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Malik, M. R.

Publications and source records attributed to Malik, M. R..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Effect of crossflow on Goertler instability in incompressible boundary layers

Linear stability theory is used to study the effect of crossflow on Goertler instability in incompressible boundary layers. The results cover a wide range of sweep angle, pressure gradient, and wall curvature parameters. It is shown that the crossflow stabilizes Goertler disturbances by reducing the maximum growth rate and shrinking the unstable band of spanwise wave numbers. On the other hand, the effect of concave wall curvature on crossflow instability is destabilizing. Calculations show that the changeover from Goertler to crossflow instabilities is a function of Goertler number, pressure gradient, and sweep angle. The results demonstrate that Goertler instability may still be relevant in the transition process on swept wings even at large angles of sweep if the pressure gradient is sufficiently small. The influence of pressure gradient and sweep can be combined by defining a crossflow Reynolds number. Thus, the changeover from Goertler to crossflow instability takes place at some critical crossflow Reynolds number whose value increases with Goertler number.

Zurigat, Y. H.↗
NASA NTRS1993

Transition correlation in subsonic flow over a flat plate

A 2D subsonic flow over a flat plate with a freestream Mach number M(infinity) up to 0.8 is considered. The flow can experience continuous uniform suction through the wall and the wall can be heated or cooled continuously with a fixed wall temperature. For a specific combination of M(infinity), suction velocity, and level of heat transfer, the mean flow problem is solved and linear stability calculations are performed to compute the location on the flat plate where the factor representing the integration of growth rates reaches nine. These calculations are repeated for several combinations of flow parameters and the theoretically predicted transition location is presented in the form of a correlation that can account for the effect of wall suction, heat transfer, and Mach number.

Masad, J. A.↗
NASA NTRS1993

Inviscid instability of streamwise corner flow

Linear stability of the incompressible flow along a stream wise corner is studied by solving the two-dimensional eigenvalue problem governed by partial differential equations. It is found that this fully three-dimensional flow is subject to inviscid instability due to the inflectional nature of the stream wise velocity profile. The higher growth rates for the inviscid instability mode, which is symmetric about the corner bisector, as compared to the viscous Tollmien-Schlichting instability operative away from the corner is consistent with the experimental findings that the corner flow transitions to turbulence earlier than the two-dimensional Blasius flow away from the corner.

Balachandar, S.↗
NASA NTRS1993

Linear stability of three-dimensional boundary layers - Effects of curvature and non-parallelism

In this paper we study the effect of in-plane (wavefront) curvature on the stability of three-dimensional boundary layers. It is found that this effect is stabilizing or destabilizing depending upon the sign of the crossflow velocity profile. We also investigate the effects of surface curvature and nonparallelism on crossflow instability. Computations performed for an infinite-swept cylinder show that while convex curvature stabilizes the three-dimensional boundary layer, nonparallelism is, in general, destabilizing and the net effect of the two depends upon meanflow and disturbance parameters. It is also found that concave surface curvature further destabilizes the crossflow instability.

Malik, M. R.↗
NASA NTRS1992

Instability and transition in three-dimensional supersonic boundary layers

Linear stability of three-dimensional flow past a 5 deg semi-vertex sharp cone at 2 deg incidence in Mach 3.5 free-stream is studied. Computed laminar mean flow profiles along the leeward line of symmetry are highly inflectional and, hence, much more unstable than the profiles along the windward line of symmetry. Accordingly, transition occurs much earlier along the leeward line both in the present calculations (based upon eN approach) and in the experiments of King (1991) performed in NASA Langley 'quiet' tunnel. Boundary-layer transition in the region between the two symmetry lines is influenced by the crossflow generated due to the angle of attack and, as a consequence, it progressively moves upstream with increasing azimuthal angle measured from the windward line. The computed transition front is qualitatively similar to the experimental results, although some differences remain.

