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At least 991 records · Page 55
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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 NTRS1986

Simulation experiments for testing the assimilation of geostationary satellite temperature retrievals into a numerical prediction model

A simulation experiment is presented which tests a procedure that assimilates temperature soundings from geostationary satellites using a method developed by Gal-Chen (1983). The simulation is used to decide whether the increased temporal resolution of geostationary satellite data can be used to improve numerical simulation of a baroclinically unstable wave, and to assess the impact of gaps in the satellite sounding fields on the model simulations. Background information on the simulation experiment is presented, including discussion of the variational approach utilized, the numerical model, updating procedures, and control run. The simulation results indicate that, for the case of a baroclinically unstable wave, considerable improvements in the short-range forecast may be realized if geostationary satellite data are inserted with a frequency near 1 hr during a 6 hr analysis cycle compared with a single insertion.

Gal-Chen, T.↗
NASA NTRS1986

Numerical solution of random singular integral equation appearing in crack problems

The solution of several elasticity problems, and particularly crack problems, can be reduced to the solution of one-dimensional singular integral equations with a Cauchy-type kernel or to a system of uncoupled singular integral equations. Here a method for the numerical solution of random singular integral equations of Cauchy type is presented. The solution technique involves a Chebyshev series approximation, the coefficients of which are the solutions of a system of random linear equations. This method is applied to the problem of periodic array of straight cracks inside an infinite isotropic elastic medium and subjected to a nonuniform pressure distribution along the crack edges. The statistical properties of the random solution are evaluated numerically, and the random solution is used to determine the values of the stress-intensity factors at the crack tips. The error, expressed as the difference between the mean of the random solution and the deterministic solution, is established. Values of stress-intensity factors at the crack tip for different random input functions are presented.

Sambandham, M.↗
NASA NTRS1987

Numerical simulation of compressible flow around complex two-dimensional cavities

Compressible viscous flow around two-dimensional cavities, that model the midplane flow in and around an airborne telescope cavity, are obtained through numerical simulation. Numerical solutions using the patched grid CSCM scheme for compressible, unsteady flow are presented for the cavities, with and without blowing. The time evolving solutions show interesting flow features. Relevant results for a limited number of problems presented here show the unsteady nature of the flow and its dependence on various parameters such as Reynolds number, the wall conditions, etc. The voluminous data of time evolving flow field solutions are analyzed through movies of the velocity vectors, and contours of other flow variables.

Venkatapathy, Ethiraj↗
NASA NTRS1987

Numerical simulation of transition, compressible turbulence, and reacting flows

Some of the recent work at NASA Langley on transition, turbulence, and reacting flows is summarized. Much of this effort has been motivated by outstanding technological problems in high-speed flow. A class of numerical algorithms for these problems has been developed and a variety of physical problems have been simulated. Descriptions are provided of the basic mathematical models, the nature of the numerical methods, and some of the recent simulations.

Zang, T. A.↗
NASA NTRS1987

Numerical simulation of a plane turbulent mixing layer, with applications to isothermal, rapid reactions

A hybrid method has been developed for the numerical prediction of turbulent mixing in a spatially-developing, free shear layer. Most significantly, the computation incorporates the effects of large-scale structures, Schmidt number and Reynolds number on mixing, which have been overlooked in the past. In flow field prediction, large-eddy simulation was conducted by a modified 2-D vortex method with subgrid-scale modeling. The predicted mean velocities, shear layer growth rates, Reynolds stresses, and the RMS of longitudinal velocity fluctuations were found to be in good agreement with experiments, although the lateral velocity fluctuations were overpredicted. In scalar transport, the Monte Carlo method was extended to the simulation of the time-dependent pdf transport equation. For the first time, the mixing frequency in Curl's coalescence/dispersion model was estimated by using Broadwell and Breidenthal's theory of micromixing, which involves Schmidt number, Reynolds number and the local vorticity. Numerical tests were performed for a gaseous case and an aqueous case. Evidence that pure freestream fluids are entrained into the layer by large-scale motions was found in the predicted pdf. Mean concentration profiles were found to be insensitive to Schmidt number, while the unmixedness was higher for higher Schmidt number. Applications were made to mixing layers with isothermal, fast reactions. The predicted difference in product thickness of the two cases was in reasonable quantitative agreement with experimental measurements.

Lin, P.↗
NASA NTRS1986

A numerical simulation of the inviscid flow through a counterrotating propeller

The results of a numerical simulation of the time-averaged inviscid flow field through the blade rows of a multiblade row turboprop configuration are presented. The governing equations are outlined along with a discussion of the solution procedure and coding strategy. Numerical results obtained from a simulation of the flow field through a modern high-speed turboprop will be shown.

Celestina, M. L.↗
NASA NTRS1986

Numerical study of sink-flow boundary layers

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 x 10 to the -6th and 3.0 x 10 to the -6th, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically, using a spectral method, with about one million degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder (1972) is observed. The two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of R(theta) for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6th, corresponding to a Reynolds number R(theta) of about 330.

Spalart, Philippe R.↗
NASA NTRS1986

Formulation of numerical procedures for dynamic analysis of spinning structures

The paper presents the descriptions of recently developed numerical algorithms that prove to be useful for the solution of the free vibration problem of spinning structures. First, a generalized procedure for the computation of nodal centrifugal forces in a finite element owing to any specified spin rate is derived in detail. This is followed by a description of an improved eigenproblem solution procedure that proves to be economical for the free vibration analysis of spinning structures. Numerical results are also presented which indicate the efficacy of the currently developed procedures.

