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At least 379 records · Page 21

On the stability of swept wing laminar boundary layers including curvature effects

A linear stability analysis that encompasses curvature effects has been conducted in wind tunnel experiments on a swept NACA 64(2)-A015 wing, and published transition-onset results have been correlated with computed N-factor values. A strong stabilizing influence is noted upon the growth of the crossflow disturbance, when the flow is accelerated in regions of high body curvature. The maximum amplified crossflow disturbances were in all cases travelling waves; when TS waves reached their maximum, the N-factors at transition lay in the 9.9-13.8 range. Stabilization due to curvature effects was less pronounced in cases where acceleration occurred over a large portion of chord.

Viken, J.↗

Assessing Uncertainties in Boundary Layer Transition Predictions for HIFiRE-1 at Non-zero Angles of Attack

Boundary layer stability was analyzed for the HIFiRE-1 flight vehicle geometry for ground tests conducted at the CUBRC LENS I hypersonic shock test facility and the Langley Research Center (LaRC) 20- inch Mach 6 Tunnel. Boundary layer stability results were compared to transition onset location obtained from discrete heat transfer measurements from thin film gauges during the CUBRC test and spatially continuous heat transfer measurements from thermal phosphor paint data during the LaRC test. The focus of this analysis was on conditions at non-zero angles of attack as stability analysis has already been performed at zero degrees angle of attack. Also, the transition onset data obtained during flight testing was at nonzero angles of attack, so this analysis could be expanded in the future to include the results of the flight test data. Stability analysis was performed using the 2D parabolized stability software suite STABL (Stability and Transition Analysis for Hypersonic Boundary Layers) developed at the University of Minnesota and the mean flow solutions were computed using the DPLR finite volume Navier-Stokes computational fluid dynamics (CFD) solver. A center line slice of the 3D mean flow solution was used for the stability analysis to incorporate the angle of attack effects while still taking advantage of the 2D STABL software suite. The N-factors at transition onset and the value of Re(sub theta)/M(sub e), commonly used to predict boundary layer transition onset, were compared for all conditions analyzed. Ground test data was analyzed at Mach 7.2 and Mach 6.0 and angles of attack of 1deg, 3deg and 5deg. At these conditions, the flow was found to be second mode dominant for the HIFiRE-1 slender cone geometry. On the leeward side of the vehicle, a strong trend of transition onset location with angle of attack was observed as the boundary layer on the leeward side of the vehicle developed inflection points at streamwise positions on the vehicle that correlated to angle of attack. Inflection points are a strong instability mechanism that lead to rapid breakdown and transition to turbulence. The transition onset location on the windward side of the vehicle displayed no trend with angle of attack or freestream Reynolds number and transition was observed farther down the vehicle than observed on the leeward side of the vehicle. In analysis of both windward and leeward sides of the vehicle, use of the N factor methodology to develop trends to predict boundary layer transition onset showed improvements over the Re(sub theta)/M(sub e) empirical correlation methodology. Stronger correlations and less scatter in the data were observed when using the N factor method for these cases.

Marek, Lindsay C.↗

Higher modes of the Orr-Sommerfeld problem for boundary layer flows

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented.

Lakin, W. D.↗

On the application of linear stability theory to the problem of supersonic boundary-layer transition

Linear stability theory is used to calculate the amplitude ratio of constant-frequency disturbances as a function of Reynolds number for insulated and cooled-wall flat-plate boundary layers between Mach numbers 1.3 and 5.8. The growth curves are used to examine the consequences of using a fixed amplitude of the most unstable frequency as a transition criterion. The effect of free-stream Mach number on insulated-wall boundary layers is calculated, assuming that the initial disturbance level is constant, is proportional to the square of the free-stream Mach number and to the square root of the energy density of the one-dimensional power spectra of free-stream disturbances measured in supersonic wind tunnels.

Mack, L. M.↗

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.↗

Effects of compressibility on design of subsonic fuselages for natural laminar flow

Compressible linear boundary-layer stability analyses of two representative axisymmetric fuselage geometries indicate that a favorable effect will be exerted on the characteristics of a fuselage's axisymmetric boundary layer by compressibility. A freestream Mach number increase from 0.6 to 0.8 significantly reduces TS wave growth rates in the laminar boundary layer of the fuselages analyzed. The generally destabilizing effect of increasing length Re number on boundary layer stability can be overpowered by the favorable effects of compressibility on the fluid.

Vijgen, P. M. H. W.↗

Efficient computation of the stability of three-dimensional compressible boundary layers

Methods for the computer analysis of the stability of three-dimensional compressible boundary layers are discussed and the user-oriented Compressible Stability Analysis (COSAL) computer code is described. The COSAL code uses a matrix finite-difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, M. R.↗

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.↗

CFD validation of a supersonic laminar flow control concept

A three-dimensional Navier-Stokes code is used in conjunction with a linear compressible stability analysis code to develop a numerical procedure for prediction of laminar flow transition. The procedure is applied to a modified F-16XL fighter with a laminar flow control glove at supersonic speed. Details of boundary layer stability analysis indicate that, computationally, laminar flow could be realized on the highly swept wing in the absence of the leading edge attachment-line contamination. Effects of the three-dimensionality of the flow were shown to be important in the boundary layer stability analysis. The numerically predicted surface pressures compare favorably with the flight test data.

