Flat Plate Turbulent Boundary Layer Research Articles

Error estimation of a homogenized streamwise periodic boundary layer

This work concerns the simulation of a homogenized streamwise periodic boundary layer which reduces the computational cost of direct numerical simulations of incompressible flat plate turbulent boundary layers. It expands upon the understanding of how the transpiration velocity changes dependent on whether a blending function is used to account for inner and outer self-similar scaling effects. With this rescaling correction, lower Reynolds number effects on the transpiration velocity are captured by the homogenized streamwise periodic boundary layer simulation.

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

Direct numerical simulation of the flow around a sphere immersed in a flat-plate turbulent boundary layer

This study investigates flow past a sphere immersed in a flat-plate turbulent boundary layer by using direct numerical simulations, with the objective of clarifying the effects of a wall-proximity sphere on turbulent coherent structures and turbulence statistics. Three cases are evaluated with gap ratios (G/D) of 0.1, 0.25, and 0.5 at a Reynolds number of ReD=2500, where D is the diameter of the sphere and G is the gap width between the bottom of the sphere and the flat plate. The results show that the wake of the sphere plays an important role in the streamwise region 0<x/D<10. The near-wall streaks break into small-scale point-like or patch-like structures in the near-wake region, with the most significant effect at G/D=0.1. This can be attributed to the interactions between the shedding vortex behind the sphere and vortical structures within the flat-plate boundary layer. Detail analysis of turbulence statistics indicates that the flat-plate boundary layer thickness is increased at x/D<−0.5 owing to the blockage effect of the sphere, whereas it is decreased at x/D>0.5 because of the high-speed jet flow around it. In addition, the presence of a wall-proximity sphere significantly affects the skin friction coefficient. The budgets of the turbulent kinetic energy show that turbulence production and viscous dissipation are augmented due to the formation of small-scale vortices and interactions among them in the near-wake region, especially at G/D=0.1.

Surface roughness effects on film-cooling effectiveness in a fan-shaped cooling hole

Large eddy simulations (LES) were carried out to investigate the influence of surface roughness, which was applied to the inner walls of a cooling hole, on cooling performance and flow structures. The cooling hole was a 30-degree inclined, baseline 7-7-7 fan-shaped hole relative to a turbulent flat plate boundary layer of the mainstream. Numerical simulations were performed at two different blowing ratios (M=1.5 and 3.0) and at a constant density ratio (DR=1.5) for various configurations of surface roughness. In order to numerically consider the effects of surface roughness, the equivalent sand-grain roughness model was utilized. Different correlations between the equivalent sand-grain roughness height and arithmetic average roughness height were numerically tested to find an accurate correlation compared to the measurements. The time-averaged numerical results were validated by experiments looking at the velocity and thermal fields for the smooth and rough cooling holes. Results revealed that increasing the surface roughness applied to the cooling hole, increases the thickness of the boundary layers within the hole, especially at the higher blowing ratio. This leads to a higher jet core flow at the cooling hole exit and lower cooling effectiveness at the flat plate surface compared with a smooth cooling hole. The minimum area-averaged film-cooling performance showed a 58% reduction compared to a smooth hole in the case of the highest blowing ratio (M=3.0) and the largest surface roughness height. In addition, the time-space evaluation of the velocity fluctuations showed greater flow unsteadiness and increased wavy patterns within the cooling hole in the case of rough holes.

Characteristics of wall-shear stress fluctuations in shock wave and turbulent boundary layer interaction

The wall-shear stress (WSS) fluctuations in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer are investigated by means of direct numerical simulation (DNS) at Mach 2.25. The numerical results agree very well with previous experiments and DNS data in terms of turbulence statistics, wall pressure, and skin friction. The fluctuating WSS characteristics, including probability density function (PDF), frequency spectrum, space–time correlation, and convection velocity, are analysed systematically. It is found that the positively skewed PDF shape of the streamwise WSS fluctuations is significantly changed due to the presence of a separation bubble, while the PDF shape of the spanwise component is slightly affected, exhibiting a symmetric behaviour across the interaction. The weighted power-spectrum density map indicates that the low-frequency unsteadiness associated with the separated shock - exhibits little influence on the spectrum for either component, and no enhancement of the low-frequency energy is observed. A significant reduction in the spatial extent of the two-point correlation is observed, causing spanwise elongated coherence for the streamwise WSS fluctuations in the separation region. Moreover, the elliptic behaviour of the space–time correlations is essentially preserved throughout the interaction, and this is accompanied by a sudden reduction of the convection velocity in the separation bubble.