Gupta, K. K.↗
NASA NTRS1987

Numerical simulations of unsteady airfoil-vortex interactions

Numerical methods based on the thin layer Navier-Stokes, Euler and transonic small disturbance equations, all three of which use the perturbation form of an implicit numerical algorithm, are used to formulate the unsteady interactions of a moving vortex with a stationary airfoil. Results are presented for both transonic and subsonic flows, as well as for weak and strong interactions. In general, the results exhibit an overwhelming influence of the vortex on the flow field around the airfoil, especially when the convecting vortex is within one chord of the airfoil. It is noted that even the ostensibly weak interactions produced vortex/shock-induced boundary layer separation.

Srinivasan, G. R.↗
NASA NTRS1987

Albedos of homogeneous semi-infinite canopies - Comparison of two-stream analytic and numerical solutions

The albedo of plant canopies is treated as a problem in radiative transfer. Albedos calcualted from an iterative multistream numerical model are compared with those calculated with an analytic two-stream solution. With the assumption of a randomly homogeneous distribution of leaf positions and orientations and isotropic scattering by individual leaves, the single-scattering albedo of the canopy can be found analytically. This single-scattering solution is incorporated into the two-stream solution and used to benchmark the multistream numerical model in the single-scattering limit. Relative errors so established in the multistream model are O(0.3 percent) or less. The two-stream model is also found to be remarkably accurate, with the error in multiply scattered radiation O(5 percent) or less, corresponding to absolute errors in visible albedo of less than 0.001 and near-infrared albedo of less than or equal to 0.01. Thus the two-stream model should be adequate for many purposes, such as climate modeling, provided the assumptions of homogeneous canopy and isotropic scattering are not too unrealistic.

Dickinson, Robert E.↗
NASA NTRS1987

A comparison of numerical flux formulas for the Euler and Navier-Stokes equations

Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.

Van Leer, Bram↗
NASA NTRS1987

Numerical simulation of transonic propeller flow using a three-dimensional small disturbance code employing novel helical coordinates

The numerical simulation of three-dimensional transonic flow about propeller blades is discussed. The equations for the unsteady potential flow about propellers is given for an arbitrary coordinate system. From this the small disturbance form of the equation is derived for a new helical coordinate system. The new coordinate system is suited to propeller flow and allows cascade boundary conditions to be applied straightforward. A numerical scheme is employed which solves the steady flow as an asymptotic limit of unsteady flow. Solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an eight bladed cascade. Both high and low advance ratio cases are given which include a lifting case as well as nonlifting cases. The nonlifting cases are compared to solutions from a Euler code.

Snyder, Aaron↗
NASA NTRS1987

Numerical study of ribbon-induced transition in Blasius flow

The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. The agreement with experimental and theoretical results is discussed.

Spalart, Philippe R.↗
NASA NTRS1987

A VAS-numerical model impact study using the Gal-Chen variational approach

A numerical study based on the use of a variational assimilation technique of Gal-Chen (1983, 1986) was conducted to assess the impact of incorporating temperature data from the VISSR Atmospheric Sounder (VAS) into a regional-scale numerical model. A comparison with the results of a control forecast using only conventional data indicated that the assimilation technique successfully combines actual VAS temperature observations with the dynamically balanced model fields without destabilizing the model during the assimilation cycle. Moreover, increasing the temporal frequency of VAS temperature insertions during the assimilation cycle was shown to enhance the impact on the model forecast through successively longer forecast periods. The incorporation of a nudging technique, whereby the model temperature field is constrained toward the VAS 'updated' values during the assimilation cycle, further enhances the impact of the VAS temperature data.

Aune, Robert M.↗
NASA NTRS1987

Numerical observations of dynamic behavior in two-dimensional compressible convection

Using numerical simulations of the anelastic partial differential equations, convective flow in a two-dimensional polytropic atmosphere is investigated. Fixing the aspect ratio at unity and choosing the viscosity as the order parameter, the numerical solutions have indicated a variety of dynamic behavior including (1) oscillatory motion with a period of order the eddy turnover time, (2) quasi-periodic motion with a long period much longer than an eddy turnover time, and (3) at least two branches of solutions in certain regimes.

Ginet, G. P.↗
NASA NTRS1986

Numerical modeling of on-orbit propellant motion resulting from an impulsive acceleration

In-space docking and separation maneuvers of spacecraft that have large fluid mass fractions may cause undersirable spacecraft motion in response to the impulsive-acceleration-induced fluid motion. An example of this potential low gravity fluid management problem arose during the development of the shuttle/Centaur vehicle. Experimentally verified numerical modeling techniques were developed to establish the propellant dynamics, and subsequent vehicle motion, associated with the separation of the Centaur vehicle from the shuttle orbiter cargo bay. Although the shuttle/Centaur development activity was suspended, the numerical modeling techniques are available to predict on-orbit liquid motion resulting from impulsive accelerations for other missions and spacecraft.

Aydelott, John C.↗
NASA NTRS1987

Comparison of two numerical techniques for aerodynamic model identification

A new algorithm, called the Minimal Residual QR algorithm, is presented to solve subset regression problems. It is shown that this new scheme can be used as a numerically reliable implementation of the stepwise regression technique, which is widely used to identify an aerodynamic model from flight test data. This capability as well as the numerical superiority of this scheme over the stepwise regression technique is demonstrated in an experimental simulation study.

Verhaegen, M. H.↗