Boundary Layer Bypass Transition Research Articles

An efficient spectral method based on an orthogonal decomposition of the velocity for transition analysis in wall bounded flow

As a consequence of the Helmholtz–Hodge theorem, any divergence-free vector field can be decomposed in two L 2-orthogonal, solenoidal vector fields expressed in terms of projections of the velocity and vorticity fields, on an arbitrary direction in space. Based on this type of decomposition and the choice of the wall-normal direction, an efficient spectral code is developed for incompressible flows developing between two parallel walls. The method relies on a weak formulation of the Navier–Stokes equations in the two corresponding divergence-free subspaces. The approximation is based on Fourier expansions in two directions and on the Chebyshev basis proposed by Moser et al. in the third direction in order to satisfy the wall boundary conditions. The method accuracy is validated for the plane Poiseuille linear stability problem and compared with the case of a spectral collocation method. Simulations of by-pass transition in boundary layers developing between two parallel walls are then presented. Since, by construction, the two orthogonal vector fields of the decomposition are associated respectively to the Orr–Sommerfeld and the Squire modes of the linear stability theory, the method makes it possible to evaluate kinetic energy transfers due to the coupling between these two scalar modes and their interactions with the base flow. The decomposition is also used to describe the structure of finite-length streaks in the earlier stages of transition.

Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer

A nominally-zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 940. Transition which is completed at approximately Reθ = 750 was triggered by intermittent localized disturbances arising from patches of isotropic turbulence introduced periodically from the free stream at Reθ = 80. Streamwise pressure gradient is quantified with several measures and is demonstrated to be weak. Blasius boundary layer is maintained in the early transitional region of 80 < Reθ < 180 within which the maximum deviation of skin friction from the theoretical solution is less than 1%. Mean and second-order turbulence statistics are compared with classic experimental data, and they constitute a rare DNS dataset for the spatially developing zero-pressure-gradient turbulent flat-plate boundary layer. Our calculations indicate that in the present spatially developing low-Reynolds-number turbulent flat-plate boundary layer, total shear stress mildly overshoots the wall shear stress in the near-wall region of 2–20 wall units with vanishing normal gradient at the wall. Overshoots as high as 10% across a wider percentage of the boundary layer thickness exist in the late transitional region. The former is a residual effect of the latter. The instantaneous flow fields are vividly populated by hairpin vortices. This is the first time that direct evidence (in the form of a solution of the Navier–Stokes equations, obeying the statistical measurements, as opposed to synthetic superposition of the structures) shows such dominance of these structures. Hairpin packets arising from upstream fragmented Λ structures are found to be instrumental in the breakdown of the present boundary layer bypass transition.

Numerical Simulation of Bypass Transition by the Approach of Intermittency Transport Equation

This paper deals with the development of a numerical approach to predict freestream turbulence-induced (FST-induced) boundary layer bypass transition using an intermittency transport equation. An intermittency based transition model, which is critical for invoking transition onset according to Abu-Ghannam and Shaw correlation, is implemented into the proven Reynolds-Averaged N-S (RANS) solver. The intermittent behavior of the transitional flow is incorporated into the computation by modifying the eddy viscosity t µ , obtained from a turbulence model. Wilcox low Reynolds k ω − turbulence model is employed to calculate the eddy viscosity and others turbulent quantities. For validation, the present transition model is applied to the benchmark experiments of flat plate test cases of ERCOFTAC series and to predictions of a modern Low Pressure (LP) turbine flow. It follows from the detail comparisons of the calculated results with the relevant experimental data and other researchers’ simulations that the present model is capable to make a reasonable prediction of FST-induced bypass transition.

Stochastic approach to the receptivity problem applied to bypass transition in boundary layers

To study the flow behavior in the presence of external disturbances of chaotic nature, a stochastic approach is pursued. In particular, transition to turbulence in boundary layers exposed to high levels of free-stream turbulence is considered. The late stages of this transition scenario, characterized by the growth and breakdown of streamwise-elongated streaks, are examined by considering the linear evolution of perturbations to a base flow consisting of the Blasius profile and the streaks. A stochastic initial condition is considered where the free-stream perturbations are described by the correlations of isotropic homogeneous turbulence. The spatial correlation of the excited flow at later times can be computed by the numerical solution of a Lyapunov equation. It is shown that free-stream turbulence has the necessary features to excite secondary energy growth, thus playing a central role in the transition to turbulence. The method proposed here can be used to examine the receptivity of other flows to external noise whose statistical properties are known or can be modeled.

