Boundary-Layer Instability and Transition Prediction
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transition prediction↗
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Transition prediction in external flows via linear stability theory
Linear stability theory results are presented for flight and low-disturbance wind tunnels, at low and high speeds, and for T-S, Gortler, and cross-flow modes. Results show that, in the absence of Morkovin 'bypasses', transition at low background disturbance levels corresponds to N-factors of the order of 9 to 11, provided that phenomena such as curvature effects are included. The results point to a wider range of applicability for the e exp N method than previously conjectured, and suggest that the e exp N method can be used to parametrize transition predictions as a function of parameters which affect the mean flow profiles for such purposes as LFC and minimum drag design.
Bushnell, D. M.↗
Roles of Engineering Correlations in Hypersonic Entry Boundary Layer Transition Prediction
Efforts to design and operate hypersonic entry vehicles are constrained by many considerations that involve all aspects of an entry vehicle system. One of the more significant physical phenomenon that affect entry trajectory and thermal protection system design is the occurrence of boundary layer transition from a laminar to turbulent state. During the Space Shuttle Return To Flight activity following the loss of Columbia and her crew of seven, NASA's entry aerothermodynamics community implemented an engineering correlation based framework for the prediction of boundary layer transition on the Orbiter. The methodology for this implementation relies upon the framework of correlation techniques that have been in use for several decades. What makes the Orbiter boundary layer transition correlation implementation unique is that a statistically significant data set was acquired in multiple ground test facilities, flight data exists to assist in establishing a better correlation and the framework was founded upon state of the art chemical nonequilibrium Navier Stokes flow field simulations. The basic tenets that guided the formulation and implementation of the Orbiter Return To Flight boundary layer transition prediction capability will be reviewed as a recommended format for future empirical correlation efforts. The validity of this approach has since been demonstrated by very favorable comparison of recent entry flight testing performed with the Orbiter Discovery, which will be graphically summarized. These flight data can provide a means to validate discrete protuberance engineering correlation approaches as well as high fidelity prediction methods to higher confidence. The results of these Orbiter engineering and flight test activities only serve to reinforce the essential role that engineering correlations currently exercise in the design and operation of entry vehicles. The framework of information-related to the Orbiter empirical boundary layer transition prediction capability will be utilized to establish a fresh perspective on this role, to illustrate how quantitative statistical evaluations of empirical correlations can and should be used to assess accuracy and to discuss what the authors' perceive as a recent heightened interest in the application of high fidelity numerical modeling of boundary layer transition. Concrete results will also be developed related to empirical boundary layer transition onset correlations. This will include assessment of the discrete protuberance boundary layer transition onset data assembled for the Orbiter configuration during post-Columbia Return To Flight. Assessment of these data will conclude that momentum thickness Reynolds number based correlations have superior coefficients and uncertainty in comparison to roughness height based Reynolds numbers, aka Re(sub k) or Re(sub kk). In addition, linear regression results from roughness height Reynolds number based correlations will be evaluated, leading to a hypothesis that non-continuum effects play a role in the processes associated with incipient boundary layer transition on discrete protuberances.
Campbell, Charles H.↗
Evaluation of two-equation turbulence models for predicting transitional flows
An evaluation of the capabilities and limitations of four low-Reynolds number two-equation turbulence models for predicting bypass transition on a flat plate has been conducted. The ability of these models to reproduce the effect of the free-stream turbulence on transition was tested. The strengths and deficiencies of these models have been identified systematically. It is found that the k-epsilon models are capable of predicting the qualitative aspects of transition. However, the predictions are found to be sensitive to the initial conditions. Also, the start and end of transition were found to depend on the damping functions used in the low-Reynolds number versions of the k-epsilon models.
