Simulation Of Turbulent Boundary Layer Research Articles

Wall-Modeled Large-Eddy Simulation of Turbulent Boundary Layer with Spatially Varying Pressure Gradients

Wall-modeled large-eddy simulations of turbulent boundary layers subjected to spatially varying streamwise pressure gradients are conducted to assess the predictive performance of three wall models: ordinary differential equation equilibrium, integral nonequilibrium, and partial differential equation (PDE) nonequilibrium models. The test case is based on experiments conducted by Volino (Journal of Fluid Mechanics, Vol. 897, Aug. 2020, p. A2), where the flow is subjected successively to zero pressure gradient (ZPG), favorable pressure gradient (FPG), recovery ZPG, and adverse pressure gradient (APG) regions. Skin friction is overpredicted in FPG by all the wall models. For equilibrium and integral models, this overprediction is attributed to the strong deviation of mean velocity profiles within FPG from the log law, used explicitly in the equilibrium and implicitly in the integral model. The overprediction is more pronounced for the PDE model, which is attributed to dynamic correction of wall-model eddy viscosity for resolved stresses and a lack of correction for pressure gradient. Potential remedies to mitigate this problem are proposed. Grid refinement improves wall-stress predictions in both FPG and APG but only affects the outer profiles in APG, revealing that accurate wall-flux modeling is more critical for APG. Anisotropic grid analysis shows streamwise grid refinement to be more crucial than spanwise for the convergence of skin-friction, outer velocity, and Reynolds stress profiles.

On the unsteady Reynolds-averaged Navier–Stokes capability of simulating turbulent boundary layers under unsteady adverse pressure gradients

Predictive capabilities of unsteady Reynolds-averaged Navier–Stokes (URANS) techniques using the k−ω shear stress transport and Spalart–Allmaras models are assessed for the simulation of turbulent boundary layers under unsteady adverse pressure gradients by comparing their results with direct numerical simulation (DNS) results. Simulations are conducted for separating and reattaching turbulent boundary layers under periodic adverse pressure gradients. Phase-wise comparisons of the velocity, the Reynolds stress, and the skin friction coefficient obtained by URANS simulations and DNS are carried out. URANS techniques are found to qualitatively well predict the formation of the separation bubble and the phase response of the shear layer height, while they predict earlier separation and a larger recirculation bubble compared with those in DNS. Phase responses of the skin friction predicted by URANS simulations are found not to be an accurate indication of flow separation and reattachment of the turbulent boundary layer. The main causes of discrepancies among DNS and URANS results in the near-wall region are attributed to the different anisotropy of the Reynolds stress, which can be characterized by a barycentric map.

Simulating unsteady flows in a compressor using immersed boundary method with turbulent wall model

Computations of unsteady turbulent flows in turbomachine are still challenging due to the complexity of geometry and relative motion between rotor and stator. A potential solution is using the immersed boundary method (IBM) for its advantages in simulating moving boundary problems, but it loses efficiency with increasing Reynolds number. In the present work, to accurately simulate unsteady flows in a compressor, the well-established turbulent wall model is adopted with the hierarchical Cartesian grid in IBM to alleviate the requirements of grid spacing for turbulent boundary layer simulation. First, verification of the flow solver on two-dimensional (2D) stationary cases of the non-inclined/inclined flat plate and zero attack NACA 0012 were conducted. Furthermore, the Tamaki et al. wall model which had been only validated in stationary problems was first extended to solve the moving boundary problem, i.e. plunging airfoil. Finally, the new immersed boundary solver employed Tamaki et al. wall model was used to simulate the classic rotor/stator interaction. The unsteady normal forces on stator blade of a low-speed compressor were examined with two different sizes of axial gap, i.e. 10% chord and 30% chord. With the large gap, the predicted phase and magnitude of the unsteady aerodynamic force agree with the measurements well. With the more challenging small gap, although the predicted phase of the peak force is lagged slightly with the measurements, the magnitude of the peak force is captured. The agreements between numerical results and measurements indicate the ability of the developed IBM solver based on Tamaki et al. wall model and hierarchical Cartesian grid in dealing with simulations of unsteady flows in turbomachine.

