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Transition Prediction for the 30P30N Airfoil and the CRM-HL using FUN3D

The ability to accurately model transition over high-lift configurations can lead to improved agreement between stationary Reynolds-Averaged Navier-Stokes (RANS) computations and experimental measurements. In this work, selected transport-equation-based RANS models for transition prediction in the NASA FUN3D flow solver are used to simulate flow over the 30P30N three-element airfoil and the High-Lift Common Research Model (CRM-HL). The primary RANS-based transition model is the Langtry-Menter (LM) 𝜸-Re𝜽𝒕 model coupled with the Menter shear-stress transport model. Additionally, the existing capability for transition prediction based on linear stability correlations is used to allow the modeling of transition over multiple elements of the 30P30N configuration. This approach pairs an algebraic transition model with the Spalart-Allmaras (SA) turbulence model that relies on an imposed transition location in FUN3D and the parabolized stability equations as implemented in the LASTRAC code. Predictions based on these different transition prediction approaches and models are compared with each other, experimental data, and previous simulations by evaluating the lift and drag coefficients, the surface-pressure/skin-friction distributions, and the locations of transition onset. Results are presented for multiple angles of attack for the 30P30N airfoil and CRM-HL. For the CRM-HL, a grid resolution study is performed for the LM transition model and the SA turbulence model.

High Lift↗

DOE OSTI2026

Boundary-layer receptivity to oblique freestream vorticity waves for a high-enthalpy hypersonic flow

The receptivity of a Mach 15 straight-cone boundary layer to oblique freestream vorticity waves is investigated using direct numerical simulation (DNS) alongside linear stability theory and the linear parabolized stability equations. A thermochemical nonequilibrium gas model is used. Oblique freestream vorticity waves at frequencies of 400, 800, and 1200 kHz are considered, with incident angles ranging from 0° to 29.4° at 400 kHz, 0° to 15.7° at 800 kHz, and 0° to 20.6° at 1200 kHz. The 400 kHz case is of primary interest due to the strong second-mode amplification at this frequency. Although the underlying base flow is axisymmetric, the oblique vorticity waves lead to a fully three-dimensional boundary-layer disturbance whose characteristics vary depending on the azimuthal ray relative to the freestream wave. Moving downstream within the second-mode instability region, some clear trends emerge in terms of the boundary-layer disturbance amplitudes; that is, disturbance amplitudes are highest at the leeward ray (relative to the freestream wave), but weakest about halfway between the windward and leeward rays. Increasing the incident angle causes the amplitudes to increase on the leeward ray and decrease on the windward ray. Moreover, the boundary-layer disturbance throughout contains a wide spectrum of azimuthal wavenumbers in which the disturbance energy falls off at higher wavenumbers. Increasing the incident angle causes the azimuthal spectrum of the boundary-layer disturbance to broaden overall. Qualitatively similar results are found for the two higher frequencies leading up to the peak-amplitude locations corresponding to the second-mode instability.

42 ENGINEERING↗

NASA NTRS1992

High speed transition prediction

The main objective of this work period was to develop, acquire and apply state-of-the-art tools for the prediction of transition at high speeds at NASA Ames. Although various stability codes as well as basic state codes were acquired, the development of a new Parabolized Stability Equation (PSE) code was minimal. The time that was initially allocated for development was used on other tasks, in particular for the Leading Edge Suction problem, in acquiring proficiency in various graphics tools, and in applying these tools to evaluate various Navier-Stokes and Euler solutions. The second objective of this work period was to attend the Transition and Turbulence Workshop at NASA Langley in July and August, 1991. A report on the Workshop follows. From July 8, 1991 to August 2, 1991, the author participated in the Transition and Turbulence Workshop at NASA Langley. For purposes of interest here, analysis can be said to consist of solving simplified governing equations by various analytical methods, such as asymptotic methods, or by use of very meager computer resources. From the composition of the various groups at the Workshop, it can be seen that analytical methods are generally more popular in Great Britain than they are in the U.S., possibly due to historical factors and the lack of computer resources. Experimenters at the Workshop were mostly concerned with subsonic flows, and a number of demonstrations were provided, among which were a hot-wire experiment to probe the boundary layer on a rotating disc, a hot-wire rake to map a free shear layer behind a cylinder, and the use of heating strips on a flat plate to control instability waves and consequent transition. A highpoint of the demonstrations was the opportunity to observe the rather noisy 'quiet' supersonic pilot tunnel in operation.

