Wall-normal Velocity Components Research Articles

Assessment of Machine Learning Wall Modeling Approaches for Large Eddy Simulation of Gas Turbine Film Cooling Flows: An a Priori Study

Abstract In this work, a priori analysis of machine learning (ML) strategies is carried out with the goal of data-driven wall modeling for large eddy simulation (LES) of gas turbine film cooling flows. High-fidelity flow datasets are extracted from wall-resolved LES (WRLES) of flow over a flat plate interacting with the coolant flow supplied by a single row of 7-7-7 shaped cooling holes inclined at 30 degrees with the flat plate at different blowing ratios (BR). The WRLES are performed using the high-order Nek5000 spectral element computational fluid dynamics (CFD) solver. Light gradient boosting machine (LightGBM) is employed as the ML algorithm for the data-driven wall model. Parametric tests are conducted to systematically assess the influence of a wide range of input flow features (velocity components, velocity gradients, pressure gradients, and fluid properties) on the accuracy of ML wall model with respect to prediction of wall shear stress. In addition, the use of spatial stencil and time delay is also explored within the ML wall modeling framework. It is shown that features associated with gradients of the streamwise and spanwise velocity components have a major impact on the prediction fidelity of wall model, while the effect of gradients of wall-normal velocity component is found to be negligible. Moreover, adding flow feature information from an x-y-z spatial stencil significantly improves the ML model accuracy and generalizability compared to just using local flow features from the matching location. Overall, highest prediction accuracy is achieved when both spatial stencil and time delay features are incorporated within the data-driven wall modeling paradigm.

A viscous vortex model for predicting the drag reduction of riblet surfaces

This paper introduces a viscous vortex model for predicting the optimal drag reduction of riblet surfaces, eliminating the need for expensive direct numerical simulations (DNSs) or experiments. The footprint of a typical quasi-streamwise vortex, in terms of the spanwise and wall-normal velocities, is extracted from smooth-wall DNS flow fields in close proximity to the surface. The extracted velocities are then averaged and used as boundary conditions in a Stokes-flow problem, wherein riblets with various cross-sectional shapes are embedded. Here, the same smooth-wall-based boundary conditions can be used for riblets, as we observe from the DNSs that the quasi-streamwise vortices remain unmodified apart from an offset. In particular, the position of these vortices remain unpinned above small riblets. The present approach is compared with the protrusion-height model of Luchini et al. (J. Fluid Mech., vol. 228, 1991, pp. 87–109), which is also based on a Stokes calculation, but represents the vortex with only a uniform spanwise velocity boundary condition. The key novelty of the present model is the introduction of a wall-normal velocity component into the boundary condition, thus inducing transpiration at the riblet crests, which becomes relevant as the riblet size increases. Consequently, the present model allows for the drag-reduction prediction of riblets up to the optimal size. The present approach does not rely on the scale separation formally required by homogenisation techniques, which are only applicable for vanishingly small riblets.

The mean wall-normal velocity in turbulent boundary layer flows under pressure gradient

Using a combination of proper variable transformation and integral methods, we rigorously derive an analytical formulation for the mean wall-normal velocity in turbulent boundary layers (TBLs) subjected to arbitrary pressure gradients. The accuracy and robustness of this novel formulation are validated extensively through comparisons with two independent sets of numerical simulation data, demonstrating excellent agreement in both near-equilibrium and non-equilibrium TBLs. In addition, the robustness of the analytical formulations to various choices of boundary-layer edge definition is further confirmed in non-equilibrium TBLs. Our formulation includes a streamwise derivative term, which has minimal significance in near-equilibrium TBLs but plays a crucial role in determining the mean wall-normal velocity in non-equilibrium TBLs. Moreover, we investigate the physical significance of the pre-factors associated with the mean wall-normal velocity components, and unveil a close connection between a previously defined pressure gradient parameter and the ratio of these pre-factors in the analytical equation governing the mean wall-normal velocity. The insights gained from the examination of the pre-factors and their connection to the pressure gradient parameter offer valuable knowledge for interpreting and predicting the behaviour of turbulent boundary layers in various practical applications.

