Turbulent Boundary Layer Flow Research Articles

Bayesian conditional diffusion models for versatile spatiotemporal turbulence generation

Turbulent flows, characterized by their chaotic and stochastic nature, have historically presented formidable challenges to predictive computational modeling. Traditional eddy-resolved numerical simulations often require vast computational resources, making them impractical or infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. In this study, we introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence under various conditions. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, as well as scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We evaluate and showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: (1) the synthesis of Large Eddy Simulations (LES) simulated instantaneous flow sequences from unsteady Reynolds-Averaged Navier–Stokes (URANS) inputs; (2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; (3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation.

Experimental assessment of square-wave spatial spanwise forcing of a turbulent boundary layer

We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise direction, thereby generating a steady spatial square-wave forcing. Stereoscopic particle image velocimetry in the streamwise–wall-normal plane is used to investigate the impact of actuation on the flow in terms of turbulence statistics, drag performance characteristics, and spanwise velocity profiles, for a non-dimensional wavelength of λx+=397\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _x^+ = 397$$\\end{document}. In line with reported numerical studies, we confirm that a significant flow control effect can be realised with this type of forcing. The scalar fields of the higher-order turbulence statistics show a strong attenuation of stresses and production of turbulence kinetic energy over the first belt already, followed by a more gradual decrease to a steady-state energy response over the second belt. The streamwise velocity in the near-wall region is reduced, indicative of a drag-reduced flow state. The profiles of the higher-order turbulence statistics are attenuated up to a wall-normal height of y+≈100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y^+ \\approx 100$$\\end{document}, with a maximum streamwise stress reduction of 45% and a reduction of integral turbulence kinetic energy production of 39%, for a non-dimensional actuation amplitude of A+=12.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^+ = 12.7$$\\end{document}. An extension of the classical laminar Stokes layer theory is introduced, based on the linear superposition of Fourier modes, to describe the non-sinusoidal boundary condition that corresponds to the current case. The experimentally obtained spanwise velocity profiles show good agreement with this extended theoretical model. The drag reduction was estimated from a linear fit in the viscous sublayer in the range 2≤y+≤5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \\le y^+\\le 5$$\\end{document}. The results are found to be in good qualitative agreement with the numerical implementations of Viotti et al. (Phys Fluids 21, 2009), matching the drag reduction trend with A+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^+$$\\end{document}, and reaching a maximum of 20%.Graphical abstract

Polydisperse sea spray effect on the vertical momentum transport in hurricanes

Abstract This study focuses on the influence of the sea spray polydispersity on the vertical transport of momentum in a turbulent marine atmospheric boundary layer in high-wind conditions of a hurricane. The Eulerian multifluid model treating air and spray droplets of different sizes as interacting inter-penetrating continua is developed and its numerical solutions are analyzed. Several droplet size distribution spectra and correlation laws relating wind speed and spray production intensity are considered. Polydisperse model solutions have confirmed the difference between the roles small and large spray droplets play in modifying the turbulent momentum transport that have been previously identified by monodisperse spray models. The obtained results have also provided a physical explanation for the previously unreported phenomenon of the formation of thin low-eddy-viscosity “sliding” layers in strongly turbulent boundary layer flows laden with predominantly fine spray.

Self-similarity in over-tripped turbulent boundary-layer flows

The scaling universality of structure functions is studied for artificially thickened turbulent boundary-layer flows in over-tripped impacts by using hot-wire measurement datasets. The self-similarity behaviours in the inner and outer regions are examined from the viewpoint of different flow mechanisms. In the inner region, the relative ratios between structure functions for the energy-containing range of scales exhibit universality behaviour, in accordance with Townsend's attached eddy hypothesis. This universality of the energy-containing range of scales extends further away from the wall by increasing the tripping intensity. On the other hand, the impact of the external intermittency on the self-similarity of small-scale turbulence is examined through the intermittent zone in over-tripped conditions. Towards the boundary-layer edge, the structure functions exhibit a growing departure from self-similarity and analytical prediction, and it is demonstrated that the departure is primarily due to external intermittency. Moreover, based on the conditional statistics concentrated in the turbulent regimes, it is revealed that the small scales in the turbulence regime are homogenized in a self-similar behaviour, which is independent of the current tripping conditions.