Spatial-scaling method and modified large eddy simulation to examine rough-wall turbulence

Direct numerical simulations of turbulent boundary layers with roughness elements on a wall were performed to investigate the spatial characteristics of rough-wall turbulence and establish a corresponding prediction method. When the roughness height was larger than the buffer layer, the rough-wall turbulence exhibited different spatial characteristics of the turbulence structures from those pertaining to a smooth wall. A novel spatial scaling method was established to examine the universal spatial characteristics of turbulence structures in the presence and absence of wall roughness. Specifically, the viscous length was determined by modifying the definition of the friction velocity in the region in which the roughness influenced the flow. The rough-wall turbulence could be accurately predicted by performing large eddy simulations using the subgrid scale model with the filter width, which was modified using the proposed spatial scaling method. The proposed model can be used to design more efficient fluid machinery in engineering applications.

Large-Eddy Simulations of Stratified Atmospheric Boundary Layers: Comparison of Different Subgrid Models

The development and assessment of subgrid-scale (SGS) models for large-eddy simulations of the atmospheric boundary layer is an active research area. In this study, we compare the performance of the classical Smagorinsky model, the Lagrangian-averaged scale-dependent (LASD) model, and the anisotropic minimum dissipation (AMD) model. The LASD model has been widely used in the literature for 15 years, while the AMD model was recently developed. Both the AMD and the LASD models allow three-dimensional variation of SGS coefficients and are therefore suitable to model heterogeneous flows over complex terrain or around a wind farm. We perform a one-to-one comparison of these SGS models for neutral, stable, and unstable atmospheric boundary layers. We find that the LASD and the AMD models capture the logarithmic velocity profile and the turbulence energy spectra better than the Smagorinsky model. In stable and unstable boundary-layer simulations, the AMD and LASD model results agree equally well with results from a high-resolution reference simulation. The performance analysis of the models reveals that the computational overhead of the AMD model and the LASD model compared to the Smagorinsky model is approximately 10% and 30% respectively. The LASD model has a higher computational and memory overhead because of the global filtering operations and Lagrangian tracking procedure, which can result in bottlenecks when the model is used in extensive simulations. These bottlenecks are absent in the AMD model, which makes it an attractive SGS model for large-scale simulations of turbulent boundary layers.

Advanced simulations of turbulent boundary layers under pressure-gradient conditions

A high-Reynolds-number turbulent boundary layer experiencing pressure gradients is simulated with Reynolds-averaged Navier-Stokes (RANS) and hybrid RANS/LES (Large Eddy Simulation) advanced turbulence modeling approaches, namely, two eddy viscosity models, two Reynolds Stress models (RSMs), and Zonal Detached Eddy Simulation (ZDES) mode 3 which corresponds to a wall-modeled LES approach. Such a study is the first of its kind to the authors’ best knowledge. The test-case considered is the experimental work of Cuvier et al. [“Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology,” J. Turbul. 18, 929–972 (2017)]. Some modifications of the top wall geometry have been proposed to take into account the blockage effect of the boundary layers developing over the wind tunnel side walls so that statistically two-dimensional simulations are possible. Comparisons have shown that there are some difficulties in properly predicting the mean skin friction and the Reynolds stresses in the adverse-pressure-gradient region for the ZDES and RSMs. The mean velocity profiles in this region are, however, poorly reproduced by all models. The atypical profiles experimentally observed at the beginning of the favorable-pressure-gradient region are well reproduced by RSMs, one eddy viscosity model, and ZDES for the mean velocity; however, only ZDES is able to satisfactorily predict the Reynolds stresses at this station. A spectral analysis of streamwise velocity fluctuations and Reynolds shear stress by means of ZDES has allowed us to identify external energetic turbulent structures at y ≈ 0.5δ and of size λx ≈ 3δ which are probably responsible for these atypical profiles. The present numerical test-case may constitute a development base for turbulence modeling under pressure gradient effects.

