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NASA NTRS1985

Numerical Techniques in Acoustics

This is the compilation of abstracts of the Numerical Techniques in Acoustics Forum held at the ASME's Winter Annual Meeting. This forum was for informal presentation and information exchange of ongoing acoustic work in finite elements, finite difference, boundary elements and other numerical approaches. As part of this forum, it was intended to allow the participants time to raise questions on unresolved problems and to generate discussions on possible approaches and methods of solution.

Baumeister, K. J.↗

NASA NTRS1985

A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects

Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.

Korkan, K. D.↗

NASA NTRS1986

A numerical simulation of the inviscid flow through a counter-rotating 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

Analytical and numerical studies of the thermocapillary flow in a uniformly floating zone

The microgravity environment of an orbiting vehicle permits crystal growth experiments in the presence of greatly reduced buoyant convection in the liquid melt. Crystals grown in ground-based laboratories do not achieve their potential properties because of dopant variations caused by flow in the melt. The floating zone crystal growing system is widely used to produce crystals of silicon and other materials. However, in this system the temperature gradient on the free sidewall surface of the melt is the source of a thermocapillary flow which does not disappear in the low-gravity environment. The idea of using a uniform rotation of the floating zone system to confine the thermocapillary flow to the melt sidewall leaving the interior of the melt passive is examined. A cylinder of fluid with an axial temperature gradient imposed on the cylindrical sidewall is considered. A half zone and the linearized, axisymmetric flow in the absence of crystal growth is examined. Rotation is found to confine the linear thermocapillary flow. A simplified model is extended to a full zone and both linear and nonlinear thermocapillary flows are studied theoretically. Analytical and numerical methods are used for the linear flows and numerical methods for the nonlinear flows. It was found that the linear flows in the full zone have more complicated and thicker boundary layer structures than in the half zone, and that these flows are also confined by the rotation. However, for the simplified model considered and for realistic values for silicon, the thermocapillary flow is not linear. The fully nonlinear flow is strong and unsteady (a weak oscillation is present) and it penetrates the interior. Some non-rotating flow results are also presented. Since silicon as a large value of thermal conductivity, one would expect the temperature fields to be determined by conduction alone. This is true for the linear and weakly nonlinear flows, but for the stronger nonlinear flow the results show that temperature advection is also important. Uniform rotation may still be a means of confining the flow and the results obtained define the procedure to be used to examine this hypothesis.

Fowlis, W. W.↗

NASA NTRS1985

Numerical weather prediction in low latitudes

Based on the results of a number of numerical prediction experiments, the differential heating between land and ocean is an important and critical factor for investigation of phenomenon such as the onset of monsoons over the Indian subcontinent. The pre-onset period during the month of May shows a rather persistent flow field in the monsoon region. At low levels the circulation exhibits anticyclonic excursions over the Arabian Sea, flowing essentially parallel to the west coast of India from the north. Over the Indian subcontinent the major feature is a shallow heat low over northern India. As the heat sources commence a rapid northwestward movement toward the southern edge of the Tibetan Plateau, an interesting configuration of the large-scale divergent circulation occurs. A favorable configuration for a rapid exchange of energy from the divergent to the rotational kinetic energy develops. Strong low level monsoonal circulations evolve, attendant with that the onset of monsoon rains occurs. In order to test this observational sequence, a series of short-range numerical prediction experiments were initiated to define the initial heat sources.

Krishnamurti, T. N.↗

NASA NTRS1985

Advances in parameterization of cumulus convection in numerical models

Observational studies over the last decade have revealed new sources of difficulty in the already complex problem of parameterization of precipitating cumulus convection in large scale numerical weather prediction models. The structure of mesoscale updrafts and downdrafts and the difficulties they present for cumulus parameterization is reviewed. An approach is proposed which follows Kuo (1974) but includes cumulus and mesoscale downdrafts in the vertical distributions of heating and moistening. The development of a realistic life cycle behavior in the numerical prediction of a mesoscale convective complex will be shown.

Molinari, J.↗

NASA NTRS1986

Advances in numerical and applied mathematics

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

South, J. C., Jr.↗

NASA NTRS1986

Development of a numerical procedure to map a general 3-d body onto a near-circle

Conformal mapping is a classical technique utilized for solving problems in aerodynamics and hydrodynamics. Conformal mapping is utilized in the construction of grids around airfoils, engine inlets and other aircraft configurations. These shapes are transformed onto a near-circle image for which the equations of fluid motion are discretized on the mapped plane and solved numerically by utilizing the appropriate techniques. In comparison to other grid-generation techniques such as algerbraic or differential type, conformal mapping offers an analytical and accurate form even if the grid deformation is large. One of the most appealing features is that the grid can be constrained to remain orthogonal to the body after the transformation. Hence, the grid is suitable for analyzing the supersonic flow past a blunt object. The associated shock as a coordinate surface adjusts its position in the course of computation until convergence is reached. The present work applied conformal mapping to 3-D bodies with no axis of symmetry such as the Aerobraking Flight Experiment (AFE) vehicle, transforming the AFE shape onto a near-circle image. A numerical procedure and code are used to generate grids around the AFE body.