Abid, Ridha↗
Roles of Engineering Correlations in Hypersonic Entry Boundary Layer Transition Prediction
Efforts to design and operate hypersonic entry vehicles are constrained by many considerations that involve all aspects of an entry vehicle system. One of the more significant physical phenomenon that affect entry trajectory and thermal protection system design is the occurrence of boundary layer transition from a laminar to turbulent state. During the Space Shuttle Return To Flight activity following the loss of Columbia and her crew of seven, NASA's entry aerothermodynamics community implemented an engineering correlation based framework for the prediction of boundary layer transition on the Orbiter. The methodology for this implementation relies upon similar correlation techniques that have been is use for several decades. What makes the Orbiter boundary layer transition correlation implementation unique is that a statistically significant data set was acquired in multiple ground test facilities, flight data exists to assist in establishing a better correlation and the framework was founded upon state of the art chemical nonequilibrium Navier Stokes flow field simulations. Recent entry flight testing performed with the Orbiter Discovery now provides a means to validate this engineering correlation approach to higher confidence. These results only serve to reinforce the essential role that engineering correlations currently exercise in the design and operation of entry vehicles. The framework of information related to the Orbiter empirical boundary layer transition prediction capability will be utilized to establish a fresh perspective on this role, and to discuss the characteristics which are desirable in a next generation advancement. The details of the paper will review the experimental facilities and techniques that were utilized to perform the implementation of the Orbiter RTF BLT Vsn 2 prediction capability. Statistically significant results for multiple engineering correlations from a ground testing campaign will be reviewed in order to describe why only certain correlations were selected for complete implementation to support the Shuttle Program. Historical Orbiter flight data on early boundary layer transition due to protruding gap fillers will be described in relation to the selected empirical correlations. In addition, Orbiter entry flight testing results from the BLT Flight Experiment will be discussed in relation to these correlations. Applicability of such correlations to the entry design problem will be reviewed, and finally a perspective on the desirable characteristics for a next generation capability based on high fidelity physical models will be provided.
Campbell, Charles H.↗
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.↗
Enhancements to Linear Stability-Based, CFD-integrated Transition Prediction for High-Speed Flows
Combining linear stability calculations with computational fluid dynamics (CFD) simulations has great potential for the automated modeling of high-speed flows, especially when adequate information about the configuration and the disturbance environment is available. However, a significant impediment to the applicability of this technique is the lack of an efficient method to calculate the crucial amplification ratio corresponding to the onset of transition in hypersonic flows. This ratio, also known as the "transition N-factor," is dependent upon the freestream disturbance environment as well as the surface properties of the test article. In response to the need for an engineering solution to predict the transition N-factor within conventional hypersonic wind tunnels, this paper presents a data-driven correlation that expands the existing correlations from straight circular cones with a narrow range of half angles to a broader array of axisymmetric configurations. Furthermore, when tested against a chosen dataset that was not used in its calibration, the suggested correlation shows good predictive accuracy with an RMS error of only 6.9%. Although similar accuracy may also be achieved via existing correlations based on similar datasets, predictions based on the proposed correlation have the advantage of not requiring an extensive amount of configuration-specific data. Practical applications often have access to the input parameters needed for this correlation, such as the freestream disturbance intensity, Mach number, and body-based slenderness Reynolds number. Additionally, this correlation outperforms the traditional assumption of a constant N-factor, particularly for configurations with blunted nose geometries. The development of this correlation is grounded in an extensive dataset encompassing conical models with body half-angles varying between 5 degrees and 16 degrees, Mach numbers ranging from 5 to 14, and nosetip-based Reynolds numbers approaching the transition reversal limit for blunt-nosed cones.
CFD↗
Enhancements to Linear Stability-Based, CFD-integrated Transition Prediction for High-Speed Flows
Combining linear stability calculations with computational fluid dynamics (CFD) simulations has great potential for the automated modeling of high-speed flows, especially when adequate information about the configuration and the disturbance environment is available. However, a significant impediment to the applicability of this technique is the lack of an efficient method to calculate the crucial amplification ratio corresponding to the onset of transition in hypersonic flows. This ratio, also known as the "transition N-factor," is dependent upon the freestream disturbance environment as well as the surface properties of the test article. In response to the need for an engineering solution to predict the transition N-factor within conventional hypersonic wind tunnels, this paper presents a data-driven correlation that expands the existing correlations from straight circular cones with a narrow range of half angles to a broader array of axisymmetric configurations. Furthermore, when tested against a chosen dataset that was not used in its calibration, the suggested correlation shows good predictive accuracy with an RMS error of only 6.9%. Although similar accuracy may also be achieved via existing correlations based on similar datasets, predictions based on the proposed correlation have the advantage of not requiring an extensive amount of configuration-specific data. Practical applications often have access to the input parameters needed for this correlation, such as the freestream disturbance intensity, Mach number, and body-based slenderness Reynolds number. Additionally, this correlation outperforms the traditional assumption of a constant N-factor, particularly for configurations with blunted nose geometries. The development of this correlation is grounded in an extensive dataset encompassing conical models with body half-angles varying between 5 degrees and 16 degrees, Mach numbers ranging from 5 to 14, and nosetip-based Reynolds numbers approaching the transition reversal limit for blunt-nosed cones.
