Turbulent Boundary Layer Wall Research Articles

Stochastic modelling of the instantaneous velocity profile in rough-wall turbulent boundary layers

The statistical properties of uniform momentum zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatiotemporally resolved velocity dataset, covering a field of view of $8 \times 9\,{\rm m}^2$ , was obtained in the atmospheric surface layer using super-large-scale particle image velocimetry (SLPIV), as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA). Wind tunnel data from a previous study are included for comparison (Heisel et al., J. Fluid Mech., vol. 887, 2020, R1). The probability density function of UMZ attributes such as their thickness, modal velocity and averaged vertical velocity are built at varying elevations and modelled using log-normal and Gaussian distributions. Inverse transform sampling of the distributions is used to generate synthetic step-like velocity profiles that are spatially and temporally uncorrelated. Results show that in the wide range of wall-normal distances and $Re_\tau$ up to $\sim O(10^6)$ investigated here, shear velocity scaling is manifested in the velocity jump across shear interfaces between adjacent UMZs, and attached eddy behaviour is observed in the linear proportionality between UMZ thickness and their wall normal location. These very same characteristics are recovered in the generated instantaneous profiles, using both fully stochastic and data-driven hybrid stochastic (DHS) models, which address, in different ways, the coupling between modal velocities and UMZ thickness. Our method provides a stochastic approach for generating an ensemble of instantaneous velocity profiles, consistent with the structural organisation of UMZs, where the ensemble reproduces the logarithmic mean velocity profile and recovers significant portions of the Reynolds stresses and, thus, of the streamwise and vertical velocity variability.

A Residual Thermodynamic Analysis of Turbulence – Part 1: Theory

A new theoretical groundwork for the analysis of wall-bounded turbulent flows is offered, the application of which is presented in a parallel paper. First, it is proposed that the turbulence phenomenon is connected to the onset of an irreversible process – specifically the action of a slip flow – by which a new fundamental model can be derived. Fluid cells with specific dimensions – of length connected with the local slip length and thickness connected with the distance between two parallel slipping flows – can be hypothetically constructed, in which a specific kinetic energy dissipation can be considered to occur. Second, via a maximum entropy production process a self-organized grouping of cells occurs – which results in the distinct zones viscous sublayer, buffer layer, and the log-law region to be built up. It appears that the underlying web structure may take the form of either representing a perfect web structure without any visible swirls, or a partially defect web structure where unbalanced forces may result in the generation of apparent swirls – which in turn might grow into larger turbulent eddies. Third, on the transition from laminar to turbulent flows, a nominal connection between the onset of a turbulent wall boundary layer (in a pipe flow), the Reynolds number as well as the wall surface roughness can be derived.

Fluctuating Pressure Beneath Smooth Wall Boundary Layers in Nonequilibrium Pressure Gradients

An experimental investigation is made of smooth wall turbulent boundary layers under a family of continually varying streamwise pressure gradient distributions. In general, the effects of these pressure gradient cases on the boundary layer are found to be nonlocal and dependent on upstream history effects. However, the friction Reynolds number grows independent of applied pressure gradient and appears to be dependent only on the origin of the turbulent boundary layer. Special attention is paid to the statistics of the fluctuating pressure on the immersed surface, and it is found that there is a spectral-region-dependent relationship between pressure gradient and the fluctuating wall pressure, indicating the lack of a universal overlap region and providing insight into the impact of pressure gradient history on turbulence evolution. The classical viscous inner scaling of the pressure spectra appears universal as does a proposed mixed variable low-frequency scaling. The impact of the pressure gradients on the pressure space-time correlations and convection velocities is more locally dependent. The implications of these observations on our understanding of nonequilibrium flows are explored, and it is postulated that such flows may be describable as a three-dimensional space governing the mean growth, pressure gradient effect, and nonequilibrium effect, respectively.

