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NASA NTRS1990

Some theoretical aspects of boundary layer stability theory

Increased understanding in recent years of boundary layer transition has been made possible by the development of strongly nonlinear stability theories. After some twenty or so years when nonlinear stability theory was restricted to the application of the Stuart-Watson method (or less formal amplitude expansion procedures), there now exist strongly nonlinear theories which can describe processes which have an 0(1) effect on the basic state. These strongly nonlinear theories and their possible role in pushing theoretical understanding of transition ever further into the nonlinear regime are discussed.

Hall, Philip↗

NASA NTRS2019

Boundary Layer Stability and Transition in a Chemically Reacting Martian Atmosphere Using LASTRAC

The Thermal Protection System (TPS) is a significant portion of the mass of reentry vehicles, planetary probes, and Martian entry vehicles. Reducing this mass has benefits in terms of decreased fuel requirements and increased payload; however, due to the high risk and uncertainty, the TPS or heat shields are designed conservatively by assuming fully turbulent flow. Laminar flow results in reduced heat flux, and improved transition prediction has the potential to reduce TPS mass and uncertainty in aerothermodynamic predictions. Limited previous research exists examining the problem of transition prediction for Martian atmospheric entry, with studies available on transition on the Mars Science Laboratory TPS. Although transition was demonstrated in wind-tunnel tests, uncertainty in the transition location resulted in a TPS designed for fully turbulent flow, and therefore greater mass than required for a partially laminar condition. In this work, we extend the boundary layer stability code LASTRAC, recently modified to include chemical and thermal nonequilibrium capabilities, to a model of the Martian atmosphere. LASTRAC provides Parabolized Stability Equations (PSE) as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semi-empirical e(sup N) methods. Results included in this work compare disturbance growth characteristics between air and Martian atmosphere at similar non-dimensional freestream conditions on a simple flat plate geometry. Both chemical nonequilibrium and thermochemical nonequilibrium, as well as both PSE and LST, are used.

Kline, H. L.↗

NASA NTRSDate not supplied

Boundary Layer Stability and Transition in a Chemically Reacting Martian Atmosphere using LASTRAC

The Thermal Protection System (TPS) is a significant portion of the mass of reentry vehicles, planetary probes, and Martian entry vehicles. Reducing this mass has benefits in terms of decreased fuel requirements and increased payload; however, due to the high risk and un-certainty, the TPS or heat shields are designed conservatively by assuming fully turbulent flow. Laminar flow results in reduced heat flux, and improved transition prediction has the potential to reduce TPS mass and uncertainty in aerothermodynamic predictions. Limited previous research exists examining the problem of transition prediction for Martian atmospheric entry, with studies available on transition on the Mars Science Laboratory TPS. Although transition was demonstrated in wind-tunnel tests, uncertainty in the transition location resulted in a TPS designed for fully turbulent flow, and therefore greater mass than required for a partially-laminar condition. In this work, we extend the boundary layer stability code LASTRAC, recently modified to include chemical and thermal nonequilibrium capabilities, to a model of the Martian atmosphere. LASTRAC provides Parabolized Stability Equations (PSE) as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semi-empirical eN methods. Results included in this work compare disturbance growth characteristics between air and Martian atmosphere at similar nondimensional freestream conditions on a simple flat plate geometry. Both chemical nonequilibrium and thermochemical nonequilibrium, as well as both PSE and LST, are used.

Heather L Kline↗

NASA NTRS1987

Effects of forebody geometry on subsonic laminar boundary layer stability

The effect of forebody geometry on the stability of the laminar boundary layer on axisymmetric body shapes at Reynolds numbers typical of small and medium sized aircraft in low-subsonic cruise flight is investigated. It is found that small nose radii are important in obtaining n-factors of 9 on axisymmetric bodies of fineness ratio of about 6 at large nondimensional axial distances downstream. Results for the effect of the steepness of the pressure gradient and the value of the minimum pressure on the extent of laminar flows on an axisymmetric body at a given Reynolds number are also presented.

