Engineering Papers⌕ Search

Engineering topics

Liu, C. H.

Publications and source records attributed to Liu, C. H..

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Comparison of uniform perturbation and numerical solutions for some potential flows past slender bodies

Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.

Wong, T.-C.↗
NASA NTRS1985

Algorithmic and theoretical results on computation of incompressible viscous flows by finite element methods

Primitive variable as well as streamfunction-vorticity and pure streamfunction formulations are discussed. For the primitive variable case alternative choices of the viscous stress term are shown to produce natural boundary conditions which are well suited for matching to various far field conditions. For the other cases recent analytical results, including error estimates are described, and an optical algorithm for pressure recovery as well as treatment for multiply connected domains are given.

Gunzburger, M. D.↗
NASA NTRS1984

Some recent developments in the interpretation of MST radar returns from clear air (keynote paper), part 2

Mesosphere-stratosphere-troposphere (MST) radar returns from clear air come about through the interaction of electromagnetic waves with the inhomogeneous structures of refractive index in the atmosphere. In order to interpret the data correctly to obtain information concerning the dynamics of the atmosphere, one must first know how the various refractive index structures can affect the propagation and scattering of the radio waves. This can be achieved through theoretical and model studies. On the other hand, in order to carry out realistic theoretical studies, realistic models of the inhomogeneous structures of the atmospheric refractive index are needed. These are available only through observational data. Therefore the close interplays between theoretical and observational investigations are essential in making progress in this area. Some results on certain aspects of the problem are presented with emphasis on those aspects that may lead to new developments.

Liu, C. H.↗
NASA NTRS1984

Gravity-wave spectra in the atmosphere observed by MST radar, part 4.2B

A universal spectrum of atmospheric buoyancy waves is proposed based on data from radiosonde, Doppler navigation, not-wire anemometer and Jimsphere balloon. The possible existence of such a universal spectrum clearly will have significant impact on several areas in the study of the middle atmosphere dynamics such as the parameterization of sub-grid scale gravity waves in global circulation models; the transport of trace constituents and heat in the middle atmosphere, etc. Therefore, it is important to examine more global wind data with temporal and spatial resolutions suitable for the investigation of the wave spectra. Mesosphere-stratosphere-troposphere (MST) radar observations offer an excellent opportunity for such studies. It is important to realize that radar measures the line-of-sight velocity which, in general, contains the combination of the vertical and horizontal components of the wave-associated particle velocity. Starting from a general oblique radar observation configuration, applying the dispersion relation for the gravity waves, the spectrum for the observed fluctuations in the line-of-sight gravity-wave spectrum is investigated through a filter function. The consequence of the filter function on data analysis is discussed.

Scheffler, A. O.↗
NASA NTRS1984

Interpretation and modeling of quasiperiodic diffraction patterns observed in equatorial VHF scintillation due to plasma bubbles

Quasiperiodic diffraction patterns have been observed in VHF scintillation recorded at Ascension Island in 1981. The patterns occur most often at the beginning or end of a scintillation patch and are shown to be consistent with those expected from irregularities having east-west scale sizes of a few hundred meters that are associated with the walls (edges) of equatorial plasma bubbles. By adjusting the geophysical parameters in a computer simulation of the amplitude fluctuations expected simultaneously at VHF, L-Band and C-Band, we model a specific event in detail. The model contains information on the size and strength of the structures that cause the regular fading patterns. In addition, multi-frequency diffraction patterns are computed for a 'phase screen' model based on high resolution measurements of a structured plasma bubble wall made using the AE-E satellite. The results are qualitatively very similar to the observations. Finally, implications of the model results for the extraction of information about the vertical structure of the irregularities are discussed.

Franke, S. J.↗
NASA NTRS1984

Comparison of uniform perturbation solutions and numerical solutions for some potential flows past slender bodies

Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.

Wong, T. C.↗
NASA NTRS1984

Numerical studies of motion of vortex filaments - Implementing the asymptotic analysis

A computational code is developed for the integro-differential equations governing the motion of the centerlines of vortex filaments submerged in a background potential flow. These equations, which are derived from the method of matched asymptotic analysis, include the effect of the decaying large-magnitude circumferential and axial velocity components in the vortical cores. Numerical examples are presented to assess the effect of a large axial velocity and that of nonsimilar initial profiles in the vortical cores. The initial configurations of the filaments are chosen so as to fulfill the basic assumption of the asymptotic analysis, which is that the effective vortical core size is much smaller than all the other length scales in the flowfield, e.g., the radius of curvature and the interfilament distance. The computations are continued until the basic assumption is no longer valid, that is when the merging or intersection of filaments has begun. A classification of the various types of local or global merging or intersection of filaments is made and demonstrated by numerical examples. It is then shown that the asymptotic solution not only provides the initial data but also can be used to formulate the appropriate boundary conditions for the numerical solution of a merged region.

Liu, C. H.↗
NASA NTRS1984

Navier-Stokes calculations for the vortex of a rotor in hover

An efficient finite-difference scheme for the solution of the incompressible Navier-Stokes equation is used to study the vortex wake of a rotor in hover. The solution Procedure uses a vorticity-stream function formulation and incorporates an asymptotic far-field boundary condition enabling the size of the computational domain to be reduced in comparison to other methods. The results from the present method are compared with experimental data obtained by smoke flow visualization and hot-wire measurements for several rotor blade configurations.