Drag reduction of the turbulent boundary layer over divergent sawtooth riblets surface with a superhydrophobic coat

Energy conservation and environmental protection have become pivotal components of the green economy. In recent years, underwater drag reduction technology has garnered significant interest. This study discusses a novel composite surface that combines divergent riblets with a superhydrophobic coating (D-rib&SHS) to enhance the drag reduction rate. Alongside this new surface, a riblet surface with a superhydrophobic coating (rib&SHS, without yaw angles) and a smooth surface are used as comparison groups. The turbulent boundary layer flow of these three surfaces is measured using a two-dimensional particle image velocimetry system. The results indicated that the maximum drag reduction rate of D-rib&SHS is approximately 27% higher than that of rib&SHS, and the drag reduction range is increased to Reθ≈4100 compared to rib&SHS (Reθ≈2200). Using correlation algorithms, it observed that the spacing between low-speed streaks over D-rib&SHS is larger than that of rib&SHS and the smooth surface. This finding suggested that the spacing between the hairpin vortex legs of D-rib&SHS is wider. The increased spacing between the hairpin vortex legs reduces the likelihood of vortex head formation between the two quasi-streamwise vortices, ultimately suppressing the auto-generation of hairpin vortices. Consequently, the development of hairpin vortex packets over D-rib&SHS is also inhibited. These phenomena observed over D-rib&SHS can be attributed to the combined effects of velocity slip on the superhydrophobic coating and the secondary flow over the divergent riblets near the wall. In addition, unlike divergent riblets that are not covered with a superhydrophobic coating, where the drag reduction effect is more pronounced with a yaw angle of 30° compared to 10°, D-rib&SHS with a 10° yaw angle demonstrated a superior drag reduction effect compared to D-rib&SHS with a 30° yaw angle. This innovative composite surface enhances the drag reduction effect and expands the drag reduction Reynolds number range, offering a new approach to mitigating drag in turbulent boundary layer flows.

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

The impact of bulk viscosity is unclear with considering the increased dilatational dissipation and compressibility effects in hypersonic turbulence flows. In this study, we employ direct numerical simulations to conduct comprehensive analysis of the effect of bulk viscosity on hypersonic turbulent boundary layer flow over a flat plate. The results demonstrate that the scaling relations remain valid even when accounting for large bulk viscosity. However, the wall-normal velocity fluctuations $v_{rms}^{\prime \prime }$ decrease significantly in the viscous sublayer due to the enhanced bulk dilatational dissipation. The intensity of travelling-wave-like alternating positive and negative structures of instantaneous pressure fluctuations $p_{rms}^{\prime }$ in the near-wall region decreases distinctly after considering the bulk viscosity, which is attributed mainly to the reduction of compressible pressure fluctuations $p_{c,rms}^{+}$ . Furthermore, the velocity divergence $\partial u_{i} / \partial x_{i}$ undergoes a significant decrease by bulk viscosity. In short, our results indicate that bulk viscosity can weaken the compressibility of the hypersonic turbulent boundary layer and becomes more significant as the Mach number increases and the wall temperature decreases. Notably, when the bulk-to-shear viscosity ratio of the gas reaches a few hundred levels ( $\mu _b/\mu =O(10^2)$ ), and mechanical behaviour of the near-wall region ( $\kern 0.06em y^+\le 30$ ) is of greater interest, the impact of bulk viscosity on the hypersonic cold-wall turbulent boundary layer may not be negligible.

