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Ting, L.

Publications and source records attributed to Ting, L..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Acoustic field in unsteady moving media

In the interaction of an acoustic field with a moving airframe the authors encounter a canonical initial value problem for an acoustic field induced by an unsteady source distribution, q(t,x) with q equivalent to 0 for t less than or equal to 0, in a medium moving with a uniform unsteady velocity U(t)i in the coordinate system x fixed on the airframe. Signals issued from a source point S in the domain of dependence D of an observation point P at time t will arrive at point P more than once corresponding to different retarded times, Tau in the interval (0, t). The number of arrivals is called the multiplicity of the point S. The multiplicity equals 1 if the velocity U remains subsonic and can be greater when U becomes supersonic. For an unsteady uniform flow U(t)i, rules are formulated for defining the smallest number of I subdomains V(sub i) of D with the union of V(sub i) equal to D. Each subdomain has multiplicity 1 and a formula for the corresponding retarded time. The number of subdomains V(sub i) with nonempty intersection is the multiplicity m of the intersection. The multiplicity is at most I. Examples demonstrating these rules are presented for media at accelerating and/or decelerating supersonic speed.

Bauer, F.↗
NASA NTRS1989

Optimum shape of a blunt forebody in hypersonic flow

The optimum shape of a blunt forebody attached to a symmetric wedge or cone is determined. The length of the forebody, its semi-thickness or base radius, the nose radius and the radius of the fillet joining the forebody to the wedge or cone are specified. The optimum shape is composed of simple curves. Thus experimental models can be built readily to investigate the utilization of aerodynamic heating for boundary layer control. The optimum shape based on the modified Newtonian theory can also serve as the preliminary shape for the numerical solution of the optimum shape using the governing equations for a compressible inviscid or viscous flow.

Maestrello, L.↗
NASA NTRS1988

Motion, decay and merging of vortex filaments

The asymptotic solutions of Navier-Stokes equations for vortex filaments of finite strength with small effective vortical cores are summarized. Emphases are placed on the physical meaning and the practical limit to the applicability of the asymptotic solution. Finite-difference solutions of Navier-Stokes equations for the merging of the filament(s) are described. It is focused on the development of the approximate boundary conditions for the computational domain.

Liu, C. H.↗
NASA NTRS1988

Interaction and merging of vortex filaments

The asymptotic solutions of Navier-Stokes equations for vortex filaments of finite strength with small effective vortical cores are summarized with special emphasis placed on the physical meaning and the practical limit to the applicability of the asymptotic solution. Finite-difference solutions of Navier-Stokes equations for the marging of the filament(s) are described with a focus on the development of the approximate boundary conditions for the computational domain. An efficiency study employing a model problem is used to assess the advantages of the present approximate boundary condition method over previously used techniques. Applications of the present method are presented for the motion and decay of a 3:1 elliptic vortex ring, and for the merging process of a pair of coaxial vortex rings. A numerical procedure for the problem of local merging of vortex filaments, which requires the asymptotic analysis as well as the numerical Navier-Stokes solver, is also presented.

Liu, C. H.↗
NASA NTRS1987

Calculating Sonic-Boom Propagation

Nonlinear effects included, enabling more-realistic modeling. Modified Method of Characteristics Sonic Boom Extrapolation Program (MMOC) is computer program for sonic-boom propagation that includes shock coalescence and incorporates effects of asymmetries due to volume and lift. Numerically integrates nonlinear governing equations using data on initial data line approximately one body length from aircraft and yields sonic-boom pressure at ground as function of time or of position at given time. MMOC written in FORTRAN IV.

Darden, C. M.↗
NASA NTRS1986

Numerical studies of motion and decay of vortex filaments

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 decaying large-magnitude circumferential and axial velocity components in the vortical cores. Numerical examples are presented to assess the effect of large axial velocity and of nonsimilar initial profiles in vortical cores. The initial configurations of the filaments are chosen so as to fulfill the basic assumption of asymptotic analysis, which is the effective vortical core size is much smaller than all other length scales in the flowfield, e.g., the radius of curvature and interfilament distance. The computations are continued until the basic assumption is no longer valid, that is, when the merging or intersection of filaments have begun. Various types of local or global merging or intersection of filaments are classified and demonstrated by numerical examples.

Liu, C. H.↗
NASA NTRS1986

Numerical studies of the margin of vortices with decaying cores

The merging of vortices to a single one is a canonical incompressible viscous flow problem. The merging process begins when the core sizes or the vortices are comparable to their distances and ends when the contour lines of constant vorticity lines are circularized around one center. Approximate solutions to this problem are constructed by adapting the asymptotic solutions for distinct vortices. For the early stage of merging, the next-order terms in the asymptotic solutions are added to the leading term. For the later stage of merging, the vorticity distribution is reinitialized by vortices with overlapping core structures guided by the 'rule of merging' and the velocity of the 'vortex centers' are then defined by a minimum principle. To show the accuracy of the approximate solution, it is compared with the finite-difference solution.