Dodbele, S. S.↗

NASA NTRS1990

On the continuous spectra of the compressible boundary layer stability equations

The branch cuts in the complex frequency plane (omega) that correspond to the continuous spectrum of the two-dimensional compressible boundary layer stability equations are computed by looking for solutions that are pure oscillatory in the free-stream. In the complex omega-plane there are three compressible and one incompressible branch cuts. The compressible branch cuts are given as solutions of third order polynomials. Computations are made for a range of Reynolds and Mach numbers, and also for several streamwise wavenumbers.

Ashpis, David E.↗

NASA NTRS1996

Hypersonic Boundary-Layer Stability Experiments on a Flared-Cone Model at Angle of Attack in a Quiet Wind Tunnel

An experimental investigation of the effects of angle of attack on hypersonic boundary-layer stability on a flared-cone model was conducted in the low-disturbance Mach-6 Nozzle-Test Chamber Facility at NASA Langley Research Center. This unique facility provided a 'quiet' flow test environment which is well suited for stability experiments because the low levels of freestream 'noise' minimize artificial stimulation of flow-disturbance growth. Surface pressure and temperature measurements documented the adverse-pressure gradient and transition-onset location. Hot-wire anemometry diagnostics were applied to identify the instability mechanisms which lead to transition. In addition, the mean flow over the flared-cone geometry was modeled by laminar Navier-Stokes computations. Results show that the boundary layer becomes more stable on the windward ray and less stable on the leeward ray relative to the zero-degree angle-of-attack case. The second-mode instability dominates the transition process at a zero-degree angle of attack, however, on the windward ray at an angle of attack this mode was completely stabilized. The less-dominant first-mode instability was slightly destabilized on the windward ray. Non-linear mechanisms such as saturation and harmonic generation are identified from the flow-disturbance bispectra.

Doggett, Glen P.↗

NASA NTRS1960

Effects of Sweep Angle on the Boundary-Layer Stability Characteristics of an Untapered Wing at Low Speeds

An investigation was conducted in the Ames 12-Foot Low-Turbulence Pressure Tunnel to determine the effects of sweep on the boundary-layer stability characteristics of an untapered variable-sweep wing having an NACA 64(2)A015 section normal to the leading edge. Pressure distribution and transition were measured on the wing at low speeds at sweep angles of 0, 10, 20, 30, 40, and 50 deg. and at angles of attack from -3 to 3 deg. The investigation also included flow-visualization studies on the surface at sweep angles from 0 to 50 deg. and total pressure surveys in the boundary layer at a sweep angle of 30 deg. for angles of attack from -12 to 0 deg. It was found that sweep caused premature transition on the wing under certain conditions. This effect resulted from the formation of vortices in the boundary layer when a critical combination of sweep angle, pressure gradient, and stream Reynolds number was attained. A useful parameter in indicating the combined effect of these flow variables on vortex formation and on beginning transition is the crossflow Reynolds number. The critical values of crossflow Reynolds number for vortex formation found in this investigation range from about 135 to 190 and are in good agreement with those reported in previous investigations. The values of crossflow Reynolds number for beginning transitions were found to be between 190 and 260. For each condition (i.e., development of vortices and initiation of transition at a given location) the lower values in the specified ranges were obtained with a light coating of flow-visualization material on the surface. A method is presented for the rapid computation of crossflow Reynolds number on any swept surface for which the pressure distribution is known. From calculations based on this method, it was found that the maximum values of crossflow Reynolds number are attained under conditions of a strong pressure gradient and at a sweep angle of about 50 deg. Due to the primary dependence on pressure gradient, effects of sweep in causing premature transition are generally first encountered on the lower surfaces of wings operating at positive angles of attack.