A new equivalent sand grain roughness relation for two-dimensional rough wall turbulent boundary layers

The effects of different geometries of two-dimensional (2-D) roughness elements in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) on turbulence statistics and drag coefficient are assessed using single hot-wire anemometry. Three kinds of 2-D roughness are used: (i) circular rods with two different heights, $k= 1.6$ and 2.4 mm, and five different streamwise spacing of $s_{x}= 6k$ to $24k$ , (ii) three-dimensional (3-D) printed triangular ribs with heights of $k= 1.6$ mm and spacing of $s_{x}= 8k$ and (iii) computerized numerical control (CNC) machined sinewave surfaces with two different heights, $k= 1.6$ and 2.4 mm, and spacing of $s_{x}= 8k$ . These roughnesses cover a wide range of ratios of the boundary layer thickness to the roughness height ( $23 < \delta /k < 41$ ), where $\delta$ is the boundary layer thickness. All roughnesses cause a downward shift on the wall-unit normalised streamwise mean velocity profile when compared with the smooth wall profiles agreeing with the literature, with a maximum downward shift observed for $s_{x}= 8k$ . In the fully rough regime, the drag coefficient becomes independent of the Reynolds number. Changing the roughness height while maintaining the same spacing ratio $s_{x}/k$ exhibits little influence on the drag coefficient in the fully rough regime. On the other hand, the effective slope $(ES)$ and the height skewness $(k_{sk})$ appear to be major surface roughness parameters that affect the drag coefficient. These parameters are used in a new expression for $k_{s}$ , the equivalent sand grain roughness, developed for 2-D uniformly distributed roughness in the fully rough regime.

Modeling of Cube Array Roughness: RANS, Large Eddy Simulation, and Direct Numerical Simulation

AbstractFlow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using direct numerical simulation (DNS) and large eddy simulation (LES), the ability of sublayer-resolved Reynolds-averaged Navier–Stokes (RANS) to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case: a low Reynolds number k–ϵ model, the Menter k–ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

Near Source Modeling of Pollutant Emissions From an Elevated Source Over an Urban Area Under Cross High Ventilation

Abstract Due to the rapid urbanization of many cities around the world, industrial manufacturing plants have grown rapidly, thus leading to the release of large amounts of pollutants into the environment. This is the main reason for the degradation of the local air quality, resulting in an increased risk of unfavorable sanitary conditions for city dwellers. Understanding the dispersion of pollutants in local population environments, meteorological conditions and other physical characteristics is fundamental for predicting and evaluating air quality. This paper provides comprehensive details on the study of flow patterns and pollutant dispersion processes in urban areas. Several factors which include building geometry, local atmospheric effects, structural obstructions, and velocity of exhaust pollutants are examined considering field data, wind tunnel tests, operational simulation techniques, and computational fluid dynamics. Good agreements are noticeable. Simultaneous evolutions of the velocity, thermal and scalar mass fraction fields of the pollutant emitting from a three-dimensional elevated source around a rectangular obstacle placed on a turbulent boundary layer wall, and also downstream the obstacle, have been successfully carried out. The most serious pollutant levels in urban areas under various high wind velocities are identified.

Spatial resolution effects on measurements in a rough wall turbulent boundary layer

Spatial resolution effects on measurements in a rough wall turbulent boundary layer

The Development and Application of a Kinetic Theory for Modeling Dispersed Particle Flows

Abstract This Freeman Scholar article reviews the formulation and application of a kinetic theory for modeling the transport and dispersion of small particles in turbulent gas-flows. The theory has been developed and refined by numerous authors and now forms a rational basis for modeling complex particle laden flows. The formalism and methodology of this approach are discussed and the choice of closure of the kinetic equations involved ensures realizability and well posedness with exact closure for Gaussian carrier flow fields. The historical development is presented and how single-particle kinetic equations resolve the problem of closure of the transport equations for particle mass, momentum, and kinetic energy/stress (the so-called continuum equations) and the treatment of the dispersed phase as a fluid. The mass fluxes associated with the turbulent aerodynamic driving forces and interfacial stresses are shown to be both dispersive and convective in inhomogeneous turbulence with implications for the build-up of particles concentration in near wall turbulent boundary layers and particle pair concentration at small separation. It is shown how this approach deals with the natural wall boundary conditions for a flowing particle suspension and examples are given of partially absorbing surfaces with particle scattering and gravitational settling; how this approach has revealed the existence of contra gradient diffusion in a developing shear flow and the influence of the turbulence on gravitational settling (the Maxey effect). Particular consideration is given to the general problem of particle transport and deposition in turbulent boundary layers including particle resuspension. Finally, the application of a particle pair formulation for both monodisperse and bidisperse particle flows is reviewed where the differences between the two are compared through the influence of collisions on the particle continuum equations and the particle collision kernel for the clustering of particles and the degree of random uncorrelated motion (RUM) at the small scales of the turbulence. The inclusion of bidisperse particle suspensions implies the application to polydisperse flows and the evolution of particle size distribution.