Turbulent/non-turbulent interface of the turbulent boundary-layer over a spanwise-heterogeneous converging/diverging riblets rough wall

Turbulent boundary layer (TBL) flows over various spanwise-heterogeneous rough walls exhibit spanwise variations in turbulence statistics, implying modifications of the turbulent/non-turbulent interface (T/NTI). In this work, based on the datasets of TBL flows over a spanwise-alternating converging/diverging riblets wall, we investigate behavior of T/NTI, properties of ‘bubble’ and ‘drop’ that are associated with T/NTI, as well as connections between T/NTI and large-scale structures within the boundary layer. The flow datasets were obtained through stereoscopic particle image velocimetry measurements on the cross-stream plane of the TBL flow at a Reynolds number Reθ = 1.3 × 104. The T/NTI and associated ‘bubble’ and ‘drop’ are identified using a kinetic energy criterion, while the large-scale structures by a streak detection algorithm. It is observed that the T/NTI height and the occurrence of ‘bubble’ and ‘drop’ display a spanwise-heterogeneous feature, with lower T/NTI height and higher occurrence probability of ‘bubble’ over the diverging section of riblets than over the converging section of riblets. Results of conditional average show that the ‘bubble’ is associated with positive streamwise fluctuations, common-down flow and a pair of counter-rotating streamwise vortices, while the ‘drop’ with negative streamwise fluctuation, common-up flow and a pair of counter-rotating streamwise vortices. Probability density functions of the ‘bubble’ size and fractal dimensions of the T/NTI are found similar for both the riblets and smooth wall flows. Furthermore, it is observed that the large-scale low-speed structures occurring preferentially over the converging section of riblets play a role in elevating T/NTI while the large-scale high-speed ones over the diverging section of riblets lowering down T/NTI.

PARAMETRIC STUDY OF SUCTION OR BLOWINGEFFECTS ON TURBULENT FLOW OVER A FLATPLATE

The two-dimensional, incompressible, and turbulent boundary layer flow over a flat plate with suction or blowing from a spanwise slot is examined numerically. The mathematical modeling involves the derivation of the governing partial differential equations of the problems. These are the continuity, the momentum, the energy and the (K-ε) turbulence model. Besides, the perfect gas law is also used. A numerical solution of the governing equations is approximated by using a finite volume method, with staggered grid and modified SIMPLE algorithm. A computer program in FORTRAN 90 is built to perform the numerical solution.The developed computational algorithm is tested for the flow over a flat plate (4m) long with uniform suction or blowing velocity ratios of (V/U∞ =± 0.0185, ± 0.0463 and ±0.0925 m/s) are imposed on the slot for Reynolds number of (1.36 x 107 ), based on the plate length. The position of the slot change in the range of (X/L=1/4, 1/2 and 3/4) from leading edge and also, change width of slot in the value equal (0.12, 0.2 and 0.28m).The plate temperature is (70 °C), with the free stream velocity and temperature are (8.6m/s) and (25 °C) respectively. In addition, the effects of pitch angles on the flow field are investigated in the range of (30о   150о).The numerical results show that, for a uniform blowing, location of slot equal (X/L=1/4) from leading edge, a significant reduction of skin friction coefficient, wall shear stress and boundary layer thickness [displacement and momentum] to occur. While, an increase in boundary layer shape factor. Reynolds stress (uv) is more decreased than [(uu) and (vv)], mean velocity profiles in wall coordinates and dimensionless distance (U+, y+) decreases. When slot location is moved downstream to locations (X/L=1/2 or 3/4) a similar behavior can be said and most effective slot is obtained as (slot at X/L= 3m) from leading edge. While width of slot equal (0.28m) is better than values equal (0.12m and 0.2m). An opposite observations for the case of suction. The numerical results are compared with available numerical results and experimental data and a satisfactory results are obtained.

On the maximum velocity profile of wave boundary layer flows in the very rough turbulent regime

The maximum velocity profile in turbulent wave boundary layer flows has been experimentally investigated under both regular and irregular wave conditions. Four types of seabed models are adopted, i.e., smooth, sand-covered, uniform-sphere-covered and nonuniform-stone covered. The results show that the maximum overshoot increases with the decreasing A/ks (A is the semi-excursion of fluid particles in the free stream and ks is the bottom roughness), but it is not notably influenced by the irregularity of the waves nor the nonuniformity of bottom roughness elements. Two-dimensional numerical simulations are carried out to reveal the physics behind the large overshoot behavior. It is found that the gap flow accelerates around roughness elements and subsequently contributes to the overshoot. A three-parameter defect function is proposed that well describes the maximum velocity profile, and all three model parameters are correlated with the governing flow parameter A/ks.