Improved convergence of the spectral proper orthogonal decomposition through time shifting

Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to response modes from resolvent analysis. The SPOD, coupled with the Welch method for spectral estimation, may require long time-resolved datasets. In this work, a linearised Ginzburg–Landau model is considered in order to study the method's convergence. Spectral proper orthogonal decomposition modes of the white-noise forced equation are computed and compared with corresponding response resolvent modes. The quantified error is shown to be related to the time length of Welch blocks (spectral window size) normalised by a convective time. Subsequently, an algorithm based on a temporal data shift is devised to further improve SPOD convergence and is applied to the Ginzburg–Landau system. Next, its efficacy is demonstrated in a numerical database of a boundary layer subject to bypass transition. The proposed approach achieves substantial improvement in mode convergence with smaller spectral window sizes with respect to the standard method. Furthermore, SPOD modes display growing wall-normal and spanwise velocity components along the streamwise direction, a feature which had not yet been observed and is also predicted by a global resolvent calculation. The shifting algorithm for the SPOD opens the possibility for using the method on datasets with time series of moderate duration, often produced by large simulations.

Analytic investigation of the compatibility condition and the initial evolution of a smooth velocity field for the Navier–Stokes equation in a channel configuration

A partial differential equation has usually a regular solution at the initial time if the initial condition is smooth in space, fulfills the governing equations and is compatible with the boundary condition. In the case of the Navier–Stokes equation, the initial velocity field must also be divergence–free. It is common belief that the initial condition is compatible with the boundary condition if the initial condition fulfills the boundary condition but this is not sufficient. Such a field does not necessarily fulfill the full compatibility condition of the Navier–Stokes equation. If the condition is violated, the solution is not regular at the initial time (). This issue has been known for a while but not in the full breadth of the engineering fluid dynamics community. In this paper, a practical calculation method is presented for checking the compatibility condition. Furthermore, a smooth initial condition is presented in a periodic channel flow that violates the compatibility condition and has therefore no smooth solution at the initial instant. The calculations were performed in an analytical framework. The results for a channel configuration show that in the absence of wall–normal velocity the condition is always fulfilled and the problem has a regular solution. If the wall–normal velocity component is non-zero, the condition is usually not fulfilled but exceptional cases, fulfilling the compatibility condition can be generated with optimization methods. The generation procedure of such a field is useful to provide correct initial conditions for such time-dependent numerical flow simulations, where the very first instances are important from an engineering point of view. The presented methods can provide insight about the applicability of the chosen initial conditions.

Control effects on coherent structures in a non-uniform adverse-pressure-gradient boundary layer

We examine the effects of three basic but effective control strategies, namely uniform blowing, uniform suction, and body-force damping, on the intense Reynolds-stress events in the turbulent boundary layer (TBL) developing on the suction side of a NACA4412 airfoil. This flow is subjected to a non-uniform adverse pressure gradient (APG), which substantially modifies its turbulence statistics with respect to a zero-pressure-gradient (ZPG) boundary layer, and it also changes how control strategies affect the flow. The strong APG results in intense events that are shorter and more often detached from the wall than in ZPG TBLs. In a quadrant analysis, ejections remain the most relevant structures, but sweeps become more important than in ZPG TBLs, a fact that results in a lower contribution to the wall-normal velocity from intense Reynolds-stress events. Control effects are relatively less important on intense events than on the turbulent statistics. Uniform blowing has an impact similar to that of an even more intense APG, while uniform suction has more complex effects, most likely due to the particular behavior of the wall-normal velocity component near the wall. Body-force damping also reduces the probability of occurrence of very-large attached structures and that of intense events in the proximity of the actuation region. Our results show that intense Reynolds-stress events are robust features of the flow. If control strategies do not target directly these structures, their effects on the strong events is less pronounced than the effects on the mean flow.

