Transient growth in the flow past a three-dimensional smooth roughness element

This work provides a global optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of smooth three-dimensional roughness elements. Amplification mechanisms are described which can bypass the asymptotical growth of Tollmien–Schlichting waves. Smooth axisymmetric roughness elements of different height have been studied, at different Reynolds numbers. The results show that even very small roughness elements, inducing only a weak deformation of the base flow, can localize the optimal disturbance characterizing the Blasius boundary-layer flow. Moreover, for large enough bump heights and Reynolds numbers, a strong amplification mechanism has been recovered, inducing an increase of several orders of magnitude of the energy gain with respect to the Blasius case. In particular, the highest value of the energy gain is obtained for an initial varicose perturbation, differently to what found for a streaky parallel flow. Optimal varicose perturbations grow very rapidly by transporting the strong wall-normal shear of the base flow, which is localized in the wake of the bump. Such optimal disturbances are found to lead to transition for initial energies and amplitudes considerably smaller than sinuous optimal ones, inducing hairpin vortices downstream of the roughness element

Numerical lnvestigation of Disturbance Environments in Low Pressure Turbines

Using a series of direct numerical simulations, the individual and cumulative effects of various disturbance environments existing in a low pressure turbine (LPT) are investigated. In particular, the effects of free-stream turbulence (FST), unsteady wakes, roughness and blade oscillations on the separation-induced transition on the suction surface of a low pressure turbine blade are analyzed. Two configurations are considered: (i) a flat plate subjected to streamwise pressure gradient representative of the suction surface of a low pressure turbine blade, (ii) a flat plate subjected to a convecting free-stream vortex of fixed strength and at a fixed height over the plate. The first configuration represents the ‘ultra high-lift’ blades for the next generation low pressure turbine. The local pressure gradient induced by the convecting vortex in the second configuration is representative of the adverse pressure gradient on the suction surface of a low pressure turbine blade. The results are validated against existing experimental or numerical data and it is demonstrated that the numerical framework has captured most of the phenomena to a reasonable level of accuracy. A kernel experiment for bypass transition is simulated for the vortex-induced instability. The effect of the convection speed and strength of the vortex are discussed and the paths of transition adopted are distinguished. At low disturbance levels, the transition to turbulence is primarily due to the breakdown of ‘Kelvin-Helmholtz’ roll up vortices. In the presence of aeroelastic blade oscillations, unsteady wakes, free-stream turbulence and roughness, transition takes the bypass route and the results show evidence of streamwise streaks. These streaks impart spanwise waviness to the separated shear layer and cause early destabilisation. The blade oscillation has an effect in reducing the separated region and hence, the profile loss, which is further accentuated in the presence of free-stream turbulence. A blade fluctuating at higher reduced frequency is found to be more effective in shrinking the separation region. Blade vibration is found to increase the level of pre-transitional fluctuations, without having a significant influence on the growth beyond separation. There is a cumulative effect in suppressing the separation region when blade oscillation and free-stream turbulence are studied in conjunction, although the additional effect of free-stream turbulence is marginal. A secondary separation bubble, noted in the unperturbed flow, is reduced in size with blade oscillation and further reduced in the presence of free-stream turbulence. The vortex-induced instability has been proposed to be a unit process of free-stream turbulence, the effect of which is studied in the presence of a discrete roughness element (similar in functionality to a trip wire). The roughness element triggers early transition by destabilizing the mean flow. Streaks are observed in the presence of the convecting and rotating cylinder, generating a vortex of fixed strength, and are enhanced by the presence of roughness in the pre-transitional zone. Enhanced spanwise waviness is noted with the roughness, leading to earlier breakdown to turbulence. The route of transition and the origin of three-dimensionality marked by the prominence of the vortex stretching is shown. An optimum range of convection speeds of the free-stream vortex is obtained and the maximum receptivity is noted at a speed of 0.386, which concurs with prior experiments on a periodic convecting vortex (Kendall, 1987). The unsteady wake has a direct effect on the velocity profile. A lag is noted between the wake passing and transition. While the wake convects at the local free-stream velocity, its impression in the boundary layer convects much slower, between 50% and 70% of the local free-stream velocity. Both unsteady wakes and blade oscillation promote near-wall mixing. The unsteady wakes and blade oscillations have a conjunctive effect on reducing the size of separation bubble. The secondary separation bubble observed in the unperturbed flow is reduced with the presence of wakes and is completely suppressed with the addition of the blade oscillation. Turbulent kinetic energy production increases with increasing perturbation levels, with the maximum effect seen for the combination of wakes and oscillation. A receptivity method based on disturbance enstrophy transport equation (DETE) is proposed. The disturbance enstrophy is evaluated as the difference between the instantaneous and mean enstrophies, and while these are positive definite quantities, the difference may not be so. This aspect of disturbance enstrophy has been used meaningfully to obtain new information about the flow instability, such as segmenting regions of flow instabilities into those dictated by positive growth rates of disturbance enstrophy, and those due to its negative counterpart. The positive growth rates are associated with large scale coherence in the free-stream whereas the negative growth rates are found to be arising in near-wall viscous structures (Sengupta et al., 2019a,b). The extension of this method to structure detection and comparison against existing vortex identification methods, indicates the ability of the DETE method to capture small-scale structures induced by the viscous term of the Navier- Stokes equation. DETE has been used for the two configurations operating with varying perturbation levels and valuable insight pertaining to the flow dynamics has been attained with respect to its budget terms. In particular, the role of vortex stretching in leading the flow to three-dimensionality is highlighted. The global and local spatio-temporal receptivity analysis of flows perturbed by plate oscillations, wakes and free-stream excitation yields a spatio-temporal wave front to be the causal mechanism for flow transition. This is essentially representative of the nonmodal part of the disturbance spectrum. While this flow instability has already been established for geophysical flows such as tsunami and other fluid dynamical problems such as for zero pressure gradient boundary layer formed over a semi-infinite flat plate excited from inside the shear layer, its role for pressure gradient dominated flows (such as in LPTs) is shown for the first time. The importance of nonlinearity and its dispersion effects is shown, specifically for flows excited at the free stream, even when the onset of disturbances follows a linear mechanism. The need for using a global, nonlinear, spatio-temporal setup is established in order to capture all pertinent flow physics.Cambridge India Ramanujan Scholarshi

