Mean Flow Properties Research Articles

Supersonic Boundary Layers with Periodic Surface Roughness

In the present study, the effects of large-scale periodic surface roughness on a high-speed (M = 2.86), high Reynolds number (Re θ ≈ 60,000), supersonic turbulent boundary layer was examined. Two roughness topologies (square and diamond) were compared with an aerodynamically smooth wall. The measurements included planar contours of the mean and fluctuating velocity, pitot pressure profiles, pressure-sensitive paint, and schlieren photography. The local strain-rate distortion parameters for the square roughness pattern were small (∼-0.01), and the mean and turbulent flow properties followed the canonical rough-wall boundary-layer trends. The diamond-shaped roughness topology produced a pattern of attached oblique shocks and expansion waves that led to strong distortion parameters. The distortions varied from -0.3 to 0.4 across the roughness elements, which resulted in localized extra turbulence production that generated large periodic variations in the turbulence levels across individual roughness elements that spanned the boundary-layer thickness; for example, the Reynolds shear stress varied by ∼100%. This result demonstrated a mechanism for altering the turbulence in supersonic boundary layers.

Influence of a Coflowing Ambient Stream on a Turbulent Axisymmetric Buoyant Jet

This paper reports numerical results on turbulent buoyant axisymmetric jets in a coflowing ambient stream. The objective of this study is to compare the performance of the Reynolds stress algebraic model (ASM) with that of the k-ε turbulence model in predicting the flow field. A finite difference method has been used to solve a system of coupled partial differential equations. A comparison has been carried out between the numerical results obtained in the present work and experimental and numerical data reported in the literature. It has been found that the two investigated models reasonably predict the mean flow properties of the flow field. Nevertheless, the ASM proves to be better than the k-ε method to predict the effects of buoyancy and the turbulence structure. It has been found that the increase of the coflow can slow the development of the jet to the state of similarity of mean characteristic profiles. A jet with a ratio of coflow velocity u¯∞ to jet discharge velocity u¯0 less than 0.05 has developed to closely approximate a free jet in a stagnant medium while a jet with higher u¯∞∕u¯0 ratio never reaches a similarity state. In buoyant jets, only a flow with u∝∕u0⩽0.05 reaches a similarity state. Buoyancy ensures that the similarity region begins at a distance closer to the nozzle exit than if the medium is stagnant.

The Effects of Canopy Leaf Area Index on Airflow Across Forest Edges: Large-eddy Simulation and Analytical Results

The structure of turbulent flows along a transition between tall-forested canopies and forest clearings continues to be an active research topic in canopy turbulence. The difficulties in describing the turbulent flow along these transitions stem from the fact that the vertical structure of the canopy and its leaf area distribution cannot be ignored or represented by an effective roughness length. Large-eddy simulation (LES) runs were performed to explore the effect of a homogeneous variation in the forest leaf area index (LAI) on the turbulent flow across forest edges. A nested grid numerical method was used to ensure the development of a deep boundary layer above the forest while maintaining a sufficiently high resolution in the region close to the ground. It was demonstrated that the LES here predicted first-order and second-order mean velocity statistics within the canopy that agree with reported Reynolds-Averaged Navier–Stokes (RANS) model results, field and laboratory experiments. In the simulations reported here, the LAI was varied between 2 and 8 spanning a broad range of observed LAI in terrestrial ecosystems. By increasing the forest LAI, the mean flow properties both within the forest and in the clearing near the forest edge were altered in two fundamental ways: near the forest edge and into the clearing, the flow statistical properties resembled the so-called back-facing step (BFS) flow with a mean recirculation zone near the edge. Another recirculation zone sets up downstream of the clearing as the flow enters the tall forest canopy. The genesis of this within-forest recirculation zone can be primarily described using the interplay between the mean pressure gradients (forcing the flow) and the drag force (opposing the flow). Using the LES results, a simplified analytical model was also proposed to explain the location of the recirculation zone inside the canopy and its dependence on the forest LAI. Furthermore, a simplified scaling argument that decomposes the mean velocity at the outflow edge into a superposition of ‘exit flow’ and BFS-like flow with their relative importance determined by LAI was explored.

