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NASA NTRS1990

Numerical methods for hypersonic boundary layer stability

Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.

Malik, M. R.↗

NASA NTRS1986

Boundary-layer stability and airfoil design

Several different natural laminar flow (NLF) airfoils have been analyzed for stability of the laminar boundary layer using linear stability codes. The NLF airfoils analyzed come from three different design conditions: incompressible; compressible with no sweep; and compressible with sweep. Some of the design problems are discussed, concentrating on those problems associated with keeping the boundary layer laminar. Also, there is a discussion on how a linear stability analysis was effectively used to improve the design for some of the airfoils.

Viken, Jeffrey K.↗

NASA NTRSDate not supplied

Three-Dimensional Nonequilibrium Boundary Layer Stability & Transition Analysis For Martian Entry

In this work, we apply the boundary layer stability code LASTRAC, modified to include chemical and thermal nonequilibrium capabilities, to a simulated test case based on literature, with three-dimensional effects. LASTRAC provides Parabolized Stability Equations (PSE)as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semiempirical eN methods. Tests of the Mars Science Laboratory (MSL)indicated a range of laminar to transitional flow conditions. In order to reduce the weight of Thermal Protection Systems (TPS), reliable prediction of transition and an understanding of the environmental factors that contribute to transition are necessary. This work is a step towards addressing this need, including the effects of thermochemical nonequilibrium but neglecting radiation, ablation, and ionization effects. Our results indicate that an oblique first mode produces maximum N-Factors on the symmetry plane, however with N-Factors too small to explain transition. Although we are able to show nonequilibrium three-dimensional PSE results inCO2, further study with improved mean flow solutions, accounting for some of the uncertainties inherent in this analysis, or evaluation of alternative transition mechanisms is needed to explain transition in the wind tunnel cases examined here.

H L Kline↗

NASA NTRS2012

Boundary-Layer Stability Analysis of the Mean Flows Obtained Using Unstructured Grids

Boundary-layer stability analyses of mean flows extracted from unstructured-grid Navier- Stokes solutions have been performed. A procedure has been developed to extract mean flow profiles from the FUN3D unstructured-grid solutions. Extensive code-to-code validations have been performed by comparing the extracted mean ows as well as the corresponding stability characteristics to the predictions based on structured-grid solutions. Comparisons are made on a range of problems from a simple at plate to a full aircraft configuration-a modified Gulfstream-III with a natural laminar flow glove. The future aim of the project is to extend the adjoint-based design capability in FUN3D to include natural laminar flow and laminar flow control by integrating it with boundary-layer stability analysis codes, such as LASTRAC.

Liao, Wei↗

NASA NTRS1986

Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers

An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.

Berry, S. A.↗

NASA NTRS1996

An Experimental Investigation of Wall-Cooling Effects on Hypersonic Boundary-Layer Stability in a Quiet Wind Tunnel

One of the primary reasons for developing quiet tunnels is for the investigation of high-speed boundary-layer stability and transition phenomena without the transition-promoting effects of acoustic radiation from tunnel walls. In this experiment, a flared-cone model under adiabatic- and cooled-wall conditions was placed in a calibrated, 'quiet' Mach 6 flow and the stability of the boundary layer was investigated using a prototype constant-voltage anemometer. The results were compared with linear-stability theory predictions and good agreement was found in the prediction of second-mode frequencies and growth. In addition, the same 'N=10' criterion used to predict boundary-layer transition in subsonic, transonic, and supersonic flows was found to be applicable for the hypersonic flow regime as well. Under cooled-wall conditions, a unique set of continuous spectra data was acquired that documents the linear, nonlinear, and breakdown regions associated with the transition of hypersonic flow under low-noise conditions.

Blanchard, Alan E.↗

NASA NTRS1981

Compressible boundary-layer stability calculations for sweptback wings with suction

The stability of the laminar boundary layers on two transonic wings of infinite span with distributed suction is investigated with the compressible, parallel-flow stability theory. Both wings have supercritical airfoil sections; one has a sweep angle of 23 deg, the other of 35 deg. Zero-frequency disturbances are used to represent cross-flow instability, and disturbances with the wavenumber vector aligned with the local flow direction represent traveling-wave instability. In both cases, the maximum spatial amplification rate is used as a measure of the instability. For the suction, distributions with constant mass flux downstream of the starting point are used. The main objective is to determine how the maximum amplification rate varies with the magnitude and starting point of the suction. It is found for both types of disturbances that the maximum amplification rate varies almost linearly with the suction magnitude up to at least the point where the amplification rate is halved. Different starting locations for the suction in the first 4% of the chord were found to affect cross-flow instability, but to have little influence on traveling-wave instability.

Mack, L. M.↗

NASA NTRS1990

Correlation of boundary layer stability analysis with flight transition data

Recently, NASA completed a boundary-layer transition flight test on an F-14 aircraft which has variable-sweep capability. Transition data were acquired for a wide variety of sweep angles, pressure distributions, Mach numbers, and Reynolds numbers. In this paper, the F-14 flight test is briefly described and N-factor correlations with measured transition locations are presented for one of two gloves flown on the F-14 wing in the flight program; a thin foam and fiberglass glove which provided a smooth sailplane finish on the basic F-14, modified NACA 6-series airfoil. For these correlations, an improved linear boundary-layer stability theory was utilized that accounts for compressibility and surface and streamline curvature effects for the flow past swept wings.