Development of Prediction Method of Boundary Layer Bypass Transition using Intermittency Transport Equation

Development of Prediction Method of Boundary Layer Bypass Transition using Intermittency Transport Equation

G304 間欠度方程式を用いた境界層バイパス遷移の予測法に関する研究(1)(GS3 可視化,境界層,一般セッション)

G304 間欠度方程式を用いた境界層バイパス遷移の予測法に関する研究(1)(GS3 可視化,境界層,一般セッション)

626 圧力勾配を伴う境界層のバイパス遷移の数値予測(乱流の数値シミュレーション,OS26 乱流の数値シミュレーション)

Bypass transition of boundary layers with pressure gradients is predicted using a second-moment closure proposed by Shima and Kobayashi. In the turbulence model, the stress redistribution is modeled by using a wall effect vector which is obtained as the solution of an elliptic equation with a simple wall boundary condition. Overall, the prediction is in good agreement with experimental data, though the model does not fully reproduce the streamwise development of the normal stress component perpendicular to the wall.

311 間欠度方程式を用いた境界層バイパス遷移の予測に関する研究(流体工学III・材料工学II)

311 間欠度方程式を用いた境界層バイパス遷移の予測に関する研究(流体工学III・材料工学II)

Experimental Studies on Wake-Induced Bypass Transition of Flat-Plate Boundary Layers under Favorable and Adverse Pressure Gradients

This study investigates wake-induced bypass transition of boundary layers on a flat plate which is subjected to favorable and adverse pressure gradients. Inlet free-stream turbulence level is controlled with a turbulence grid. Detailed boundary layer measurements are executed by use of a single hot-wire probe. The main focus of this paper is on how and to what extent the wake-induced bypass transition of a flatplate boundary layer can be affected by favorable - adverse pressure gradient as well as enhanced turbulence intensity. A spoked-wheel-type wake generator creates periodic wakes in front of the flat plate. Two types of the wakes are generated by altering the direction of the movement of the wake-generating bars. Instantaneous velocity signals successfully reveal the flow events associated with the wake passage happening inside the boundary layer, such as the emergence of turbulent spots and calmed regions behind them. Noticeable differences in the transitional behavior due to the wake passage also appear between these two types of the wakes.

外部擾乱に起因する境界層バイパス遷移に関する研究 : 境界層制御の効果(S22-5 境界層,管内流の制御-1,S22 流れ制御の技術)

外部擾乱に起因する境界層バイパス遷移に関する研究 : 境界層制御の効果(S22-5 境界層,管内流の制御-1,S22 流れ制御の技術)

On the receptivity of the by-pass transition to the length scale of the outer stream turbulence

The effect of length scale on flat-plate by-pass boundary layer transition under free stream turbulence conditions has been investigated. Plane grids generated a constant value of 3 percent intensity turbulent fluctuations and five values of the dissipation length parameter in the range of 2.2 mm to 33.3 mm at 5 m/s flow velocity in the plane of the leading edge of the flat plate. The investigated boundary layer corresponds to the ERCOFTAC Test Case T3A+. Distributions of integral parameters as well as the statistical characteristics of the turbulent fluctuations were measured. They document a significant effect of turbulence length scale on the onset and the end of by-pass transition. It was found that the onset of the final stage of transition comes on later in `fine-grained' turbulence than in the case of large free stream turbulence length scale. At the same time, the extent of the transition region shortens with decreasing length scale. Nevertheless, the transition process terminates sooner in a flow with a large turbulence length scale than in a flow with a small one. An attempt has been made to describe these observations quantitatively.

