Engineering topics

Liu, G. C.

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

7 records

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

Upwind Navier-Stokes solutions for separated periodic flows

The application of an upwind implicit approximate factorization Navier-Stokes algorithm to highly separated flow is described. Using both the thin-layer and complete forms of the Navier-Stokes equations, the low Reynolds number laminar flow around a circular cylinder with periodic shedding is solved. The effect of grid density, grid extent, and time step on the Strouhal number is shown. Results from both sets of equations agree within the experimental data band. Unsteady, laminar flow computations around inclined plates and separated airfoils are also described. Strouhal numbers agree to within 5 percent of experiments for inclined plates. Differences between the complete equations and the thin-layer approximation for separated periodic flows are discussed. Computations of an impulsively started circular cylinder and airfoil yield time-accurate flowfield shapes in good agreement with experimental flow visualizations. The turbulent computation of an airfoil at a high angle-of-attack is massively separated, but shows no evidence of periodicity.

Rumsey, C. L.↗

NASA NTRS1986

Numerical studies of interacting vortices

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

Liu, G. C.↗

NASA NTRS1985

Numerical studies of interacting vortices

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two dimensional vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

Liu, G. C.↗

NASA NTRS1984

Calculation of vertical and ramp-assisted takeoffs for supersonic cruise fighters

A procedure that allows rapid preliminary evaluations of the vertical, short, and normal takeoff performance of supersonic cruise aircraft concepts was developed into a numerical computer program. The program is used to determine the effects on takeoff performance of various parameters, such as thrust-weight ratio, wing loading, thrust vector angle, and flap setting. Ramp-assisted takeoffs for overloaded configurations typical of a ground-attack mission are included. The effects of wind on the takeoff performance are also considered.

Liu, G. C.↗

NASA NTRS1984

Canonical solutions for unsteady flow fields

The initial value problem of one-dimensional gas-dynamics involving discontinuous, nonuniform initial data is discussed. Canonical solutions which are valid in a small x, t region aroung a discontinuity, and which include the first order effects of nonuniformities in the data, are derived explicitly. The theory is derived by considering a group of elementary piston problems. Solutions with a shock or with a centered expansion wave are worked out individually in order to relate initial flow properties and their gradients to the speed and acceleration of the discontinuity waves. They are then combined to represent the solution of a general initial value problem by regarding the piston path as a contact line. In addition, problems with chemical reaction are discussed in terms of elementary piston problems which involve strong detonation waves, Chapman-Jouguet detonation waves, and deflagration waves.

Liu, G. C.↗

NASA NTRS1983

Performance of high-altitude, long-endurance, turboprop airplanes using conventional or cryogenic fuels

An analytical study has been conducted to evaluate the potential endurance of remotely piloted, low speed, high altitude, long endurance airplanes designed with 1990 technology. The baseline configuration was a propeller driven, sailplane like airplane powered by turbine engines that used JP-7, liquid methane, or liquid hydrogen as fuel. Endurance was measured as the time spent between 60,000 feet and an engine limited maximum altitude of 70,000 feet. Performance was calculated for a baseline vehicle and for configurations derived by varying aerodynamic, structural or propulsion parameters. Endurance is maximized by reducing wing loading and engine size. The level of maximum endurance for a given wing loading is virtually the same for all three fuels. Constraints due to winds aloft and propulsion system scaling produce maximum endurance values of 71 hours for JP-7 fuel, 70 hours for liquid methane, and 65 hours for liquid hydrogen. Endurance is shown to be strongly effected by structural weight fraction, specific fuel consumption, and fuel load. Listings of the computer program used in this study and sample cases are included in the report.

Liu, G. C.↗