Turbulence Characteristics of Open-Channel Flow with Bed Suction

The influence of bed suction on the characteristics of turbulent open channel flow is studied in a laboratory flume using a two-component laser Doppler velocimeter. The experimental results show how bed suction significantly affects the mean flow properties, turbulence levels, and Reynolds stress distributions. The data reveal the presence of a more negative vertical (downward) velocity. The results also show how the horizontal and vertical turbulence intensities and Reynolds shear stresses respond to suction. All these properties are found to reduce with increasing relative suctions: decreasing more rapidly around the bed region than that near the free surface. In the downstream direction, the flow structure in the suction zone undergoes a process of rapid readjustment within a transitional region. Beyond this region, the turbulence flow structures asymptotes toward an “equilibrium” region.

Corotating Disk Assembly with Turbulent Through Flow

Turbulent flow in a paired corotating disk assembly with through flow is studied numerically. A RANS equation with near wall turbulence model is used in conjunction with an isotropic eddy viscosity model to disclose the mean and turbulent flow properties. The velocities and the mean shear vectors change directions continuously as they move away from wall. The lag angle between them is up to 31° within the log layer and precludes the use of log laws to bridge the near wall flow. A wake less wall law represents the resultant velocity profile in terms of wall coordinates. The disks' moment coefficient is lower than the one found for free-disk flows but it follows the same tendency. The turbulent flow properties are in qualitative agreement with recent experimental measurements and DNS on disk flows.

Interaction of waves, surface currents, and turbulence: the application of surface-following coordinate systems

Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, either implicitly or explicitly. In order to calculate the effect of wind forcing on waves and currents, and vice versa, it is necessary to employ a consistent formulation of the energy and momentum balance within the airflow, wave field, and water column. It is very advantageous to apply surface-following coordinate systems, whereby the steep gradients in mean flow properties near the air-water interface in the cross-interface direction may be resolved over distances which are much smaller than the height of the waves themselves. We may account for the waves explicitly by employing a numerical spectral wave model, and applying a suitable theory of wave-mean flow interaction. If the mean flow is small compared with the wave phase speed, perturbation expansions of the hydrodynamic equations in a Lagrangian or generalized Lagrangian mean framework are useful: for stronger flows, such as for wind blowing over waves, the presence of critical levels where the mean flow velocity is equal to the wave phase speed necessitates the application of more general types of surface-following coordinate system. The interaction of the flow of air and water and associated differences in temperature and the concentration of various substances (such as gas species) gives rise to a complex boundary-layer structure at a wide range of vertical scales, from the sub-millimetre scales of gaseous diffusion, to several tens of metres for the turbulent Ekman layer. The balance of momentum, heat, and mass is also affected significantly by breaking waves, which act to increase the effective area of the surface for mass transfer, and increase turbulent diffusive fluxes via the conversion of wave energy to turbulent kinetic energy.

CFD simulation of bubbly flows: Random dispersion model

Three-dimensional CFD simulations of two-phase flow in a vertical pipe, a square cross-sectional bubble column and a large-scale plume are presented. A random dispersion model (RDM) is used to generate an instantaneous turbulent fluctuating velocity field by assuming that it is comprised of eddies, lifetimes and length-scales of which can be deduced from local mean flow properties. The RDM is used to describe turbulent dispersion of bubbles, and is validated here against the experimental data, and compared with predictions obtained by imposing an empirical turbulent dispersion force (TDF), but without introducing adjustable coefficients. The strictly mechanistic approach to bubble dispersion can offer better opportunities for the development of trustworthy, two-phase flow models.

A study of swirling turbulent pipe and jet flows

Axially rotating turbulent pipe flow is an example in which the rotation strongly affects the turbulence, which then also influences the mean flow properties. For instance, in the fully developed flow as well, the fluid is not in solid body rotation due to the influence of the cross-stream Reynolds stress. The present paper reports new measurements from a rotating pipe flow and the streamwise mean velocity distribution is compared with recent scaling ideas of Oberlack [J. Fluid Mech. 379, 1 (1999)] and good agreement is found. A second part of the paper deals with the initial stages when the flow leaves the pipe and forms a swirling jet. The measurements in the jet show that at some distance downstream (approximately five jet diameters) the central part of the jet actually rotates in the opposite direction as compared to the rotation of the pipe. This effect is explained by the influence of the cross-stream Reynolds shear stress.

