Zero-pressure Gradient Boundary Layer Research Articles

Role of streak secondary instabilities on free-stream turbulence-induced transition

We study the stability of a zero-pressure gradient boundary layer subjected to free-stream disturbances by means of local stability analysis. The dataset under study corresponds to a direct numerical simulation (DNS) of a flat plate with a sharp leading edge in realistic wind tunnel conditions, with a turbulence level of 3.45 % at the leading edge. We present a method to track the convective evolution of the secondary instabilities of streaks by performing sequential stability calculations following the wave packet, connecting successive unstable eigenfunctions. A scattered nature, in time and space, of secondary instabilities is seen in the stability calculations. These instabilities can be detected before they reach finite amplitude in the DNS, preceding the nucleation of turbulent spots, and whose appearance is well correlated to the transition onset. This represents further evidence regarding the relevance of secondary instabilities of streaks in the bypass transition in realistic flow conditions. Consistent with the spatio-temporal nature of this problem, our approach allows us to integrate directly the local growth rates to obtain the spatial amplification ratio of the individual instabilities, where it is shown that instabilities reaching an $N$ -factor in the range [2.5,4] can be directly correlated to more than 65 % of the nucleation events. Interestingly, it is found that high amplification is not only attained by modes with high growth rates, but also by instabilities with sustained low growth rates for a long time.

Investigation of non-ideal effects in compressible boundary layers of dense vapors through direct numerical simulations

In this work, we present an investigation about the sources of dissipation in adiabatic boundary layers of non-ideal compressible fluid flows. Direct numerical simulations (DNS) of transitional, zero-pressure gradient boundary layer flows are performed for two fluids characterized by different complexity of the fluid molecules, namely, “air” and siloxane MM. Different sets of thermodynamic free-stream boundary conditions are selected to evaluate the influence of the fluid state on both the frictional loss and the dissipation mechanisms. The thermophysical properties of siloxane MM are calculated with a state-of-the-art equation of state. Results show that the dissipation due to both time-mean strain field, irreversible heat transfer, and turbulent dissipation differs significantly depending on both the molecular complexity of the fluid and its thermodynamic state. The dissipation coefficient calculated from the DNS results is then compared against the one obtained using a reduced-order model (ROM), which solves the two-dimensional boundary layer flow equations for an arbitrary fluid [M. Pini and C. De Servi, “Entropy generation in laminar boundary layers of non-ideal fluid flows,” in 2nd International Seminar on Non-Ideal Compressible Fluid Dynamics for Propulsion and Power (Springer, 2020), pp. 104–117]. Results from both the DNS and the ROM show that low values of the overall dissipation are observed in the case of fluids made of simple molecules, e.g., air, and if the fluid is at a thermodynamic state in the proximity of that of the vapor–liquid critical point.

Effect of free-stream turbulence properties on different transition routes for a zero-pressure gradient boundary layer

The natural and bypass routes to boundary-layer transition to turbulence are traditionally investigated independently in fluid mechanics applications. Nevertheless, in certain flow regimes both mechanisms could coexist and interact. In this work, large-eddy simulations (LES) were performed for a zero-pressure gradient boundary layer developing over a flat plate to investigate the transition mechanism for variable free-stream turbulent properties. Four different combinations of turbulence intensity and integral length scale were analyzed, and two main transition mechanisms were observed. High free-stream turbulence intensity instigates pure bypass transition through the amplification of a continuous Orr–Sommerfeld (O–S) mode that breaks down after secondary instability. Instead, at low free-stream turbulence intensity, discrete and continuous O–S modes interact and are both involved in the transition process. Visual inspection of the LES snapshots provides a detailed insight in Tollmien–Schlichting (TS) waves–streaks mutual interaction and clearly identifies two main mechanisms involved in turbulence breakdown. On one hand, TS waves trigger varicose instability of streaky structures. On the other hand, streaks cause secondary instability of TS waves with emerging Λ-structure formation. Then, dynamic mode decomposition (DMD) is applied to extract the main stability properties for both types of transition route and to highlight coherent structure dynamics, which is hardly observable in the literature. Specifically, for low-medium free-stream turbulence levels, DMD extracts unstable modes clearly related to streaks–TS waves interaction and leading to the formation of Λ structures. Therefore, the streaks–TS waves interaction is proved to be destabilizing and to trigger secondary instability leading to turbulence breakdown.

