Analysis Of Turbulent Boundary Layer Research Articles

Multi-scaling analysis of turbulent boundary layers over an isothermally heated flat plate with zero pressure gradient

A meticulous investigation into turbulent boundary layers over an isothermally heated flat plate with zero pressure gradient has been conducted. Eight distinct turbulence models, including algebraic yPlus, standard k-ω, standard k-ε, length-velocity, Spalart-Allmaras, low Reynolds number k-ε, shear stress transport, and v2-f turbulence models, are carefully chosen for numerical simulation alongside thermal energy and Reynolds-Averaged Navier-Stokes equations. A comparative analysis has determined that the Spalart-Allmaras model exhibits remarkable agreement with the results from direct numerical simulation, making it a reliable tool for predicting turbulent heat transfer and fluid flow, particularly at higher Prandtl and Reynolds numbers. Subsequently, a multi-scale investigation employs a comprehensive four-layer structure scheme and encompasses various momentum thickness Reynolds numbers of 1432, 2522, and 4000, and Prandtl numbers of 0.71, 2, and 5. The subsequent investigation reveals the governing non-dimensional numbers' substantial impact on the distribution and magnitude of mean thermal and flow characteristics. Notably, the scaling of mean thermal and momentum fields discloses the existence of a meso or intermediate layer characterized by a logarithmic nature unique to itself. The multi-scaling analysis of the flow field demonstrates greater conformity with the selected scaling variables primarily relying on the Reynolds number. Furthermore, the scaling of the energy field yields compelling outcomes within the inner and intermediate layers. However, according to the four-layer theory, minor discrepancies are observed in the outer layer when using the current scaling.

A GPU-Accelerated Particle Advection Methodology for 3D Lagrangian Coherent Structures in High-Speed Turbulent Boundary Layers

In this work, we introduce a scalable and efficient GPU-accelerated methodology for volumetric particle advection and finite-time Lyapunov exponent (FTLE) calculation, focusing on the analysis of Lagrangian coherent structures (LCS) in large-scale direct numerical simulation (DNS) datasets across incompressible, supersonic, and hypersonic flow regimes. LCS play a significant role in turbulent boundary layer analysis, and our proposed methodology offers valuable insights into their behavior in various flow conditions. Our novel owning-cell locator method enables efficient constant-time cell search, and the algorithm draws inspiration from classical search algorithms and modern multi-level approaches in numerical linear algebra. The proposed method is implemented for both multi-core CPUs and Nvidia GPUs, demonstrating strong scaling up to 32,768 CPU cores and up to 62 Nvidia V100 GPUs. By decoupling particle advection from other problems, we achieve modularity and extensibility, resulting in consistent parallel efficiency across different architectures. Our methodology was applied to calculate and visualize the FTLE on four turbulent boundary layers at different Reynolds and Mach numbers, revealing that coherent structures grow more isotropic proportional to the Mach number, and their inclination angle varies along the streamwise direction. We also observed increased anisotropy and FTLE organization at lower Reynolds numbers, with structures retaining coherency along both spanwise and streamwise directions. Additionally, we demonstrated the impact of lower temporal frequency sampling by upscaling with an efficient linear upsampler, preserving general trends with only 10% of the required storage. In summary, we present a particle search scheme for particle advection workloads in the context of visualizing LCS via FTLE that exhibits strong scaling performance and efficiency at scale. Our proposed algorithm is applicable across various domains, requiring efficient search algorithms in large, structured domains. While this article focuses on the methodology and its application to LCS, an in-depth study of the physics and compressibility effects in LCS candidates will be explored in a future publication.

Large-eddy simulation and streamline coordinate analysis of flow over an axisymmetric hull