Gasperas, Gediminis↗

NASA NTRS1991

Analysis of the linear stability of compressible boundary layers using the PSE

The application of linearized parabolic stability equations (PSE) to compressible flow is considered. The effect of mean-flow nonparallelism is found to be weak on 2D waves and strong on 3D waves. Results for a single choice of free-stream parameters that corresponds to the atmospheric conditions at 15,000 m above sea level are presented.

Bertolotti, F. P.↗

NASA NTRS1992

The transition prediction toolkit: LST, SIT, PSE, DNS, and LES

The e(sup N) method for predicting transition onset is an amplitude ratio criterion that is on the verge of full maturation for three-dimensional, compressible, real gas flows. Many of the components for a more sophisticated, absolute amplitude criterion are now emerging: receptivity theory, secondary instability theory, parabolized stability equations approaches, direct numerical simulation and large-eddy simulation. This paper will provide a description of each of these new theoretical tools and provide indications of their current status.

Zang, Thomas A.↗

NASA NTRS1993

Stability and transition on swept wings

This paper describes the extension and application of the Parabolized Stability Equations (PSE) to the stability and transition of the supersonic three-dimensional laminar boundary layer on a swept wing. The problem formulation uses a general coordinate transformation for arbitrary curvilinear body-fitted computational grids. Some testing using these coordinates is briefly described to help validate the software used for the investigation. The disturbance amplitude ratios as a function of chord position for supersonic (Mach 1.5) boundary layers on untapered, untwisted wings of different sweep angles are then presented and compared with those obtained from local parallel analyses.

Stuckert, Greg↗

NASA NTRS1993

Effects of free-stream turbulence on boundary-layer transition

Traditional methods for the prediction of the transition location rest either on lump parameters like the momentum thickness or on N factors obtained from the approximate linear stability characteristics of the flow. These methods account for the effects of the disturbance environment by empirical correlation with observed transition locations. We have developed a highly efficient and accurate approach to stability analysis and transition simulation based on parabolized stability equations (PSE). Here we present a first application of this approach to realistic problems of practical interest. We study the effects of the turbulence level on transition and heat transfer in flows over flat plates, curved plates, and the stator blade of a gas-turbine model. We discuss the formulation of an input model for the PSE analysis in the light of the present knowledge of receptivity mechanisms. The input model is used to compute transition locations for various configurations and flow conditions. The results compare favorably with experimental data.

Herbert, TH.↗

NASA NTRS1993

Non-parallel stability of compressible boundary layers

Linear and nonlinear stability of compressible growing boundary layers is studied using parabolized stability equations (PSE). Linear PSE calculations are performed for Mach 1.6 and 4.5 plate-plate flow, and the results are compared with the predictions of the multiple-scales approach. In general, the nonparallel effect appears to be less significant for oblique waves near the lower neutral branch but it progressively becomes important at higher Reynolds numbers near the upper branch. In contrast, the nonparallel effect is more pronounced near the lower branch for two-dimensional first-mode waves. The PSE and multiple-scales results agree for the first mode waves, but in the first-second mode transition region, the latter approach tends to break down. Comparison with the first (oblique) and second mode growth rate data from Kendall's (1967) experiment shows good agreement; however, the peak second mode growth rate is over-predicted. Similar conclusions are drawn for the second mode experiment of Stetson et al. (1983) for Mach 8 flow past a sharp cone. We conjecture that the lower experimental growth rate is due to nonlinear saturation and provide supporting calculations.

Chang, Chau-Lyan↗

NASA NTRS1993

Higher-order accurate Osher schemes with application to compressible boundary layer stability

Two fourth order accurate Osher schemes are presented which maintain higher order accuracy on nonuniform grids. They use either a conservative finite difference or finite volume discretization. Both methods are successfully used for direct numerical simulations of flat plate boundary layer instability at different Mach numbers. Results of growth rates of Tollmien-Schlichting waves compare well with direct simulations of incompressible flow and for compressible flow with results obtained by solving the parabolic stability equations.

