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NASA NTRS1990

Stability theory for chemically reacting flows

Linear stability theory for chemically reacting (equilibrium and nonequilibrium) flows is applied to study the stability of hypersonic boundary layers under the equilibrium assumption. The results for Mach 15 flow indicate that the second mode instability shifts to lower frequencies, as compared to the perfect gas results. The peak second mode growth rate is also increased for the equilibrium gas model. However, the results for Goertler instability show very little real gas effect. The present theory has been applied to a sphere-cone flight transition experiment performed at freestream Mach of about 20.

Malik, Mujeeb R.↗
NASA NTRS2003

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Chang, Chau-Lyan↗
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 NTRS2019

Effects of Wall Cooling on Supersonic Modes in High-Enthalpy Hypersonic Boundary Layers over a Cone

High-enthalpy hypersonic boundary-layer transition plays an important role in many entry/descent vehicles. Aerothermodynamic performance of these vehicles strongly depends on the transition location on the surface. However, detailed transition flow physics in these chemically reacting boundary layers are poorly understood and transition estimates during the design phase rely heavily on empirically-derived transition criteria such as 𝑹𝒆(𝜽)/𝑴(𝒆). One of the most intriguing characteristics in hypersonic boundary layers is the presence of unstable supersonic modes, first identified in the 1990s. Due to a recent surge in hypersonic applications, there has been renewed interest in studying the flow physics of supersonic modes using either theory or direct numerical simulations. This paper investigates the rise of supersonic modes in a high-enthalpy hypersonic flow over a 𝟓° half-angle cone at various wall temperatures using both quasiparallel linear stability theory and linear PSE. It was found that supersonic modes exist in all wall temperature conditions including the adiabatic wall case. Cooler wall temperature causes the second Mack mode to become an unstable supersonic mode naturally downstream of the upper-branch neutral location when the wall is sufficiently cooled. In terms of the integrated growth, the second mode is still the dominant mode. Nonetheless, supersonic modes can cause additional series of relatively weaker growth than that of the second mode beyond the peak amplitude location. According to the present linear PSE results, contrary to what was speculated in the literature, supersonic-mode pressure disturbance structure radiated into the freestream is nonacoustic in nature and the formation of unstable supersonic modes is mainly associated with the synchronization of phase speed between the instability and acoustic waves in a nonp ayer, not due to nonlinear modal interaction as suggested in the literature.

Chang, Chau-Lyan↗
NASA NTRS1975

A numerical method for the prediction of high-speed boundary-layer transition using linear theory

A method is described of estimating the location of transition in an arbitrary laminar boundary layer on the basis of linear stability theory. After an examination of experimental evidence for the relation between linear stability theory and transition, a discussion is given of the three essential elements of a transition calculation: (1) the interaction of the external disturbances with the boundary layer; (2) the growth of the disturbances in the boundary layer; and (3) a transition criterion. The computer program which carried out these three calculations is described. The program is first tested by calculating the effect of free-stream turbulence on the transition of the Blasius boundary layer, and is then applied to the problem of transition in a supersonic wind tunnel. The effects of unit Reynolds number and Mach number on the transition of an insulated flat-plate boundary layer are calculated on the basis of experimental data on the intensity and spectrum of free-stream disturbances. Reasonable agreement with experiment is obtained in the Mach number range from 2 to 4.5.