A new perspective on the analysis of turbulent boundary layers on streamlined bodies is provided by deriving the axisymmetric Reynolds-averaged Navier–Stokes equations in an orthogonal coordinate system aligned with streamlines, streamline-normal lines and the plane of symmetry. Wall-resolved large-eddy simulation using an unstructured overset method is performed to study flow about the axisymmetric DARPA SUBOFF hull at a Reynolds number of $Re_L = 1.1 \times 10^{6}$ based on the hull length and free-stream velocity. The streamline-normal coordinate is naturally normal to the wall at the hull surface and perpendicular to the free-stream velocity far from the body, which is critical for studying bodies with concave streamwise curvature. The momentum equations naturally reduce to the differential form of Bernoulli's equation and the $s$ – $n$ Euler equation for curved streamlines outside of the boundary layer. In the curved laminar boundary layer at the front of the hull, the streamline momentum equation represents a balance of the streamwise advection, streamwise pressure gradient and viscous stress, while the streamline-normal equation is a balance between the streamline-normal pressure gradient and centripetal acceleration. In the turbulent boundary layer on the mid-hull, the curvature terms and streamwise pressure gradient are negligible and the results conform to traditional analysis of flat-plate boundary layers. In the thick stern boundary layer, the curvature and streamwise pressure gradient terms reappear to balance the turbulent and viscous stresses. This balance explains the characteristic variation of static pressure observed for thick boundary layers at the tails of axisymmetric bodies.

The effects of wall curvature and adverse pressure gradient on air ducts in HVAC systems using turbulent entropy generation analysis

Abstract In the present study, entropy generation analysis of turbulent boundary layer was carried out to examine the effects of the wall curvature and adverse pressure gradient (APG) on air distribution ducts in HVAC systems considering both individual and simultaneous effects of these parameters and using the empirical data. Six walls, including straight wall (A), convex curved wall (B1), concave curved wall (B2), straight wall with APG (D), convex curved wall with APG (C1), and concave curved wall with APG (C2) were investigated. The air distribution ducts can be divided into various geometries, including straight duct (A*), curved duct (B*), straight diffuser (D*), and curved diffuser (C*). Furthermore, for walls with APG (D, C1, and C2), the divergence angle was chosen in such a way that no flow separation occurred in the range under consideration. The findings showed that the entropy generation resulted from turbulence dissipation was highly important in the regions near the boundary layer edge, so that the ratio of the entropy generation rate due to the turbulence dissipation to the total entropy generation rate in the regions near the boundary layer edge approximates 0.9. In fact, in these regions, a large portion of the total entropy generation rate was related to turbulence dissipation. Consequently, the turbulence dissipation in these regions was too large to be ignored. Thus, in order to achieve a more precise criterion of the dissipation of air distribution ducts in HVAC systems, the turbulence dissipation should be taken into account.

Non-unique turbulent boundary layer flows having a moderately large velocity defect: a rational extension of the classical asymptotic theory

The classical analysis of turbulent boundary layers in the limit of large Reynolds number Re is characterised by an asymptotically small velocity defect with respect to the external irrotational flow. As an extension of the classical theory, it is shown in the present work that the defect may become moderately large and, in the most general case, independent of Re but still remain small compared to the external streamwise velocity for non-zero pressure gradient boundary layers. That wake-type flow turns out to be characterised by large values of the Rotta–Clauser parameter, serving as an appropriate measure for the defect and hence as a second perturbation parameter besides Re. Most important, it is demonstrated that also this case can be addressed by rigorous asymptotic analysis, which is essentially independent of the choice of a specific Reynolds stress closure. As a salient result of this procedure, transition from the classical small defect to a pronounced wake flow is found to be accompanied by quasi-equilibrium flow, described by a distinguished limit that involves the wall shear stress. This situation is associated with double-valued solutions of the boundary layer equations and an unconventional weak Re-dependence of the external bulk flow—a phenomenon seen to agree well with previous semi-empirical studies and early experimental observations. Numerical computations of the boundary layer flow for various values of Re reproduce these analytical findings with satisfactory agreement.

Turbulent Boundary Layer Under the Influence of Adverse Pressure Gradient

AbstractThe paper deals with the experimental analysis of turbulent boundary layer at the flat plate for large value of Reynolds number equal Reθ ≈︁ 3000. The adverse pressure gradient generated by curvature of the upper wall corresponded to the case of pressure variation in axial compressor. The fully developed structure of turbulence was achieved by proper triggering of the boundary layer. The mean and turbulent flow‐fields were investigated with the use of hot‐wire technique while mean and instantaneous pressure fields were examined with piezoelectric transducers. The scaling and turbulence structure of fully developed turbulent boundary layer under the influence of adverse pressure gradient revealed the more pronounced contribution of outer region to the downstream development of turbulent boundary layer. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental analysis of turbulent boundary layer under the influence of adverse pressure gradient