Boltz, Frederick W.↗

NASA NTRS1991

Analysis of flight-measured boundary-layer stability and transition data

The paper concentrates on the computational analysis of both the Tollmien-Schlichting and crossflow-type instabilities using the results of a boundary-layer transition flight experiment on a smooth swept test surface. In addition, the effect of nonadiabatic wall conditions is analyzed using the measured surface temperature distribution on the boundary-layer development and stability growth. The computational methods utilized in analyzing the boundary-layer stability characteristics are discussed: one approach analyzes the Tollmien-Schlichting and crossflow instabilities independently with maximum Tollmien-Schlichting n-factors near nine and maximum crossflow n-factors near six at transition onset for separate cases, while the second approach analyzes the instabilities for maximum growth regardless of the type. As much as a 27-percent increase in n-factor is found at transition onset due to an increased Tollmien-Schlichting instability.

Obara, Clifford J.↗

NASA NTRS1987

Higher eigenmodes in the Blasius boundary-layer stability problem

The higher spatial-stability eigenmodes for the Blasius boundary layer are examined by using asymptotic theory, and an infinite number of modes are found. The asymptotic results are shown to be in close agreement with results from a direct numerical solution of the Orr-Sommerfeld problem. The asymptotic theory would therefore provide an efficient tool in exploratory searches for the eigenvalues.

Hultgren, Lennart S.↗

NASA NTRS1986

Variable Sweep Transition Flight Experiment (VSTFE)-Parametric Pressure Distribution Boundary Layer Stability Study and Wing Glove Design Task

The Variable Sweep Transition Flight Experiment (VSTFE) was initiated to establish a boundary-layer transition data base for laminar flow wing design. For this experiment, full-span upper-surface gloves will be fitted to a variable sweep F-14 aircraft. The results of two initial tasks are documented: a parametric pressure distribution/boundary-layer stability study and the design of an upper-surface glove for Mach 0.8. The first task was conducted to provide a data base from which wing-glove pressure distributions could be selected for glove designs. Boundary-layer stability analyses were conducted on a set of pressure distributions for various wing sweep angles, Mach numbers, and Reynolds number in the range of those anticipated for the flight-test program. The design procedure for the Mach 0.8 glove is described, and boundary-layer stability calculations and pressure distributions are presented both at design and off-design conditions. Also included is the analysis of the clean-up glove (smoothed basic wing) that will be flight-tested initially and the analysis of a Mach 0.7 glove designed at the NASA Langley Research Center.

Rozendaal, Rodger A.↗

NASA NTRS1996

Hypersonic Boundary Layer Stability over a Flared Cone in a Quiet Tunnel

Hypersonic boundary layer measurements were conducted over a flared cone in a quiet wind tunnel. The flared cone was tested at a freestream unit Reynolds number of 2.82x106/ft in a Mach 6 flow. This Reynolds number provided laminar-to-transitional flow over the model in a low-disturbance environment. Point measurements with a single hot wire using a novel constant voltage anemometry system were used to measure the boundary layer disturbances. Surface temperature and schlieren measurements were also conducted to characterize the laminar-to-transitional state of the boundary layer and to identify instability modes. Results suggest that the second mode disturbances were the most unstable and scaled with the boundary layer thickness. The integrated growth rates of the second mode compared well with linear stability theory in the linear stability regime. The second mode is responsible for transition onset despite the existence of a second mode sub-harmonic. The sub-harmonic wavelength also scales with the boundary layer thickness. Furthermore, the existence of higher harmonics of the fundamental suggests that non-linear disturbances are not associated with high free stream disturbance levels.

Lachowicz, Jason T.↗

NASA NTRS1990

Effect of nose bluntness on boundary layer stability and transition

The effect of nose bluntness on boundary layer instability is studied theoretically for a Mach 8 flow past a 7 degree semivertex cone. The basic flow is computed by solving the parabolized Navier-Stokes equations. Linear stability analysis of the basic flow reveals that, with small amount of bluntness, the critical Reynolds number for the onset of instability increases by an order of magnitude compared to the sharp cone value. The computed second mode frequencies are also in reasonable agreement with the experimental results. The results are used to explain the effect of unit Reynolds number on transition present in the quiet aeroballistic range data.