Hommel, M. J.↗

NASA NTRS1986

Numerical simulation of boundary layers. Part 2: Ribbon-induced transition in Blasius flow

The early three-dimensional stages of transition in Blasius boundary layers are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and random low-amplitude three-dimensional 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 wave number 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. Agreement with experimental and theoretical results is discussed.

Spalart, P.↗

NASA NTRS1986

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

Sidi, A.↗

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

The influence of surface roughness of deserts on the July circulation - A numerical study

The effect of the low surface roughness characteristics of deserts on atmospheric circulation in July is examined using numerical simulations with the GCM of the Goddard Laboratory for Atmospheric Science (GLAS). Identical sets of simulations were carried out with the model starting from the initial state of the atmosphere on June 15, for the years 1979 and 1980. The first simulation included a surface roughness factor of 45 cm, and the second set had a surface roughness factor of 0.02 cm for desert regions, and 45 cm for all other land. A comparative analysis of the numerical data was carried out in order to study the variations for the desert regions. It is shown that rainfall in the Sahara desert was reduced significantly in the data set with the nonuniform surface roughness factor in comparison with the other data set. The inter-tropical convergence zone (ITCZ) moved southward to about 15 degrees, which was close to its observed location at about 10 degrees N. In other deserts, the North American Great Plains, Rajputana in India, and the Central Asian desert, no similar changes were observed. Detailed contour maps of the weather conditions in the different desert regions are provided.

Sud, Y. C.↗

NASA NTRS1985

Numerical simulation of transonic flow over porous airfoils

A numerical study was made to examine the effect of a porous surface on the aerodynamic performance of a transonic airfoil. The pressure jump across the normal shock wave on the upper surface of the airfoil was reduced by making the surface below the shock porous. The weakened shock is preceded by an oblique shock at the upstream end of the porous surface where air is blown out of the cavity. The lambda shock structure shown in the numerical result qualitatively agrees with that observed in the wind tunnel. According to the present analysis, the porous airfoil has a smaller drag and a higher lift than the solid airfoil.

Chow, C.-Y.↗

NASA NTRS1985

Numerical simulation of self-excited oscillations in a ramjet inlet-diffuser flow

This paper describes numerical simulations of self-excited oscillations in a two-dimensional transonic inlet-diffuser flow by solving the Navier-Stokes equations with a two-equation turbulence model. The calculated amplitudes of oscillations for the terminal shock and the velocity fields compare well with experimental measurements; however, the predicted frequency of oscillations is about 50 percent higher. The formation of a pair of downstream-traveling, counter-rotating vortices at each cycle of velocity fluctuations, as reported experimentally, is vividly revealed by the numerical results.

Hsieh, T.↗

NASA NTRS1985

Numerical schemes for a model for nonlinear dispersive waves

A description is given of a number of numerical schemes to solve an evolution equation (Korteweg-deVries) that arises when modelling the propagation of water waves in a channel. The discussion also includes the results of numerical experiments made with each of the schemes. It is suggested, on the basis of these experiments, that one of the schemes may have (discrete) solitary-wave solutions.

Bona, J. L.↗

NASA NTRS1986

Numerical simulation of unsteady flow in an axisymmetric shear layer

Numerical simulation of unsteady flow in an axisymmetric subsonic shear layer is accomplished by solving the time-dependent compressible Navier-Stokes equations. The objective of the effort is to investigate by numerical means the influence of various flow parameters on the shear layer behavior. The parameters investigated include the velocity ratio of two streams, total temperature, and nozzle lip thickness. The computations are performed on a CRAY-IS computer using McCormack's explicit finite difference scheme. The computed results generally show qualitative agreement with experimental data.

Scott, J. N.↗

NASA NTRS1986

A numerical study of three-dimensional incompressible flow around multiple posts

The incompressible laminar flow around single and double rows of an infinite number of posts between two flat plates has been calculated numerically. A C-grid with periodic boundary conditions has been used. The angle of attack, measured from the line normal to the row of posts, was varied between zero and less than 90 deg. The pressure loading was computed for all of the posts in each of these cases. Most of these calculations have been carried out on the Numerical Aerodynamic Simulation Cray 2 at NASA Ames Research Center.

Rogers, S. E.↗

NASA NTRS1986

Numerical study of vortex breakdown

The incompressible axisymmetric steady Navier-Stokes equations and the Euler equations are solved numerically to model the breakdown of a vortex. Although the solutions obtained for the Euler equations show a 'vortex breakdown-like' structure, their behavior is very different from that of the Navier-Stokes equations. The details of the numerical algorithmms used are presented, and the results obtained are compared to those in the literature.

Hafez, M.↗