Improved wall model treatment for aerodynamic flows in LBM

The article deals with an improved treatment of wall models for the simulation of turbulent flows in the framework of Immersed Wall Boundaries on Cartesian grids. The emphasis is put on the implementation in a Lattice-Boltzmann Method solver without loss of generality, since the proposed approach can be used in Navier–Stokes-based solvers in a straightforward way. The proposed improved wall model implementation relies on the combination of several key elements, namely i) the removal of grid points too close to the solid surface and ii) an original computation of wall normal velocity gradient and iii) the interpolation scheme. The new method is successfully assessed considering URANS simulations focusing on steady solutions of the Zero Pressure Gradient turbulent flat plate boundary layer and the turbulent flow around a NACA0012 airfoil at several angles of attack.

Explicit Algebraic Reynolds-Stress Modeling of Pressure-Induced Separating Flows in the Presence of Sidewalls

AbstractReynolds-averaged Navier–Stokes (RANS) approach is used to simulate the steady-state of a family of pressure-induced turbulent separation bubbles in the presence of sidewalls. Different turbulence models are employed with a specific emphasis on the baseline explicit algebraic Reynolds stress model (BSL-EARSM) and the simulations are compared with experimental data. The separation and reattachment of a flat-plate turbulent boundary layer are generated through a combination of adverse and favorable pressure gradients (APG-FPG) by numerically reproducing the geometry of the wind-tunnel test section used for the experiments. Three cases are considered a large (LB) and a medium (MB) bubble presenting mean backflow, and a small bubble (SB) without mean-flow reversal. This is achieved by varying the streamwise position of the APG/FPG transition. Good agreement between the BSL-EARSM-computed solutions and the experimental results are obtained for wall-pressure and skin-friction distributions on the centerline plane of the test section as well as for the overall three-dimensional flow topology. However, both detachment and reattachment are predicted too early and the bubble length is slightly overestimated for cases LB and MB. For case LB, the streamwise Reynolds stress is estimated fairly well but its production is somewhat delayed. Normal and shear stresses are in good agreement with the experiments in the upstream part of the bubble but are significantly over-estimated in the reattachment region. The k−ω shear-stress transport (SST) model with the so-called reattachment modification performs better than the other tested linear-eddy-viscosity models but it is still unable to reproduce accurately the three-dimensional flow topology even for the “simplest” case SB. Overall, the results suggest that BSL-EARSM is the most suitable turbulence model for this flow configuration.

Predictive accuracy of wall-modelled large-eddy simulation on unstructured grids

The predictive accuracy of wall-modelled LES is influenced by a combination of the subgrid model, the wall model, the numerical dissipation induced primarily by the convective numerical scheme, and also by the density and topology of the computational grid. The latter factor is of particular importance for industrial flow problems, where unstructured grids are typically employed due to the necessity to handle complex geometries. Here, a systematic simulation-based study is presented, investigating the effect of grid-cell type on the predictive accuracy of wall-modelled LES in the framework of a general-purpose finite-volume solver. Following standard practice for meshing near-wall regions, it is proposed to use prismatic cells. Three candidate shapes for the base of the prisms are considered: a triangle, a quadrilateral, and an arbitrary polygon. The cell-centre distance is proposed as a metric to determine the spatial resolution of grids with different cell types. The simulation campaign covers two test cases with attached boundary layers: fully-developed turbulent channel flow, and a zero-pressure-gradient flat-plate turbulent boundary layer. A grid construction strategy is employed, which adapts the grid metric to the outer length scale of the boundary layer. The results are compared with DNS data concerning mean wall shear stress and profiles of flow statistics. The principle outcome is that unstructured simulations may provide the same accuracy as simulations on structured orthogonal hexahedral grids. The choice of base shape of the near-wall cells has a significant impact on the computational cost, but in terms of accuracy appears to be a factor of secondary importance.

