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At least 289 records · Page 16

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NASA NTRS1979

Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows

An analysis is presented for the linear stability of water boundary-layer flows over nonuniformly flat plates. Included in the analysis are disturbances due to velocity, pressure, temperatures, density, and transport properties as well as variations of the liquid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow. In contrast with previous analyses, the nonsimilarity of the mean flow is taken into account. No analysis agrees, even qualitatively, with the experimental data when similar profiles are used. However, both the parallel and nonparallel results qualitatively agree with the experimental results of Strazisar and Reshotko when nonsimilar profiles are used.

Nayfeh, A. H.↗

NASA NTRS1979

Stability of three-dimensional boundary layers

A theory is presented for the three-dimensional stability of boundary layers. Equations are derived for the evolution of a disturbance having a given frequency and originating at a given curve. These equations are used to determine the rays along which the disturbance energy propagates. It is shown that the results can be obtained by using the saddle-point method, or kinematic wave theory, or the method of multiple scales. Extension of the theory to the case of a wave packet is also presented.

Nayfeh, A. H.↗

NASA NTRS1979

Secondary instability in boundary-layer flows

The stability of a secondary Tollmien-Schlichting wave, whose wavenumber and frequency are nearly one half those of a fundamental Tollmien-Schlichting instability wave is analyzed using the method of multiple scales. Under these conditions, the fundamental wave acts as a parametric exciter for the secondary wave. The results show that the amplitude of the fundamental wave must exceed a critical value to trigger this parametric instability. This value is proportional to a detuning parameter which is the real part of k - 2K, where k and K are the wavenumbers of the fundamental and its subharmonic, respectively. For Blasius flow, the critical amplitude is approximately 29% of the mean flow, and hence many other secondary instabilities take place before this parametric instability becomes significant. For other flows where the detuning parameter is small, such as free-shear layer flows, the critical amplitude can be small, thus the parametric instability might play a greater role.

Nayfeh, A. H.↗

NASA NTRS1979

solar thermal power systems advanced solar thermal technology project, advanced subsystems development

The preliminary design for a prototype small (20 kWe) solar thermal electric generating unit was completed, consisting of several subsystems. The concentrator and the receiver collect solar energy and a thermal buffer storage with a transport system is used to provide a partially smoothed heat input to the Stirling engine. A fossil-fuel combustor is included in the receiver designs to permit operation with partial or no solar insolation (hybrid). The engine converts the heat input into mechanical action that powers a generator. To obtain electric power on a large scale, multiple solar modules will be required to operate in parallel. The small solar electric power plant used as a baseline design will provide electricity at remote sites and small communities.

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NASA NTRS1979

Effect of streamwise vortices on Tollmien-Schlichting waves

The method of multiple scales is used to determine a first order uniform expansion for the effect of counter rotating steady streamwise vortices in growing boundary layers on Tollmien-Schlichting waves. The results show that such vortices have a strong tendency to amplify three dimensional Tollmien-Schlichting waves having a spanwise wavelength that is twice the wavelength of the vortices. An analytical expression is derived for the growth rates of these waves. These growth rates increase linearly with increasing amplitudes of the vortices.

Nayfeh, A. H.↗

NASA NTRS1980

Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis

A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined.

El-Hady, N. M.↗

NASA NTRS1980

Nonlinear interaction of two waves in boundary-layer flows

First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.

Nayfeh, A. H.↗

NASA NTRS1980

On the stability of three-dimensional compressible nonparallel boundary layers

A compressible linear stability theory is presented for three-dimensional nonuniform boundary layers. The amplitude, phase, and wavenumber equations which govern the motion of the disturbance are obtained by using the method of multiple scales. Group velocity trajectories are used to identify the disturbance growth direction. The spatial stability theory is applied to the flow on a laminar flow control supercritical sweptback wing of infinite span. Three different methods are used to calculate the absolute maximum logarithmic amplitude ratio N. In the front crossflow instability region, the method of maximum spatial growth rate predicts large difference in N compared with the method of fixed wavelength and the method of fixed spanwise component of wavelength. This difference decreases in the middle streamwise instability region, and almost vanishes in the rear crossflow instability region. Compressibility of the medium reduces N by about 15% in both the front and rear regions, and by about 40% in the middle region of the wing. Nonuniformity of the medium has large effects specially in the rear region.

El-Hady, N. M.↗

NASA NTRS1980

A comparison of experiment and theory for sound propagation in variable area ducts

An experimental and analytical program has been carried out to evaluate sound suppression techniques in ducts that produce refraction effects due to axial velocity gradients. The analytical program employs a computer code based on the method of multiple scales to calculate the influence of axial variations due to slow changes in the cross-sectional area as well as transverse gradients due to the wall boundary layers. Detailed comparisons between the analytical predictions and the experimental measurements have been made. The circumferential variations of pressure amplitudes and phases at several axial positions have been examined in straight and variable area ducts, with hard walls and lined sections, and with and without a mean flow. Reasonable agreement between the theoretical and experimental results has been found.

