Pre-transitional Boundary Layer Research Articles

Experimental study of a separated shear layer transition under acoustic excitation

The paper discusses experimental results on the effect of broadband acoustic excitation on laminar-to-turbulent transition in a separated shear layer developing on a flat plate subjected to an adverse pressure gradient (APG) and freestream turbulence level equal to Tu ≅ 1 %. The study encompasses the influence of Reynolds number (Rex = 185 000 and 370 000) and sound pressure level (SPL). The inherent complexity of the problem is simplified by providing an acoustic excitation from a controlled source (loudspeaker), acting on the boundary layer developing on the flat plate with a given streamwise pressure gradient. Two types of instabilities were identified in the pre-transitional boundary layer in unexcited flows. One was related to the inviscid Kelvin-Helmholtz (K-H) instability, while the second one was associated with formation of streamwise-oriented Klebanoff streaks (so-called Klebanoff mode).In the low Reynolds number case (Rex = 185 000), the K-H was responsible for transition onset, while in the high Reynolds number flow (Rex = 370 000), the Klebanoff distortions dominated the turbulent breakdown with the minor effect of the K-H instability. In addition to the naturally developing boundary layer, the flow was exposed to a pink noise characterized by SPL = 125 dB and 135 dB. In the low Reynolds number case, the acoustic excitation enhanced the K-H instability. It resulted in an earlier laminar-to-turbulent transition in case with higher sound pressure level (135 dB). In the high Reynolds number flow, the acoustic excitation enhanced the mixed-type transition mechanism with dominant role of the Klebanoff streaks. Shrinking or complete suppression of the separation bubbles was observed, depending on the applied sound pressure level (125 and 135 dB).

Instability mechanisms and intermittency distribution in adverse pressure gradient attached and separated boundary layers

Direct numerical simulation has been carried out on one attached and two separated boundary layer flows (involving small and large separation) under the influence of an adverse pressure gradient. A unified picture of the pre-transitional boundary layer for the three cases has been provided that reveals a “mixed-mode” instability, involving contribution from instability waves and streamwise streaks. A time-frequency analysis of the transitional velocity signals has been performed which shows that as the Reynolds number decreases, the character of the time traces evolves continuously from a “spotty” behavior (exhibiting distinct turbulent spots) for the attached case to a “non-spotty” behavior (involving more “uniform” distribution of turbulent fluctuations in time) for the large-separation case, encompassing the entire spectrum of transition scenarios. The variation of the intermittency factor within the transition zone is seen to compare well with the Narasimha universal intermittency distribution. We find that although the time variation of velocity for large separation is non-spotty (or more “uniform”), the spanwise variation of velocity is spotty, showing a clear clustering of high-wavenumber fluctuations separated by quasi-laminar regions. Thus, all three cases exhibit spottiness in the transition zone with different manifestations. We present a physical cartoon for the transition scenarios for the attached and separated cases, using the ideas of vortex-wall interaction and instability of spanwise vortical structures. We find that concentrated breakdown is exhibited by all the three cases near the transition onset, and the spot breakdown processes are broadly consistent with the postulates underlying the universal intermittency distribution.

Identification of a Pressure–Strain Correlation-Based Bypass Transition Onset Marker

Abstract Temporally developing direct numerical simulations (T-DNS) are performed for freestream turbulence induced bypass transition flow with zero-pressure gradient over a flat-plate boundary layer for a range of freestream turbulence intensities (Tu) of 1.4% to 6%. The objective is to understand the role of pressure–strain terms on bypass transition onset and to propose and validate a phenomenological hypothesis for the identification of a robust transition onset marker for use in transition-sensitive Reynolds-averaged Navier–Stokes (RANS) simulations. Results show that transition initiates at a location where the slow pressure–strain term becomes more dominant than the rapid term in the pretransitional boundary layer region. A simple transition onset marker based on one-point statistical quantities is derived from the scaling of the ratio of the slow and rapid pressure fluctuation source terms. The critical value of the marker is found to vary within a narrow range (±2.8%) and satisfies previously identified criteria for a robust transition onset marker.