Reflected shock/turbulent boundary layer interaction structure analysis based on large eddy simulation

In order to understand the physical phenomenon of the reflected shock/turbulent boundary layer interaction, the Large Eddy Simulation (LES) is conducted to investigate shock wave and turbulent boundary layer interaction in a 12° compression ramp with inlet high Mach number of 2.9. Rescaling/recycling method is used as inflow turbulence generation technique and validated on a supersonic flat plate turbulent boundary layer. The flow field of recycling plane in the plate computation domain is obtained to give the inlet boundary condition for the LES computation. This paper focuses on the reflected shock/turbulent boundary layer interaction region, where the fine flow structure and instantaneous flow field are analyzed in detail. It is found that the unsteady motion of the shock wave leads to the increase of wall pressure fluctuation.

Verification of Drag Reduction Effect of Flat Plate Turbulent Boundary Layer with Inclined Blowing Using Mainstream Dynamic Pressure

Verification of Drag Reduction Effect of Flat Plate Turbulent Boundary Layer with Inclined Blowing Using Mainstream Dynamic Pressure

Unsteady heat transfer characteristics downstream of a vortex generator attached on the flat plate turbulent boundary layer

Unsteady heat transfer characteristics downstream of a vortex generator attached on the flat plate turbulent boundary layer

A high-resolution floating-element force balance for friction drag measurement

A high-resolution floating-element (FE) force balance is developed, along with a calibration method, which is demonstrated to be able to capture reliably very small wall shear stress (WSS), in the order of 10–4N in a smooth flat-plate turbulent boundary layer (TBL). Based on the lever principle, the WSS on the FE is greatly amplified and converted to a vertical force, which can be measured by a load cell. A thorough investigation is performed to document the possible error sources of the system, in light of which countermeasures are taken to minimize the errors. The balance-measured friction coefficient cf deviates by no more than 1.9% from the Coles–Fernholz correlation for the friction Reynolds number Reτ of 570 ~ 1487, thus providing a validation for this technique. This force balance is applied to measure the WSS in a TBL over a smooth flat plate with and without plasma-generated wall-normal blowing through two spanwise slots at Reτ = 570, capturing a friction drag as small as 2.56 × 10–4 ~ 1.81 × 10–4 N, corresponding to a drag reduction (DR) of 0.9 × 10–5 to 8.4 × 10–5 N, in agreement with the estimate from the integration of hot-wire-measured local DR over the same FE area.

Aero-optical suppression for supersonic turbulent boundary layer

Aero-optical reduction in flat-plate turbulent boundary layer has been widely concerned due to critical application for high-speed target-seeking vehicles. From the perspective of disciplinary intersection between aerodynamic and optical engineering, the turbulence-aberrated optical behaviour, in high-Reynolds-number supersonic freestream, is numerically investigated using the in-house code High-Order SimulaTor for Aerodynamics (HOSTA) and ray-tracing scheme. To evaluate the efficiency of wall cooling strategy to reduce the detrimental aero-optical distortions, the authors leverage the theoretical equation deduced from Sutton statistic model for mutual verification with the simulative results. Additionally, based on the beneficial wall cooling effects on turbulent aero-optical reduction, comparison suggests that refrigeration directly towards the turbulence section is the most effective rather than cooling the laminar or transitional region. In further discussion, wall blowing, suction and combinational blowing and suction schemes are issued. Results reveal the rationality of employing proper suction amplitude to modify the flow into laminar state, and sufficiently high suction intensity is also promising in turbulent aero-optical reduction despite the fact of low efficiency currently. The current study puts an eye on the simulation concerning three-dimensional supersonic turbulent flow in high-Reynolds-number freestream and the application of statistic model, and future investigation is suggested for higher effectiveness of aero-optical suppression.