3D Simulations and MLT. I. Renzini’s Critique

Abstract Renzini wrote an influential critique of “overshooting” in mixing-length theory (MLT), as used in stellar evolution codes, and concluded that three-dimensional fluid dynamical simulations were needed. Such simulations are now well tested. Implicit large eddy simulations connect large-scale stellar flow to a turbulent cascade at the grid scale, and allow the simulation of turbulent boundary layers, with essentially no assumptions regarding flow except the number of computational cells. Buoyant driving balances turbulent dissipation for weak stratification, as in MLT, but with the dissipation length replacing the mixing length. The turbulent kinetic energy in our computational domain shows steady pulses after 30 turnovers, with no discernible diminution; these are caused by the necessary lag in turbulent dissipation behind acceleration. Interactions between coherent turbulent structures give multi-modal behavior, which drives intermittency and fluctuations. These cause mixing, which may justify use of the instability criterion of Schwarzschild rather than the Ledoux. Chaotic shear flow of turning material at convective boundaries causes instabilities that generate waves and sculpt the composition gradients and boundary layer structures. The flow is not anelastic; wave generation is necessary at boundaries. A self-consistent approach to boundary layers can remove the need for ad hoc procedures of “convective overshooting” and “semi-convection.” In Paper II, we quantify the adequacy of our numerical resolution in a novel way, determine the length scale of dissipation—the “mixing length”—without astronomical calibration, quantify agreement with the four-fifths law of Kolmogorov for weak stratification, and deal with strong stratification.

Numerical simulation of turbulent boundary layers with foreign gas transpiration using OpenFOAM

Transpiration cooling in combination with porous high-temperature materials is a promising technique for thermal protection of highly-loaded aerospace applications. In this study, we present a modified OpenFOAM solver which is applied to the simulation of a turbulent channel flow with boundary layer blowing. Different models for porous wall injection of air, argon, and helium into a main flow of air are proposed and evaluated. Subsequently, same and foreign gas transpiration is simulated for cold and heated main flow conditions and the results are compared to experimental data and correlations from literature. A very good overall agreement is found for velocity and temperature boundary layer profiles as well as the dimensionless parameters for wall shear stress and heat transfer.

Influence of pressure gradients on wall pressure beneath a turbulent boundary layer

This study investigates the effects of a pressure gradient on the wall pressure beneath equilibrium turbulent boundary layers. Excitation of the walls of a vehicle by turbulent boundary layers indeed constitutes a major source of interior noise and it is necessary to take into account the presence of a pressure gradient to represent the effect of the curvature of the walls. With this aim, large-eddy simulations of turbulent boundary layers in the presence of both mild adverse and mild favourable pressure gradients are carried out by solving the compressible Navier–Stokes equations. This method provides both the aeroacoustic contribution and the hydrodynamic wall-pressure fluctuations. A critical comparison with existing databases, including recent measurements, is conducted to assess the influence of a free stream pressure gradient. The analyses of wall-pressure spectral densities show an increase in the low-frequency content from adverse to favourable conditions, yielding higher integrated levels of pressure fluctuations scaled by the wall shear stress. This is accompanied by a steeper decay rate in the medium-frequency portion for adverse pressure gradients. No significant difference is found for the mean convection velocity. Frequency–wavenumber spectra including the subconvective region are presented for the first time in the presence of a pressure gradient. A scaling law for the convective ridge is proposed, and the acoustic domain is captured by the simulations. Direct acoustic emissions have similar features in all gradient cases, even if slightly higher levels are noted for boundary layers subjected to an adverse gradient.

Direct numerical simulations of a wall-attached cube immersed in laminar and turbulent boundary layers

A wall-attached cube immersed in a zero pressure gradient boundary layer is studied by means of Direct Numerical Simulations (DNS) at various Reynolds numbers ReH (based on the cube height and the free-stream velocity) ranging from 500 to 3000. The cube is either immersed in a laminar boundary layer (LBL) or in a turbulent boundary layer (TBL), with the aim to understand the mechanisms of the unsteady flow structures generated downstream of the wall-attached cube. The mean locations of the stagnation and recirculation points around the cube immersed in a TBL are in good agreement with reference experimental and numerical data, even if in those studies the cube was immersed in a turbulent channel. In the TBL simulation, a vortex shedding can be identified in the energy spectra downstream of the cube, with Strouhal number of St=0.14. However, the frequency of the vortex shedding is different in the LBL simulations, showing a significant dependence on the Reynolds number. Furthermore, in the TBL simulation, a low frequency peak with St=0.05 can be observed far away from the boundary layer, at long streamwise distances from the cube. This peak cannot be identified in the LBL simulations nor in the baseline TBL simulation without the wall-attached cube.