Van Der Vegt, J. J. W.↗

NASA NTRS1993

High speed transition prediction

The main objective of this work period was to develop, maintain and exercise state-of-the-art methods for transition prediction in supersonic flow fields. Basic state and stability codes, acquired during the last work period, were exercised and applied to calculate the properties of various flowfields. The development of a code for the prediction of transition location using a currently novel method (the PSE or Parabolized Stability Equation method), initiated during the last work period and continued during the present work period, was cancelled at mid-year for budgetary reasons. Other activities during this period included the presentation of a paper at the APS meeting in Tallahassee, Florida entitled 'Stability of Two-Dimensional Compressible Boundary Layers', as well as the initiation of a paper co-authored with H. Reed of the Arizona State University entitled 'Stability of Boundary Layers'.

Gasperas, Gediminis↗

NASA NTRS1993

Higher-order accurate Osher schemes with application to compressible boundary layer stability

Vandervegt, J. J. W.↗

NASA NTRS1993

Vortex generation and wave-vortex interaction over a concave plate with roughness and suction

The generation and amplification of vortices by surface homogeneities, both in the form of surface waviness and of wall-normal velocity, is investigated using the nonlinear parabolic stability equations. Transients and issues of algebraic growth are avoided through the use of a similarity solution as initial condition for the vortex. In the absence of curvature, the vortex decays as the square root of 1/x when flowing over streamwise aligned riblets of constant height, and grows as the square root of x when flowing over a corresponding streamwise aligned variation of blowing/suction transpiration velocity. However, in the presence of wall inhomogeneities having both streamwise and spanwise periodicity, the growth of the vortex can be much larger. In the presence of curvature, the vortex develops into a Gortler vortex. The 'direct' and 'indirect' interaction mechanisms possible in wave-vortex interaction are presented. The 'direct' interaction does not lead to strong resonance with the flow conditions investigated. The 'indirect' interaction leads to K-type transition.

Bertolotti, Fabio↗

NASA NTRS1994

Numerical simulation of receptivity and transition in a boundary layer on a flat plate with a suction hole

A Navier-Stokes solver has been modified to allow for unsteady boundary conditions to be imposed at the inflow boundary. Because the streamwise derivatives are discretized with three-point compact differences, there is no need for special treatment of the points adjacent to the inflow boundary, provided that all necessary derivatives are properly specified at the boundary points. The unsteady boundary conditions can be obtained from a previous computation, from a solution of the parabolized stability equations (PSE), or from an analytical exact or approximate solution of the Navier-Stokes equations, e.g. an asymptotic expansion solution to model a sound wave interacting with the boundary layer.

Fasel, Hermann F.↗

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 NTRS1994

Numerical simulation of supersonic boundary layer transition

The present contribution reviews some of the recent progress obtained at our group in the direct numerical simulation (DNS) of compressible boundary layer transition. Elements of the different simulation approaches and numerical techniques employed are surveyed. Temporal and spatial simulations, as well as comparisons with results obtained from Parabolized Stability Equations, are discussed. DNS results are given for flat plate boundary layers in the Mach number range 1.6 to 4.5. A temporal DNS at Mach 4.5 has been continued through breakdown all the way to the turbulent stage. In addition results obtained with a recently developed extended temporal DNS approach are presented, which takes into account some nonparallel effects of a growing boundary layer. Results from this approach are quite close to those of spatial DNS, while preserving the efficiency of the temporal DNS.

Guo, Y.↗

NASA NTRS1994

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.↗

NASA NTRS1995

Simulation of crossflow instability on a supersonic highly swept wing

A direct numerical simulation (DNS) algorithm has been developed and validated for use in the investigation of crossflow instability on supersonic swept wings, an application of potential relevance to the design of the High-Speed Civil Transport (HSCT). The algorithm is applied to the investigation of stationary crossflow instability on an infinitely long 77-degree swept wing in Mach 3.5 flow. The results of the DNS are compared with the predictions of linear parabolized stability equation (PSE) methodology. In-general, the DNS and PSE results agree closely in terms of modal growth rate, structure, and orientation angle. Although further validation is needed for large-amplitude (nonlinear) disturbances, the close agreement between independently derived methods offers preliminary validation of both DNS and PSE approaches.

Pruett, C. David↗

NASA NTRS1996

Nonlinear stability of supersonic jets

The stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations are presented. In this analysis the large scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.

Tiwari, S. N.↗