Enhanced outer peaks in turbulent boundary layer using uniform blowing at moderate Reynolds number

Uniform blowing through a permeable surface acts as an active flow control method in wall bounded flows. Such control technique was investigated in a zero pressure gradient turbulent boundary layer over a flat plate. Measurement data were obtained with the help of Laser Doppler Anemometry technique. Besides the drag reduction characteristics of such flow control method, time averaged measurement of stream-wise and wall-normal velocity components was taken at Reynolds number based on momentum thickness () of 1100–3670. Due to the difference in surface condition with and without blowing, mean properties of the boundary condition at wall influence the flow properties when scaled with outer scaling properties. Enhanced turbulence is observed in Reynolds stresses using statistical analysis including the thickening of the boundary layer.

The Wake Structure of a Stationary and a Rotary Wall-Mounted Low-Aspect-Ratio Cylinder

This paper investigates the wake structure of a low-aspect-ratio rotating cylinder mounted wall-normal to a flat plate at a diameter-based Reynolds number of . The cylinder is driven at a constant rotational rate about its respective axial coordinate. Four nondimensional rotation rates were selected: 0.5, 1, 2, and 3, representing rates based on the static cylinder’s natural shedding frequency and corresponding harmonics. Two aspect ratios were investigated: i) and ii) . The case of represents a cylinder height equal to the local boundary-layer thickness. Both streamwise and cross-stream (transverse) particle image velocimetry (PIV) planes are presented, and the resulting time-averaged flowfield is examined. Results for the rotating cylinder reveal the development of a dominant streamwise vortex that persists for several length scales downstream of the cylinder. Accompanying the streamwise vortex formation is an enhancement in the wall-normal velocity component (downwash) behind the rotating cylinder. Additionally, the maximum downwash occurs immediately behind the rotating cylinder near 0.27 diameters downstream in contradistinction to a stationary cylinder with peak downwash near 2–3 diameters. The maximum downwash, being in line with the formation of the dominant streamwise vortex, shortens the recirculation region in the cylinder’s wake, thus shifting the plate reattachment point further upstream. In the case of , where the cylinder is submerged within the boundary layer, although the length of the recirculation region reflected by the mean flow is lengthened by the rotary motion, the maximum downwash for the rotating cylinder is enhanced by a factor of 10 from that of the maximum downwash experienced by a static counterpart.

The influence of wall heating on turbulent boundary layer characteristics during mixed convection

An investigation on the modification of turbulent boundary layer characteristics by wall heating was conducted on the mixed convection turbulent boundary layer flow. The multi-plane particle image velocimetry (PIV) technique was used to characterize turbulent boundary layer dynamics. Experiments were performed over a range of mixed convection flow conditions, quantified by the Richardson number (Ri), from inertia dominant flow (RiL=0.01) to buoyancy-influenced flow (RiL=0.3). The implemented PIV technique produced multiple two-dimensional velocity fields from two orthogonal planes with respect to the mean-flow direction. From the computed velocity fields, the low-order turbulent statistics were computed where a significant modification to the wall normal stress was observed. The cause of this modification was investigated via the probability density function (PDF) of the turbulent wall-normal velocity component (v'). Results show that the PDF of v' is multi-modal in the presence of wall heating, demonstrating that the buoyancy-driven phenomena influence the turbulent boundary layer flow via intermittent bursting and rising of thermals through the boundary layer.

DNS Of entropy generation rates for turbulent flows subjected to high temperature gradients

Direct Numerical Simulations are performed to analyze the influence of key boundary conditions and flow characteristics on entropy generation rate statistics in a highly anisothermal forced convective turbulent channel flow of a thermo-dependent fluid submitted to asymmetrical heating. Each parameter is varied separately to quantify its influence compared to a reference simulation, the hot to cold wall temperature ratio from 1.5 to 3, the mean friction Reynolds number from 150 to 210, the mean thermodynamic pressure from 1bar to 3bar. Two thermal boundary condition types are also compared (fixed temperatures vs. fixed heat flux density at the walls). For each parameter that is varied, the evolution of the entropy generation rate mean, root-mean-square and correlations with the temperature and the streamwise or wall-normal velocity components are presented and discussed. All simulations have in common the thermal asymmetry and the highly non-isothermal nature of the flow: beyond the changes induced by the variation of each parameter, the common characteristics of the statistical quantity profiles are also analyzed. This work establishes how the spatial distribution of the local entropy generation rate is modified by the parameters studied, in which direction and with which sensitivity. It demonstrates the significant influence of the thermal boundary condition type on the entropy generation rate fluctuations near the walls.