The Influence of Element Thermal Conductivity, Shape, and Density on Heat Transfer in a Rough Wall Turbulent Boundary Layer With Strong Pressure Gradients

Abstract Formation mechanisms for turbine roughness are manifold, including erosion, corrosion, deposition, and spallation or more recently additive manufacturing processes. Consequently, the resulting surfaces differ remarkably not only in roughness shape, height, and density but also in element thermal conductivity. Because the roughness elements extend into the boundary layer, their temperature distribution has a direct influence on the thermal boundary layer and thus on the resulting convective heat transfer. In the current study, heat transfer distributions along a flat plate with more than 20 deterministic rough surface topographies that differ in element eccentricity, height and density are measured. For each surface roughness, measurements are conducted using two different element thermal conductivities (0.2 W/(mK) and 30 W/(mK)), two pressure distributions, four Reynolds numbers between 3 × 105 and 7.5 × 105 and various inlet turbulence intensities in the range of 1.5 % to 8 %. The pressure distributions resemble a typical suction and pressure side, respectively. Results show a heat transfer increase of up to 60 % for the high thermal conductivity surfaces and up to 50 % for the low conductivity ones. While heat transfer on the high conductivity surfaces is always higher than on the low conductivity ones, the difference becomes smaller with decreasing element density.

Reynolds number effect on the response of a rough wall turbulent boundary layer to local wall suction

Abstract

Airfoil profile surface drag reduction characteristics based on the structure of the mantis shrimp abdominal segment

To reduce the drag of fluid on a surface, the parameterized structure of the mantis shrimp abdominal segment was analyzed to design the airfoil profile, and a calculation model was established based on the biological characteristics of the mantis shrimp. By using a numerical simulation method, the change in the viscous sublayer and drag reduction of the biological surface under different flow velocities and with different numbers of airfoil profiles was analyzed, and the mechanism of the drag reduction of the biological airfoil profile was revealed. The results show that the biological surface with airfoil profiles exhibited a better drag reduction effect. With an increase in airfoil profile numbers, the drag reduction rate first decreased and then increased. When the flow velocity was 10 m/s and the number of airfoil profiles was 5, the drag reduction rate exhibited the largest value of 15.33%. This result showed that the biological airfoil profile could affect the structure of the wall turbulent boundary layer and diminish the velocity gradient of the boundary layer, which finally changed the interaction pattern between the fluid and wall. In addition, the vortex cushioning effect was created to change the friction between the fluid and the wall into a rolling friction with a lower friction coefficient, thus reducing the shear stress on the wall, which achieved drag reduction.

Assessment of the wall-adapting local eddy-viscosity model in transitional boundary layer

The main idea of this manuscript is to assess the wall-adapting local eddy-viscosity (WALE) model, which is designed for large-eddy simulation (LES) of turbulent boundary layer, in transitional flow. In contrast to many other sub-grid-scale (SGS) models, the WALE model demonstrates the asymptotic decay of the eddy viscosity in the vicinity of a solid wall in turbulent boundary layer without relying on a dynamic procedure on the SGS model coefficient. Furthermore, the WALE model yields zero eddy viscosity in pure shear flow. Such features are attractive for LES of laminar-to-turbulent transition, yet the WALE model has not been thoroughly investigated in transitional boundary layer flow. Well-resolved LES is conducted for canonical boundary layer transition triggered by sub-harmonic resonance. The model formulation is thoroughly analyzed in the transition process. The asymptotic behavior of the two major tensors, i.e., the strain rate tensor and the traceless tensor of the velocity gradient squared, are confirmed in the current well-resolved LES. The cubic decay of the eddy viscosity in the wall distance is confirmed from the asymptotic analysis on the transitional flow. The presence of the strain rate in the model formulation generates practically zero eddy viscosity in the pre-transition region, allowing interactions of small-amplitude instabilities. The traceless tensor of the velocity gradient squared escalates if small-scale eddies appear, leading to sizable eddy viscosity particularly in the log-law layer in turbulent flow. The response of the WALE model to grid resolution is also discussed. The performance of the WALE model is compared to two other SGS models, Smagorinsky and Vreman models with a constant coefficient, in the current transitional wall-bounded flow.