CFD↗
The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows
The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.
Boundary Layer Stability↗
The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows
The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.
Boundary Layer Stability↗
Predicted transition temperatures of very thin films and whiskers of superconducting semiconductors - Application to SrTiO sub 3.
Bardeen-Cooper-Schrieffer energy gap equation /with constant kernel/ approximate solution derivation for superconducting semiconductors, discussing predicted very thin film transition temperatures
Eagles, D. M.↗
Transition prediction and control in subsonic flow over a hump
The influence of a surface roughness element in the form of a two-dimensional hump on the transition location in a two-dimensional subsonic flow with a free-stream Mach number up to 0.8 is evaluated. Linear stability theory, coupled with the N-factor transition criterion, is used in the evaluation. The mean flow over the hump is calculated by solving the interacting boundary-layer equations; the viscous-inviscid coupling is taken into consideration, and the flow is solved within the separation bubble. The effects of hump height, length, location, and shape; unit Reynolds number; free-stream Mach number, continuous suction level; location of a suction strip; continuous cooling level; and location of a heating strip on the transition location are evaluated. The N-factor criterion predictions agree well with the experimental correlation of Fage; in addition, the N-factor criterion is more general and powerful than experimental correlations. The theoretically predicted effects of the hump's parameters and flow conditions on transition location are consistent and in agreement with both wind-tunnel and flight observations.
Masad, Jamal A.↗
Stability theory and transition prediction applied to a general aviation fuselage
The linear stability of a fully three-dimensional boundary layer formed over a general aviation fuselage was investigated. The location of the onset of transition was estimated using the N-factor method. The results were compared with existing experimental data and indicate N-factors of approximately 8.5 on the side of the fuselage and 3.0 near the top. Considerable crossflow existed along the side of the body, which significantly affected the unstable modes present in the boundary layer. Fair agreement was found between the predicted frequency range of linear instability modes and available experimental data concerning the spectral content of the boundary layer.
Spall, R. E.↗
Boundary-Layer Transition Prediction Through Loose Coupling of OVERFLOW and LASTRAC
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boundary layer transition↗
Transition Prediction in Three-Dimensional Flows with the Harmonic Linearized Navier-Stokes Equations
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Boundary-Layer Transition↗
Comparison of methods for prediction of transition by stability analysis
The paper compares several methods of transition prediction of linear stability analysis. The spectral stability analysis code SALLY is used to analyze flows over laminar flow control wings. It is shown that transition prediction by the envelope method and a new modified wave packet method are comparable in reliability, but that the envelope method is more efficient computationally. This is based on the results which show that the wave packet method provides N factors which are at best as consistent as those of the envelope method; since the wave packet method is at least 3 times as expensive as the envelope method, the latter is recommended for engineering design calculations.
Malik, M. R.↗
Compressible Stability Analysis Code For Transition Prediction in Three Dimensional Boundary Layers.
COSAL employs finite-difference method to solve compressible stability equations in original form. Code includes two eigenvalue search procedures. Global procedure provided for use when no initial guess available. Fast local eigenvalue search procedure provided for use when good initial guess available. COSAL written in FORTRAN IV.
Malik, M. R.↗
The harmonic linearized Navier–Stokes equations for transition prediction in three-dimensional flows
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Pedro Paredes↗