Numerical study of turbulent magnetohydrodynamic channel flow

Mean flow properties of turbulent magnetohydrodynamic channel flow with electrically insulating channel walls are studied using high-resolution direct numerical simulations. The Lorentz force due to the homogeneous wall-normal magnetic field is computed in the quasi-static approximation. For strong magnetic fields, the mean velocity profile shows a clear three-layer structure consisting of a viscous region near each wall and a plateau in the middle connected by logarithmic layers. This structure reflects the significance of viscous, turbulent, and electromagnetic stresses in the streamwise momentum balance dominating the viscous, logarithmic, and plateau regions, respectively. The width of the logarithmic layers changes with the ratio of Reynolds- and Hartmann numbers. Turbulent stresses typically decay more rapidly away from the walls than predicted by mixing-length models.

On the near-wall structure in reverse-flow and post-reattachment recovery regions of separated flow and its equivalence to the structure in wall and free-surface jets

The statistical and structural properties of two wall jets, one developing along a real wall and the other along a shear-free wall, are contrasted with the equivalent properties in the post-reattachment-recovery and reverse-flow regions of a separated backward-facing step flow, respectively. The study was motivated, principally, by the wish to isolate and understand the mechanisms responsible for the poor representation of the post-reattachment recovery returned by most RANS closures. It demonstrates a substantive commonality in the turbulent processes between, on the one hand, the real wall jet and post-reattachment recovery, and on the other hand, between the zero-wall-shear jet and the reattachment zone, as well as the reverse-flowing near-wall layer in the backward-facing-step flow. All regions under consideration are found to be characterised by an influential interaction between an outer shear layer and the wall, but an important distinction arises from the presence or absence of strong near-wall shear which introduces significant changes to the nature of this interaction: in the absence or near-absence of wall shear, the interaction is largely inviscid, associated with wall-blocking, while strong shear tends to shield the wall from the outer flow. The commonality between the two sets of flow conditions is explored by way of mean-flow properties, budgets, anisotropy maps, departures from local equilibrium, non-dimensional strain parameter, length-scale variations and structural properties. The study shows that the post-reattachment-recovery region, like the real wall jet, is far from the state of local equilibrium found in a standard boundary layer, that the recovery of the flow towards a state of equilibrium is slow, and that the near-wall region is strongly affected by turbulent diffusion associated with the migration of large-scale structures towards the wall. In statistical terms, this last process is represented by the importance of turbulent transport by third moments and pressure–velocity correlations. Within the reattachment and reverse–flow layer, near-wall shear is weak, and so is the shielding of the wall from the outer layer. In these regions, the flow shares many of the properties of the zero-wall-shear jet.

Evaluation of Detached Eddy Simulation for Turbulent Wake Applications

resolution. The results for simulations on three grids of increasing resolution for the three-dimensional square cylinder wake are compared with experimental data and to other computational studies. The comparisons of mean flow and global flow quantities to experimental data are favorable, whereas the results for second order statistics in the wake are mixed and do not always improve with increasing spatial resolution. Comparisons to large eddy simulation are also generally favorable, suggesting detached eddy simulation provides an adequate subgrid scale model. Predictions of base drag and centerline wake velocity for the supersonic wake are also good, given sufficient grid refinement. These cases add to the validation library for detached eddy simulation and support its use as an engineering analysis tool for accurate prediction of global flow quantities and mean flow properties.

Computational analysis of supersonic turbulent boundary layers over rough surfaces using the k–ω and the stress–ω models

The influence of surface roughness in the prediction of the mean flow and turbulent properties of a high-speed supersonic ( M = 2.7, Re / m = 2 × 10 7 ) turbulent boundary layer flow over a flat plate is numerically investigated. In particular, the performance of the k – ω and stress– ω turbulence models is evaluated against the available experimental data. Even though the performance of these models have been proven satisfactory in the computation of incompressible boundary layer flow over rough surfaces, their validity for high-speed compressible has not been investigated yet. It is observed from this study that, for smooth surface, both k – ω and stress– ω models perform very well in predicting the mean flow and turbulence quantities in supersonic flow. For rough surfaces, both models matched the experimental data fairly well for lower roughness heights but performed unsatisfactorily for higher roughness conditions. Overall the performance of the k – ω model is better than the stress– ω model. The stress– ω model does not show any strong advantages to make up for the extra computational cost associated with it. The predictions indicate that the ω boundary conditions at the wall in both models, especially the stress– ω model, need to be refined and reconsidered to include the geometric factor for supersonic flow over surfaces with large roughness values.