Effects of Localized Micro-blowing on a Spatially Developing Flat Turbulent Boundary Layer

Direct numerical simulation (DNS) is used to investigate the turbulent flat-plate boundary layer with localized micro-blowing. The 32 × 32 array of micro-holes is arranged in a staggered pattern on the solid wall, located in the developed turbulent region. The porosity of the porous wall is 23%, and the blowing fraction is 0.0015. The Reynolds number based on the inflow velocity is set to be 50,000. The structures of the turbulent boundary layer are carefully analyzed to understand the effects of micro-blowing and its drag reduction mechanism. The DNS results show that the drag reduction is efficient, and the local maximum rate of drag reduction achieves 40%. A low-speed “turbulent spot” near the micro-blowing region thickens the boundary layer. Some turbulent properties, such as the mean velocity profile, stream-wise vorticity and stream-wise velocity fluctuation are lifted up. Particularly, the tilting term of vorticity transport is significantly increased. Meanwhile, the visualization of 3-dimensional vortex displays several concave marks on the surface of the near-wall vortices, which is caused by the micro-jets, leading to more broken vortices and isotropic small scales. This impact travels downstream with a small distance due to the accumulation of the micro-jets, while the uplift effect will gradually disappear. In addition, FIK identity reveals that the spatial development term and mean wall-normal convection term play opposite roles in the contribution to the skin friction drag.

Microbubble effect on friction drag reduction in a turbulent boundary layer

Effects of microbubbles injection on friction drag in a turbulent boundary layer are studied using large-eddy simulation. A flat-plate turbulent boundary layer with a Reynolds number Reθ = 1430 is generated within a short distance of inflow by introducing disturbances. The parameters investigated include the gravity, the injection height, and the volume fraction of microbubbles. It is found that the mechanism for drag reduction is threefold, that is, buoyancy acting on microbubbles, the change of coherent structures, and hydrodynamic viscosity near the wall. Under different conditions, the dominant mechanism for drag reduction varies among them. With microbubbles injected above the flat plate, the primary mechanism is the lift of coherent structures from the wall and the decrease in the size and vorticity of the streamwise vortices. When microbubble volume fraction increases, the larger buoyancy acting on microbubbles leads to coherent structures shifted further away from the wall, resulting in higher drag reduction. With microbubbles injected beneath the flat plate, the dominant mechanism is a significant decrease in hydrodynamic viscosity as buoyancy pushes microbubbles gathering near the wall and forming a thin air layer. The drag reduction is higher than that of microbubbles injected above the flat plate.

Validation case for supersonic boundary layer and turbulent aero-optical investigation in high-Reynolds-number freestream by WCNS-E-5

Turbulent flat-plate boundary layer flows have been widely employed for numerical validation in the aero-optical field. In present study, the laminar-to-turbulent evolution induced by wavy roughness in high-Reynolds-number supersonic freestream is investigated using a numerical technique based on the fifth-order weighted compact nonlinear scheme (WCNS-E-5). The computational procedure and post-processing method are described in detail, and the acquired instantaneous flow structure and statistical data are compared with other theoretical, experimental, and numerical results to demonstrate the feasibility of predicting turbulence using WCNS-E-5. Further, to reduce the computational resources required to simulate turbulent flow, a velocity correlation function is introduced to decrease the computational domain in the spanwise direction. Additionally, the effects of different grid sizes on the simulation results are examined by reducing the number of cells in the streamwise, wall-normal, and spanwise directions. Finally, the authors conduct a tentative investigation into the aero-optical effects of the laminar-to-turbulent flowfield using a ray-tracing method, considering both the feasibility of aero-optical detection and the effect of grid scale on the time-averaged imaging quality, as well as a deeper probe into the characteristic structures reflected by aero-optical frequency spectrum. The results elucidated that the wall-normal grid number has the strongest influence on the transitional location, and undoubtedly affects wavefront aberrations. However, different gird scales lead to similar aero-optical spectrum, and revealed the Kolmogorov-type turbulence at small-scale regime. As a prelude to further aero-optical simulations of wall-bounded flows, the current study provides some reference for the code validation process and aero-optical interrogation.