Mack, L. M.↗
NASA NTRS2016

Measurements in a Transitioning Cone Boundary Layer at Freestream Mach 3.5

An experimental study was conducted in the Supersonic Low-Disturbance Tunnel to investigate naturally-occurring instabilities in a supersonic boundary layer on a 7 deg half- angle cone. All tests were conducted with a nominal freestream Mach number of M(sub infinity) = 3:5, total temperature of T(sub 0) = 299:8 K, and unit Reynolds numbers of Re(sub infinity) x 10(exp -6) = 9:89, 13.85, 21.77, and 25.73 m(exp -1). Instability measurements were acquired under noisy- ow and quiet- ow conditions. Measurements were made to document the freestream and the boundary-layer edge environment, to document the cone baseline flow, and to establish the stability characteristics of the transitioning flow. Pitot pressure and hot-wire boundary- layer measurements were obtained using a model-integrated traverse system. All hot- wire results were single-point measurements and were acquired with a sensor calibrated to mass ux. For the noisy-flow conditions, excellent agreement for the growth rates and mode shapes was achieved between the measured results and linear stability theory (LST). The corresponding N factor at transition from LST is N 3:9. The stability measurements for the quiet-flow conditions were limited to the aft end of the cone. The most unstable first-mode instabilities as predicted by LST were successfully measured, but this unstable first mode was not the dominant instability measured in the boundary layer. Instead, the dominant instabilities were found to be the less-amplified, low-frequency disturbances predicted by linear stability theory, and these instabilities grew according to linear theory. These low-frequency unstable disturbances were initiated by freestream acoustic disturbances through a receptivity process that is believed to occur near the branch I locations of the cone. Under quiet-flow conditions, the boundary layer remained laminar up to the last measurement station for the largest Re1, implying a transition N factor of N greater than 8:5.

King, Rudolph A.↗
NASA NTRS1989

Crossflow-vortex instability and transition on a 45 deg swept wing

A crossflow vortex experiment on a 45 deg swept wing is currently being conducted in the Arizona State University Unsteady Wind Tunnel. The experimental apparatus is designed to produce crossflow-dominated transition by simulating infinite swept wing flow using contoured end liners in a closed throat wind tunnel. Stationary fixed-wavelength crossflow vortices are observed at several chord Reynolds numbers. The vortex wavelength which is fixed for a given Reynolds number varies with Reynolds number approximately as predicted by linear stability theory, but with the predicted wavelengths about 30 percent larger than the observed wavelengths. Travelling waves are observed both in the frequency range predicted by linear stability theory and at higher frequencies. These higher frequency waves may be harmonics of the primary crossflow waves generated by a nonlinear parametric resonance phenomena.

Dagenhart, J. Ray↗
NASA NTRSDate not supplied

Exploring data-driven modeling of boundary layer transition

Prediction of laminar-turbulent transition in boundary layer flows is an important component of predicting the aerodynamic performance of a number of aerospace configurations. According to the CFD Vision 2030 [1], transition modeling represents acriticalarea in CFD simulation capability that will remain a pacing item for the foreseeable future. The fact thattransition can take placevia either one of a myriad possible paths adds to the challenges inreliable transition predictions, despite a limited knowledge of the relevant input parameters. In the low disturbance environments typical of flight applications, transition is often initiated by small amplitude disturbances in the form of linear instability waves of the laminar boundary layer. These disturbances amplify linearly at first and eventually undergo a sequence of nonlinear interactions that result in transition to turbulence. Because the nonlinear phase is rather rapid, the amplification of boundary layer instabilities is governed by the linearstability theory over a majority of the distance leading up to the onset of transition. Semi-empirical transition correlations based on the linear stability theory have been successful in explaining the observed trends in transition location within a broad class of flows. However, the application of stability theory is highly non-robust and often requires a significant domain expertise. Recent work at the NASA Langley Research Center has beenaimed at bridging the gap between physics based transition analyses such as those based on linear stability theory and practical applications that require transition prediction by users that may not be well versed in transition physics. The applications of deep learning have been at the center of these efforts. This presentation will focus on the progress achieved thus far, highlighting the applications of neural networks to selectedtransition scenarios across a range of Mach numbers and flow configuration, as well as the lessons learnedand remaining challengeswithrespect to the selection of training data and neural networks architectures, hyperparameter tuning, and the physical insights distilled from the otherwise black-box models.

M. R. Malik↗
NASA NTRS1990

Experiments on swept-wing boundary layers

Three-dimensional boundary-layer experiments are currently being conducted on a 45-deg swept wing in the Arizona State University Unsteady Wind Tunnel. Crossflow-dominated transition is produced via a model with contoured end liners to simulate infinite swept-wing flow. Fixed-wavelength stationary and traveling crossflow vortices are observed. The stationary vortex wavelengths vary with Reynolds number as predicted by linear-stability theory, but with observed wavelengths which are about 25 percent smaller than theoretically predicted. The frequencies of the most amplified moving waves are in agreement with linear stability theory; however, traveling waves at higher frequencies than predicted are also observed. These higher-frequency waves may be harmonics of the primary crossflow waves generated by a parametric resonance phenomena. Boundary-layer profiles measured at several spanwise locations show streamwise disturbance profiles characteristic of the crossflow instability.