Stochastic receptivity analysis of boundary layer flow

We utilize the externally forced linearized Navier-Stokes equations to study the receptivity of pre-transitional boundary layers to persistent sources of stochastic excitation. Stochastic forcing is used to model the effect of free-stream turbulence that enters at various wall-normal locations and the fluctuation dynamics are studied via linearized models that arise from locally parallel and global perspectives. In contrast to the widely used resolvent analysis that quantifies the amplification of deterministic disturbances at a given temporal frequency, our approach examines the steady-state response to stochastic excitation that is uncorrelated in time. In addition to stochastic forcing with identity covariance, we utilize the spatial spectrum of homogeneous isotropic turbulence to model the effect of free-stream turbulence. Even though locally parallel analysis does not account for the effect of the spatially evolving base flow, we demonstrate that it captures the essential mechanisms and the prevailing length-scales in stochastically forced boundary layer flows. On the other hand, global analysis, which accounts for the spatially evolving nature of the boundary layer flow, predicts the amplification of a cascade of streamwise scales throughout the streamwise domain. We show that the flow structures that can be extracted from a modal decomposition of the resulting velocity covariance matrix, can be closely captured by conducting locally parallel analysis at various streamwise locations and over different wall-parallel wavenumber pairs. Our approach does not rely on costly stochastic simulations and it provides insight into mechanisms for perturbation growth including the interaction of the slowly varying base flow with streaks and Tollmien-Schlichting waves.

A novel laminar kinetic energy model for the prediction of pretransitional velocity fluctuations and boundary layer transition

Boundary layer transition onset estimation and modelling are essential for the design of many engineering products across many industries. In this work, a novel model for predicting pretransitional boundary layer fluctuations is proposed. The laminar kinetic energy (LKE) concept is used to represent such fluctuations. The new LKE model is implemented in OpenFOAM within the Reynolds-Averaged Navier-Stokes (RANS) framework. Only two approaches for modelling the LKE can be found in the literature. Mayle and Schulz (1997) has the limitation of requiring an initial LKE profile. Walters and Cokljat’s (2008) approach has been found to significantly overpredict the growth of the LKE. In addition, their model is tightly coupled with the specific dissipation rate and turbulent kinetic energy equations. The new model proposed here can act as a stand-alone equation for the LKE, making it portable and potentially facilitating the development of new transition models tailored to various industrial applications. Comparison with experiments shows that the new LKE model correctly predicts the growth of pretransitional velocity fluctuations and skin friction for a flat plate at zero-pressure gradient. To illustrate its practical application for transitional flows, the LKE model is coupled with an existing k−ω model using a new approach that requires minimal modifications. The resulting model (k−ω LKE) demonstrates excellent predictive capabilities when applied to a number of validation test cases.

Data-enabled prediction of streak breakdown in pressure-gradient boundary layers

Streaks in pre-transitional boundary layers are analysed and their properties are extracted from direct numerical simulation data. Streaks that induce breakdown to turbulence via secondary instability are shown to differ from the remainder of the population in various attributes. Conditionally averaged flow fields establish that they are situated farther away from the wall, and have a larger cross-sectional area and higher peak amplitude. The analysis also shows that the momentum thickness acts as a similarity parameter for the properties of the streaks. Probability density functions of the streak amplitude, area, and shear along the streaks, collapse among the various pressure gradients when plotted as a function of the momentum thickness. A prediction scheme for laminar–turbulent transition based on artificial neural networks is presented, which can identify the streaks that will eventually induce the formation of turbulent spots. In comparison to linear stability theory, the approach achieves a higher prediction accuracy at considerably lower computational cost.

A Four-Equation Eddy-Viscosity Approach for Modeling Bypass Transition

AbstractIt is very important to predict the bypass transition in the simulation of flows through turbomachinery. This paper presents a four-equation eddy-viscosity turbulence transition model for prediction of bypass transition. It is based on the SST turbulence model and the laminar kinetic energy concept. A transport equation for the non-turbulent viscosity is proposed to predict the development of the laminar kinetic energy in the pre-transitional boundary layer flow which has been observed in experiments. The turbulence breakdown process is then captured with an intermittency transport equation in the transitional region. The performance of this new transition model is validated through the experimental cases of T3AM, T3A and T3B. Results in this paper show that the new transition model can reach good agreement in predicting bypass transition, and is compatible with modern CFD software by using local variables.

