Mean Flow Statistics Research Articles

Physically Realistic Roughness Closure Scheme to Simulate Turbulent Channel Flow over Rough Beds within the Framework of LES

A physically realistic roughness closure method for the simulation of turbulent open-channel flow over natural beds within the framework of large-eddy simulation (LES) is proposed. The description of bed roughness in LES is accomplished through a roughness geometry function together with forcing terms in the momentum equations. The major benefit of this method is that the roughness is generated from one physically measurable parameter, i.e., the mean grain diameter of the bed material. A series of flows over rough beds, for which mean flow and turbulence statistics are available from experiments, is simulated. Measured and computed values are compared to validate the proposed roughness closure approach. It is found that predicted streamwise velocity profiles, turbulence intensities, and turbulent shear stress profiles match the measured values fairly well. Furthermore, the effect of roughness on the overall flow resistance is predicted in reasonable agreement with experimental values.

Stochastic coherent adaptive large eddy simulation of forced isotropic turbulence

The stochastic coherent adaptive large eddy simulation (SCALES) methodology is a novel approach to the numerical simulation of turbulence, where a dynamic grid adaptation strategy based on wavelet threshold filtering is utilized to solve for the most ‘energetic’ eddies. The effect of the less energetic unresolved motions is simulated by a model. Previous studies have demonstrated excellent predictive properties of the SCALES approach for decaying homogeneous turbulence. In this paper the applicability of the method is further explored for statistically steady turbulent flows by considering linearly forced homogeneous turbulence at moderate Reynolds number. A local dynamic subgrid-scale eddy viscosity model based on the definition of the kinetic energy associated with the unresolved motions is used as closure model. The governing equations for the wavelet filtered velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy, are numerically solved by means of a dynamically adaptive wavelet collocation method. It is demonstrated that adaptive simulations closely match results from a reference pseudo-spectral fully de-aliased direct numerical simulation, by using only about 1% of the corresponding computational nodes. In contrast to classical non-adaptive large eddy simulation, the agreement with direct solution holds for the mean flow statistics as well as in terms of energy and enstrophy spectra up to the dissipative wavenumbers range.

The separating flow in a plane asymmetric diffuser with 8.5° opening angle: mean flow and turbulence statistics, temporal behaviour and flow structures

The flow in a plane asymmetric diffuser with an opening angle of 8.5° has been studied experimentally using time-resolving stereoscopic particle image velocimetry. The inlet condition is fully developed turbulent channel flow at a Reynolds number based on the inlet channel height and bulk velocity of Re = 38000. All mean velocity and Reynolds stress components have been measured. A separated region is found on the inclined wall with a mean separation point at 7.4 and a mean reattachment point at 30.5 inlet channel heights downstream the diffuser inlet (the inclined wall ends 24.8 channel heights downstream the inlet). Instantaneous flow reversal never occurs upstream of five inlet channel heights but may occur far downstream the point of reattachment. A strong shear layer in which high rates of turbulence production are found is located in a region outside the separation. The static wall pressure through the diffuser is presented and used in an analysis of the balance between pressure forces and momentum change. It is demonstrated that production of turbulence causes a major part of the losses of mean flow kinetic energy. The character of the large turbulence structures is investigated by means of time-resolved sequences of velocity fields and spatial auto-correlation functions. Pronounced inclined structures are observed in the spanwise velocity and it is suggested that these are due to the legs of hairpin-like vortices.

Structure of turbulent flow over 90° and 45° transverse ribs

This article reports on an experimental study of turbulent flows over periodic arrays of transverse square ribs attached to the bottom and top walls of an asymmetric converging channel preceded by an upstream parallel section. In the first and second series of experiments, the ribs on both walls were, respectively, arranged perpendicular and then at an angle of 45° to the sidewalls of the channel in a non-staggered configuration. A high-resolution particle image velocimetry system was used to conduct detailed velocity measurements in the upstream parallel and converging sections of the channel. For the 45° ribs, measurements were made at three different streamwise planes to capture the secondary motions produced by the inclined ribs. From these measurements, profiles and contours of the mean velocities, one-point turbulent statistics including the Reynolds stresses, Reynolds stress ratios, triple velocity correlations, and two-point correlation functions were obtained. These results, together with reference smooth-wall measurements in the fully developed section of a plane channel, are used to document the effects of rib roughness, pressure gradient, rib inclination, and spanwise location of the mean flow and turbulent statistics.