Malik, M. R.↗
NASA NTRS1992

Three-dimensional boundary layer stability and transition

Nonparallel and nonlinear stability of a three-dimensional boundary layer, subject to crossflow instability, is investigated using parabolized stability equations (PSEs). Both traveling and stationary disturbances are considered and nonparallel effect on crossflow instability is found to be destabilizing. Our linear PSE results for stationary disturbances agree well with the results from direct solution of Navier-Stokes equations obtained by Spalart (1989). Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble remarkably well with the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in our nonlinear calculations. Nonlinear interaction of the stationary amplitude of the stationary vortex is large as compared to the traveling mode, and the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the traveling mode dominates the downstream development owing to its higher growth rate, and there is a tendency for the stationary mode to be suppressed. The effect of nonlinear wave development on the skin-friction coefficient is also computed.

Malik, M. R.↗
NASA NTRS1992

Secondary instability in rotating-disk flow

Primary instability of the 3D boundary layer on a rotating disk introduces periodic modulation of the mean flow in the form of stationary crossflow vortices. We study the stability of this modulated mean flow with respect to secondary disturbances. Both fundamental and subharmonic resonance cases are considered, and their corresponding results indicate that the growth rate and the frequency of the secondary instability are insensitive to the exact nature of the resonance condition. The threshold primary stationary crossflow vortex amplitude for secondary instability found in this 3D incompressible boundary layer is significantly larger than that for a 2D boundary layer which is subjected to Tollmien-Schlichting instability. The secondary instability results in a pair of travelling counter-rotating vortices, tilted up and oriented at an angle to the primary stationary crossflow vortices.

Balachandar, S.↗
NASA NTRS1992

The linear stability of a flat plate boundary-layer approaching a cylindrical obstacle

The linear stability of the low-speed three-dimensional flow over a flat plate with an attached cylinder is studied. The region of interest is upstream of the initial separation point and includes the effects of both adverse and favorable pressure gradients, as well as crossflow. The resulting boundary-layer is subject to both the Tollmien-Schlichting (TS) and crossflow instabilities. Linear stability calculations, using N-factor correlations, indicate that the transition process would be dominated by TS instabilities, although for low frequencies crossflow-type disturbances are important.

Spall, R. E.↗
NASA NTRS1992

Discrete modes and continuous spectra in supersonic boundary layers

The disturbance field induced due to a harmonic point source consists of discrete eigenmodes and a continuous spectrum; these are studied by using generalized Fourier transform techniques. For a supersonic boundary layer, there exist seven branches of the continuous spectrum in the complex wavenumber space, four of which (two acoustic waves, one vorticity wave and one entropy wave) contribute to the flowfield downstream of the source. The discrete eigenmodes spring off from these branches at some critical Reynolds numbers. The results for Mach 2 and 4.5 boundary layers show that the receptivity coefficients for the stable discrete modes are much larger than that for the unstable mode. Therefore, the flow very near the source is dominated by the continuous spectrum and the stable discrete modes. However, the unstable mode takes over sufficiently far away from the source. It is shown that it is only necessary to consider the first few discrete modes to construct the solution. Calculations also show that, in a supersonic boundary layer, upstream influence from a localized disturbance is minimal.

Balakumar, P.↗
NASA NTRS1991

On the receptivity and nonparallel stability of traveling disturbances in rotating-disk flow

The generation and evolution of small amplitude long wavelength traveling disturbances in rotating-disk flow are discussed. The steady rotational speed of the disk is perturbed so as to introduce high-frequency oscillations in the flow field. Secondly, surface imperfections on the disk such as roughness elements are introduced. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations which are solved numerically. It is found that, for the class of disturbances considered here (wavelength on the order of Reynolds number), eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are preferentially excited.

Balakumar, P.↗
NASA NTRS1991

On the stability of compressible flow past axisymmetric bodies

Compressible linear stability theory for axisymmetric flows is presented. The theory is applied to flow past a cylinder and a sharp cone at a Mach number of 5 with adiabatic wall conditions. The effect of transverse curvature and body divergence is studied. It is found that transverse curvature has a stabilizing influence on axisymmetric (first and second mode) disturbances while it has a destabilizing influence on the asymmetric (oblique first mode) disturbances. The body divergence effects are stabilizing for both symmetric and asymmetric disturbances. Comparisons made with the results of planar stability theory show that, for a cylinder, curvature effects become more pronounced with increasing distance along the cylinder. For a sharp cone, these effects become less significant further away from the cone tip since the body radius increases faster than the growth of the boundary layer. The effect of cone angle on stability is also studied.