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 NTRS1996

Hypersonic Boundary Layer Stability Experiments in a Quiet Wind Tunnel with Bluntness Effects

Hypersonic boundary layer measurements over a flared cone were conducted in a Mach 6 quiet wind tunnel at a freestream unit Reynolds number of 2.82 million/ft. This Reynolds number provided laminar-to-transitional flow over the cone model in a low-disturbance environment. Four interchangeable nose-tips, including a sharp-tip, were tested. Point measurements with a single hot-wire using a novel constant voltage anemometer were used to measure the boundary layer disturbances. Surface temperature and schlieren measurements were also conducted to characterize the transitional state of the boundary layer and to identify instability modes. Results suggest that second mode disturbances were the most unstable and scaled with the boundary layer thickness. The second mode integrated growth rates compared well with linear stability theory in the linear stability regime. The second mode is responsible for transition onset despite the existence of a second mode subharmonic. The subharmonic disturbance wavelength also scales with the boundary layer thickness. Furthermore, the existence of higher harmonics of the fundamental suggests that nonlinear disturbances are not associated with 'high' free stream disturbance levels. Nose-tip radii greater than 2.7% of the base radius completely stabilized the second mode.

Lachowicz, Jason T.↗

NASA NTRS1967

Mechanics of Boundary Layer Transition. Part 5: Boundary Layer Stability theory in incompressible and compressible flow

The fundamentals of stability theory, its chief results, and the physical mechanisms at work are presented. The stability theory of the laminar boundary determines whether a small disturbance introduced into the boundary layer will amplify or damp. If the disturbance damps, the boundary layer remains laminar. If the disturbance amplifies, and by a sufficient amount, then transition to turbulence eventually takes place. The stability theory establishes those states of the boundary layer which are most likely to lead to transition, identifys those frequencies which are the most dangerous, and indicates how the external parameters can best be changed to avoid transition.

Mack, L. M.↗

NASA NTRS1989

Supersonic boundary layer stability analysis with and without suction on aircraft wings

An analysis of the boundary layer and its stability with and without suction on a supersonic cruise fighter wing having biconvex 5 percent thick airfoils is conducted for a free-stream Mach number of 2.0 and an angle of attack of 4.0 deg. It is found that the largest amplification is due to the highly oblique traveling cross flow type waves, oriented approximately 80 deg without suction, and 87.5 deg with suction, from the local external velocity vector. It is concluded that with the biconvex airfoil section on the thin swept wing, this type of instability would be the likely cause of transition. The approximate values of the frequency, wave orientation angle, and wavelength/chord ratio for the most amplified disturbance are given for the cases of suction and no suction. The largest amplifications are found for highly oblique traveling crossflow type waves oriented at approximately 80 deg without suction and 87.5 deg with suction, measured from the local external velocity vector.

Agrawal, Shreekant↗

NASA NTRS1984

Effect of curvature on three-dimensional boundary layer stability

The problem of the stability of a three-dimensional laminar boundary layer formed on a curved surface is considered. A calculation scheme, which takes account of the curvature of the flow streamlines and of the surface is proposed for the prediction of the development of small amplitude temporal disturbances. Computations have been performed for the flow over the windward face of an infinitely long yawed cylinder and comparisons have been made with experimental data. These indicate that the theory correctly predicts many of the features of the unstable laminar flow. The theory also suggests that transition, in this particular situation, is dominated by traveling disturbance waves and that, at the experimentally observed transition location, the wave which has undergone greatest total amplification has an amplitude ratio of approximately e to the 11th. When the effects of curvature are omitted the maximum amplitude ratio at transition is about e to the 17th.

Malik, M. R.↗

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.↗