A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow

Fully developed incompressible turbulent pipe flow at bulk-velocity- and pipe-diameter-based Reynolds number ReD=44000 was simulated with second-order finite-difference methods on 630 million grid points. The corresponding Kármán number R+, based on pipe radius R, is 1142, and the computational domain length is 15R. The computed mean flow statistics agree well with Princeton Superpipe data at ReD=41727 and at ReD=74000. Second-order turbulence statistics show good agreement with experimental data at ReD=38000. Near the wall the gradient of $\mbox{ln}\overline{u}_{z}^{+}$ with respect to ln(1−r)+ varies with radius except for a narrow region, 70 < (1−r)+ < 120, within which the gradient is approximately 0.149. The gradient of $\overline{u}_{z}^{+}$ with respect to ln{(1−r)++a+} at the present relatively low Reynolds number of ReD=44000 is not consistent with the proposition that the mean axial velocity $\overline{u}_{z}^{+}$ is logarithmic with respect to the sum of the wall distance (1−r)+ and an additive constant a+ within a mesolayer below 300 wall units. For the standard case of a+=0 within the narrow region from (1−r)+=50 to 90, the gradient of $\overline{u}_{z}^{+}$ with respect to ln{(1−r)++a+} is approximately 2.35. Computational results at the lower Reynolds number ReD=5300 also agree well with existing data. The gradient of $\overline{u}_{z}$ with respect to 1−r at ReD=44000 is approximately equal to that at ReD=5300 for the region of 1−r > 0.4. For 5300 < ReD < 44000, bulk-velocity-normalized mean velocity defect profiles from the present DNS and from previous experiments collapse within the same radial range of 1−r > 0.4. A rationale based on the curvature of mean velocity gradient profile is proposed to understand the perplexing existence of logarithmic mean velocity profile in very-low-Reynolds-number pipe flows. Beyond ReD=44000, axial turbulence intensity varies linearly with radius within the range of 0.15 < 1−r < 0.7. Flow visualizations and two-point correlations reveal large-scale structures with comparable near-wall azimuthal dimensions at ReD=44000 and 5300 when measured in wall units. When normalized in outer units, streamwise coherence and azimuthal dimension of the large-scale structures in the pipe core away from the wall are also comparable at these two Reynolds numbers.

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.

Effects of canopy morphology and thermal stability on mean flow and turbulence statistics observed inside a mixed hardwood forest

The influences of thermal stability and seasonal changes in canopy morphology on mean flow and turbulence statistics in a mixed hardwood forest are presented from a year long field experiment at the University of Michigan Biological Station AmeriFlux site. A secondary wind speed maximum at z/ h = 0.07 ( z is height above ground and h is mean canopy height) below the level of peak vegetation area density (VAD) in the understory (young white pines) is observed more frequently and is more pronounced in fully leafed (closed) canopy than defoliated (open) canopy, and in stable than near-neutral and unstable conditions. A secondary wind speed maximum at z/ h = 0.58 is observed only in the closed canopy below the level of peak VAD in the upper canopy (crowns of mature aspen trees), which occurs less frequently and is less pronounced than that at z/ h = 0.07. Horizontal mean winds in the forest are observed to flow to the left (counter-clockwise) of that at the canopy top. The degrees of turning of the mean winds increase with increasing depth into the forest except a reversal (clockwise) near the forest floor in the closed canopy. The degrees of turning are greater in the closed canopy than the open canopy but smaller in near-neutral than unstable and stable conditions. The attenuations of Reynolds stress, correlation coefficient and velocity variances with increasing depth into the forest are more rapid in the closed canopy and in stable conditions. But the relative turbulence intensities are greater in the closed canopy than in the open canopy and decrease with increasing stability. In near-neutral stability, the zero-plane displacement height ( d) for the closed canopy decreases with increasing wind speed (∼0.81 h on average), while d for the open canopy does not show a clear dependence on wind speed (∼0.65 h on average). The bulk drag coefficient ( C D h ) measured at the canopy top is much greater over the closed canopy than the open canopy, contrary to earlier observations over a deciduous forest. But C D h * = C D h / VAI (VAI is vegetation area index) is about the same over the closed and open canopies (∼0.03 in near-neutral stability). The drag coefficient ( C d) for the parameterization of drag force in mean momentum budget equations in closure models increases with decreasing wind speed and varies with height. The drag coefficient ( C d LES ) for the parameterization of drag force in prognostic momentum equations in large-eddy simulations of airflow in plant canopies is smaller than C d, and the ratio C d LES / C d is greater in the open canopy than closed canopy and in stable than near-neutral and unstable conditions due to smaller relative turbulence intensities. All drag coefficients decrease and the displacement height increases with increasing stability, which indicates that these estimated aerodynamic parameters are not entirely the properties of vegetation elements, but are influenced by vertical turbulent mixing of momentum. Both eddy-diffusivity and mixing-lengths for momentum transfer decrease with increasing stability. An evidence of non-local transport is shown by peak values in estimated eddy-diffusivity and mixing-lengths below the crowns of mature aspen trees in the closed canopy. Otherwise, the eddy-diffusivity decreases with increasing depth into the forest, while the mixing-lengths above the level of the peaks are greater in the open canopy and the opposite is true below the level of the peaks.