Dagenhart, J. R.↗
NASA NTRS1989

The development of crossflow vortices on a 45 degree swept wing

Three-dimensional boundary-layer experiments are currently being conducted on a 45 deg swept wing in the Arizona State University Unsteady Wind Tunnel. Crossflow-dominated transition is produced via a model with contoured end liners to simulate infinite swept-wing flow. Fixed-wavelength stationary and traveling crossflow vortex are observed. The stationary vortex wavelengths vary with Reynolds number as predicted by linear-stability theory, but with observed wavelengths which are about 25 percent smaller than theoretically predicted. The frequencies of the most-amplified moving waves are in agreement with linear-stability theory; traveling waves at higher frequencies than predicted are also observed. These higher-frequency waves may be harmonics of the primary crossflow waves generated by a parametric resonance phenomena. Boundary-layer profiles measured at several spanwise locations show streamwise disturbance profiles characteristic of the crossflow instability. Near the transition location, severe distortions of the laminar boundary-layer profiles are observed. Mean-profile measurements are compared to theoretical predictions.

Mousseux, Marc C.↗
NASA NTRS2001

Cellular Spacing Selection During the Directional Solidification of Binary Alloys. A Numerical Approach

The evolution of cellular solid/liquid interfaces from an initially unstable planar front was studied by means of a two-dimensional computer simulation. The developed numerical model makes use of an interface tracking procedure and has the capability to describe the dynamics of the interface morphology based on local changes of the thermodynamic conditions. The fundamental physics of this formulation was validated against experimental microgravity results and the predictions of the analytical linear stability theory. The performed simulations revealed that in certain conditions, based on a competitive growth mechanism, an interface could become unstable to random perturbations of infinitesimal amplitude even at wavelengths smaller than the neutral wavelength, lambda(sub c), predicted by the linear stability theory. Furthermore, two main stages of spacing selection have been identified. In the first stage, at low perturbations amplitude, the selection mechanism is driven by the maximum growth rate of instabilities while in the second stage the selection is influenced by nonlinear phenomena caused by the interactions between the neighboring cells. Comparison of these predictions with other existing theories of pattern formation and experimental results will be discussed.

Catalina, Adrian V.↗
NASA NTRS2002

Experimental Study of the Richtmyer-Meshkov Instability of Incompressible Fluids

The Richtmyer-Meshkov instability of a low Atwood number, miscible, two-liquid system is investigated experimentally. The initially stratified fluids are contained within a rectangular tank mounted to a sled that rides on a vertical set of rails. The instability is generated by dropping the sled onto a coil spring, producing a nearly impulsive upward acceleration. The subsequent freefall that occurs as the container travels upward and then downward on the rails allows the instability to evolve in the absence of gravity. The interface separating the two liquids initially has a well-defined, sinusoidal perturbation that quickly inverts and then grows in amplitude after undergoing the impulsive acceleration. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial growth rate, a(sub 0), for single-mode perturbations with the predicted amplitudes differing by less than 10% from experimental measurements up to a nondimensional time ka(sub 0)t = 0.7, where k is the wavenumber. Linear stability theory also provides excellent agreement for the individual mode amplitudes of multi-mode initial perturbations up until the interface becomes multi-valued. Comparison with previously published weakly nonlinear single-mode models shows good agreement up to ka(sub 0)t = 3, while published nonlinear single-mode models provide good agreement up to ka(sub 0)t = 30. The effects of Reynolds number on the vortex core evolution and overall growth rate of the interface are also investigated. Measurements of the overall amplitude are found to be unaffected by the Reynolds number for the range of values studied here. However, experiments carried out at lower values of Reynolds numbers were found to have decreased vortex core rotation rates. In addition, an instability in the vortex cores is observed.