A DDES Model with Subgrid-scale Eddy Viscosity for Turbulent Flow

The original (delayed) detached-eddy simulation ((D)DES), a widely used and efficient hybrid turbulence method, is confronted with some flaws containing grid-induced separation (GIS), log-layer mismatch (LLM), and slow RANS-LES transition. A novel hybrid turbulence model, namely production-limited eddy simulation (PLES), depleting the production through introducing the subarid-scale eddy viscosity is proposed. The simulation data of the zero-pressure gradient boundary layer proves that a good performance in mitigating the GIS issue is obtained from the PLES model. The results of the channel flows reveal that the PLES model has eliminated the LLM of the velocity. A good conformity is given for the backward-facing step flow in the PLES simulation, which proves that the PLES model is validated for complex flow. More turbulent scales in the shear layer are captured by the PLES model, which testifies that the PLES model has a faster RANS/LES switch than the IDDES model. The PLES model has a good performance in predicting the cylinder flow with coarser grid resolution. Due to the new LES mode, the PLES model behaves better than the IDDES model in simulating the cylinder flow. Furthermore, the PLES model allows one to use different LES model in the LES portion for other complex flows.

Exact Eddy-Viscosity Equation for Turbulent Wall Flows—Implications for Computational Fluid Dynamics Models

For turbulent channel flow, pipe flow, and zero-pressure gradient boundary layer, Heinz yielded recently analytical formulas for the eddy viscosity as a product of a function of (the wall-normal distance scaled in inner units) and a function of (the same scaled in outer units). By calculating the eddy-viscosity turbulent diffusion term, an exact high-Reynolds-number equation with one production and two dissipation terms is constructed for those flows. One dissipation term is universal, peaks near the wall, and scales mainly with . The second, smaller one, is flow dependent, peaks in the wake, and scales mainly with . The production term is flow dependent, peaks in between, and scales similarly. The universal dissipation term implies a length scale analogous to the von Karman length scale used in the scale-adaptive simulation models of Menter. This length scale also appears in the production term. This confirms the relevance of these length scales. An asymptotic analysis of all terms in the budget in the limit of infinite Reynolds numbers is provided. This yields a test bench of existing Reynolds-averaged Navier–Stokes models with a similar equation. It is shown that some models, e.g., the one of Spalart and Allmaras, do not respect the flow physics: they display a production peak in the near-wall region. The most promising model, a scale-adaptive simulation model, is modified. As a step forward toward a solution to the wall damping problem, the equation of our model behaves much more correctly in the near-wall region.

Integral measures of the zero pressure gradient boundary layer over the Reynolds number range ≤Rτ<∞

