Hypersonic Three-Dimensional Nonequilibrium Boundary-Layer Equations in Generalized Curvilinear Coordinates PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Hypersonic Three-Dimensional Nonequilibrium Boundary-Layer Equations in Generalized Curvilinear Coordinates PDF full book. Access full book title Hypersonic Three-Dimensional Nonequilibrium Boundary-Layer Equations in Generalized Curvilinear Coordinates by National Aeronautics and Space Administration (NASA). Download full books in PDF and EPUB format.
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722441920
Category :
Languages : en
Pages : 66
Get Book Here
Book Description
The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given. Lee, Jong-Hun Unspecified Center...
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722441920
Category :
Languages : en
Pages : 66
Get Book Here
Book Description
The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given. Lee, Jong-Hun Unspecified Center...
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781725635708
Category :
Languages : en
Pages : 36
Get Book Here
Book Description
A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations. Panaras, Argyris G. Ames Research Center NASA-TM-100003, A-87272, NAS 1.15:100003 RTOP 505-60...
Author: Theo Geis
Publisher:
ISBN:
Category : Boundary layer
Languages : en
Pages : 96
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 994
Get Book Here
Book Description
Author: Timothy Wade Swafford
Publisher:
ISBN:
Category : Boundary layer
Languages : en
Pages : 300
Get Book Here
Book Description
A method is presented for computing three-dimensional, time-dependent, compressible, turbulent boundary layers in nonorthogonal curvilinear coordinates. An integral method is employed in the interest of computational speed and because the three-dimensional method is an extension of an existing two-dimensional method. After presenting a detailed derivation of the integral form of the boundary-layer equations, the necessary auxiliary relations are given along with the relationships between integral lengths expressed in streamline and nonorthogonal coordinates. A time dependent approach is used to account for time accuracy (if desired) and to provide a method that is compatible with the surface grid used by an inviscid solver for use in viscous-inviscid interaction calculations. The equations are solved using a Runge-Kutta scheme with local time stepping to accelerate convergence. Stability and convergence of the numerical scheme are examined for various space differences compared with measurements and with computations of previous investigators.
Author: Joseph L. Steger
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
Get Book Here
Book Description
Author: Argyris G. Panaras
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 590
Get Book Here
Book Description
Author: Y.P. Golovachov
Publisher: Springer Science & Business Media
ISBN: 9401584907
Category : Mathematics
Languages : en
Pages : 359
Get Book Here
Book Description
The book is concerned with mathematical modelling of supersonic and hyper sonic flows about bodies. Permanent interest in this topic is stimulated, first of all, by aviation and aerospace engineering. The designing of aircraft and space vehicles requires a more precise prediction of the aerodynamic and heat transfer characteristics. Together with broadening of the flight condition range, this makes it necessary to take into account a number of gas dynamic and physical effects caused by rarefaction, viscous-inviscid interaction, separation, various physical and chemical processes induced by gas heating in the intensive bow shock wave. The flow field around a body moving at supersonic speed can be divided into three parts, namely, shock layer, near wake including base flow, and far wake. The shock layer flow is bounded by the bow shock wave and the front and lat eral parts of the body surface. A conventional approach to calculation of shock layer flows consists in a successive solution of the inviscid gas and boundary layer equations. When the afore-mentioned effects become important, implementation of these models meets difficulties or even becomes impossible. In this case, one has to use a more general approach based on the viscous shock layer concept.
Author: Denis Bergeron
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Get Book Here
Book Description