Transpired turbulent boundary layers: a general strategy for RANS turbulence models

ABSTRACTTranspired boundary layers are of major interest for many industrial applications. Although well described, there is no turbulence model specifically dedicated to the prediction of boundary layers for both blowing and suction configurations. Revisiting closure relations of turbulence models, a general strategy was established to recover Stevenson's law of the wall that described the behaviour of transpired boundary layers in the wall region. The methodology is applied to the SST turbulence model and compared to Wilcox's correction, only applicable to blowing cases. A version of the proposed correction, more suited to RANS solvers, was also derived. Several experimental boundary layer configurations with blowing or suction were computed using both versions of the correction. The good agreements observed on all cases prove the relevance and the efficiency of the present strategy.Abbreviations: l: mixing length; u: longitudinal velocity component; v: wall-normalvelocity component; : longitudinal velocity fluctuation; : wall-normal velocityfluctuation; x: longitudinal direction; y: wall-normal direction; k: turbulent kineticenergy; ω: specific dissipation; : displacement thickness; τ: shear stress; ρ: density; ν: kinematic viscosity; : eddy viscosity; μ: dynamic viscosity; κ: Kàrmàn constant; :superscript for dimensionless wall quantities; : subscript for quantities at the wall; :Reynolds average

Characterization of the Spatio-Temporal Response of a Turbulent Boundary Layer to Dynamic Roughness

The spatio-temporal response of a smooth-wall turbulent boundary layer to two-dimensional dynamic roughness forcing was investigated using flow structure-resolved particle image velocimetry. While such a flow has been extensively studied through pointwise temporal measurements, we characterize the streamwise-spatial nature of the streamwise and wall-normal velocity components of the synthetic mode excited by the roughness, which had not been previously fully characterized. Investigation of the spanwise variation of the response confirms a broad extent of two-dimensional characteristics in the streamwise and spanwise directions. Spatial amplitude modulation is observed in the synthetic structure and investigated directly through the spatial spectra. A parametric study of the influences of forcing frequency (and roughness height) leads to an empirical relationship between input frequency and resultant streamwise spatial lengthscale, which is proposed to extend the usefulness of dynamic roughness as a well-characterized input by which to probe the structure and dynamics of wall turbulence. In turn, dynamic roughness forcing may be used to study the response of complex fluid systems to these deterministic structures and explore the efficacy of possible flow control strategies in a directed manner.

Spatial Variation of Statistical and Spectral Properties of the Stream Wise and Wall-Normal Velocity Fluctuations in the Near-Neutral Atmospheric Surface Layer

Based on high-quality near-neutral atmospheric-surface-layer (ASL) data obtained from an observational site located in flat desert and existing experimental results for a friction Reynolds number Reτ 106, the change of the second-order statistics of the streamwise velocity component with height is consistent with the experimental results for Reτ < 106, while the second-order statistics of the wall-normal velocity component increase linearly with height. In combination with the experimental results for Reτ < 106, the variation of the slope of streamwise turbulence intensity with height and the variation of the slope and intercept of the wall-normal turbulence intensity with height are quantified to reveal that both the streamwise and wall-normal velocity variances follow a generalized logarithmic law, with the distribution of the streamwise and wall-normal velocity components satisfying sub- and super-Gaussian distributions. Spectral analysis shows that the variation of the wavenumber corresponding to the pre-multiplied streamwise and wall-normal spectra peaks with the ratio z/δ obeys the form $$ k_{x} \delta = a(\delta /z)^{b} $$ , where z is the height, kx is the streamwise wavenumber, and δ is the ASL thickness. For the pre-multiplied streamwise spectra, $$ b = 0.5 \pm 0.1 $$ and the value of a may have a Reynolds-number dependence, while for the pre-multiplied wall-normal spectra, $$ a = 2.2 \pm 0.09 $$ and $$ b = 1.0 \pm 0.1 $$ . The von Karman constant, the Townsend–Perry constant and other parameters also display a weak Reynolds-number dependence.