A recently developed mixing length model of the turbulent shearing stress has been shown to generate a universal velocity profile that provides an accurate approximation to incompressible pipe flow velocity profiles over a wide Reynolds number range [B. J. Cantwell, “A universal velocity profile for smooth wall pipe flow,” J. Fluid Mech. 878, 834–874 (2019)]. More recently, the same profile was shown to accurately approximate velocity profiles in channel flow, the zero pressure gradient boundary layer, and the boundary layer in an adverse pressure gradient [M. A. Subrahmanyam, B. J. Cantwell, and J. J. Alonso, “A universal velocity profile for turbulent wall flows,” AIAA Paper No. 2021-0061, 2021 and M. A. Subrahmanyam, B. J. Cantwell, and J. J. Alonso, “A universal velocity profile for turbulent wall flows including adverse pressure gradient boundary layers,” J. Fluid Mech. (unpublished) (2021)] The universal velocity profile is uniformly valid from the wall to the free stream at all Reynolds numbers from zero to infinity. At a low Reynolds number, the profile approaches the laminar channel/pipe flow limit. The primary measure of the Reynolds number used in this work is the friction Reynolds number Rτ=uτδ/ν. It is a little unusual to use Rτ for the boundary layer since it requires that the velocity profile be cutoff using an arbitrarily defined overall boundary layer thickness, δ. Because of the slow approach of the velocity to the free stream, different conventions used to define the thickness lead to different values of Rτ assigned to a given flow. It will be shown in this paper that, through its connection to channel/pipe flow, the universal velocity profile can be used to define a practically useful, unambiguous, measure of overall boundary layer thickness, called here the equivalent channel half height, δh. For Rτ>≈5000, the universal velocity profile defines a Reynolds number independent shape function that can be used to generate explicit expressions for the infinite Reynolds number behavior of all the usual integral boundary layer measures; displacement thickness, momentum thickness, energy thickness, overall boundary layer thickness, and skin friction. The friction coefficient Cf(Rδ2) generated by the universal velocity profile accurately approximates data over a wide range of momentum thickness Reynolds numbers collected by Nagib et al. [“Can we ever rely on results from wall-bounded turbulent flows without direct measurements of wall shear stress?,” AIAA Paper No. 2004-2392, 2004]. The universal velocity profile is used to integrate the von Kaŕmań boundary layer integral equation [T. von Kármán, “Uber laminaire und turbulente reibung,” Z. Angew. Math. Mech. 1, 233–252 (1921)] in order to generate the various thicknesses and friction velocity as functions of the spatial Reynolds number, Rx=uex/ν.

General method for determining the boundary layer thickness in nonequilibrium flows

While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general non-equilibrium flows. In this work, a method is developed based on a local reconstruction of the "inviscid" velocity profile $U_I[y]$ resulting from the application of the Bernoulli equation in the wall-normal direction. The boundary-layer thickness $\delta_{99}$ is then defined as the location where $U/U_I = 0.99$, which is consistent with its classical definition for the zero-pressure-gradient boundary layers (ZPGBLs). The proposed local-reconstruction method is parameter free and can be deployed for both internal and external flows without resorting to an iterative procedure, numerical integration, or numerical differentiation. The superior performance of the local-reconstruction method over various existing methods is demonstrated by applying the methods to laminar and turbulent boundary layers and two flows over airfoils. Numerical experiments reveal that the local-reconstruction method is more accurate and more robust than existing methods, and it is applicable for flows over a wide range of Reynolds numbers.

Tracking disturbances in transitional and turbulent flows: Coherent structures

Tracking transitional and turbulent flows requires methods other than the classical techniques, which capture coherent structures via locating pressure minima, after the disturbance field has evolved to late-transitional and turbulent flow stages. Keeping it in mind, transition to turbulence of zero pressure gradient flow is studied, following two routes of excitation, by solving the three-dimensional Navier-Stokes equation in derived variable formulation, with vorticity as one of the dependent variables. For such flows, disturbance structures should be traced from the receptivity to the coherent structure stage for the fully developed turbulent flow. The coherent structures in turbulent flows are identified by the Q- and λ2-criteria, based on the occurrence of pressure minima at the vortex cores. In the proposed study here, the zero pressure gradient boundary layer is excited (i) at the wall with a monochromatic source and (ii) causing transition to turbulence, by a convecting vortex in the free stream. The main aim here is to trace the incipient disturbances from the onset to the turbulent state in terms of physical quantities, such as the disturbance mechanical energy introduced by Sengupta et al. [“Vortex-induced instability of an incompressible wall-bounded shear layer,” J. Fluid Mech. 493, 277–286 (2003)] and disturbance enstrophy transport equation, as proposed by Sengupta et al. [“An enstrophy-based linear and nonlinear receptivity theory,” Phys. Fluids 30(5), 054106 (2018)]. Such methods are capable of tracing disturbance structures from the onset to the evolved stage. We compare these methods with Q- and λ2-criteria to trace disturbance evolution.