Malik, M. R.↗
NASA NTRS1991

The linear stability of three-dimensional boundary-layers over axisymmetric bodies at incidence

The linear stability of the fully three-dimensional boundary layer formed over a 6:1 prolate spheroid at 10 deg incidence is investigated using a modified version of the linear stability code COSAL. For this case, both Tollmien-Schlichting and cross flow disturbances are relevant in the transition process. The predicted location of the onset of transition using the e exp N method compares favorably with experimental results of Meier and Kreplin (1980). Using a value of N = 10, the predicted location is located approximately 10 percent upstream of the experimentally determined location. Results also indicate that the direction of disturbance propagation is dependent upon the type of disturbance, and hence the dimensional frequency.

Spall, R. E.↗
NASA NTRS1991

Waves produced from a harmonic point source in a supersonic boundary layer

The disturbance wave pattern produced by a harmonic point source in a compressible flat-plate boundary layer is computed using linear stability theory and direct numerical integration approach. Receptivity coefficients are computed for the spectrum of spanwise modes generated at the source. The effect of boundary layer growth on the development of linear waves is determined by using the method of multiple scales. Results are presented for Mach numbers of 0, 2, 4.5, and 7. It is found that disturbances spread in wedge-shaped regions behind the source and the wedge angle decreases with Mach number. The lateral spreading angle for the instability waves turns out to be quite close to the angle found experimentally for turbulence lateral contamination.

Balakumar, P.↗
NASA NTRS1991

Real gas effects on hypersonic boundary-layer stability

High-temperature effects alter the physical and transport properties of a gas, air in particular, due to vibrational excitation and gas dissociation, and thus the chemical reactions have to be considered in order to compute the flow field. Linear stability of high-temperature boundary layers is investigated under the assumption of chemical equilibrium and this gas model is labeled here as real gas model. In this model, the system of stability equations remains of the same order as for the perfect gas and the effect of chemical reactions is introduced only through mean flow and gas property variations. Calculations are performed for Mach 10 and 15 boundary layers and the results indicate that real gas effects cause the first mode instability to stabilize while the second mode is made more unstable. It is also found that the second mode instability shifts to lower frequencies. There is a slight destabilizing influence of real gas on the Goertler instability as compared to the perfect gas results.

Malik, M. R.↗
NASA NTRS1990

On the receptivity and non-parallel stability of travelling disturbances in rotating disk flow

The generation and evolution of small amplitude wavelength traveling disturbances in rotating disk flow is discussed. The steady rotational speed of the disk is perturbed so as to introduce high frequency oscillations in the flow field. Secondly, surface imperfections are introduced on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations that are solved numerically. For the class of disturbances considered (wavelength on the order of Reynolds number), it is found that eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are excited the most. The width of these roughness elements in the radial direction is about .1 r(sub 0) where r(sub 0) is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wavenumber than for a positive one. Typical wave angles found for these disturbances are about -26 degrees.

Balakumar, P.↗
NASA NTRS1990

Boundary layer transition in hypersonic flows

This paper summarizes some of the recent progress made at NASA Langley Research Center in the understanding, prediction and modeling of high speed boundary-layer transition. Linear and nonlinear theories together with large-eddy and direct numerical simulations have been used to understand various aspects of the transition problem while low disturbance 'quiet' tunnels provide means for validating the theoretical results.

Malik, M. R.↗
NASA NTRS1990

Design and operational features of low-disturbance wind tunnels at NASA Langley for Mach numbers from 3.5 to 18

The experimental and theoretical program at NASA Langley to develop high-speed low-disturbance wind tunnels for transition research is reviewed. Design and operational details of three new low-disturbance wind tunnels - the Mach-18 quiet helium, Mach-8 variable density, and Mach-3.5/Mach-6 high-speed low-disturbance tunnels, are presented. Focus is placed on the high-speed low-disturbance wind tunnel, which will have relatively large mass flows and run times from about 6 to 25 minutes. This facility is designed to provide direct simulation of low-disturbance flight conditions in the atmosphere. The Mach-8 facility will provide uniform flow conditions suitable for validation of aerodynamic codes, while the helium facility will be used for validation of boundary-layer and free shear-layer stability and transition prediction codes.

Beckwith, I. E.↗