Algebraic non-equilibrium wall-stress modeling for large eddy simulation based on analytical integration of the thin boundary-layer equation

An algebraic nonequilibrium wall-stress model for large eddy simulation is discussed. The ordinary differential equation (ODE) derived from the thin-layer approximated momentum equation, including the temporal, convection, and pressure gradient terms, is considered to form the wall-stress model. Based on the concept of the analytical wall function (AWF) for Reynolds-averaged turbulence models, the profile of the subgrid scale (SGS) eddy viscosity inside the wall-adjacent cells is modeled as a two-segment piecewise linear variations. This simplification makes it possible to analytically integrate the ODE near the wall to algebraically give the wall shear stress as the wall boundary condition for the momentum equation. By applying such integration to the wall-normal velocity component, the methodology to avoid the log-layer mismatch is also presented. Coupled with the standard Smagorinsky model, the proposed SGS-AWF shows good performance in turbulent channel flows at Reτ = 1000–5000 irrespective of the grid resolutions. This SGS-AWF is also confirmed to be superior to the traditional equilibrium wall-stress model in a turbulent backward-facing step flow.

Large-scale turbulence structures in a laboratory-scale boundary layer under steady and gusty wind inflows

Experiments on turbulence structures and features of a wind field under steady inflow and gusty wind inflows were implemented in a straight-through wind tunnel. Streamwise and wall-normal velocity components were measured using a streamline constant temperature anemometer (streamline CTA). Power spectra analyses revealed the existence of very large-scale motions (VLSMs) under both steady and gusty wind inflows; but new gusty scale motions (GSMs) were revealed under only gusty wind inflows. The GSMs might originate from an ordered external driving force that forces hairpin packets to align coherently in groups with a length scale related to the gust inflow condition. The streamwise wavelength of VLSMs is independent of inflow conditions, while the turbulent energy of VLSMs is associated with the wall-normal height and local mean streamwise velocity. In particular, the streamwise wavelength of GSMs increases linearly with the average value and period of sinusoidal gusty wind inflows, and the turbulent energy of GSMs is sensitive to the wall-normal height and all characteristic parameters of gusty wind inflows, including the average value, amplitude and period. Considerable wall-normal airflows induced by gusty wind inflows were detected and these are negatively correlated with the variation in gusty streamwise velocity, and root mean square (RMS) values of the gusty wall-normal velocity tended to increase linearly with the average value and amplitude of gusty wind inflows.

Measurements of the wall-shear stress distribution in turbulent channel flow using the micro-pillar shear stress sensor MPS3

This study investigates the wall-shear stress (WSS) distribution in turbulent channel flow at friction Reynolds numbers of Reτ=860 and 1300 using the micro-pillar shear-stress sensor (MPS3). The probability density functions and the joint probability density functions of the wall-shear stress vectors indicate that the intermittency of the flow increases for higher Reynolds numbers. Extreme events occurring at the wall, such as wall-normal velocity spikes and backflow events, are detected and analyzed based on the wall-shear stress patterns. The events representing the wall-normal spikes are conditionally sampled from the wall-normal velocity component, which is determined from the local wall-shear stress gradients. The results show that the negative velocity spikes tend to co-occur with strong streamwise wall-shear stress motions, and that the positive spikes are likely to accompany large spanwise motions. Rare backflow events are detected from the wall-shear stressdistribution for both Reynolds numbers, serving as an experimental evidence of near-wall flow reversal events in turbulent channel flow. The diameter of the detected backflow region is approximately 20 viscous units. The data confirm the results from previous numerical studies. The wall-normal velocity spikes and the backflow events are likely to be three-dimensional, suggesting an energy and momentum transfer between the viscous sublayer and the outer part of the turbulent channel flow.