Entropy generation in a transitional boundary layer region under the influence of freestream turbulence using transitional RANS models and DNS

In this study, the entropy generation process in the bypass transition scenario is investigated for a flat plate boundary layer. Here transition occurs prematurely due to the presence of strong levels of freestream turbulence. Reynolds-Averaged Navier–Stokes (RANS) models and Direct Numerical Simulations (DNS) are implemented to study the local entropy generation and energy dissipation in pre-transitional and transitional regions comprehensively. Two new transitional RANS models (SST k−ω(4eq) and k−kl−ω) were used for prediction of the onset of transition and the results are compared with DNS ones. Classical laminar theory underpredicts the observed entropy generated. In the pre-transitional boundary layer, the perturbations generated by the streaky structures modify the mean velocity profile and induce a quasi-turbulent contribution to indirect dissipation. In the transition region the pointwise entropy generation rate (S‴)+ initially increases near the wall and then decreases corresponding to the distribution predicted for a fully-turbulent boundary layer as the flow moves downstream. All the RANS models predicted transition onset prematurely and, consequently, overpredict the integral entropy generation rate and the skin friction coefficient in the transition region.

Entropy Generation in a Boundary Layer Transitioning Under the Influence of Freestream Turbulence

The objective of the present research is to develop new fundamental knowledge of the entropy generation process in laminar flow with significant fluctuations (called pre-transition) and during transition prematurely induced by strong freestream turbulence (bypass transition). Results of direct numerical simulations are employed. In the pre-transitional boundary layer, the perturbations by the streaky structures modify the mean velocity profile and induce a “quasi-turbulent” contribution to indirect dissipation. Application of classical laminar theory leads to underprediction of the entropy generated. In the transition region the pointwise entropy generation rate (S′′′)+ initially increases near the wall and then decreases to correspond to the distribution predicted for a fully-turbulent boundary layer as the flow progresses downstream. In contrast to a developed turbulent flow, the term for turbulent convection in the turbulence kinetic energy balance is significant and can play an important role in some regions of the transitioning boundary layer. More turbulent energy is produced than dissipated and the excess is convected downstream as the boundary layer grows. Since it is difficult to measure and predict true turbulent dissipation rates (and hence, entropy generation rates) exactly other than by expensive direct numerical simulations, a motivation for this research is to evaluate approximate methods for possible use in experiments and design. These new results demonstrate that an approximate technique, used by many investigators, overestimates the dissipation coefficient Cd by up to seventeen per cent. For better predictions and measurements, an integral approach accounting for the important turbulent energy flux is proposed and validated for the case studied.

A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow

An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k-ω framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretransitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in comparison with commonly used models that exhibit no capability of predicting laminar-to-turbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems.

Boundary layer receptivity measurements on compliant surfaces

This paper describes receptivity measurements in a pre-transitional boundary layer flowing over either a rigid or a compliant surface. Fluctuating velocities and frequency spectra were determined on one rigid and nine compliant surfaces. The results showed that the near wall receptivity grows linearly with Re θ . An empirical correlation of the gain frequency spectrum for a rigid wall was also established. For the compliant surfaces, the near wall gain is increased markedly near the leading edge of the plate due to the amplification of high and mid-frequencies. These frequencies are dissipated though as the flow progresses over the compliant surface such that the receptivity is lower on all the compliant surfaces than on the rigid surface at the trailing edge. An empirical correlation for the ratio of the gains on compliant and rigid surfaces in terms of the compliant surface coefficient ζ 2/ Eρ CS L 2 and Re θ was established. This correlation indicates that compliant surfaces can suppress receptivity by up to 25% for a Re θ = 400.

The influence of compliant surfaces on bypass transition

The objective of the work was to investigate the effect of compliant surfaces on the receptivity and bypass transition of a boundary layer. Hot wire measurements in the pre-transitional and transitional boundary layers on nine different compliant and one rigid surface with identical geometries were made. The experiments were conducted in air and the compliant surfaces were manufactured from gelatine covered by a 10 μm protective PVC film. The laminar boundary layer profiles and growth rate results were the same for all the surfaces. However, the receptivity of the laminar boundary layer to freestream disturbances increased close to the leading edge of each compliant surface. Further downstream the majority of the compliant surfaces were successful in reducing the receptivity to a value below that for the rigid surface. The transition onset position on the compliant surfaces ranged from 3% downstream to 20% upstream of the rigid surface position. It was concluded that compliant surfaces with optimum properties can reduce receptivity and delay transition.