Characteristics of strongly-forced turbulent jets and non-premixed jet flames

Previous researchers have demonstrated that strong pulsations of the fuel flow rate can significantly reduce the flame length and luminosity of laminar/transitional non-premixed jet flames. The physical mechanisms responsible for these changes are investigated experimentally in acoustically-forced jet flows where the peak velocity fluctuations are up to eight times the mean flow velocity. Both reacting and non-reacting flows were studied and Reynolds numbers, based on the mean flow properties, ranged from 800 to 10,000 (corresponding to peak Reynolds numbers of 1,450–23,000), and forcing frequencies ranged from 290 to 1,140 Hz. Both the first and second organ-pipe resonance modes of the fuel delivery tube were excited to obtain these frequencies. An analysis of the acoustic forcing characteristics within the resonance tube is provided in order to understand the source of the high amplitude forcing. Flow visualization of jets with first resonant forcing confirms the presence of large-scale coherent vortices and strong reverse flow near the exit of the fuel tube. With second-resonant forcing, however, vortices are not emitted from the tube as they are drawn back into the fuel tube before they can fully form. Increased fine-scale turbulence is associated with both resonant cases, but particularly at second resonance. The power spectra of the velocity fluctuations for a resonantly pulsed jet show the presence of an inertial subrange indicating that the flow becomes fully turbulent even for mean-Reynolds-number jets that are nominally laminar. It is shown that these pulsed jet flows exhibit strong similarities to synthetic jets and that the Strouhal number, based on the maximum velocity at the fuel tube exit, is the dominant parameter for scaling these flows. The Strouhal number determines the downstream location where the coherent vortices breakdown, and is found to provide better collapse of flame length data (both current and previous) than other parameters that have been used in the literature.

Dynamic self-organization in particle-laden channel flow

We study dynamic flow-structuring and mean-flow properties of turbulent particle-laden riser-flow at significant particle volume fractions of about 1.5%. We include particle–particle as well as particle–fluid interactions through inelastic collisions and drag forces, in a so-called four-way coupled description. These interactions are the origin for the emergence of coherent particle swarms in a flow. The dynamic cluster-formation and cluster-disintegration are associated with the competition between turbulent dispersion and inelastic particle collisions. We establish the basic scenario of this self-organization and investigate the dominant mean-flow aspects of the resulting turbulence modulation for particles with high Stokes response-time. Large-eddy simulations of turbulent channel flow, using dynamic subgrid models and particles at a significant volume fraction and realistic mass load are presented. These simulations indicate the development of a thinner boundary layer, a flatter velocity profile, an higher effective Von Kármán constant and an accumulation of particles near the walls. Moreover, it was found that neglecting particle–particle interactions, as done in so-called two-way coupling, leads to a modulated flow which displays a strong ‘center-channel-jet’ that is not found in physical experiments.

Computational prediction of a slightly heated turbulent rectangular jet discharged into a narrow channel crossflow using two different turbulence models

A computational investigation of three-dimensional mean flow field resulting due to the interaction of a rectangular heated jet issuing into a narrow channel crossflow has been reported in the present paper. The jet discharge slot spans more than 55% of the crossflow channel bed, leaving a small clearance between the jet edge and sidewalls. Such flow configurations are encountered in several industrial processes such as mixing product streams, drying product streams, etc. The objective of the present work was to carry out a detailed investigation of the mean flow field and flow structure, which could not be obtained in a similar two-dimensional experimental work reported in the literature. The commercial code FLUENT 6.2.16 based on the finite volume method was used to predict the mean flow and temperature fields for the jet to crossflow velocity ratio ( R) = 6. Two different turbulence models, namely, Reynolds-stress transport model (RSTM) and the standard k– ε model, were used for the computations. Different terms of the Reynolds-stress transport equation were modeled based on the proposals in the literature that are appropriate for the important flow features of the present configuration. Important flow features predicted by the two models, such as the formation of different vortical structures and their effects on the flow field are discussed. Some predicted results are compared with the available experimental data reported in the literature. The predicted mean and turbulent flow properties are shown to be in good agreement with the experimental data. However, the performance of RSTM is found to be better than that of the standard k– ε model.