Simulation of boundary layer transition induced by periodically passing wakes

The interaction between an initially laminar boundary layer developing spatially on a flat plate and wakes traversing the inlet periodically has been simulated numerically. The three-dimensional, time-dependent Navier–Stokes equations were solved with 5.24×107 grid points using a message passing interface on a scalable parallel computer. The flow bears a close resemblance to the transitional boundary layer on turbomachinery blades and was designed following, in outline, the experiments by Liu & Rodi (1991). The momentum thickness Reynolds number evolves from Reθ = 80 to 1120. Mean and second-order statistics downstream of Reθ = 800 are of canonical flat-plate turbulent boundary layers and are in good agreement with Spalart (1988).In many important aspects the mechanism leading to the inception of turbulence is in agreement with previous fundamental studies on boundary layer bypass transition, as summarized in Alfredsson & Matsubara (1996). Inlet wake disturbances inside the boundary layer evolve rapidly into longitudinal puffs during an initial receptivity phase. In the absence of strong forcing from free-stream vortices, these structures exhibit streamwise elongation with gradual decay in amplitude. Selective intensification of the puffs occurs when certain types of turbulent eddies from the free-stream wake interact with the boundary layer flow through a localized instability. Breakdown of the puffs into young turbulent spots is preceded by a wavy motion in the velocity field in the outer part of the boundary layer.Properties and streamwise evolution of the turbulent spots following breakdown, as well as the process of completion of transition to turbulence, are in agreement with previous engineering turbomachinery flow studies. The overall geometrical characteristics of the matured turbulent spot are in good agreement with those observed in the experiments of Zhong et al. (1998). When breakdown occurs in the outer layer, where local convection speed is large, as in the present case, the spots broaden downstream, having the vague appearance of an arrowhead pointing upstream.The flow has also been studied statistically. Phase-averaged velocity fields and skin-friction coefficients in the transitional region show similar features to previous cascade experiments. Selected results from additional thought experiments and simulations are also presented to illustrate the effects of streamwise pressure gradient and free-stream turbulence.

Optimal disturbances and bypass transition in boundary layers

Streamwise streaks are ubiquitous in transitional boundary layers, particularly when subjected to high levels of free-stream turbulence. Using the steady boundary-layer approximation, the upstream disturbances experiencing maximum spatial energy growth are numerically calculated. The calculations use techniques commonly employed when solving optimal-control problems for distributed parameter systems. The calculated optimal disturbances consist of streamwise vortices developing into streamwise streaks. The maximum spatial energy growth was found to scale linearly with the distance from the leading edge. Based on these results, a simple model for prediction of transition location is proposed. Available experiments have been used to correlate the single constant appearing in the model.

Bypass Transition in Boundary Layers Including Curvature and Favorable Pressure Gradient Effects

Recent experimental studies of two-dimensional boundary layers undergoing bypass transition have been reviewed to attempt to characterize the effects of free-stream turbulence level, acceleration, and wall curvature on bypass transition. Results from several studies were cast in terms of “local” boundary layer coordinates (momentum and enthalpy thickness Reynolds numbers) and compared. In unaccelerated flow on flat walls, skin friction coefficients were shown to match those from a laminar integral solution before transition and quickly adjusted to match those from a fully turbulent correlation after transition. Stanton number data also matched a correlation in the laminar region, but do not match correlation values so well in the turbulent region. The data showed that the relationship between skin friction coefficient and momentum thickness Reynolds number is unaffected by streamwise acceleration. Stanton numbers were strongly affected by acceleration, however, indicating a breakdown in Reynolds analogy. Concave curvature caused the formation of Go¨rtler vortices, which strongly influenced the skin friction. Convex curvature had an opposite, and lesser effect. The location and length of the transition region generally followed the expected trends as free-stream turbulence level, curvature, and acceleration were varied; the onset location and the transition length were extended by acceleration and convex curvature and reduced by concave curvature and enhanced turbulence. When individual cases were compared, some inconsistencies were observed. These inconsistencies indicate a need to characterize the flows to be compared more completely. Better spectral and length scale measurements of the free-stream disturbance would help in this regard. Within the transition region, the intermittency data from all the cases on flat walls (no curvature) were consistent with an intermittency distribution from the literature. Turbulent spot production rates were shown to be mostly dependent on free-stream turbulence, with a noted increase in spot production rate due to concave curvature and little effect of convex curvature. The acceleration effect on spot production rate was small for the cases studied.