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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Abolhassani, J. S.↗
NASA NTRS1986

Numerical solutions of the complete Navier-Stokes equations

Using ideas from the kinetic theory, the Navier-Stokes equations are modified in such a way that they can be cast as a set of first order hyperbolic equations. This is achieved by incorporating time dependent terms into the definition of the stress tensor and the heat flux vectors. The boundary conditions are then determined from the theory of characteristics. Because the resulting equations reduce to the traditional Navier-Stokes equations when the steady state is reached, the present approach provides a straightforward scheme for the determination of inflow and outflow boundary conditions. The method is validated by comparing its predictions with known exact solutions of the steady Navier-Stokes equations.

Hassan, H. A.↗
NASA NTRS1987

Boundary conditions for the Navier-Stokes equations

Using ideas from kinetic theory, the Navier-Stokes equations are modified in such a way that they can be cast as a set of first order hyperbolic equations. This is achieved by incorporating time dependent terms into the definition of the stress tensor and the heat flux vectors. The boundary conditions are then determined from the theory of characteristics. Because the resulting equations reduce to the traditional Navier-Stokes equations when the steady state is reached, the present approach provides a straightforward scheme for the determination of inflow and outflow boundary conditions. The method is validated by comparing its predictions with exact and numerical solutions of the steady Navier-Stokes equations.

Rudisill, Edgar N., Jr.↗
NASA NTRS1992

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Yu, Sheng-Tao↗
NASA NTRS2016

Unique Results and Lessons Learned from the TSS Missions

In 1924, Irvin Langmuir and H. M. Mott-Smith published a theoretical model for the complex plasma sheath phenomenon in which they identified some very special cases which greatly simplified the sheath and allowed a closed solution to the problem. The most widely used application is for an electrostatic, or "Langmuir," probe in laboratory plasma. Although the Langmuir probe is physically simple (a biased wire) the theory describing its functional behavior and its current-voltage characteristic is extremely complex and, accordingly, a number of assumptions and approximations are used in the LMS model. These simplifications, correspondingly, place limits on the model's range of application. Adapting the LMS model to real-life conditions is the subject of numerous papers and dissertations. The Orbit-Motion Limited (OML) model that is widely used today is one of these adaptions that is a convenient means of calculating sheath effects. The OML equation for electron current collection by a positively biased body is simply: I is approximately equal to A x j(sub eo) x 2/√𝜋(phi)(exp ½) where A is the area of the body and phi is the electric potential on the body with respect to the plasma. Since the Langmuir probe is a simple biased wire immersed in plasma, it is particularly tempting to use the OML equation in calculating the characteristics of the long, highly biased wires of an Electric Sail in the solar wind plasma. However, in order to arrive at the OML equation, a number of additional simplifying assumptions and approximations (beyond those made by Langmuir-Mott-Smith) are necessary. The OML equation is a good approximation when all conditions are met, but it would appear that the Electric Sail problem lies outside of the limits of applicability.

Stone, Nobie H.↗
NASA NTRS1982

A composite velocity procedure for the compressible Navier-Stokes equations

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Khosla, P. K.↗
NASA NTRS2016

Rethinking Use of the OML Model in Electric Sail Development

In 1924, Irvin Langmuir and H. M. Mott-Smith published a theoretical model for the complex plasma sheath phenomenon in which they identified some very special cases which greatly simplified the sheath and allowed a closed solution to the problem. The most widely used application is for an electrostatic, or "Langmuir," probe in laboratory plasma. Although the Langmuir probe is physically simple (a biased wire) the theory describing its functional behavior and its current-voltage characteristic is extremely complex and, accordingly, a number of assumptions and approximations are used in the LMS model. These simplifications, correspondingly, place limits on the model's range of application. Adapting the LMS model to real-life conditions is the subject of numerous papers and dissertations. The Orbit-Motion Limited (OML) model that is widely used today is one of these adaptions that is a convenient means of calculating sheath effects. Since the Langmuir probe is a simple biased wire immersed in plasma, it is particularly tempting to use the OML equation in calculating the characteristics of the long, highly biased wires of an Electric Sail in the solar wind plasma. However, in order to arrive at the OML equation, a number of additional simplifying assumptions and approximations (beyond those made by Langmuir-Mott-Smith) are necessary. The OML equation is a good approximation when all conditions are met, but it would appear that the Electric Sail problem lies outside of the limits of applicability.

Stone, Nobie H.↗
NASA NTRS1991

Estimation of homogeneous nucleation flux via a kinetic model

The proposed kinetic model for condensation under homogeneous conditions, and the onset of unidirectional cluster growth in supersaturated gases, does not suffer from the conceptual flaws that characterize classical nucleation theory. When a full set of simultaneous rate equation is solved, a characteristic time emerges, for each cluster size, at which the production rate, and its rate of conversion to the next size (n + 1) are equal. Procedures for estimating the essential parameters are proposed; condensation fluxes J(kin) exp ss are evaluated. Since there are practical limits to the cluster size that can be incorporated in the set of simultaneous first-order differential equations, a code was developed for computing an approximate J(th) exp ss based on estimates of a 'constrained equilibrium' distribution, and identification of its minimum.