Flow separation control over a rounded ramp with spanwise alternating wall actuation

An implicit large-eddy simulation is carried out to study turbulent boundary-layer separation from a backward-facing rounded ramp with active wall actuation control. This method, called spanwise alternating distributed strips control, is imposed onto the flat plate surface upstream of a rounded ramp by alternatively applying out-of-phase control and in-phase control to the wall-normal velocity component in the spanwise direction. As a result, the local turbulence intensity is alternatively suppressed and enhanced, leading to the creation of vertical shear-layers, which is responsible for the presence of large-scale streamwise vortices. These vortices exert a predominant influence on the suppression of the flow separation. The interaction between the large-scale vortices and the downstream recirculation zone and free shear-layer is studied by examining flow statistics. It is found that in comparison with the non-controlled case, the flow separation is delayed, the reattachment point is shifted upstream, and the length of the mean recirculation zone is reduced up to 8.49%. The optimal control case is achieved with narrow in-phase control strips. An in-depth analysis shows that the delay of the flow separation is attributed to the activation of the near-wall turbulence by the in-phase control strips and the improvement of the reattachment location is mainly due to the large-scale streamwise vortices, which enhance the momentum transport between the main flow and separated region.

Phase evolution of terms of turbulent kinetic energy transport equation in the boundary layer of a pulsating flow

Experimental data on production, dissipation, turbulent and molecular diffusion of turbulent energy have been obtained in the boundary layer of flow with forced freestream velocity fluctuations. The evolution of these terms over the pulsation phase is presented for streamwise and wall-normal velocity components. The presented results have been obtained on the basis of the dynamics of vector fields measured using a new optical SIV method with a spatial resolution comparable to the Kolmogorov scale.

Spatial characterization of turbulent channel flow via complex networks.

A network-based analysis of a turbulent channel flow numerically solved at Re_{τ}=180 is proposed as an innovative perspective for the spatial characterization of the flow field. Two spatial networks corresponding to the streamwise and wall-normal velocity components are built, where nodes represent portions of volume of the physical domain. For each network, links are active if the correlation coefficient of the corresponding velocity component between pairs of nodes is sufficiently high, thus unveiling the strongest kinematic relations. Several network measures are studied in order to explore the interrelations between nodes and their neighbors. Specifically, long-range links are localized between near-wall regions and associated with the temporal persistence of coherent patterns, namely high and low speed streaks. Furthermore, long-range links play a crucial role as intermediary for the kinematic information flow, as emerges from the analysis of indirect connections between nodes. The proposed approach provides a framework to investigate spatial structures of the turbulent dynamics, showing the full potential of complex networks. Although the network analysis is based on the two-point correlation, it is able to advance the level of information, by exploiting the texture created by active links in all directions. Based on the observed findings, the current approach can pave the way for an enhanced spatial interpretation of the turbulence dynamics.

Wall-based identification of coherent structures in wall-bounded turbulence

During the last decades, a number of reduced order models based on coherent structures have been proposed to describe wall-bounded turbulence. Many of these models emphasize the importance of coherent wall-normal velocity eddies (ν-eddies), which drive the generation of the very long streamwise velocity structures observed in the logarithmic and outer region. In order to use these models to improve our ability to control wall-bounded turbulence in realistic applications, these ν-eddies need to be identified from the wall in a non-intrusive way. In this paper, the possibility of using the pressure signal at the wall to identify these ν-eddies is explored, analyzing the cross-correlation between the wall-normal velocity component and the pressure fluctuations at the wall in a DNS of a turbulent channel flow at Reτ = 939. The results show that the cross-correlation has a region of negative correlation upstream, and a region of positive correlation backwards. In the spanwise direction the correlation decays monotonously, except very close to the wall where a change of sign of the correlation coefficient is observed. Moreover, filtering the pressure fluctuations at the wall in space results in an increase of the region where the cross-correlation is strong, both for the positively and the negatively correlated regions. The use of a time filter for the pressure fluctuations at the wall yields different results, displacing the regions of strong correlation without changing much their sizes. The results suggest that space-filtering the pressure at the wall is a feasible way to identify ν-eddies of different sizes, which could be used to trigger turbulent control strategies.