Niederhaus, Charles↗
NASA NTRS1992

The influence of bulges on boundary-layer instability

Local disturbances caused by a spanwise surface corrugation affect the position of the boundary-layer transition, and so the drag, of an object. This premature transition from laminar to turbulent flow is often associated with a separation of the laminar boundary-layer from its surface. Also the roughness-induced separation bubble provides an important link between the pressure and velocity fluctuations in the environment and the development of the disturbance in the laminar boundary-layer, i.e., the receptivity problem. To investigate the influence of a laminar separation bubble on boundary-layer instability, a separated flow generated by a velocity gradient over a flat plate was analyzed by direct numerical simulation using finite-difference solutions of the Navier-Stokes equations. The bubble acts as a strong amplifier of the instability waves and a highly nonlinear flow field is shown to develop downstream of the bubble. Consequently, the results of the direct numerical simulation differ noticeably from those of the classical linear stability theory proving the fact that the nonparallel effects together with the nonlinear interactions are crucial to this flow development. In the present paper, the effect of physical perturbations such as humps and hollows on boundary-layer instability is analyzed. This problem has been considered theoretically by several researchers (e.g., Nayfeh et al., 1987 and 1990; Cebeci et al., 1988). They used linear stability theory in their approach which does not include the nonparallel nor the nonlinear effects. Therefore, to account for these important effects in studying flow over humps and hollows the direct simulation technique is being implemented in generalized coordinates.

Elli, S.↗
NASA NTRS1990

Design optimization of natural laminar flow fuselages in compressible flow

An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions, and linear stability analysis of the compressible boundary layer. Boundary-layer transition is predicted by a 'hybrid' transition criterion based on Granville's transition criterion and a criterion using linear stability theory coupled with the e(n)-method. A tiptank of a business-jet is used as an example to illustrate that the method can be utilized to design an axisymmetric body shape with extensive natural laminar flow. Boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10 to the 6th on the original tiptank. On the designed body shape, a transition Reynolds number of 7.22 x 10 to the 6th is predicted using compressible linear stability theory coupled with e(n)-method.

Dodbele, Simha S.↗
NASA NTRS1990

Design of laminar flow bodies in compressible flow

An optimization method was developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions, and linear stability analysis of the compressible boundary-layer. Boundary-layer transition is predicted by a 'hybrid' transition criterion based on Granville's transition criterion and a criterion using linear stability theory coupled with the e(sup n)-method. A tiptank of a business jet is used as an example to illustrate that the method can be utilized to design an axisymmetric body shape with extensive natural laminar flow. On the original tiptank boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10 6 on the original tiptank. On the designed body shape a transition Reynolds number of 7.22 x 10 6 is predicted using compressible linear stability theory coupled with e n -method.

Simha S. Dodbele↗
NASA NTRS1992

Design optimization of natural laminar flow bodies in compressible flow

An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions and linear stability analysis of the compressible boundary-layer. In order to reduce the computer time, Granville's transition criterion is used to predict boundary-layer transition and to calculate the gradients of the objective function, and linear stability theory coupled with the e(exp n)-method is used to calculate the objective function at the end of each design iteration. Use of a method to design an axisymmetric body with extensive natural laminar flow is illustrated through the design of a tiptank of a business jet. For the original tiptank, boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10(exp 6). For the designed body shape, a transition Reynolds number of 7.22 x 10(exp 6) is predicted using compressible linear stability theory coupled with the e(exp n)-method.

Dodbele, Simha S.↗
NASA NTRS2010

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Li, Fei↗
NASA NTRS1987

Application of stability theory to laminar flow control - Progress and requirements

Paper briefly summarizes the current status of linear stability theory as applied to laminar flow control for aerodynamics. Results indicate that the conventional 'N factor' method of correlating stability theory and transition has a broad application range, including low- and high-speeds, two- and three-dimensional mean flow and TS, Gortler and crossflow disturbance modes. Linear theory is particularly applicable to the laminar flow control problem as, for system efficiency, control must be exercised and disturbances maintained in the linear regime. Current areas of concern for LFC, which require further stability theory research, include TS-crossflow interaction, combined disturbance fields (roughness, waviness, noise) and suction-induced disturbances. Some results on wave-interactions are presented.

Bushnell, D. M.↗