Simulation of turbulent boundary layer wall pressure fluctuations via Poisson equation and synthetic turbulence

Flat plate turbulent boundary layers under zero pressure gradient are simulated using synthetic turbulence generated by the fast random particle–mesh method. The stochastic realisation is based on time-averaged turbulence statistics derived from Reynolds-averaged Navier–Stokes simulation of flat plate turbulent boundary layers at Reynolds numbers $\mathit{Re}_{\unicode[STIX]{x1D70F}}=2513$ and $\mathit{Re}_{\unicode[STIX]{x1D70F}}=4357$. To determine fluctuating pressure, a Poisson equation is solved with an unsteady right-hand side source term derived from the synthetic turbulence realisation. The Poisson equation is solved via fast Fourier transform using Hockney’s method. Due to its efficiency, the applied procedure enables us to study, for high Reynolds number flow, the effect of variations of the modelled turbulence characteristics on the resulting wall pressure spectrum. The contributions to wall pressure fluctuations from the mean-shear turbulence interaction term and the turbulence–turbulence interaction term are studied separately. The results show that both contributions have the same order of magnitude. Simulated one-point spectra and two-point cross-correlations of wall pressure fluctuations are analysed in detail. Convective features of the fluctuating pressure field are well determined. Good agreement for the characteristics of the wall pressure fluctuations is found between the present results and databases from other investigators.

Effect of wall cooling on boundary-layer-induced pressure fluctuations at Mach 6

Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modified in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.

Direct numerical simulation of turbulent boundary layer with fully resolved particles at low volume fraction

In the present work, a direct numerical simulation (DNS) of dilute particulate flow in a turbulent boundary layer has been conducted, containing thousands of finite-sized solid rigid particles. The particle surfaces are resolved with the multi-direct forcing immersed-boundary method. This is, to the best of the authors' knowledge, the first DNS study of a turbulent boundary layer laden with finite-sized particles. The particles have a diameter of approximately 11.3 wall units, a density of 3.3 times that of the fluid, and a solid volume fraction of 1/1000. The simulation shows that the onset and the completion of the transition processes are shifted earlier with the inclusion of the solid phase and that the resulting streamwise mean velocity of the boundary layer in the particle-laden case is almost consistent with the results of the single-phase case. At the same time, relatively stronger particle movements are observed in the near-wall regions, due to the driving of the counterrotating streamwise vortexes. As a result, increased levels of dissipation occur on the particle surfaces, and the root mean square of the fluctuating velocities of the fluid in the near-wall regions is decreased. Under the present parameters, including the particle Stokes number St+ = 24 and the particle Reynolds number Rep = 33 based on the maximum instantaneous fluid-solid velocity lag, no vortex shedding behind the particle is observed. Lastly, a trajectory analysis of the particles shows the influence of turbophoresis on particle wall-normal concentration, and the particles that originated between y+ = 60 and 2/3 of the boundary-layer thickness are the most influenced.

A simple extension of digital filter-based turbulent inflow to non-uniform structured grids

The digital filter-based turbulence generator is one of the widely used synthetic turbulence inflow boundary conditions for large-scale-resolving flow simulations. However, the requirement of using uniformly-spaced Cartesian meshes and the limitation of enforcing a constant integral length scale along a given direction restrict the applicability of the method severely. The current paper describes an easy-to-implement and computationally inexpensive approach to extend the digital filter-based inflow to non-uniform structured meshes, using a mapping between the physical curvilinear mesh and a computational uniformly-spaced Cartesian mesh. The method also allows a limited control on the variation of integral length scales over the inflow plane. A zero-pressure-gradient, flat plate turbulent boundary layer is simulated using the proposed method and the distance required by the generated fluctuations to adapt into realistic turbulence is estimated to be about 10 boundary layer thicknesses. The method was developed for and has been used in simulations of turbulent boundary layers along nozzle walls for jet noise applications.