Roughness effect in an initially laminar channel flow

The possibility of generating and maintaining turbulence in an initially laminar channel flow is investigated for two Reynolds numbers and 2100 (based on bulk velocity, and half-height of the channel, ). The study is carried out through a direct numerical simulation based on the lattice Boltzmann method (LBM). The channel consists of two parallel walls separated by a distance where the roughness elements are mounted on both walls. It was observed that when the transverse square bars span half the width of the channel and are mounted in a ‘staggered’ formation, the flow becomes fully turbulent with strong similarities to fully rough wall turbulent channel flows at much higher Reynolds number, as reported in the literature. For example, the rough wall mean velocity profile exhibits a significant downward shift when compared to the smooth wall one. Also, the turbulent kinetic energy budget is similar to its counterpart in rough wall turbulent channel flows at much higher Reynolds numbers than the present ones. It is further shown that the present velocity spectra compared very well with that obtained in a rough wall turbulent boundary layer. Finally, some elements of the possible physical mechanism allowing the generation, growth and sustainability of turbulence are proposed.

Effects of wall suction on a 2D rough wall turbulent boundary layer

Hot-wire measurements carried out in a 2D rough wall turbulent boundary layer subjected to a wall suction through a porous strip show that the outer part of the boundary layer is deflected inward (toward the wall), thus impacting on the roughness elements close to the suction strip. This leads to an increased drag coefficient associated with an increased energy input, arguably, resulting from an intensified shedding of vortical structures from the roughness elements. Conversely to the smooth wall case, suction does not lead to relaminarization of the boundary layer. It also seems that suction does not alter significantly the turbulence structure of the boundary layer.

Characterization of Freestream Disturbances in Conventional Hypersonic Wind Tunnels

Although low-disturbance (“quiet”) hypersonic wind tunnels are believed to provide more reliable extrapolation of boundary-layer transition behavior from ground to flight, the presently available quiet facilities are limited to Mach 6, moderate Reynolds numbers, low freestream enthalpy, and subscale models. As a result, only conventional (“noisy”) wind tunnels can reproduce both Reynolds numbers and enthalpies of hypersonic flight configurations and must therefore be used for flight vehicle test and evaluation involving high Mach number, high enthalpy, and larger models. This paper outlines the recent progress and achievements in the characterization of tunnel noise that have resulted from the coordinated effort within the AVT-240 specialists group on hypersonic boundary-layer transition prediction. The new experimental measurements cover a range of conventional wind tunnels with different sizes and Mach numbers from 6 to 14 and extend the database of freestream fluctuations within the spectral range of boundary-layer instability waves over commonly tested models. New direct numerical simulation datasets elucidate the physics of noise generation inside the turbulent nozzle wall boundary layer, characterize the spatiotemporal structure of the freestream noise, and account for the propagation and transfer of the freestream disturbances to a Pitot-mounted sensor.

The spatial structure of the logarithmic region in very-high-Reynolds-number rough wall turbulent boundary layers

Using super-large-scale particle image velocimetry (SLPIV), we investigate the spatial structure of the near-wall region in the fully rough atmospheric surface layer with Reynolds number$Re_{\unicode[STIX]{x1D70F}}\sim O(10^{6})$. The field site consists of relatively flat, snow-covered farmland, allowing for the development of a fully rough turbulent boundary layer under near-neutral thermal stability conditions. The imaging field of view extends from 3 m to 19 m above the ground and captures the top of the roughness sublayer and the bottom of an extensive logarithmic region. The SLPIV technique uses natural snowfall as seeding particles for the flow imaging. We demonstrate that SLPIV provides reliable measurements of first- and second-order velocity statistics in the streamwise and wall-normal directions. Our results in the logarithmic region show that the structural features identified in laboratory studies are similarly present in the atmosphere. Using instantaneous vector fields and two-point correlation analysis, we identify vortex structures sharing the signature of hairpin vortex packets. We also evaluate the zonal structure of the boundary layer by tracking uniform momentum zones (UMZs) and the shear interfaces between UMZs in space and time. Statistics of the UMZs and shear interfaces reveal the role of the zonal structure in determining the mean and variance profiles. The velocity difference across the shear interfaces scales with the friction velocity, in agreement with previous studies, and the size of the UMZs scales with wall-normal distance, in agreement with the attached eddy framework.

Turbulence investigation in the roughness sub-layer of a near wall flow

The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.