Separating the effects of wall blocking and near-wall shear in the interaction between the wall and the free shear layer in a wall jet

The statistical and structural characteristics of two plane jets, one developing along a real wall and the other along a frictionless wall (equivalent to a zero-shear, nondeformable free surface) are compared by way of highly resolved LES (large eddy simulation) solutions at computational conditions close to those of DNS (direct numerical simulation). The aim is to distinguish between two types of influence of the wall on the outer shear layer: one inviscid, arising from wall blocking, and the other, associated with the near-wall shear in the boundary layer. Results are presented for mean-flow properties, second moments and budgets thereof, structural characteristics, and the integral length scale. The comparisons demonstrate that the wall affects a significant proportion of the outer shear layer to a depth of approximately 3 times the thickness of the boundary layer, with or without wall shear. Outside the immediate near-wall layer, in the interaction region, the influence of the wall is affected by an interplay between turbulence diffusion toward the wall and inviscid processes associated with pressure fluctuations and their reflection from the wall. The addition of shear modifies substantially the statistical behavior and structure within the thin sheared region. The state of anisotropy and the energy-redistribution process among the normal-stress components change drastically, the structure is dominated by small scale, elongated eddies, and the near-wall layer is observed to ‘shield’ the wall from the penetration of large-scale vortices from the outer shear layer. The role of diffusion, in particular, renders the near-wall shear layer very different from a conventional equilibrium boundary layer, its integral scale being considerably enhanced by the influence of large-scale eddies originating in the outer shear layer and migrating toward the wall.

Aero-Optic Performance of an Aircraft Forward-Facing Optical Turret

The results of three-dimensional calculations are presented for aero-optic analysis of an aircraft forward-facing optical turret. Computational-fluid-dynamics calculations, using a compressibility corrected k-e turbulence model, defined the mean flow properties. Turbulence characteristics were obtained from a three-dimensional g law equation that yielded the variance of index-of-refraction fluctuations. The characteristic scale length of the correlation function of the index-of-refraction fluctuations was calculated. Strehl ratios and wave front distortion were computed for the mean flow and turbulence aberrations for four azimuth angles, 0, 45, 90, and 120 deg. For 90 and 120 deg azimuth, a portion of the beam passes through an open cavity with large-scale turbulence and nonuniform mean flow. For the mean flow, the Strehl ratio decreased to 0.001 at 90-deg azimuth after tip, tilt, and best focus were removed for a wavelength of 1.06 μm. The loss of Strehl as a result of turbulence was not as severe. Wind-tunnel measurements of optical path differences scale favorably to this work. In addition, instantaneous far-field intensity plots for instantaneous realizations of turbulence were constructed. A deformable mirror adaptive optics system might improve the Strehl ratio for the mean flow, but probably not for turbulence.

Momentum and Heat Transfer in a Buoyant Turbulent Swirling Jet

Solutions are presented for a three-parameter model of turbulence for axisymmetric turbulent buoyant swirling jet flows in uniform and stagnant surroundings. The exit swirl number has a significant effect on the flow characteristics. The predicted results are in good agreement with experimental data. A discussion is provided for the effects of swirl and buoyancy on the growth of the jet width, the axial decay of mean flow properties, and the mass flow rates.

횡 방향 진동하는 전자기력에 대한 공간 발달하는 난류 경계층의 반응

Direct numerical simulations were performed to investigate the physics of a spatially developing turbulent boundary layer flow subjected to spanwise oscillating electromagnetic forces in the near wall region. A fully implicit fractional step method was employed to simulate the flow. The mean flow properties and the Reynolds stresses were obtained to analyze the near-wall turbulent structure. It is found that skin friction and turbulent kinetic energy can be reduced by the electromagnetic forces. The decrease in production is responsible for the reduction of turbulent kinetic energy. Instantaneous flow visualization techniques were used to observe the response of streamwise vortices and streak structures to spanwise oscillating forces. The near-wall vortical structures are affected by spanwise oscillating electromagnetic forces. Following the stopping of the electromagnetic force, the flow eventually relaxes back to a two-dimensional equilibrium boundary layer.

Measurement of developing turbulent flows in a 90-degree square bend with spanwise rotation

Mean flow and turbulence properties of developing turbulent flows in a 90 degree square bend with span-wise rotation are measured by a hot-wire anemometer. A slanted wire is rotated into 6 orientations and the voltage outputs from them are combined to obtain the mean velocity and the Reynolds stress components. Combined effects of the centrifugal and Coriolis forces due to the curvature and the rotation of the bend on the mean motion and turbulence structures are investigated experimentally. Results show that the two body forces can either enhance or counteract each other depending on the flow direction in the bend.