Wilcox, C. F.↗
NASA NTRS1952

Discussion of Boundary-Layer Characteristics Near the Wall of an Axial-Flow Compressor

The boundary-layer velocity profiles in the tip region of an axial-flow compressor downstream of the guide vanes and downstream of the rotor were measured by use of total-pressure and claw-type yaw probes. These velocities were resolved into two components: one along the streamline of the flow outside the boundary layer, and the other perpendicular to it. The affinity among all profiles was thus demonstrated with the boundary-layer thickness and the deflection of the boundary layer at the wall as the generalizing parameters. By use of these results and the momentum-integral equations, boundary-layer characteristics on the walls of an axial-flow compressor were qualitatively evaluated.

Mager, Artur↗
NASA NTRS1984

Multiple steady states for characteristic initial value problems

The time dependent, isentropic, quasi-one-dimensional equations of gas dynamics and other model equations are considered under the constraint of characteristic boundary conditions. Analysis of the time evolution shows how different initial data may lead to different steady states and how seemingly anamolous behavior of the solution may be resolved. Numerical experimentation using time consistent explicit algorithms verifies the conclusions of the analysis. The use of implicit schemes with very large time steps leads to erroneous results.

Salas, M. D.↗
NASA NTRS1993

Vibration of thermally buckled composite plates with initial deflections using triangular elements

A consistent finite element formulation is presented for the analysis of thermal postbuckling and free vibration of thermally buckled thin, laminated composite plates subjected to large temperature change. The influence of moderately large initial imperfections in deflection on the thermal postbuckling deflection and the vibration characteristics of the buckled plate is also investigated. The finite element equations of motion are derived from the principle of virtual work. These equations can be mathematically separated into two sets and solved in sequence. The first set of equations yields the particular solution of static thermal postbuckling deflection, and the second set of equations gives the homogeneous solution of vibration characteristics on the buckled plate. The first set of static equations is solved by using Newton-Raphson iteration method. The tangent stiffness matrix in the final iteration is equal to the total stiffness matrix of the second set of dynamic equations. This feature saves tremendous computation time in comparing with using the conventional approach. The influence of lamination angle, temperature distribution, plate planform of arbitrary shape, and boundary support conditions on postbuckling and vibration behavior are investigated.

Zhou, R. C.↗
NASA NTRS1985

Heat pipe modeling and simulation

Presented herein is a parametric study of the defining equations which govern the steady state operational characteristics of the Grumman Monogroove Dual Passage Heat Pipe. These defining equations are combined to develop a mathematical model which describes and predicts the operational and performance capabilities of a specific heat pipe, given the necessary physical characteristics and working fluid. Included is a brief review of the current literature, a discussion of the governing equations, and a description of both the mathematical and computer model. Final results of preliminary test runs of the model are presented and compared with experimental tests performed by Grumman on actual prototypes.

Peterson, G. P.↗
NASA NTRS1973

Vibration of Shells

The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.

Leissa, A. W.↗
NASA NTRS2003

Main Chamber Injectors for Advanced Hydrocarbon Booster Engines

Achieving the highest possible specific impulse has long been a key driver for space launch systems. Recently, more importance has been placed on the need for increased reliability and streamlined launch operations. These general factors along with more specific mission requirements have provided a new focus that is centered on the oxidizer rich staged combustion (ORSC) cycle. Despite a history of use in Russia that extends back to the 1960's, a proven design methodology for ORSC cycle engines does not exist in the West. This lack of design expertise extends to the main chamber injector, a critical subcomponent that largely determines the engine performance and main chamber life. The goals of the effort described here are to establish an empirical knowledge base to provide a fundamental understanding of main chamber injectors and for verification of an injector design methodology for the ORSC cycle. The design of a baseline injector element, derived from information on Russian engines in the open literature, is presented. The baseline injector comprises a gaseous oxidizer core flow and an annular swirling fuel flow. Sets of equations describing the steady-state and the dynamic characteristics of the injector are presented; these equations, which form the basis of the design analysis methodology, will be verified in tests later this year. On-going cold flow studies, using nitrogen and water as simulants, are described which indicate highly atomized and symmetric sprays.

Long, Matthew R.↗
NASA NTRS1973

An experimental-analytical method to study steady spray combustion.

Description of a method for determining the local parameters of the gas mixture resulting from the combustion of sprayed fuel in a gaseous oxidizer. The method is based on the measurement of local static pressures in the gas mixture and does not require the knowledge of the droplet distribution function, drag, and vaporization characteristics. A set of equations with substituted local pressure values is used for calculations. Application of the method is demonstrated on a liquid oxygen-ethanol rocket fuel.

Bracco, F. V.↗