OpenFOAM과 어댑티드 격자를 이용한 난류 경계층의 직접 수치 모사

OpenFOAM과 어댑티드 격자를 이용한 난류 경계층의 직접 수치 모사

Numerical simulation of turbulent boundary layers of surfaces covered with foul release and antifouling coatings

In order to compare the frictional resistance of three kinds of ship’s hull coatings (Foul Release, SPC copper, SPC TBT) in the unfouled conditions, the numerical studies have been made. Simulations have been carried out for different Reynolds numbers in the range of 2.85 × – 5.5 × based on the plate length and flow velocity. Antifouling coatings have a larger mean roughness than Foul Release. The results have indicated that frictional resistance coefficient of Foul Release test plate is lower than SPC copper and SPC TBT test plates. The total resistance obtained by computational fluid dynamics has been compared with the experimental data and good agreement in results has been found which those have shown the ability of CFD modeling in calculating of fluid flow resistance by considering the coating characteristics.

Direct numerical simulation of turbulent boundary layer with heat transfer

A direct numerical simulation was conducted of an incompressible, nominally zero-pressure-gradient flat-plate boundary layer from momentum thickness Reynolds numbers 80–1150. Heat transfer was considered with a constant-temperature solid boundary and the Prandtl number Pr=0.71. Both the temperature boundary layer thickness and the Stanton number compared well to experimental data. The mean temperature distributions, the root-mean-square of the temperature fluctuations and the correlations between the velocity fluctuations and the temperature fluctuations have good agreements with previous investigations. One of the main focuses of the present paper is the statistical behavior of the velocity and temperature fluctuations in the wall-normal direction from the sub-layer region to the outer region of the boundary layer. Probability density functions (PDF) are presented to investigate the statistical characteristics near the wall. In addition, the near-wall temperature streaky structures are presented, and the coherence of the turbulent structures between the velocity and the temperature fields is discussed.

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.

Free-stream coherent structures in growing boundary layers: a link to near-wall streaks

In a recent paper, Deguchi & Hall (J. Fluid Mech., vol. 752, 2014a, pp. 602–625) described a new kind of exact coherent structure which sits at the edge of an asymptotic suction boundary layer at high values of the Reynolds number $Re$. At a distance $\ln Re$ from the wall, the structure is driven by the fully nonlinear interaction of tiny rolls, waves and streaks convected downstream at almost the free-stream speed. The interaction problem satisfies the unit-Reynolds-number three-dimensional Navier–Stokes equations and is localized in a layer of the same depth as the unperturbed boundary layer. Here, we show that the interaction problem is generic to any boundary layer that approaches its free-stream form through an exponentially small correction. It is shown that away from the layer where it is generated the induced roll–streak flow is dominated by non-parallel effects which now play a major role in the streamwise evolution of the structure. The similarity with the parallel boundary layer case is restricted only to the layer where it is generated. It is shown that non-parallel effects cause the structure to persist only over intervals of finite length in any growing boundary layer and lead to a flow structure reminiscent of turbulent boundary layer simulations. The results found shed light on a possible mechanism to couple near-wall streaks with coherent structures located towards the edge of a turbulent boundary layer. Some discussion of how the mechanism adapts to a three-dimensional base flow is given.

Analysis of conditional statistics obtained near the turbulent/non-turbulent interface of turbulent boundary layers

Direct numerical simulations of turbulent boundary layers (TBL) along a flat plate are used to study the properties of turbulent/non-turbulent (T/NT) interface of the TBL. The values of the momentum-thickness-based Reynolds numbers, Reθ, used for this study, are 500–2200. Analysis of the conditional statistics near the interface of the TBL shows that there are a small peak in the spanwise vorticity, and an associated small jump in streamwise velocity. It is shown that the interfacial layer has an inertia-viscous double structure which consists of a turbulent sublayer with a thickness of the order of the Taylor micro-scale and its outer boundary with a thickness of the order of the Kolmogorov length scale. The velocity jump near the T/NT interface of the TBL is of the order of the rms value of velocity fluctuations near the interface. Conditional cross correlations of the streamwise or the wall-normal velocity fluctuations change sharply across the interface, which are consistent with the blocking mechanism of the interface.