THEORETICAL STUDY OF A THREE-DIMENSIONAL TURBULENT BOUNDARY LAYER OVER A ROTATING CONE OR DISK

In this study, we investigated turbulent boundary layer flow due to a rotating cone or disk. A comprehensive theoretical analysis was performed and the results for several physical quantities of significant interest are presented. The problem was modeled such that both cone and disk cases could be achieved under the same formulation. In most situations, comparisons were made with the experimental results available in the literature. A primary objective of this study was to present reliable results of a rotating cone or disk with respect to several physical quantities of significant interest in order to facilitate future studies. The results were obtained at 45° and 60° angles in the cone case and at a 90° angle in the disk case. The Keller-box method was applied to numerically solve the Reynolds-averaged Navier-Stokes equations. The mixing-length turbulent model was implemented to incorporate the turbulence effects. The validity of this method was first confirmed by comparing the obtained solution for the disk case with the existing literature produced by different researchers. Circumferential and radial velocity distributions and polar plots in the cone and disk cases are presented for Reynolds numbers up to Re<i><sub>r</sub></i> = 1 × 10<sup>6</sup>. However, the circumferential and radial skin-friction coefficients, combined friction coefficient, moment coefficient, boundary layer thickness, displacement thickness, velocity shape factor, flow rate, and flow swirl angle are provided up to Re<i><sub>r</sub></i> = 1 × 10<sup>8</sup>. We also noted that the asymptotic nature of velocities can be achieved by setting the value of grid parameter <i>K</i>.

Large‐eddy simulation of plume dispersion in a turbulent boundary layer flow generated by a dynamically controlled recycling method

AbstractWhen conducting large‐eddy simulations (LESs) of plume dispersion in the atmosphere, crucial issue is to prescribe time‐dependent turbulent inflow data. Therefore, several techniques for driving LESs have been proposed. For example, in the original recycling (OR) method developed by Kataoka and Mizuno (Wind and Structures, 2002, 5, 379–392), a mean wind profile is prescribed at the inlet boundary, the only fluctuating components extracted at the downstream position are recycled to the inlet boundary. Although the basic turbulence characteristics are reproduced with a short development section, it is difficult to generate target turbulent fluctuations consistent with realistic atmospheric turbulence. In this study, we proposed a dynamically controlled recycling (DCR) method that is a simple extension of the OR procedure. In this method, the magnitude of turbulent fluctuations is dynamically controlled to match with the target turbulent boundary layer (TBL) flow using a turbulence enhancement coefficient based on the ratio of the target turbulence statistics to the computed ones. When compared to the recommended data of Engineering Science Data Unit (ESDU) 85020, the turbulence characteristics generated by our proposed method were quantitatively reproduced well. Furthermore, the spanwise and vertical plume spreads were also simulated well. It is concluded that the DCR method successfully simulates plume dispersion in neutral TBL flows.

Prediction model based on artificial neural network and bivariate spectral quasi-linearization method for compressible turbulent boundary-layer flow over a smooth flat surface

The compressible two-dimensional turbulent flow solutions at an arbitrary point in time and space by incorporating the mass, momentum, and energy conservation equations over a smooth flat surface and parallel free stream with unfavorable pressure gradient are studied. The Falkner–Skan transformation is applied to the turbulent boundary-layer equations and related boundary conditions, and the resulting nonlinear coupled system of partial differential equations is solved by the bivariate spectral quasi-linearization method. Moreover, to predict the thermal distribution of the flow, an artificial neural network model has been developed with the Nusselt number as target values. Several plots have been depicted, it is evaluated that the mean squared error value is 6.41 × 10−7, the overall coefficient of determination (R) is 0.997 52, and the average error rate is 0.68% for the said model, indicating the attainment of high accuracy for estimation.