Large-scale motions in a plane wall jet

The plane wall jet (PWJ) is a wall-bounded flow in which a wall shear layer develops in the presence of extremely energetic flow structures of the outer free-shear layer. The structure of a PWJ, developing in still air, was studied with the focus on the large scales in the flow. Wall-normal hot-wire anemometry (HWA) measurements along with double-frame particle image velocimetry (PIV) measurements (wall-normal–streamwise plane) were carried out at streamwise distances up to $162b$, where $b$ is the slot width of the PWJ exit. The nominal PWJ Reynolds number based on exit parameters was $Re_{j}\approx 5940$. Comparisons with a zero-pressure-gradient boundary layer (ZPGBL) at nominally matched friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ were also carried out as appropriate, to highlight key features of the PWJ structure. Consistent with previous work, the PWJ showed a dependence of the peak turbulent stresses on the jet exit Reynolds number. The turbulent production showed a peak corresponding to the near-wall cycle similar to the peak seen in the ZPGBL. However, another turbulent production peak was observed in the outer free-shear layer that was an order of magnitude larger than the inner one. Along with the change in sign of the viscous and Reynolds shear stresses, the PWJ was shown to have a region of very low turbulent production between these two peaks. The dissipation rate increased over the PWJ layer with a peak also in the outer region. Visualizations of the flow and two-point correlations reveal that the most energetic large-scale structures within a PWJ are vortical motions in the wall-normal–streamwise plane similar to those structures seen in free-shear layers. These structures are referred to as J (for jet) type structures. In addition two-point correlations reveal the existence of large-scale structures in the wall region which have a signature similar to those structures seen in canonical boundary layers. These structures are referred to as W (for wall) type structures. Instantaneous PIV realizations and flow visualizations reveal that these W type large-scale features are consistent with the paradigm of hairpin vortex packets in the wall region. The J type structures were seen to intrude well into the wall region while the W type structures were also seen to extend into the outer shear layer. Further, these large-scale structures were shown to modulate the amplitude of the finer scales of the flow.

Is Tollmien-Schlichting wave necessary for transition of zero pressure gradient boundary layer flow?

Comprehensive understanding of the routes of instability and transition for many flows is not complete yet. For a zero pressure gradient (ZPG) boundary layer, linear spatial theory predicted Tollmien-Schlichting (TS) waves, which have been experimentally verified by vortically exciting the flow by a monochromatic source. This is the well-known frequency response of dynamical system theory. Natural transition in real flows occurs due to polychromatic excitation, and to simulate such transition, the ZPG boundary layer has been excited via an impulse response in some of our recent direct numerical simulations. Such impulse responses cause transition even when TS waves are not excited. In the present exercise, we show the theoretical basis of natural transition by spatiotemporal stability analysis, as used in the work of Sengupta et al. [“Spatiotemporal growing wave fronts in spatially stable boundary layers,” Phys. Rev. Lett. 96(22), 224504 (2006)], by invoking finite start-up of the frequency response to wall excitation. There appear to be different instability mechanisms active for the frequency and the impulse responses to localized wall excitation. Here, we show that in both the frequency and impulse responses, the spatiotemporal wave-front (STWF) is the common element. Additionally, we also consider cases, where following different start-ups, the wall excitation remains constant, which also show the presence of the STWF. The presented results for the ZPG boundary layer show that the TS wave is not necessary for transition to turbulence and help us to re-evaluate our understanding of the transition mechanism for this canonical flow.