Flow past a near-wall retrograde rotating cylinder at varying rotation and gap ratios

The flow past a circular cylinder that is rotating retrograde near a turbulent wall boundary layer at Re = 10 000 has been investigated experimentally using particle image velocimetry (PIV). The cylinder rotates in retrograde direction with different rotation ratios from α = 0 to 2, where α is defined as the ratio of the peripheral speed on the cylinder surface divided by the free-stream velocity. The gap ratio, G* = G/D, is varied between 0 and 1.6, where G is the gap between the cylinder and the plane wall, and D is the cylinder diameter. The flow structure is greatly modified due to the influence of wall proximity and cylinder rotation, notably the onset/suppression, frequency and strength of vortex shedding. Similar to a near-wall stationary cylinder, there exists a critical gap ratio (about 0.4) below which periodic vortex shedding from the cylinder is suppressed. On the other hand, the cylinder rotation causes vortex shedding to cease at α ≥ 1.6, which is slightly lower than the reported value of α ≈ 2 in the literature on rotating cylinder in uniform flow. However, reducing G* and increasing α do not always favor the suppression of vortex shedding. In fact, cylinder rotation promotes vortex shedding over a certain range (α < 1). As α increases, the length of recirculation region behind the cylinder, which is indicated by the movement of the mean saddle point, decreases almost linearly. The effects of wall proximity and cylinder rotation are also evident on the ensemble-averaged flow field, such as the turbulent kinetic energy and Reynolds shear stress.

КОМПЛЕКСНИЙ МЕТОД РОЗРАХУНКУ ОПОРУ ТЕРТЯ І ТЕПЛООБМІНУ НА ПОВЕРХНІ ЛЬОТНИХ ОСЕСИМЕТРИЧНИХ ОБ’ЄКТІВ ПРИ ПОЛЬОТІ ПО ТРАЄКТОРІЇ З НАЯВНІСТЮ В ПРИСТІННОМУ ПРИКОРДОННОМУ ШАРІ НЕІЗОТЕРМІЧНОСТІ, СТИСЛИВОСТІ, ЛАМІНАРНО-ТУРБУЛЕНТНОГО ПЕРЕХОДУ ТА РЕЛАМІНАРІЗАЦІЇ

The complex method of calculation of aerodynamic resistance of friction and heating on the surface of flight axisymmetric bodies of rotation like a jet uncontrollable shell is developed. The method allows to carry out calculations from the moment of start to landing in limits to-, a trance- and supersonic speeds of flight. Range of speeds corresponds to М∞ ≤ 3,0 Mach numbers. When calculating the phenomena of a non-isothermicity, compressibility, laminar-turbulenttransition and a relaminarization which occur on streamline surfaces when flying on a trajectory are considered. The method is based on use of the asymptotic theory ofa wall turbulent boundary layer ofS.S. Kutateladze and A. І. Leontyeva in combination with results of the linearized theory of flow of bodies of rotation, the theory of turbulent spots of Emmons of a transitionalboundary layer and data on Reynolds numbers of the beginning of laminar-turbulenttransition received by results of flight experiments. On the basis of the carried-out calculations of parameters of a stream on a streamline surface of a shell when flying on a trajectory from the moment of start to landing in limits to-, a trance- and supersonic speeds of flight with use of the boundary numbers of laminar-turbulent transitionreceived in flight experiments it is established that flow of a considerable part of a surface of a shell happens in the conditions of laminar-turbulent transition and a relaminarization which occupy an essential part of the general time of flight. Existence of a reverse of laminar-turbulent transition is established by a settlement way. The analysis of values of temperature on a surface of a head part of a rocket when flying on a settlement trajectory has shown that for rather short period there is an aerodynamic heating of a surface which significantly influences the aerodynamic resistance of friction by a non-isothermicity in a wall boundary layer. The conclusion is drawn that the linearized theory of calculations of flow of rather thin bodies of rotation can be used for calculation of parameters on external border of boundary layer of axisymmetric bodies of rotation like a jet uncontrollable shell in limits to-, a trance- and supersonic speeds of flight for the purpose of account longitudinal to pressure gradient when calculating friction and heating. Use of the linearized theory of flow for calculation of parameters on external border of boundary layer in limits to-, a trance- and supersonic speeds of flight allows to create a "fast" algorithm of calculation of resistance of friction and heating taking into account a longitudinal gradient of pressure existing on the streamline surfaces of axisymmetric bodies of rotation. Numerical results of calculations of parameters of a nonviscous current on external border of boundary layerfor the linearized theory, coefficient of a intermittency, temperature of heating of a surface of a shell and resistance of friction from the start moment before landing are given

Prediction of Rough Wall Turbulent Boundary Layer with DNS and Proposal of an Observation Method

Prediction of Rough Wall Turbulent Boundary Layer with DNS and Proposal of an Observation Method