Properties of the Wind Field within the Oklahoma City Park Avenue Street Canyon. Part I: Mean Flow and Turbulence Statistics

Abstract Velocity data were obtained from sonic anemometer measurements within an east–west-running street canyon located in the urban core of Oklahoma City, Oklahoma, during the Joint Urban 2003 field campaign. These data were used to explore the directional dependence of the mean flow and turbulence within a real-world street canyon. The along-canyon vortex that is a key characteristic of idealized street canyon studies was not evident in the mean wind data, although the sensor placement was not optimized for the detection of such structures. Instead, surface wind measurements imply that regions of horizontal convergence and divergence exist within the canopy, which are likely caused by taller buildings diverting the winds aloft down into the canopy. The details of these processes appear to be dependent on relatively small perturbations in the prevailing wind direction. Turbulence intensities within the canyon interior appeared to have more dependence on prevailing wind direction than they did in the intersections. Turbulence in the intersections tended to be higher than was observed in the canyon interior. This behavior implies that there are some fundamental differences between the flow structure found in North American–style cities where building heights are typically heterogeneous and that found in European-style cities, which generally have more homogeneous building heights. It is hypothesized that the greater three-dimensionality caused by the heterogeneous building heights increases the ventilation of the urban canopy through mean advective transport as well as enhanced turbulence.

Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGS model. The resulting so-called adaptive local deconvolution method (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper, ALDM is evaluated for the separated flow through a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2,808 and Re = 10,595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered physically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.

Numerical simulations of cellular secondary currents and suspended sediment transport in open-channel flows over smooth-rough bed strips

The flow and transport of suspended sediment in open-channel flows over smooth-rough bed strips were simulated numerically. The flow equations were solved with the aid of the Reynolds stress model. Simulated flow structures are provided and compared with measured data available in the literature. The comparisons indicate that the numerical model successfully predicts the mean flow and turbulence statistics. The sediment distribution of suspended particles in such flows was also simulated. The transport equation for suspended sediment was solved using the eddy diffusivity concept. The computed results show that flows with higher concentration occur over the smooth strips as observed in a river flow during the floods. The eddy diffusivity profile was also obtained and compared with that from an analytical expression reported byWang and Cheng [Advances inWater Resources. 28 (2005) 441–450]

Validation of a Large-Eddy Simulation Model to Simulate Flow in Pump Intakes of Realistic Geometry

This paper describes efforts toward developing a reliable numerical model to predict pump intake flow and associated vortices. Numerical prediction of these flows characterized by the formation of unsteady (meandering) intermittent vortices and presence of massive separation is very challenging. Successful prediction of these phenomena and their effects on the mean flow fields requires numerical methods and turbulence models that can accurately capture the dynamics of the main coherent structures in these flows. In the present work, large-eddy simulation (LES) in conjunction with an accurate nondissipative nonhydrostatic Navier-Stokes massively parallel solver is used to predict the flow and vortical structures in a pressurized pump intake of complex geometry. The LES model is validated using particle image velocimetry data recently collected on a laboratory model of a realistic geometry pump intake. To better put in perspective the predictive performance of the LES model, results from steady simulations employing the shear stress transport (SST) Reynolds-averaged-Navier-Stokes (RANS) model are presented and compared with LES. It is shown that even if SST can fairly successfully capture the mean velocity distribution and mean vortical structures in some regions, overall LES can more accurately predict the mean flow and turbulence statistics compared to the steady SST model.

