux splitting method, second order central difference scheme for the diffusion terms, an...
متن کاملExact Solutions for Two-Dimensional Reactive Flow for Verification of Numerical Algorithms
New exact solutions of oblique detonations are developed for the supersonic irrotational flow of an inviscid calorically perfect ideal gas which undergoes a one-step, irreversible, exothermic, zero activation energy reaction as it passes through a straight shock over a curved wedge. A full exact solution gives expressions for the velocity, pressure, density, temperature, and position as paramet...
متن کامل