An Experimental Study of Roughness-Induced Instabilities in a Supersonic Boundary Layer

Progress on an experimental study of laminar-to-turbulent transition induced by an isolated roughness element in a supersonic laminar boundary layer is reported in this paper. Here, the primary focus is on the effects of roughness planform shape on the instability and transition characteristics. Four different roughness planform shapes were considered (a diamond, a circle, a right triangle, and a 45 degree fence) and the height and width of each one was held fixed so that a consistent frontal area was presented to the oncoming boundary layer. The nominal roughness Reynolds number was 462 and the ratio of the roughness height to the boundary layer thickness was 0.48. Detailed flow- field surveys in the wake of each geometry were performed via hot-wire anemometry. High- and low-speed streaks were observed in the wake of each roughness geometry, and the modified mean flow associated with these streak structures was found to support a single dominant convective instability mode. For the symmetric planform shapes - the diamond and circular planforms - the instability characteristics (mode shapes, growth rates, and frequencies) were found to be similar. For the asymmetric planform shapes - the right-triangle and 45 degree fence planforms - the mode shapes were asymmetrically distributed about the roughness-wake centerline. The instability growth rates for the asymmetric planforms were lower than those for the symmetric planforms and therefore, transition onset was delayed relative to the symmetric planforms

Recent insights into instability and transition to turbulence in open-flow systems

Roads to turbulence in open-flow shear layers are interpreted as sequences of often competing instabilities. These correspond to primary and higher order restructurings of vorticity distributions which culminate in convected spatial disorder (with some spatial coherence on the scale of the shear layer) traditionally called turbulence. Attempts are made to interpret these phenomena in terms of concepts of convective and global instabilities on one hand, and of chaos and strange attractors on the other. The first is fruitful, and together with a review of mechanisms of receptivity provides a unifying approach to understanding and estimating transition to turbulence. In contrast, current evidence indicates that concepts of chaos are unlikely to help in predicting transition in open-flow systems. Furthermore, a distinction should apparently be made between temporal chaos and the convected spatial disorder of turbulence past Reynolds numbers where boundary layers and separated shear layers are formed