Direct numerical simulation of turbulent channel flow under a uniform magnetic field for large-scale structures at high Reynolds number

A direct numerical simulation (DNS) of turbulent channel flow with high Reynolds number has been carried out to show the effects of the magnetic field. In this study, the Reynolds number for channel flow based on bulk velocity Ub, viscosity ν, and channel width 2δ was set to be constant; Reb=2δUb∕ν=45818. A uniform magnetic field was applied in the direction of the wall normal. The value of the Hartmann number, Ha were 32.5 and 65, where Ha=2δB0σ∕ρν. The turbulent quantities such as the mean flow, turbulent stress, and turbulent statistics were obtained by DNS. Although the influence of the magnetohydrodynamic dissipation terms in the turbulent kinetic energy budget was small, large-scale turbulent structures, e.g., vertical structures, low-speed streaks, ejection, and sweep, were found to decrease at the central region of the channel. Consequently, the difference between production and dissipation in the turbulent kinetic energy decreased with increasing Hartmann number at the central region and large-scale structures at this region were reduced.

An Idealized Nonlinear Model of the Northern Hemisphere Winter Storm Tracks

Abstract In this paper, a nonlinear dry model, forced by fixed radiative forcing alone, has been constructed to simulate the Northern Hemisphere winter storm tracks. A procedure has been devised to iterate the radiative equilibrium temperature profile such that at the end of the iterations the model climate closely resembles the desired target climate. This iterative approach is applied to simulate the climatological storm tracks in January. It is found that, when the three-dimensional temperature distribution in the model resembles the observed distribution, the model storm tracks are much too weak. It is hypothesized that this is due to the fact that eddy development is suppressed in a dry atmosphere, owing to the lack of latent heat release in the ascending warm air. To obtain storm tracks with realistic amplitudes, the static stability of the target climate is reduced to simulate the enhancement in baroclinic energy conversion due to latent heat release. With this modification, the storm tracks in the model simulation closely resemble those observed except that the strength of the Atlantic storm track is slightly weaker than observed. The model, when used as a forecast model, also gives high-quality forecasts of the evolution of observed eddies. The iterative approach is applied to force the model to simulate climate anomalies associated with ENSO and the interannual variations of the winter Pacific jet stream/storm tracks. The results show that the model not only succeeds in simulating the climatology of storm tracks, but also produces realistic simulations of storm track anomalies when the model climate is forced to resemble observed climate anomalies. An extended run of the control experiment is conducted to generate monthly mean flow and storm track statistics. These statistics are used to build a linear statistical model relating storm track anomalies to mean flow anomalies. This model performs well when used to hindcast observed storm track anomalies based on observed mean flow anomalies, showing that the storm track/mean flow covariability in the model is realistic and that storm track distribution is not sensitive to the exact form of the applied forcings.

Mean Flow and Turbulence Statistics Over Groups of Urban-like Cubical Obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant ‘dispersive stress’ whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

Numerical investigations of mean flow and turbulence structures of partly-vegetated open-channel flows using the Reynolds stress model

A Reynolds stress model for the numerical simulation of partly-vegetated flows is presented. The model uses Speziale, Sarkar, and Gatski's model for the pressure–strain correlation, Mellor and Herring's model and Rotta's model for the diffusion and the dissipation rate of the Reynolds stress, respectively. The model is applied to partly-vegetated rectangular open-channel flows, and simulated results are compared with experimental data. The model satisfactorily predicts mean flow and turbulence statistics. Through numerical experiments, the evolution of secondary current patterns and mean flow structure are presented for different densities of vegetation. A budget analysis of the streamwise vorticity equation is also performed to investigate the mechanism by which secondary currents in a partly-vegetated open-channel flow are generated. In the vegetated zone, the production by anisotropy is important in generating secondary currents over the entire depth, except for regions close to the free surface and the bottom where Reynolds shear stress plays a key role. This is different from the vortical structure of plain open-channel flows.

Shear-induced mixing and transport from a rectangular cavity

Measurements were conducted in the vicinity and downstream of two-dimensional cavities filled with a dense miscible fluid subjected to purging by an overlying wall-bounded turbulent shear flow. Two cavities with aspect ratios 1 and 2 were used, based on previous observations that the mechanism for entraining dense fluid into the flow above is different for these cases. Scaling for the downstream variation of the vertical concentration (buoyancy) distribution of dense fluid is advanced based on dimensional arguments and tested using laser-induced fluorescence measurements, The mean flow and turbulent statistics in the vicinity and downstream of the cavity were also measured. A notable increase of shear stress and turbulent intensities was observed above the higher aspect ratio cavity due to intense vertical exchange between the cavity and the flow above. The influence of the cavity could be detected for several cavity widths, or distances equal to several eddy turnover times. However, the flow above the lower aspect ratio cavity exhibits dramatically less vertical exchange between the cavity and the flow above, as indicated by subtle wisps of fluid transported downstream by the free-stream flow. The shear stress and turbulent intensities for this case have only a minor influence of the cavity.