The three-dimensional impulse response of a boundary layer to different types of wall excitation

Here we report a study of the physical mechanism behind the creation of perturbation of a boundary layer by direct numerical simulation (DNS) of an incompressible Navier-Stokes equation (NSE) that leads to eventual three-dimensional (3D) transition. By considering two different types of impulsive wall-excitations which are similar to dip-slip and strike-slip events in the seismological terminology for a zero pressure gradient (ZPG) boundary layer, we show that initial events and the evolution of the resultant wave-packet bear a close resemblance with the physical mechanism for the creation of tsunamis. This is due to the significant differences in the characteristics and dynamics of the wall-bounded and oceanic boundary layer at deep-ocean. Here we particularly seek out the impulse response of a ZPG boundary layer as demonstrated recently in the work of S. Bhaumik and T. K. Sengupta [“Impulse response and spatio-temporal wave-packets: The common feature of rogue waves, tsunami, and transition to turbulence,” Phys. Fluids 29, 124103 (2017)], by considering a specific boundary motion similar to dip-slip events for the creation of tsunamis. The precursor of flow transition, noted as the spatiotemporal wave front, has been shown to be very effectively created by the dip-slip type of boundary motion, first reported in the work of Sengupta et al. [“Spatiotemporal growing wave-fronts in spatially stable boundary layers,” Phys. Rev. Lett. 96, 224504 (2006)], from both linear and nonlinear analyses of NSE. In this study, receptivity of the boundary layer to these two types of subduction motions is contrasted. This is performed for the first time using 3D DNS of NSE. It is shown that the dip-slip event displays stronger receptivity than the strike-slip event.

Impulse response and spatio-temporal wave-packets: The common feature of rogue waves, tsunami, and transition to turbulence

Here, we present the impulse response of the canonical zero pressure gradient boundary layer from the dynamical system approach. The fundamental physical mechanism of the impulse response is in creation of a spatio-temporal wave-front (STWF) by a localized, time-impulsive wall excitation of the boundary layer. The present research is undertaken to explain the unit process of diverse phenomena in geophysical fluid flows and basic hydrodynamics. Creation of a tsunami has been attributed to localized events in the ocean-bed caused by earthquakes, landslides, or volcanic eruptions, whose manifestation is in the run up to the coast by surface waves of massive amplitude but of very finite fetch. Similarly rogue waves have often been noted; a coherent account of the same is yet to appear, although some explanations have been proposed. Our studies in both two- and three-dimensional frameworks in Sengupta and Bhaumik [“Onset of turbulence from the receptivity stage of fluid flows,” Phys. Rev. Lett. 107(15), 154501 (2011)] and Bhaumik and Sengupta [“Precursor of transition to turbulence: Spatiotemporal wave front,” Phys. Rev. E 89(4), 043018 (2014)] have shown that the STWF provides the central role for causing transition to turbulence by reproducing carefully conducted transition experiments. Here, we furthermore relax the condition of time behavior and use a Dirac-delta wall excitation for the impulse response. The present approach is not based on any simplification of the governing Navier-Stokes equation (NSE), which is unlike solving a nonlinear shallow water equation and/or nonlinear Schrödinger equation. The full nonlinear Navier-Stokes equation (NSE) is solved here using high accuracy dispersion relation preserving numerical schemes and using appropriate formulation of the NSE which minimizes error. The adopted numerical methods and formulation have been extensively validated with respect to various external and internal 2D and 3D flow problems. We also present results from the Orr-Sommerfeld equation to show that the origin of the STWF is via a linear mechanism. Nonlinearity and nonparallelism play the central role in causing these phenomena of geophysics and transition to turbulence.

A consistent steady state CFD simulation method for stratified atmospheric boundary layer flows

An effective methodology for CFD simulations of stratified atmospheric boundary layer flows is presented, based on the Poiseuille-type zero pressure gradient boundary layer. The concept of precursor inflow generation is applied in the scope of Reynolds Averaging Navier-Stokes (RANS) simulations, and combined with mean temperature control via explicit global heat correction in the energy equation. We thus obtain solutions that are fully consistent with the equation system in a one-dimensional computational domain, which then serve as inlet profiles for the three-dimensional calculation.The resulting inflow profiles are furthermore utilized for turbulence model validation and the calibration of the modeling parameters. This yields an extension of the standard k-ε turbulence model, incorporating buoyancy induced turbulence production and dissipation terms. Additionally, modified turbulent wall functions are applied, which consistently model wall roughness and heat transfer, in agreement with the similarity law. We demonstrate that the obtained turbulence model reproduces the expected analytical profiles from the Monin-Obukhov similarity theory, and also that the representation of turbulent kinetic energy shows a realistic evolution over a wide range of stratification parameters.The presented method is then applied to study flow over inhomogeneous surfaces, among others a cosine shaped hill and ridge, where lee wave patterns are observed in the expected range of Obukhov lengths. The final validation demonstrates quantitatively good agreement of the simulation results at a complex on-shore site in Germany with data from a 200 m met mast.