A Computational Fluid Dynamics (CFD) Analysis of the Aerodynamic Effects of the Seams on a Two-Dimensional Representation of a Soccer Ball

Most major sports today use a dedicated ball or projectile with specific shape, size, and surface geometry, except for soccer. Over the history of the sport, the surface geometry and design stayed relatively unchanged, sewn together using 32 pentagonal and hexagonal panels. However, recent innovations in panel designs differ substantially from the traditional 32 panel ball. The effects these new designs have on the aerodynamic characteristics of the ball have remained largely unknown, even with the influx of experimental research completed in the past decade. Experimental studies have been broad in scope, analyzing an entire ball in wind tunnels or full flow paths in trajectory analyses. Computational efforts have been too assumptive in flow conditions, such as a fully turbulent flow field, which has not yielded accurate representations of the flow phenomenon. This study investigates the aerodynamic effects of the seam on a two-dimensional representation of a non-rotating soccer ball using Computational Fluid Dynamics (CFD). By applying a transitional solver to the narrowed scope of a two-dimensional flow domain, with a single seam in cross-flow, the effects of the seam on the boundary layer and overall transient flow structure can be more accurately modeled. Data analysis suggests the seam produces a local effect on skin friction, however, that effect does not materialize into a premature boundary layer transition or delayed separation point, as predicted by literature. A detailed flow visualization is consistent with this result, displaying expected symmetric vortex shedding similar to a smooth cylinder, but not fully capturing the effects of the seam, reinforcing the need for expanding computational research efforts in this field

Direct numerical simulation of instabilities in parallel flow with spherical roughness elements

Results from a direct numerical simulation of laminar flow over a flat surface with spherical roughness elements using a spectral-element method are given. The numerical simulation approximates roughness as a cellular pattern of identical spheres protruding from a smooth wall. Periodic boundary conditions on the domain's horizontal faces simulate an infinite array of roughness elements extending in the streamwise and spanwise directions, which implies the parallel-flow assumption, and results in a closed domain. A body force, designed to yield the horizontal Blasius velocity in the absence of roughness, sustains the flow. Instabilities above a critical Reynolds number reveal negligible oscillations in the recirculation regions behind each sphere and in the free stream, high-amplitude oscillations in the layer directly above the spheres, and a mean profile with an inflection point near the sphere's crest. The inflection point yields an unstable layer above the roughness (where U''(y) is less than 0) and a stable region within the roughness (where U''(y) is greater than 0). Evidently, the instability begins when the low-momentum or wake region behind an element, being the region most affected by disturbances (purely numerical in this case), goes unstable and moves. In compressible flow with periodic boundaries, this motion sends disturbances to all regions of the domain. In the unstable layer just above the inflection point, the disturbances grow while being carried downstream with a propagation speed equal to the local mean velocity; they do not grow amid the low energy region near the roughness patch. The most amplified disturbance eventually arrives at the next roughness element downstream, perturbing its wake and inducing a global response at a frequency governed by the streamwise spacing between spheres and the mean velocity of the most amplified layer

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Global stability analysis and direct numerical simulation (DNS) are performed to study boundary layer flows with an isolated roughness element. Wall-attached cuboids with aspect ratios $\eta=1$ and $\eta=0.5$ are investigated for fixed ratio of roughness height to displacement boundary layer thickness $h/\delta^*=2.86$. Global stability analysis is able to capture the frequency of the primary vortical structures. For $\eta=1$, only varicose instability is seen. For the thinner roughness element ($\eta=0.5$), the varicose instability dominates the sinuous instability, and the sinuous instability becomes more pronounced as $Re_h$ increases, due to increased spanwise shear in the near-wake region. The unstable modes mainly extract energy from the central streak, although the lateral streaks also contribute. The DNS results show that different instability features lead to different behavior and development of vortical structures in the nonlinear transition process. For $\eta=1$, the varicose mode is associated with the shedding of hairpin vortices. As $Re_h$ increases, the breakdown of hairpin vortices occurs closer to the roughness and sinuous breakdown behavior promoting transition to turbulence is seen in the farther wake. A fully-developed turbulent flow is established in both the inner and outer layers farther downstream when $Re_h$ is sufficiently high. For $\eta=0.5$, the sinuous wiggling of hairpin vortices is prominent at higher $Re_h$, leading to stronger interactions in the near wake, as a result of combined varicose and sinuous instabilities. A sinuous mode captured by dynamic mode decomposition (DMD) analysis, and associated with the `wiggling' of streaks persists far downstream