The paper deals with the experimental analysis of turbulent boundary layer at the flat plate for large value of Reynolds number equal Re θ ≈3000. The adverse pressure gradient is generated by curvature of the upper wall and corresponds to the case of pressure variation in axial compressor. The analysis is concentrated on the problem of scaling of turbulent boundary layer and on the physical background behind scaling laws being compared. The results obtained suggest, that boundary layer at APG conditions requires two velocity scales, i.e. inner (imposed by inner boundary condition) and outer (imposed by outer layer) velocity scales.

LES analysis of turbulent boundary layer over 3D steep hill covered with vegetation

Large eddy simulation (LES) is carried out to investigate the turbulent boundary-layer type of flows over a hill-shaped model with a steep slope. Also, we focus on the surface condition of a hill, such as vegetation effects as well as curvature effects. In order to model the vegetation effects for LES, we employ the feedback forcing method proposed by Goldstein et al. (1993, Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105, 354–366). In this model, the equation of motion for trees or grasses are coupled with the Navier–Stokes equation, so turbulence in the vegetation canopy can be numerically expressed. Instantaneous velocity profile of turbulent boundary layer on the corresponding surface is imposed at inflow boundary. Both the computed results over the hill with and without vegetation are in good agreement with Meng and Hibi's (1998. An experimental study of turbulent boundary layer over steep hills. In: Proceedings of 15th National Symposium on Wind Engineering, pp. 61–66.) experimental data for a rough and a smooth hill. Also, the effects of vegetation on turbulence statistics, such as high intensity due to the coherent flow structures at the top of the vegetation and reduction of turbulence inside the vegetation, are clarified.

Velocity and turbulence measurements in a separating boundary layer with and without passive flow control

The present paper reports the results of a detailed experimental study on low profile vortex generators (VGs) used to control boundary layer separation on a large-scale flat plate with prescribed adverse pressure gradients. This activity is part of a joint European research program on Aggressive Intermediate Duct Aerodynamics. The inlet turbulent boundary layer and the pressure gradient over the flat plate are representative of aggressive turbine intermediate ducts. By regulating the inclination of the wall opposite to the flat plate, different pressure gradients, typical of turbine intermediate ducts, can be obtained. To avoid separation on the movable wall, boundary layer suction is applied. Previous measurements showed the effectiveness of VGs in delaying separation and revealed their optimum configuration for the different prescribed pressure gradients. In the present work, laser Doppler velocimetry (LDV) is applied to the most significant pressure gradient case, in order to obtain a more thorough knowledge of the near-wall flow field. Velocity and turbulence profiles are determined up to the near-wall region in order to provide an in-depth analysis of turbulent boundary layer at separation conditions, with and without application of control devices. LDV allowed high spatial resolution and accurate statistical analysis of the boundary layer velocities. The results show velocity and turbulence profiles typical of separated turbulent boundary layers for the baseline case, and non-conventional unseparated boundary layer profiles when VGs are installed on the flat plate.

Bed shear in equilibrium scour around a circular cylinder embedded in a loose bed

The bed shear stress for a horseshoe vortex in the equilibrium scour hole around the base of a circular cylinder, embedded in a loose bed with a uniform approach flow under a clear water regime, is computed from turbulent boundary layer analysis by integrating the Navier—Stokes equations. Inside the thin boundary layer, which is developed by the reverse flow at the bed due to swirl motion, Pohlhausen's method is applied with an arbitrary 1/7th power distribution of velocity, as was assumed by Weber in solving turbulent boundary layer. Outside the boundary layer, the expressions of 3-D flow field given by Dey are used. Finally the above technique produces two unknowns, namely bed shear stress and boundary layer thickness. The expression of wall shear stress given by Blasius for turbulent flow in pipes as well as over flat plates is assumed for solving boundary layer thickness, and subsequently bed shear stress. The computational results of bed shear stress and boundary layer thickness are presented.

