Boundary-Layer Equations in Generalized Curvilinear Coordinates


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...







Hypersonic Three-Dimensional Nonequilibrium Boundary-Layer Equations in Generalized Curvilinear Coordinates


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...







Chemically Reacting Flow


Book Description

A guide to the theoretical underpinnings and practical applications of chemically reacting flow Chemically Reacting Flow: Theory, Modeling, and Simulation, Second Edition combines fundamental concepts in fluid mechanics and physical chemistry while helping students and professionals to develop the analytical and simulation skills needed to solve real-world engineering problems. The authors clearly explain the theoretical and computational building blocks enabling readers to extend the approaches described to related or entirely new applications. New to this Second Edition are substantially revised and reorganized coverage of topics treated in the first edition. New material in the book includes two important areas of active research: reactive porous-media flows and electrochemical kinetics. These topics create bridges between traditional fluid-flow simulation approaches and transport within porous-media electrochemical systems. The first half of the book is devoted to multicomponent fluid-mechanical fundamentals. In the second half the authors provide the necessary fundamental background needed to couple reaction chemistry into complex reacting-flow models. Coverage of such topics is presented in self-contained chapters, allowing a great deal of flexibility in course curriculum design. • Features new chapters on reactive porous-media flow, electrochemistry, chemical thermodynamics, transport properties, and solving differential equations in MATLAB • Provides the theoretical underpinnings and practical applications of chemically reacting flow • Emphasizes fundamentals, allowing the analyst to understand fundamental theory underlying reacting-flow simulations • Helps readers to acquire greater facility in the derivation and solution of conservation equations in new or unusual circumstances • Reorganized to facilitate use as a class text and now including a solutions manual for academic adopters Computer simulation of reactive systems is highly efficient and cost-effective in the development, enhancement, and optimization of chemical processes. Chemically Reacting Flow: Theory, Modeling, and Simulation, Second Edition helps prepare graduate students in mechanical or chemical engineering, as well as research professionals in those fields take utmost advantage of that powerful capability.




Three-Dimensional Attached Viscous Flow


Book Description

Viscous flow is treated usually in the frame of boundary-layer theory and as two-dimensional flow. Books on boundary layers give at most the describing equations for three-dimensional boundary layers, and solutions often only for some special cases. This book provides basic principles and theoretical foundations regarding three-dimensional attached viscous flow. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers. This wider scope is necessary in view of the theoretical and practical problems to be mastered in practice. The topics are weak, strong, and global interaction, the locality principle, properties of three-dimensional viscous flow, thermal surface effects, characteristic properties, wall compatibility conditions, connections between inviscid and viscous flow, flow topology, quasi-one- and two-dimensional flows, laminar-turbulent transition and turbulence. Though the primary flight speed range is that of civil air transport vehicles, flows past other flying vehicles up to hypersonic speeds are also considered. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers, as this wider scope is necessary in view of the theoretical and practical problems that have to be overcome in practice. The specific topics covered include weak, strong, and global interaction; the locality principle; properties of three-dimensional viscous flows; thermal surface effects; characteristic properties; wall compatibility conditions; connections between inviscid and viscous flows; flow topology; quasi-one- and two-dimensional flows; laminar-turbulent transition; and turbulence. Detailed discussions of examples illustrate these topics and the relevant phenomena encountered in three-dimensional viscous flows. The full governing equations, reference-temperature relations for qualitative considerations and estimations of flow properties, and coordinates for fuselages and wings are also provided. Sample problems with solutions allow readers to test their understanding.







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