Large-Eddy Simulation Inflow Conditions for Coupling with Reynolds-Averaged Flow Solvers

Hybrid approaches using a combination of Reynolds-averaged Navier-Stokes (RANS) approaches and large eddy simulations (LES) have become increasingly popular. One way to construct a hybrid approach is to apply separate flow solvers to components of a complex system and to exchange information at the interfaces of the domains. For the LES flow solver, boundary conditions then have to be defined on the basis of the Reynolds-averaged flow statistics delivered by a RANS flow solver. This is a challenge, which also arises, for instance, when defining LES inflow conditions from experimental data. The problem for the coupled RANS-LES computations is further complicated by the fact that the mean flow statistics at the interface may vary in time and are not known a priori but only from the RANS solution. The present study defines a method to provide LES inflow conditions through auxiliary, a priori LES computations, where an LES inflow database is generated. The database is modified to account for the unsteadiness of the interface flow statistics

Velocity statistics and flow structures observed in bypass transition using stereo PTV

It is known from smoke visualizations that in a transitional boundary layer subjected to free-stream turbulence, streaks appear and eventually break down to turbulence after wavy motions. In order to observe the streaky structures directly, a stereo particle-tracking velocimetry system using hydrogen bubbles in a water channel has been developed and validated against laser Doppler velocimetry. Mean flow statistics show good agreement with previous results. With the developed measurement system, the instantaneous spanwise distribution of the streamwise and wall-normal velocities can be measured fast enough to resolve the time development of the streaky structures. Measurements of instantaneous spanwise distributions of the streamwise and wall-normal velocity disturbances show strong negative correlation between the wall-normal and streamwise velocities in the streaks.

Dependence of Statistics of Low-Reynolds Number Compressible Turbulent Channel Flow on Non-Dimensional Parameters 1st Report Mean Flow Feild and Turbulence Statistics.

The dependence of mean flow and turbulence statistics on the non-dimensional parameters, the Mach number and the Reynolds number, is investigated using direct numerical simulation (DNS) of the low-Reynolds number compressible turbulent channel flow between isothermal walls. The Mach number M is based on the bulk velocity and sound speed at the wall. The Reynolds number Re is based on the bulk density, bulk velocity, channel half-width, and viscosity at the wall. Five computational cases are considered. The computational cases of Re=2000 with M=1.0, 1.25 and 1.5 are Cases A, B and C, respectively. The computational cases of M=1.5 with Re=2 000, 2500 and 3000 are Cases C, D and E, respectively. The main results of this report are as follows : (1) As M increases, the semi-local friction Reynolds number based on the local density and viscosity, semi-local friction velocity, channel half-width becomes larger in y*l3 and smaller in y*g3, where y* is the semi-local wall unit. (2) The mean dilatation profile depends on Re and M, even if the variable property effect is taken into account. (3) The region where the compressibility affects on the near-wall asymptotic behavior of wall-normal velocity intensity becomes wider with the increase of M and the decrease of Re.

Contribution to the Large Eddy Simulation of Flows in Electromagnetic Stirrers for Continuous Casting

A numerical study in cylindrical coordinates of the statistically steady turbulent flow in a laboratory setup for modeling the rotational inductive stirring in continuous casting of round strands is presented using the large eddy simulation method. For simulation of the velocity increase in the flow-mechanically stable layers the turbulent viscosity of the Smagorinsky model is reduced by a term depending on the r-derivative of the angular momentum, which characterize the stability. The explicit discretization scheme is applied for the time integration with implicit calculation of the diffusive terms in the azimuthal direction in order to obtain a greater maximal admissible time step. On the z-axis unique interpolated velocity values are used in the finite difference equations. The pressure Poisson equation is solved applying the fast Fourier transform and a supplementary pressure gradient is introduced to vanish the axial flow rate resulted by the use of axial periodic boundary conditions. Comparisons with experimental data show good agreements for both mean velocity and flow statistics.