Localized Blowing for Near-Wake Flow and Vortical Structure Control in Turbulent Boundary Layers Over Periodic 2D Roughness

Abstract Volumetric three-component flow measurements were made to investigate localized blowing (injection) as a control strategy for turbulent boundary layers over k-type 2D roughness. The flow measurements were made using particle tracking velocimetry at a Reynolds number of 100,000. The roughness occupied ~ 13% of the boundary layer thickness and consisted of transverse square bars positioned periodically at a pitch to height ratio of 11. Two cases were considered: a baseline case without blowing and a case with blowing through five spanwise jets issuing from the downstream face of the 11th bar. The results highlight the effectiveness of blowing in reducing the size of the recirculation zone and turbulence past the bar. Specifically, the spanwise-averaged flow field for the blowing case shows a 40% reduction in the reattachment length and ~ 25% reduction in the maximum Reynolds shear stress relative to the baseline case. Moreover, visualizations of the vortical structures past the bars for the baseline case display coherent spanwise vortices similar to those observed past isolated 2D bars and backward-facing steps. Blowing disrupts these spanwise vortices and produces new weaker vortical structures with a wall-normal sense of rotation. As such, blowing results in a reduction in the spanwise-averaged spanwise vorticity characteristic of the flow over k-type 2D roughness. The disruption of the spanwise vortices and the reduction in the size of the recirculation zone are likely responsible for the reduction in the Reynolds shear stress and turbulent kinetic energy in the near wake.

Neutral and stratified turbulent boundary‐layer flow over low mountains

AbstractA theory for flow over gentle hills using a mixing‐length turbulence closure is developed to describe the transition from turbulent orographic form drag to gravity wave drag. It confirms that the first is associated with downstream sheltering, and the second with upstream blocking and strong downslope winds. It shows that the altitude at which the incident flow needs to be taken to calculate the drag is the inner layer scale at which dissipation equilibrates disturbance advection. It also shows that the parameter that controls the transition, here a Richardson number, compares the mountain length with the altitude of the turning points above which the upward‐propagating gravity waves become evanescent. Our solutions are also used to show that the downslope winds penetrate well into the inner layer and that a good fraction of the drag is deposited in the inner layer: all of it in the neutral case, a large fraction in the intermediate cases when there are trapped lee waves, and even in stable situations without trapping part of the gravity wave drag is eroded in the inner layer. Some discussion on how to combine neutral and stratified effects in the parametrization of subgrid scale orography in large‐scale models is given.

Advancing airborne Doppler lidar wind profiling in turbulent boundary layer flow – an LES-based optimization of traditional scanning-beam versus novel fixed-beam measurement systems

Abstract. There is a need for improved wind measurements inside the planetary boundary layer (PBL), including the capability to sample turbulent flow. Airborne Doppler lidar (ADL) provides unique capabilities for spatially resolved and targeted wind measurements in the PBL. However, ADL wind profiling in the PBL is challenging, as turbulence violates the flow homogeneity assumption used in wind profile retrieval and thereby introduces error in the retrieved wind profiles. As turbulence is a dominant source of error it is necessary to investigate and optimize ADL wind profiling capabilities in turbulent PBL flow. This study investigates the potential of a novel multiple-fixed-beam ADL system design to provide improved wind information in turbulent PBL flow compared to traditional single-scanning-beam ADL systems. To achieve this, an LES-based (LES: large eddy simulation) airborne Doppler lidar simulator presented in Gasch et al. (2020) is employed and extended in this study. Results show that a multiple-fixed-beam system with settings comparable to those of commonly used single-scanning-beam systems offers distinct advantages. Advantages include overall reduced wind profile retrieval error due to turbulence and improved spatial representation alongside higher wind profile availability. The study also offers insight into the dependence of the retrieval error on system setup parameters and retrieval parameters for both fixed-beam and scanning-beam systems. When using a fixed-beam system, an order of magnitude higher wind profile resolution appears possible compared to traditional scanning systems at comparable retrieval accuracy. Thus, using multiple-fixed-beam systems opens the door to better sampling of turbulent PBL flow. Overall, the simulator provides a cost-effective tool to investigate and optimize wind profile error characteristics due to turbulence and to optimize system setup and retrieval strategies for ADL wind profiling in turbulent flow.