Woan, Chung-Jin↗

Geometric Effects on the Amplification of First Mode Instability Waves

The effects of geometric changes on the amplification of first mode instability waves in an external supersonic boundary layer were investigated using numerical techniques. Boundary layer stability was analyzed at Mach 6 conditions similar to freestream conditions obtained in quiet ground test facilities so that results obtained in this study may be applied to future test article design to measure first mode instability waves. The DAKOTA optimization software package was used to optimize an axisymmetric geometry to maximize the amplification of the waves at first mode frequencies as computed by the 2D STABL hypersonic boundary layer stability analysis tool. First, geometric parameters such as nose radius, cone half angle, vehicle length, and surface curvature were examined separately to determine the individual effects on the first mode amplification. Finally, all geometric parameters were allowed to vary to produce a shape optimized to maximize the amplification of first mode instability waves while minimizing the amplification of second mode instability waves. Since first mode waves are known to be most unstable in the form of oblique wave, the geometries were optimized using a broad range of wave frequencies as well as a wide range of oblique wave angles to determine the geometry that most amplifies the first mode waves. Since first mode waves are seen most often in flows with low Mach numbers at the edge of the boundary layer, the edge Mach number for each geometry was recorded to determine any relationship between edge Mach number and the stability of first mode waves. Results indicate that an axisymmetric cone with a sharp nose and a slight flare at the aft end under the Mach 6 freestream conditions used here will lower the Mach number at the edge of the boundary layer to less than 4, and the corresponding stability analysis showed maximum first mode N factors of 3.

Kirk, Lindsay C.↗

Linear stability theory and three-dimensional boundary layer transition

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

Spall, Robert E.↗

The stability of a three dimensional laminar boundary layer over a swept flat plate

The linear stability of the laminar boundary layer on a swept flat plate with an imposed favorable pressure gradient was studied utilizing a linear stability model which accounts for streamline curvature for three-dimensional incompressible flows. Calculations were performed for a leading-edge sweep angle of 45 degrees and freestream valocity of 19 m/s. Computed disturbance amplification rates and wavelengths for stationary crossflow vortices were compared with available experimental results.

Mueller, B.↗

Transition correlations in three-dimensional boundary layers

The stability and transition characteristics of three-dimensional boundary-layer flows are examined. First, the flow over a rotating cone is considered computationally. An increase of stagnation temperature is found to be only slightly stabilizing. Parameter studies on the simple rotating-cone geometry provide a large database of three-dimensional boundary-layer profiles and associated stability characteristics. To determine the possibility of correlating transition location with parameters based purely on basic-state three-dimensional boundary-layer profile characteristics, an empirical transition location of N = 9 is assumed. Transition location does not correlate with the traditional crossflow Reynolds number. A more appropriate definition for crossflow Reynolds number is found and termed R(sub cf(new)). This new parameter appears to correlate for transition location when plotted against maximum crossflow velocity. Then, the flow over a yawed cone is considered experimentally. The correlation results obtained from the rotating-cone work are applied to the actual measured transition locations on two different yawed-cone models under various angle-of-attack conditions in two different experimental facilities and are verified. This correlation is only suggested as a tool for preliminary transition prediction and design in three-dimensional boundary layers; once a preliminary shape is selected, further linear stability theory or parabolized stability equation calculations are strongly urged.

Reed, Helen L.↗

Determination of Stability and Translation in a Boundary Layer

Reducing the infinite degrees of freedom inherent in fluid motion into a manageable number of modes to analyze fluid motion is presented. The concepts behind the center manifold technique are used. Study of the Blasius boundary layer and a precise description of stability within the flow field are discussed.

Crepeau, John↗

Data Analysis for the NASA/Boeing Hybrid Laminar Flow Control Crossflow Experiment

The Hybrid-Laminar Flow Control (HLFC) Crossflow Experiment, completed in 1995. generated a large database of boundary layer stability and transition data that was only partially analyzed before data analysis was abruptly ended in the late 1990's. Renewed interest in laminar flow technologies prompted additional data analysis, to integrate all data, including some post-test roughness and porosity measurements. The objective is to gain new insights into the effects of suction on boundary layer stability. A number of challenges were encountered during the data analysis, and their solutions are discussed in detail. They include the effect of the probe vibration, the effect of the time-varying surface temperature on traveling crossflow instabilities, and the effect of the stationary crossflow modes on the approximation of wall location. Despite the low turbulence intensity of the wind tunnel (0.01 to 0.02%), traveling crosflow disturbances were present in the data, in some cases at amplitudes up to 1% of the freestream velocity. However, the data suggests that transition was dominated by stationary crossflow. Traveling crossflow results and stationary data in the presence of suction are compared with linear parabolized stability equations results as a way of testing the quality of the results.

Eppink, Jenna L.↗

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

Equations↗

Spurious frequencies as a result of numerical boundary treatments

The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues is a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a 2-D cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. A more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions is reported.

Abarbanel, Saul↗