Streamwise evolution of drag reduced turbulent boundary layer with polymer solutions

The effect of local polymer solution injection on the evolution of a flat-plate turbulent boundary layer has been investigated experimentally. Polyethylene oxide (PEO) solutions were injected through an inclined slot. The influence of polymer injection on boundary layer development downstream of the slot is assessed at three different concentrations (100 ppm, 500 ppm, and 1000 ppm) using planar velocity field and concentration measurements. A local drag reduction (DR) of up to 60% was obtained in the vicinity of the slot. A systematic change observed in the inverse of the von Kármán constant (k = 1/κ) with an increase in DR is used to define the sub-regimes of the high DR regime, and a linear relation between k and DR is shown to persist over a wide range of Reynolds numbers. The analysis of combined velocity and concentration measurements provides added insight into the associated changes in the boundary layer characteristics and the underlying flow physics.

Asymptotic scaling of drag in flat-plate turbulent boundary layers

A new asymptotic −1/2 power-law scaling is derived from the momentum integral equation for the drag in flat-plate turbulent boundary layers. In the limit of infinite Reynolds number, the appropriate velocity scale for drag is found to be M/ν, where M is the boundary layer kinematic momentum rate and ν is the fluid kinematic viscosity. Data covering a wide range of Reynolds numbers remarkably collapse to a universal drag curve in the new variables. Two models, discrete and continuous, are proposed for this universal drag curve, and a robust drag estimation method, based on these models, is also presented.

Boundary layer measurements over a body of revolution using long-distance particle image velocimetry

This study reports the development and application of long-distance high magnification Particle Image Velocimetry (PIV) to measure the mean and fluctuating velocity components in a turbulent boundary layer over a body of revolution. A 400 mm lens coupled with an extension tube and a novel aperture control mechanism has enabled high resolution images at a working distance of 1.5 m. The body of revolution used in the investigation is representative of a conventional submarine hull without appendages, as per (Joubert, 2006). The flow over the model was measured at a nominal Reynolds number, ReL=4.0 × 106, based on the length of the body. A comparison of single-point statistics from the PIV experiments were found to compare well with pitot probe and hot-wire measurements. Further, the boundary layer thickness and mean streamwise velocity were found to conform closely with a traditional flat plate turbulent boundary layer in the parallel mid-body section of the geometry. However, a comparison of the streamwise and wall-normal Reynolds stresses with Direct Numerical Simulations (DNS) of a turbulent boundary layer on a flat plate with zero pressure gradient indicated lower turbulence levels. This was partly attributed to the spatial averaging evident both in the hot-wire and PIV measurements. We also report that in the tail section of the model, the boundary layer rapidly grows and departs from the flat plate solution due to the conical section and adverse pressure gradient imposed on the flow.

Effects of favorable pressure gradient on turbulence structures and statistics of a flat-plate supersonic turbulent boundary layer

A Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a moderate favorable pressure gradient (FPG) induced by external expansion waves is investigated through direct numerical simulation and compared with a zero pressure gradient (ZPG) boundary layer. It is found that under FPG, the logarithmic region in the van Driest transformed velocity profile is lifted above the log law, while the wake region deviates below its ZPG counterpart. The near-wall streaks are elongated in the streamwise direction with wider spanwise spacing, which leads to an attenuated meandering effect compared to the ZPG case. Although small-scale motions in the outer layer are evidently suppressed, they survive mostly in the inner layer. On the other hand, large-scale motions tend to correlate further with the lifted fluid from upstream due to bulk dilatation. However, their relative locations within the boundary layer remain unchanged. Different responses of turbulence structures in the inner and the outer layer to FPG show that this two-layer feature within the boundary layer is mainly associated with the bulk dilatation rather than the wall curvatures. The profiles of turbulent kinetic energy (TKE) and turbulent Mach number also show a two-layer behavior, where the reduction in turbulence in the outer layer is more prominent than in the inner. Positive convection occurs from the buffer to the outer layer according to the TKE budget analysis, which compensates the production and resists the decrease in the turbulence level.