Surrogate‐based optimization for active drag reduction of turbulent boundary layer flows

AbstractTwo surrogate‐based optimization strategies using support vector regression (SVR) and Gaussian process regression (GPR) as surrogates are investigated to guide the design of actuation parameters for active drag reduction techniques in turbulent boundary layer flows encountered at civil airplanes in cruise flight and high‐speed trains. As an approximation, the turbulent flow over a flat plate subjected to spanwise traveling transversal sinusoidal surface waves is simulated by wall‐resolved large‐eddy simulations (LESs). These simulation data are used to model the dependence of the objective drag reduction on the actuation parameters, that is, the optimization variables. In this work, the previous purely exploitative approach of SVR‐based ridgeline optimization is extended to GPR‐based Bayesian optimization to further automate the simulation‐driven tuning of the actuation parameters.

Spectral Characteristics of Fluctuating Aerodynamic Forces Acting on Rectangular Prisms

The present work is devoted to the role of boundary layer turbulence on the spectral characteristics of fluctuating wind loads on large aspect-ratio rectangular prisms. Seven rectangular rigid models with different side ratios (1/4~4) were created, and simultaneous pressure experiments were conducted under the boundary layer turbulence flows. Using the measured data, the power spectrums of the fluctuating aerodynamic forces were calculated, and then, the spectral characteristics under different turbulent boundary layer flows were analyzed. In contrast to the typical power spectrum model, the main factors affecting the spectral characteristics of the fluctuating aerodynamic loads are presented and discussed in this study. The power spectrum of the rectangular prism was significantly impacted by the turbulent wind field, primarily because higher turbulence intensity levels result in a lower spectral peak and a wider spectral bandwidth, which also redistributes spectral energy. In particular, the effect on the spectral properties of across-wind fluctuating loads was stronger, and the turbulent disturbance modified the lateral separation flow structure, causing the reattachment phenomenon to occur earlier on rectangular prisms with small side ratios, which effectively altered the spectral properties. Thus, a normalized across-wind fluctuating wind load spectrum model is proposed, taking into account the effects of incoming turbulence, the side ratio, vortex shedding, separation reattachment flow-induced spectral bandwidth changes, and high-frequency fluctuations.

Universal law of skin-friction coefficient in a fully developed zero pressure gradient axisymmetric turbulent boundary layer flow

Understanding the skin friction in an axisymmetric turbulent boundary layer (ATBL) flow is a key to designing and optimising the flow past axisymmetric bodies, for example, a rocket engine nozzle and a submarine hull. In this study, we propose a universal law of the skin-friction coefficient in an ATBL flow. The flow is steady and fully developed with a zero pressure gradient. The governing equation for the ATBL flow is derived by methodically applying the boundary layer approximation. Subsequently, the scaling law of the Reynolds shear stress, caused by turbulent eddies, at the surface tangential to the wall roughness summits is derived by incorporating the role of transverse curvature. The skin-friction coefficient in a smooth ATBL flow is found to depend on two parameters, namely, the Reynolds number based on the cylinder radius, Rea, and the ratio of boundary layer thickness to cylinder radius, δ/a. The analysis predicts a simple form of the skin-friction coefficient as ${C_f} = 4.56 \times {10^{ - 2}}{[R{e_a}\ln (1 + \delta /a)]^{ - 1/4}}$ , which agrees satisfactorily with the available experimental data and the numerical simulations in all the axisymmetric flow regimes. The proposed law, in the limit of infinite radius, is consistent with the classical law of the skin-friction coefficient in a plane turbulent boundary layer flow as ${C_{f0}}\sim Re_\delta ^{ - 1/4}$ , where Reδ is the Reynolds number based on the boundary layer thickness. This study reveals that, for δ/a < 1, the relative skin-friction coefficient, $({C_f} - {C_{f0}})/{C_{f0}}$ , follows a linear law with δ $/$ a.