Liu, G. C.↗
NASA NTRS1986

Numerical studies of the merging of vortices

A newly improved method has been employed to study the roll-up and decay of trailing vortex sheets. This method is obtained by using a scheme formulated recently Liu et al., Sept. 1985 to improve the accuracy of the boundary data. The scheme is much more efficient than the previous one used by Weston and Liu (1982). Comparisons of the present numreical results with other numerical solutions of the Navier-Stokes equations are presented.

Weston, R. P.↗
NASA NTRS1986

Interaction of decaying trailing vortices in ground shear

The drift of trailing vortices in a cross wind near to the ground is modeled by an unsteady, two-dimensional, rotational flowfield with a concentration of large vorticity in spots having finite total strength. The problem is analyzed by a combination of the method of matched asymptotic analyses for the decay of the vortical spots and the Euler solution for the unsteady rotational flow. A primary feature of the numerical scheme is that the grid size and time step depend only the length and velocity scales of the background flow and is independent of the effective core size of a vortical spot which can be much smaller than the grid size. Numerical results are presented to demonstrated the strong interaction between the trajectjories of the vortical spots and the redistribution of vorticity in the background flowfield.

Liu, C. H.↗
NASA NTRS1985

Vortex-dominated flow with viscous core structure

Recent theoretical studies of vortex-dominated flows are reviewed with special emphasis on those for which the viscous core structures play an important role. The problems to be described are: The interaction and merging of two-dimensional vortices and of curved vortex filaments, the roll-up and decay of trailing far wakes, and the initiation of vortex breakdown. The analysis utilizes finite-difference solutions of the Navier-Stokes equations complemented by asymptotic expansion techniques.

Liu, C. H.↗
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

Analysis of active control by surface heating

The excitation of boundary-layer disturbances by active, localized periodic heating of the flow surfaces is investigated analytically. A triple-deck model is used in the matched-asymptotics approach, and the incompressible case with small temperature variations, a linearized 3-deck problem, is considered. This case corresponds to the experimental (water-tunnel) conditions of Liepmann et al. (1982), who demonstrated that the induced disturbances can be used to enhance or suppress the Tollmien-Schlichting waves. Here the energy equation is uncoupled from the momentum and continuity equations to permit definition of the thermal-sublayer temperature profile by superposition of canonical solutions, which are presented in an appendix. A diagram of the 3-deck structure and graphs of calculated results are included.

Maestrello, L.↗
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.↗
NASA NTRS1980

Sound propagation through parallel jets exhausting from ducts

The method of matched asymptotic expansions is employed to construct the solution for the propagation of sound through parallel jets which exit from long ducts and are surrounded by a uniform parallel stream. Parts of the duct walls are lined with acoustically absorbent material. The small parameter for the expansion is the ratio of the inner jet thickness to the accoustic wavelength. The problem is further simplified when the condition is imposed that the speed of the outer stream, which accounts for the forward motion speed of the ducts, is much smaller than the speeds of the jets. This condition is valid during landing and takeoff operations. Farfield pressure distributions are obtained for the case in which the inner jet is much faster than the outer jet and the case in which the two jets are the same.

Ting, L.↗
NASA NTRS1979

Radiation of an acoustic source near the trailing edge of a wing in forward motion

The acoustic sources simulating engine or jet noise are located near the trailing edge. During landing or take-off operations the flap angle is not small. Solutions for the scattering of the acoustic sources, monopoles, dipoles or quadrupoles, by the wing with the flap at finite angle are constructed for the case that the acoustic wave length is much larger than the length of the flap but may be of the same order as the chord. For each given geometry of the flap and the position of the singularities, critical orientations of the dipoles and the quadrupoles are defined along which the noise becomes 'suppressed', i.e., the far field pressure becomes one order smaller.

Ting, L.↗
NASA NTRS1978

Sonic boom research

It is demonstrated that a supersonic airplane configuration weighing over half a million pounds while creating a maximum sonic boom of less than 1 p.s.f. can be designed. New experimental techniques are developed in the wind tunnel and experiments for the sonic boom measurements were carried out. Theoretical analyses were performed for the effects of sonic boom on structures and pollution problems associated with supersonic flights were investigated. Numerical programs were generated for the sonic boom propagations from the near field of an airplane in supersonic flight at high altitude to the ground, taking into account the nonlinear effects and the asymmetric effects due to lift and the spacewise distributions of lift and volume.

Ting, L.↗