Receptivity to Harmonic Excitation Following Nonimpulsive Start for Boundary-Layer Flows

It has been shown in recent times that transition to turbulence occurs following two- and three-dimensional routes primarily by what is called the spatiotemporal wave front, for the canonical problem of a zero-pressure gradient boundary layer excited harmonically at the wall following an impulsive start. This paper shows that this onset process of disturbance growth continues also for a varying range of nonimpulsive wall excitation onset that is switched on smoothly. This is important because this will dispel any idea that a spatiotemporal wave front is totally due to impulsive start of wall excitation. This paper distinguishes between high- and low-frequency excitation cases to follow qualitatively different transition routes.

On the accuracy of RANS simulations with DNS data.

Simulation results conducted for incompressible planar wall-bounded turbulent flows with the Reynolds-Averaged Navier-Stokes (RANS) equations with no modeling involved are presented. Instead, all terms but the molecular diffusion are represented by the data from direct numerical simulation (DNS). In simulations, the transport equations for velocity moments through the second order (and the fourth order where the data are available) are solved in a zero-pressure gradient boundary layer over a flat plate and in a fully-developed channel flow in a wide range of Reynolds numbers using DNS data from Sillero et al. (2013), Lee & Moser (2015), and Jeyapaul et al. (2015). The results obtained demonstrate that DNS data are the significant and dominant source of uncertainty in such simulations (hereafter, RANS-DNS simulations). Effects of the Reynolds number, flow geometry, and the velocity moment order as well as an uncertainty quantification technique used to collect the DNS data on the results of RANS-DNS simulations are analyzed. New criteria for uncertainty quantification in statistical data collected from DNS are proposed to guarantee the data accuracy sufficient for their use in RANS equations and for the turbulence model validation.

Amplitude modulation of pressure in turbulent boundary layer

The interaction between pressure fluctuations associated with large- and small-scale motions is studied. Using a small pressure probe, both static pressure and wall pressure fluctuations were measured inside the zero-pressure gradient boundary layer at relatively high Reynolds numbers. How the large scales in the log-region affect the small scales near the wall is analyzed by means of an amplitude modulation procedure. Analyzing the wall pressure fluctuations, it was found that the large scale interacts with the small scale but there is a time-lag between them.

Coherent structures in a zero-pressure-gradient and a strongly decelerated boundary layer

Coherent structures in a strongly decelerated large-velocity-defect turbulent boundary layer (TBL) and a zero pressure gradient (ZPG) boundary layer are analysed by direct numerical simulation (DNS). The characteristics of the one-point velocity stastistics are also considered. The adverse pressure gradient (APG) TBL simulation is a new one carried out by the present authors. The APG TBL begins as a zero pressure gradient boundary layer, decelerates under a strong adverse pressure gradient, and separates near the end of the domain in the form of a very thin separation bubble. The one-point velocity statistics in the outer region of this large-defect boundary layer are compared to those of two other large-velocity-defect APG TBLs (one in dynamic equilibrium, the other in disequilibrium) and a mixing layer. In the upper half of the large-defect boundary layers, the velocity statistics are similar to those of the mixing layer. The dominant peaks of turbulence production and Reynolds stresses are located in the middle of the boundary layers. Three-dimensional spatial correlations of (u, u) and (u, v) show that coherence is lost in the streamwise and spanwise directions as the velocity defect increases. Near-wall streaks tend to disappear in the large-defect zone of the flow to be replaced by more disorganized u motions. Near-wall sweeps and ejections are also less numerous. In the outer region, the u structures tend to be shorter, less streaky, and more inclined with respect to the wall than in the ZPG TBL. The sweeps and ejections are generally bigger with respect to the boundary layer thickness in the large-defect boundary layer, even if the biggest structures are found in the ZPG TBL. Large sweeps and ejections that reach the wall region (wall-attached) are less streamwise elongated and they occupy less space than in the ZPG boundary layer. The distinction between wall-attached and wall-detached structures is not as pronounced in the large-defect TBL.