Liu, C. H.↗
NASA NTRS1984

Navier-Stokes calculations for unsteady three-dimensional vortical flows in unbounded domains

Finite-difference Navier-Stokes calculations for unsteady, three-dimensional, incompressible, viscous flows induced by initial vorticity distributions are presented and discussed in this paper. The initial vorticity distributions are assumed to be embedded in a flow field of infinite extent that is quiescent at infinity. These vorticity distributions are typical of vortex rings and other closed vortical tubes or structures. Such structures are important elements in fluid flows such as jets, atmospheric convection and the far-field wakes of aircraft; studies of their interaction may aid in an understanding of complex fluid flows. The calculations employ a method recently proposed by Ting to approximate the infinite-domain boundary value problem with a finite boundary computational domain, and this method is shown to yield accurate three-dimensional results for reasonable expenditures of computer time. Because of the efficiency of the boundary condition technique and the resulting Navier-Stokes code, a 16-bit minicomputer with virtual memory was capable of performing the calculations for the unsteady motion of two obliquely colliding vortex rings. The results of these calculations are presented in the paper.

Chamberlain, J. P.↗
NASA NTRS1983

Interpretation of MST radar returns from clear air

The nature of the scattering and reflection mechanisms that give rise to the MST radar echoes from the clear air is essential in the correct interpretation of the data about winds, waves, turbulence and stability in the atmosphere. There are two main aspects: the nature of the targets the radar sees and their generation mechanisms; and the signatures of the radar signals returned from the different targets. Volume scatterings from isotropic or anisotropic turbulence, and partial reflections from horizontally stratified, sharp refractive index gradients are believed the main contributors to radar echoes. Combined effects from all the mechanisms probably produce the observed data. The signature of the echo signals for these different scatterers under realistic experimental conditions should be studied. It is hoped from these studies, the nature of the targets can be better understood, and related to atmospheric dynamic processes.

Liu, C. H.↗
NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Gunzburger, M. D.↗
NASA NTRS1983

Navier-Stokes calculations for the vortex wake of a rotor in hover

An efficient finite-difference scheme for the solution of the incompressible Navier-Stokes equation is used to study the vortex wake of a rotor in hover. The solution procedure uses a vorticity-stream function formulation and incorporates an asymptotic far-field boundary condition enabling the size of the computational domain to be reduced in comparison to other methods. The results from the present method are compared with experimental data obtained by smoke flow visualization and hot-wire measurements for several rotor blade configurations.

Liu, C. H.↗
NASA NTRS1983

A finite element method for diffusion dominated unsteady viscous flows

A general conforming finite element scheme for computing viscous flows is presented which is of second-order accuracy in space and time. Viscous terms are treated implicitly and advection terms are treated explicitly in the time marching segment of the algorithm. A method for solving the algebraic equations at each time step is given. The method is demonstrated on two test problems, one of them being a plane vortex flow for which asymptotic methods are used to obtain suitable numerical boundary conditions at each time step.

Gunzburger, M. D.↗
NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

Gunzburger, M. D.↗
NASA NTRS1982

Supersonic jet noise generated by large scale instabilities

The role of large scale wavelike structures as the major mechanism for supersonic jet noise emission is examined. With the use of aerodynamic and acoustic data for low Reynolds number, supersonic jets at and below 70 thousand comparisons are made with flow fluctuation and acoustic measurements in high Reynolds number, supersonic jets. These comparisons show that a similar physical mechanism governs the generation of sound emitted in he principal noise direction. These experimental data are further compared with a linear instability theory whose prediction for the axial location of peak wave amplitude agrees satisfactorily with measured phased averaged flow fluctuation data in the low Reynolds number jets. The agreement between theory and experiment in the high Reynolds number flow differs as to the axial location for peak flow fluctuations and predicts an apparent origin for sound emission far upstream of the measured acoustic data.

Seiner, J. M.↗
NASA NTRS1982

Approximate boundary condition procedure for the two-dimensional numerical solution of vortex wakes

Research on efficient computational methods for general vorticity fields has been conducted in connection with a need for basic research on vortex-dominated flows. The present investigation is concerned with the evolution of vortex wakes behind aircraft wings. An efficient procedure is presented for the calculation of the boundary values used in the numerical solution of the unsteady, incompressible, two-dimensional Navier-Stokes equations for an unbounded flow field. The extent of the computational grid can be reduced compared to methods utilizing standard boundary conditions, without loss of accuracy. The efficiencies realized make it feasible to calculate the vortex wake development for realistic wing configurations, including the merging of multiple vortices, for Reynolds numbers of about 10,000 based on wing chord.

Weston, R. P.↗
NASA NTRS1982

Numerical solution of viscous flow in unbounded fluid

Incompressible viscous flow fields induced by initial vorticity distributions with bounded support or exponential decay in the far field are investigated. A numerical scheme for the solution of the vorticity distribution and the velocity field is presented with special emphasis on the treatment of the boundary data. The efficiency of the scheme is demonstrated. The present method has been applied to the study of the merging and collision of vortex rings.

Liu, C. H.↗