Development and Application of Quadratic Constitutive Relation and Transitional Crossflow Effects in the Wray-Agarwal Turbulence model

Computational Fluid Dynamics (CFD) has now become an almost indispensable tool for modern engineering analysis of fluid flow over aircrafts, turbomachinery, automobiles, and many other industrial applications. Accurate prediction of turbulent flows remains a challenging problem. The most popular approach for simulating turbulent flows in complex industrial applications is based on the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations. RANS equations introduce the so called “Reynolds or turbulent stresses” which are generally modeled using the Boussinesq approximation known as “Turbulence modeling.” Despite their development over a century, the turbulence models used with RANS equations still need much improvement. The first part of this research introduces the Quadratic Constitutive Relations (QCR), which is a nonlinear approach to approximating the turbulent stresses in eddy-viscosity class of turbulence models. In Boussinesq approximation, turbulent stresses are assumed to be linearly proportional to the strain with eddy viscosity being the proportionality constant. In recent years it has been found that linear eddy viscosity models are not accurate for prediction of vortical flows and wall bounded flows with mild separation with regions of recirculating flows. Such flows occur in junctions of aerodynamic surfaces e.g. the wing-body junction and in inlets and ducts with corners. The accurate prediction of these flows is needed for design improvements and better product performance. To remedy some of the shortcomings of the linear eddy-viscosity models, the Quadratic Constitutive Relation (QCR) for eddy viscosity is investigated to test its capability for predicting non-equilibrium turbulence effects. QCR is implemented in Spalart-Allmaras (SA), SST k-ω and Wray-Agarwal (WA) turbulence models and is applied to several applications involving large recirculating regions. It is demonstrated That QCR improves the results compared to linear eddy viscosity models. Another shortcoming of RANS models is their inability to accurately predict regions of transitional flow in a flow field. Many flow regions in industrial applications contain the transitional flow regime e.g. flows over aircraft wings and fuselages, past wind turbines and in gas turbines engines to name a few. The second part of this research has been on the development of a transitional model by suitably combining a correlation based intermittency-γ equation with the WA turbulence model; this new model is designated as Wray-Agarwal-γ (WA-γ) transition model. The WA-γ is extensively validated by computing a number of benchmark cases. The WA-γ model is also extended to include the crossflow-instability induced transition which is a dominant mode of transition in flows involving three-dimensional boundary layers, e.g. flow past swept wings and ellipsoids. This modified WA-γ model is validated using a benchmark test case for analyzing crossflow-induced transition

Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer

International audienceAn experimental and theoretical investigation aimed at describing the nonmodal growth of steady and spanwise periodic streamwise streaks in a flat plate boundary layer is presented. Stable laminar streaks are experimentally generated by means of a spanwise periodic array of small cylindrical roughness elements fixed on the plate. The streamwise evolution of the streaks is measured and it is proved that, except in a small region near the roughness elements, they obey the boundary layer scalings. The maximum achievable amplitude is mainly determined by the relative height of the roughness elements. Results are compared with numerical simulations of optimal and suboptimal boundary layer streaks. The theory is able to elucidate some of the discrepancies recently noticed between experimentally realizable nonmodal growth and optimal perturbation theory. The key factor is found to be the wall normal location and the extension of the laminar standing streamwise vortices inducing the streaks. The differences among previous experimental works can be explained by different dominating streak generation mechanisms which can be linked to the geometry and to the ratio between the roughness height and the boundary layer scale. © 2004 American Institute of Physics