Impact of orifice orientation on a finite-span synthetic jet interaction with a crossflow

The formation and evolution of flow structures associated with a finite-span synthetic jet issued into a zero-pressure gradient boundary layer were investigated experimentally using stereoscopic particle image velocimetry. A synthetic jet with an aspect ratio of AR = 18 was mounted on a flat plate and its interaction with a free stream, having a velocity of U∞ = 10 m/s (Reδ = 2000) at momentum coefficients of Cμ = 0.08, 0.33, and 0.75, was studied. The effect of the orifice pitch (α = 20∘–90∘) and skew (β = 0∘–90∘) angles on vortex formation as well as the global impact of the synthetic jet on the flow field was explored in detail. It was found that the orifice orientation had a significant impact on the steady and unsteady flow structures. Different orifice skew and pitch angles could result in several types of vortical structures downstream, including: no coherent vortex structure, a single (positive or negative) strong vortex, or a symmetric vortex pair. In all cases, the velocity near the wall was increased; however, cases with higher blockage (i.e., more wall-normal, transverse orifice) resulted in a strong velocity deficit in the free stream where orifices with lower pitch angles yielded in an increase in velocity throughout. The analysis is concluded with a summary of quantitative metrics that allude to flow control effectiveness.

リブレットの抵抗低減効果を模擬する乱流モデルの構築

For practical CFD-aided design of riblets on aircrafts, we are aiming to develop a Reynolds-Averaged Navier-Stokes (RANS) turbulence model which can simulate drag reduction effects without resolving fine-scale flows near the riblets. Wilcox's rough wall boundary condition for Menter's SST model is modified to reproduce velocity shift in logarithmic region corresponding to riblet's drag reduction effects. Two basic relations for this model are derived from available experimental data and parametric analysis, and are validated in zero-pressure gradient boundary layers with two different-geometry riblets. Drag reduction rates corresponding to experimental results can be obtained with these relations. The new model, however, underestimates the effects of riblet mounted on NACA0012, which suggests that further improvement of the model is needed to account for influences of pressure gradient.

Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions

The flow around a wall-mounted square cylinder of side d is investigated by means of direct numerical simulation (DNS). The effect of inflow conditions is assessed by considering two different cases with matching momentum-thickness Reynolds numbers Reθ ≃ 1000 at the obstacle: the first case is a fullyturbulent zero pressure gradient boundary layer, and the second one is a laminar boundary layer with prescribed Blasius inflow profile further upstream. An auxiliary simulation carried out with the pseudo-spectral Fourier–Chebyshev code SIMSON is used to obtain the turbulent time-dependent inflow conditions which are then fed into the main simulation where the actual flow around the cylinder is computed. This main simulation is performed, for both laminar and turbulent-inflows, with the spectral-element method code Nek5000. In both cases the wake is completely turbulent, and we find the same Strouhal number St ≃ 0.1, although the two wakes exhibit structural differences for x > 3d downstream of the cylinder. Transition to turbulence is observed in the laminar-inflow case, induced by the recirculation bubble produced upstream of the obstacle, and in the turbulent-inflow simulation the streamwise fluctuations modulate the horseshoe vortex. The wake obtained in our laminar-inflow case is in closer agreement with reference particle image velocimetry measurements of the same geometry, revealing that the experimental boundary layer was not fully turbulent in that dataset, and highlighting the usefulness of DNS to assess the quality of experimental inflow conditions.