Numerical Analysis of Turbulent Boundary Layers with Injection and Suction through a Slit

A numerical analysis is made on the turbulent boundary layers with injection and suction through a slit using five different turbulence models. The five models are three eddy viscosity models (zero-, one- and two-equation models) and two different types Reynolds stress model. Published experimental data on the skin friction factor, the mean velocity profiles, and Reynolds stress profiles are used to assess the performance of the model calculations. Applicabilities of these models to the turbulent boundary layers with injection and suction are investigated. For flow with injection, the Reynolds stress model gives good agreement with the experimental data. The zero-equation model provides very accurate prediction for suction flow.

Numerical Analysis of Turbulent Boundary Layers with Injection and Suction through a Slit.

A numerical analysis is made on the turbulent boundary layers with injection and suction through a slit using the five different turbulent models. The five models are three eddy viscosity models (zero-, one- and two-equation models) and two different types of Reynolds stress model. Published experimental data on the skin friction factor, the mean velocity profiles, and Reynolds stress profiles are used to assess the performance of the model calculations. The applicabilities of these models on the turbulent boundary layers with injection and suction are discussed.

Difference Methods for Initial-Boundary-Value Problems and Flow Around Bodies

the boundary-layer differential equations. Included are the effects of suction and injection as well as heat and mass transfer and compressible boundary layers. The treatment of turbulent boundary layers is preceeded by a discussion of transition including a short outline of stability theory and presentation of experimental information. In turbulent flow, considerable space is provided for the modeling of the turbulent transport process, including time mean flow formulations (models of the inner and outer region), models based on turbulent kinetic energy, on energy and length scale (k-e models), and on Reynolds stress. Chapters are devoted to turbulent-free shear layers, boundary layers with variable density, and heat and mass transfer. The book presents a well-rounded and up-to-date introduction to our present knowledge of boundary-layer flow and its analysis. The author offers the book as text for upper division undergraduate and first-year graduate courses for mechanical, chemical, aeronautical, civil, and ocean engineering students. This reviewer suspects that the treatment, especially of the turbulent modeling, is too short for students to perform computer analysis of turbulent boundary layers without supporting material. Some detailed remarks: With the many parameters appearing in the text, it would be helpful to include their definitions in the section NOTATION or to refer to the pages where they are introduced. Notations in figures are sometimes not defined (e.g., in Figs. 6-11 and 7-38). The notations in Figs. 1-8, C and D, are identical—what is the difference? Such shortcomings should be removed in a second edition. In summary, the book is an excellent introduction to boundary-layer theory for those wanting information about our present knowledge of boundary-layer flow and our ability to predict its character. It can also be recommended as a textbook when additional supporting material is provided. E. R. G. Eckert University of Minnesota

Flow pattern transition and heat transfer of inverted annular flow

The characteristics of flow pattern transitions and heat transfer of a steady inverted annular flow (IAF) in a vertical tube are studied experimentally and analytically using freon R-113 as a working fluid. The heat transfer characteristics are divided into three regions and a heat transfer characteristic map is proposed. Flow patterns along the tube change from IAF to dispersed flow (DF) through inverted slug flow (ISF) for lower mass fluxes and through agitated inverted annular flow (AIAF) for higher mass fluxes. A flow pattern map is proposed and the boundaries of the flow patterns agree well with those of the heat transfer characteristic map. A turbulent boundary layer analysis is applied to IAF using modified Reichardt equations. Radial velocity and temperature profiles of both the gas and liquid phases are obtained. The predicted heat transfer coefficients agree well with the experimental results. The flow pattern transition criterion from IAF to AIAF is predicted by the analytical results and the Kelvin-Helmholtz instability and that from AIAF to DF is predicted by a previous drift flux model and a void fraction of 0.7. The predicted criteria agree well with the experimental results.

Plasma behavior in the boundary layer near a railgun surface

Viscous flow and thermal characteristics are theoretically analyzed for the plasma behind a moving projectile inside a railgun. When only convective effects are included in the turbulent boundary layer analysis, the results suggest a temperature maximum in the wall region for very-high-velocity flow. The case of radiative as well as convective transport has also been investigated for an optically thick boundary layer flow by application of an approximate method. Results show a sizable effect of radiation on the flow characteristics, especially on the heat transfer rate to the railgun surface. Specifically, the theory predicts that the heat flux to the wall is proportional to the square root of the sum of the radiation and convection parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of Turbulent Boundary Layer on Cascade and Rotor Blades of Turbomachinery

The momentum integral technique for predicting the boundary-layer growth in three-dimensi onal flow has been extended to include the entrainment equation as the closure model. The numerical solution is compared with the cascade, inducer, compressor, and fan rotor blade data from various sources. The agreement is found to be excellent in all cases, with the exception of the separated flow. Both the momentum thickness and the limiting streamline angle predicted from this analysis compare well with the measured data for a rotor blade. The technique is extremely useful in engineering design, analysis, and performance prediction.