Collier, F. S., Jr.↗

NASA NTRS1991

Compressible stability of growing boundary layers using parabolized stability equations

The parabolized stability equation (PSE) approach is employed to study linear and nonlinear compressible stability with an eye to providing a capability for boundary-layer transition prediction in both 'quiet' and 'disturbed' environments. The governing compressible stability equations are solved by a rational parabolizing approximation in the streamwise direction. Nonparallel flow effects are studied for both the first- and second-mode disturbances. For oblique waves of the first-mode type, the departure from the parallel results is more pronounced as compared to that for the two-dimensional waves. Results for the Mach 4.5 case show that flow nonparallelism has more influence on the first mode than on the second. The disturbance growth rate is shown to be a strong function of the wall-normal distance due to either flow nonparallelism or nonlinear interactions. The subharmonic and fundamental types of breakdown are found to be similar to the ones in incompressible boundary layers.

Chang, Chau-Lyan↗

NASA NTRS1979

Summary of past experience in natural laminar flow and experimental program for resilient leading edge

The potential of natural laminar flow for significant drag reduction and improved efficiency for aircraft is assessed. Past experience with natural laminar flow as reported in published and unpublished data and personal observations of various researchers is summarized. Aspects discussed include surface contour, waviness, and smoothness requirements; noise and vibration effects on boundary layer transition, boundary layer stability criteria; flight experience with natural laminar flow and suction stabilized boundary layers; and propeller slipstream, rain, frost, ice and insect contamination effects on boundary layer transition. The resilient leading edge appears to be a very promising method to prevent leading edge insect contamination.

Carmichael, B. H.↗

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 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 NTRS1987

Nonparallel stability of boundary layers

The asymptotic formulations of the nonparallel linear stability of incompressible growing boundary layers are critically reviewed. These formulations can be divided into two approaches. The first approach combines a numerical method with either the method of multiple scales, or the method of averaging, of the Wentzel-Kramers-Brillouin (WKB) approximation; all these methods yield the same result. The second approach combined a multi-structure theory with the method of multiple scales. The first approach yields results that are in excellent agreement with all available experimental data, including the growth rates as well as the neutral stability curve. The derivation of the linear stability of the incompressible growing boundary layers is explained.

Nayfeh, Ali H.↗

NASA NTRS1990

Effects of forebody geometry on subsonic boundary-layer stability

As part of an effort to develop computational techniques for design of natural laminar flow fuselages, a computational study was made of the effect of forebody geometry on laminar boundary layer stability on axisymmetric body shapes. The effects of nose radius on the stability of the incompressible laminar boundary layer was computationally investigated using linear stability theory for body length Reynolds numbers representative of small and medium-sized airplanes. The steepness of the pressure gradient and the value of the minimum pressure (both functions of fineness ratio) govern the stability of laminar flow possible on an axisymmetric body at a given Reynolds number. It was found that to keep the laminar boundary layer stable for extended lengths, it is important to have a small nose radius. However, nose shapes with extremely small nose radii produce large pressure peaks at off-design angles of attack and can produce vortices which would adversely affect transition.

Dodbele, Simha S.↗

NASA NTRS1990

Boundary-layer stability analysis of flight-measured transition data

Correlation of in-flight boundary-layer transition experiments with linear boundary-layer stability theory contributes both to the validation of the numerical methods as well as the analysis of the measured transition process. Transition results obtained in a recent flight experiment, in which the extent of laminar flow and the transition process on the wing of a business-jet fitted with an instrumented glove section were determined, are analyzed. The experiment was conducted at freestream Mach numbers from 0.55 to 0.82, chord Reynolds numbers from 10 to 20 x 10 to the 6th, and leading-edge sweep angles 17 deg to 20 deg. The growth of both Tollmien-Schlichting and crossflow instabilities are predicted using the e exp n method for several flight conditions and the calculated n-factors at transition onset are correlated. Comparison of the measured dominant boundary-layer disturbance frequencies and the predicted unstable frequencies shows fair agreement for several of the flight conditions studied.

Obara, Clifford J.↗

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 NTRS1979

Aeroelastic stability and response of horizontal axis wind turbine blades

Coupled flap-lag-torsion equations of motion of an isolated horizontal axis wind turbine (HAWT) blade have been formulated. The analysis neglects blade-tower coupling. The final nonlinear equations have periodic coefficients. A new and convenient method of generating an appropriate time-dependent equilibrium position, required for the stability analysis, has been implemented and found to be computationally efficient. Steady-state response and stability boundaries for an existing (typical) HAWT blade are presented. Such stability boundaries have never been published in the literature. The results show that the isolated blade under study is basically stable. The tower shadow (wake) has a considerable effect on the out-of-plane response but leaves blade stability unchanged. Nonlinear terms can significantly affect linearized stability boundaries; however, they have a negligible effect on response, thus implying that a time-dependent equilibrium position (or steady-state response), based completely on the linear system, is appropriate for the type of HAWT blades under study.

Kottapalli, S. B. R.↗

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.↗