Nayfeh, A. H.↗

NASA NTRS1979

Perturbation solutions of combustion instability problems

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Googerdy, A.↗

NASA NTRS1980

Semiconductor devices for optical communications in 1 micron band of wavelength

Crystal growth and the characteristics of semiconductor lasers and diodes for the long wavelength band used in optical communications are examined. It is concluded that to utilize the advantages of this band, it is necessary to have a large scale multiple wavelength communication, along with optical cumulative circuits and optical exchangers.

Suematsu, Y.↗

NASA NTRS1981

On the effect of boundary layer growth on the stability of compressible flows

The method of multiple scales is used to describe a formally correct method based on the nonparallel linear stability theory, that examines the two and three dimensional stability of compressible boundary layer flows. The method is applied to the supersonic flat plate layer at Mach number 4.5. The theoretical growth rates are in good agreement with experimental results. The method is also applied to the infinite-span swept wing transonic boundary layer with suction to evaluate the effect of the nonparallel flow on the development of crossflow disturbances.

El-Hady, N. M.↗

NASA NTRS1980

Three-dimensional stability of growing boundary layers

A theory is developed for the linear stability of three-dimensional growing boundary layers. The method of multiple scales is used to derive partial-differential equations describing the temporal and spatial evolution of the complex amplitudes and wavenumbers of the disturbances. In general, these equations are elliptic unless certain conditions are satisfied. For a monochromatic disturbance, these conditions demand that the ratio of the components of the complex group velocity be real and thereby relate the direction of growth of the disturbance to the disturbance wave angle. For a nongrowing boundary layer, this condition reduces to d-alpha/d-beta being real, in agreement with the result obtained by using the saddle-point method. For a wavepacket, these conditions demand that the components of the group velocity be real.

Nayfeh, A. H.↗

NASA NTRS1980

A perturbation solution for transverse pressure-sensitive combustion instability in an annulus

A method for analysis of combustion instability in rocket motors based on a combination of the Galerkin method and the two-variable (or multiple-scales) perturbation method is developed. The method is illustrated by applying it to the problem of pressure-sensitive combustion instability in a liquid-fuel annular combustion chamber. To the order of approximation inherent in the method it is found that the complete linear stability analysis and most of the nonlinear stability analysis can be carried out in closed form. The results thus obtained are used to clarify several aspects of the interpretation of numerical solutions obtained by previous investigators.

Googerdy, A.↗

NASA NTRS1981

Nonparallel stability of three-dimensional flows

The linear stability of three-dimensional incompressible, isothermal, nonparallel boundary-layer flows has been investigated. The method of multiple scales is used to derive the partial-differential equations that describe the spatial modulations of the amplitude, phase and wavenumber of a disturbance. Group velocities are used to determine the disturbance growth direction. The envelope method is used to calculate the logarithmic amplitude growth rate N. The theory is applied to the flows over a swept-back tapered wing with boundary-layer suction. Results of such analysis for the X-21 wing are discussed. It is found that the nonparallel effects for this wing is substantial.

Padhye, A. R.↗

NASA NTRS1981

Effect of streamwise vortices on Tollmien-Schlichting waves

The method of multiple scales is used to determine a first-order uniform expansion for the effect of counter-rotating steady streamwise vortices in growing boundary layers on oblique Tollmien-Schlichting waves. The results show that such vortices have a strong tendency to amplify oblique Tollmien-Schlichting waves having a spanwise wavelength that is twice the wavelength of the vortices. An analytical expression is derived for the growth rates of these waves. These exponential growth rates increase linearly with increasing amplitudes of the vortices. Numerical results are presented. They suggest that this mechanism may dominate the instability.

Nayfeh, A. H.↗

NASA NTRS1982

Stability of compressible three-dimensional boundary-layer flows

For compressible three-dimensional flow, the method of multiple scales to formulate the three-dimensional stability problem and determine the partial-differential equations governing variations of the amplitude and complex wavenumbers is used. A method for following one specific wave along its trajectory to ascertain the characteristics of the most unstable disturbance is proposed. Numerical results using the flow over the X-21 wing as calculated from the Kaups-Cebeci code will be presented.

Reed, H. L.↗

NASA NTRS1983

On the shock cell structure and noise of supersonic jets

A linear solution modeling the shock cell structure of an axisymmetric supersonic jet operated at off-design conditions is developed by the method of multiple-scales. The model solution takes into account the gradual spatial change of the mean flow in the downstream direction. Turbulence in the mixing layer of the jet has the tendency of smoothing out the sharp velocity and density gradients induced by the shocks. To simulate this effect, eddy viscosity terms are incorporated in the model. It is known that the interaction between the quasi-periodic shock cells and the downstream propagating large turbulence structures in the mixing layer of the jet is responsible for the generation of broadband shock associated noise. Experimentally, the dominant part of this noise has been found to originate from the part of the jet near the end of the potential core. Calculated shock cell spacing at the end of the jet core according to the present model is used to estimate the peak frequencies of the shock associated noise for a range of observation angles. Very favorable agreement with experimental measurements is found.

Tam, C. K. W.↗