Boundary-Layer Equations in Generalized Curvilinear Coordinates PDF Download
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781725635708
Category :
Languages : en
Pages : 36
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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: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781725635708
Category :
Languages : en
Pages : 36
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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: Argyris G. Panaras
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722441920
Category :
Languages : en
Pages : 66
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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: Denis Bergeron
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Author: Denis Bergeron
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Joseph L. Steger
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722000967
Category :
Languages : en
Pages : 28
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Book Description
This is a working paper in which a formulation is given for solving the boundary-layer equations in general body-fitted curvilinear coordinates while retaining the original Cartesian dependent variables. The solution procedure does not require that any of the coordinates be orthogonal, and much of the software developed for many Navier-Stokes schemes can be readily used. A limited number of calculations has been undertaken to validate the approach. Steger, Joseph L. and Vandalsem, William R. and Panaras, Argyris G. and Rao, K. V. Ames Research Center ...
Author: Stuart Eames Rogers
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 52
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Author: Timothy Wade Swafford
Publisher:
ISBN:
Category : Boundary layer
Languages : en
Pages : 300
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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: Theo Geis
Publisher:
ISBN:
Category : Boundary layer
Languages : en
Pages : 96
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