Drag reduction using bionic groove surface for underwater vehicles.

Introduction: The reduction of drag is a crucial concern within the shipping industry as it directly influences energy consumption. This study addresses this issue by proposing a novel approach inspired by the unique ridge structure found on killer whale skin. The objective is to develop a non-smooth surface drag reduction method that can effectively decrease drag and improve energy efficiency for ships. Methods: The study introduces a technique involving the creation of transverse bionic groove surfaces modeled after the killer whale skin's ridge structure. These grooves are aligned perpendicular to the flow direction and are intended to modify the behavior of turbulent boundary layer flows that form around the ship's hull. Numerical simulations are employed using the Shear Stress Transport k-ω model to analyze the effects of the proposed groove surface across a wide range of flow conditions. The research investigates the impact of various parameters, such as the width-to-depth ratio (λ/A), groove depth, and inlet velocity, on the drag reduction performance of the bionic groove surface. Results: The study reveals several key findings. Optimal shape parameters for the bionic groove surface are determined, enabling the most effective drag reduction. The numerical simulations demonstrate that the proposed groove surface yields notable drag reduction benefits within the velocity range of 2∼12m/s. Specifically, the friction drag reduction ratio is measured at 26.91%, and the total drag reduction ratio at 9.63%. These reductions signify a substantial decrease in the forces opposing the ship's movement through water, leading to enhanced energy efficiency. Discussion: Comparative analysis is conducted between the performance of the bionic groove surface and that of a smooth surface. This investigation involves the examination of velocity gradient, streamwise mean velocity, and turbulent intensity. The results indicate that the bionic groove structure effectively mitigates viscous stress and Reynolds stress, which in turn reduces friction drag. This reduction in drag is attributed to the alteration in flow behavior induced by the non-smooth surface. Conclusion: The study proposes a novel approach for drag reduction in the shipping industry by emulating the ridge structure of killer whale skin. The transverse bionic groove surface, aligned perpendicular to flow direction, demonstrates promising drag reduction outcomes across diverse flow conditions. Through systematic numerical simulations and analysis of key parameters, the research provides insights into the drag reduction mechanism and identifies optimal design parameters for the groove surface. The potential for significant energy savings and improved fuel efficiency in maritime transportation underscores the practical significance of this research.

Near-wall numerical coherent structures and turbulence generation in wall-modelled large-eddy simulation

Near-wall turbulence structures and generation in the wall-modelled large-eddy simulation (WMLES) are revealed. To elucidate the turbulence structures driving a near-wall turbulence generation in the WMLES, flat-plate turbulent boundary-layer flows calculated by the WMLES and direct numerical simulation (DNS) are closely investigated. A conditional-averaging technique is applied to the instantaneous flow fields and the near-wall statistical structures of the ejection and sweep pairs, which produce the turbulence, are revealed to exist even in the WMLES although the structures are non-physically elongated compared with those obtained by the DNS. Since the near-wall turbulence structures in the WMLES are revealed not to be disordered, but to be coherent structures with low- and high-speed fluids alternating in the spanwise direction, it is suggested that the near-wall turbulence generation in the WMLES is explained by the numerically elongated coherent structures. Furthermore, the Reynolds number effects of wall-bounded turbulent flows, i.e. the appearance of the outer peak in the energy spectrum of the streamwise velocity fluctuations at increasing Reynolds numbers, is found not to be reproduced by the WMLES, and the origin of the outer peak is discussed in association with the inner–outer-layer interactions. The near-wall turbulence structures in the WMLES could depend heavily on the computational grids and the numerical methods. Therefore, additional cases varying the grid resolutions and the numerical methods (numerical schemes and sub-grid-scale models) are also conducted to confirm the consistency of the present conclusions.