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Predicting Transition in Turbomachinery—Part I: A Review and New Model Development

Here we report on an effort to include an empirically based transition modeling capability in a Reynolds Averaged Navier-Stokes solver. Well known empirical models for both attached- and separated-flow transition were tested against cascade data and found unsuitable for use in turbomachinery design. Consequently, a program was launched to develop models with sufficient accuracy for use in design. As a first step, accurate prediction of free stream turbulence development was identified as a prerequisite for accurate modeling. Additionally, a demonstrated capability to capture the effects of free stream turbulence on pre-transitional boundary layers became an impetus for the work. A computational fluid dynamics (CFD)-supplemented database of 104 experimental cascade cases was constructed to explore the development of new correlations. Dimensional analyses were performed to guide the work, and appropriate non-dimensional parameters were then extracted from CFD predictions of the laminar boundary layers existing on the airfoil surfaces prior to either transition onset or incipient separation. For attached-flow transition, onset was found to occur at a critical ratio of the boundary-layer diffusion time to a time scale associated with the energy-bearing turbulent eddies. In the case of separated-flow transition, it was found that the length of a separation bubble prior to turbulent reattachment was a simple function of the local momentum thickness at separation and the overall surface length traversed by a fluid element prior to separation. Both the attached- and separated-flow transition models were implemented into the design system as point-like trips.

Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer

This paper is concerned with the effect of free-stream turbulence on the pretransitional flat-plate boundary layer. It is assumed that either the turbulent Reynolds number or the downstream distance (or both) is small enough that the flow can be linearized. The dominant disturbances in the boundary layer, which are of the Klebanoff type, are governed by the linearized unsteady boundary-region equations, i.e. the linearized Navier–Stokes equations with the streamwise derivatives neglected in the viscous and pressure-gradient terms. The turbulence is represented as a superposition of vortical free-stream Fourier modes and the corresponding Fourier component solutions to the boundary-region equations are obtained numerically. The results are then superposed to compute the root mean square of the fluctuating streamwise velocity in the boundary layer produced by the actual free-stream turbulence. It is found that the disturbances computed with isotropic free-stream turbulence do not reach the levels measured in experiments. However, good quantitative agreement is obtained with the relatively low turbulent Reynolds number data of Kendall when the measured strong anisotropy of the low-frequency portion of his spectrum is accounted for. Data at higher turbulent Reynolds numbers are affected by nonlinearity, which manifests itself through the generation of small spanwise length scales. We attempt to model this within the context of the linear theory by choosing a free-stream spectrum whose energy is concentrated at larger transverse wavenumbers and achieve very good agreement with the data. The results suggest that even small deviations from pure isotropy can be an important factor in explaining the large amplitudes of the Klebanoff modes in the pre-transitional boundary layer, and also point to the importance of nonlinear effects. We discuss some additional effects that may need to be accounted for in order to obtain a complete description of the Klebanoff modes.

1997 Best Paper Award—Heat Transfer Committee: The Turbulence That Matters

A unified expression for the spectrum of turbulence is developed by asymptotically matching known expressions for small and large wave numbers, and a formula for the one-dimensional spectral function, which depends on the turbulence Reynolds number Reλ, is provided. In addition, formulas relating all the length scales of turbulence are provided. These relations also depend on Reynolds number. The effects of free-stream turbulence on laminar heat transfer and pretransitional flow in gas turbines are re-examined in light of these new expressions using our recent thoughts on an “effective” frequency of turbulence and an “effective” turbulence level. The results of this are that the frequency most effective for laminar heat transfer is about 1.3 U/2πLe, where U is the free-stream velocity and Le is the length scale of the eddies containing the most turbulent energy, and the most effective frequency for producing pretransitional boundary layer fluctuations is about 0.3 U/2πη, where η is Kolmogorov’s length scale. In addition, the role of turbulence Reynolds number on stagnation heat transfer and transition is discussed, and new expressions to account for its effect are provided.

Application of Turbulence Models to Bypass Transition

The present study considers the use of low-Reynolds number, single-point closures for transition prediction at high levels of free-stream turbulence. The work is focused on two differential Reynolds Stress Transport models, which are compared with the k – ε model of Launder and Sharma. Calculations are carried out for attached boundary layer flow on a flat plate equipped with a sharp leading edge at zero-pressure gradient and for various free-stream turbulence levels. Comparisons with results from a large eddy simulation reveal significant shortcomings in the modeling of the dissipation, with a large overprediction in the pretransitional boundary layer. The present results are in some cases in conflict with other results reported in the literature, and it is shown that the discrepancies can be ascribed to the implementation of the free-stream boundary conditions.