Fundamental Studies of Turbulent Boundary Layers with Injection or Suction through Porous Walls : 2nd Report, Theoretical and Experimental Analysis of Turbulent Boundary Layers with Injection and Adverse Pressure Gradients

In this report, Truckenbrodt's method of analyzing the turbulent boundary layer with adverse pressure gradients has been extended to explain the properties of the turbulent boundary layers with injection. Applying the Truckenbrodt's method, and based on the fact of the One-Parameter Family advocated by Doenhoff and the others, the author intended to find a method of calculating the velocity profiles from the momentum thickness θ and the shape parameter H(=δ*/θ). As it was confirmed through many experiments that the concept of One-Parameter Family is applicable to the velocity profiles of turbulent boundary layers with injection, the author established a simple analytical method of calculating θand H from the momentum equation and the energy equation. Accordingly, the velocity profiles are easily determined as functions of given Reynolds number (Rx=u0 x/ν). Here, the theoretical equations of θ and H were examined by the author, and it is confirmed that the semi-empirical values of θ and H are in good agreement with measured ones. Moreover shearing stress at the wall and frictional work in the turbulent boundary layer were examined for the turbulent boundary layer with injection.

A Two-Region Model of the Turbulent Boundary Layer, With Emphasis on Interfacial Conditions

Presented herein is a turbulent boundary-layer analysis which is based on a two-region characterization for eddy viscosity. The eddy viscosity for the inner region is described with the usual wall law whereas the outer region, which is characterized by large eddy scales, is treated through an application of Prandtl’s eddy viscosity model for free shear flows. A similarity solution for the outer region is obtained for a linearized motion equation and suitably joined to the inner solution by requiring continuity of shear stress and eddy viscosity. The present matching criteria for the two regions result in the preservation of the velocity profile shape in the defect plane while simultaneously yielding the correct longitudinal development of all layer parameters. It is shown that interfacial conditions are, collectively, the particular feature of incompressible flow which can serve as the point of reference for variable density transformations. A simple, parametric density scaling of the eddy viscosity is employed to demonstrate that the inner layer is much less sensitive to the density variation than the outer region. An improved compressibility transformation, based on ρε = ρ¯ε¯, is advanced.

Fundamental Studies of Turbulent Boundary Layers with Injection or Suction through Porous Wall : 1st Report, Analysis of Turbulent Boundary Layers on Flat Plate with Injection

This report presents the results of a basic research into turbulent boundary layers with injection. The research was conducted solely from considerations of fluid dynamics. It is intended to solve technical problems concerned with a sweat cooling system for gas turbine blades. In the first stage, a theoretical formula for velocity profile in a turbulent inner layer without injection was formed from a basic equation of motion by applying to it the Prandtl's mixing length theory. Separately from this, a turbulent outer layer along a flat plate is understood as one which is featured by the phenomenon of intermittency. Then, the intermittency theory has been amplified to substantiate that the phenomenon in the outer layer can be solved by statistic means. In the next stage, the same theory has been utilized to explain the whole region of turbulent boundary layers with injection. In addition, correlations among factors, which symbolize the velocity profile for turbulent boundary layers, have been found from experimental values. Finally it was proved that the theoretical velocity profile and the mean skin friction for turbulent boundary layers can be calculated simply by using correlative and momentum equations.

Separation Prediction for Conical Diffusers

A method of incompressible turbulent boundary-layer analysis based on the D parameter introduced by D. Ross is applied to conical-diffuser flow. The separation conditions are shown to depend on the initial momentum-thickness Reynolds number and a distance parameter involving the initial momentum thickness, the initial radius, and the diffuser length. Comparison with experimental information on diffuser separation indicates that the predictions are reliable, but conservative.