Ratio Of Friction Velocity Research Articles

Effects of laminar burning velocity to friction velocity ratio on turbulent premixed flame-wall interaction within turbulent boundary layers

Direct numerical simulation of flame-wall interaction (FWI) for two flame configurations under different laminar burning velocity to nonreacting wall friction velocity ratio, SL/uτNR, have been performed. The first configuration considered is a V-flame in a turbulent channel flow with isothermal inert walls and represents oblique wall interaction. The second configuration is representative of head-on interaction (HOI) of a planar flame interacting with a wall in a fully developed turbulent boundary layer. In the case of the V-flame with SL/uτNR=0.4, a smaller flame angle is obtained when compared with that of the V-flame with SL/uτNR=0.7. This is a consequence of the differences in the turbulent burning velocities between the two V-flame cases, where the case with SL/uτNR=0.4 has a lower turbulent burning velocity when compared with that of the case with SL/uτNR=0.7. By contrast, the ratio of turbulent to laminar burning velocity is higher for the SL/uτNR=0.4 HOI case when compared to the corresponding HOI case with SL/uτNR=0.7. The flame orientations with respect to the streamwise component of velocity and wall-normal direction in addition to the SL/uτNR values have been found to have a significant impact on the variations of wall heat flux, wall shear stress, and wall friction velocity in premixed FWI within turbulent boundary layers. The behaviors of nondimensional streamwise velocity, u+, and nondimensional temperature using wall units, T+, have also been investigated for different SL/uτNR ratios and it is found that the standard log-law profiles in the case of u+ and T+ are not valid for the two configurations and the two SL/uτNR ratios considered. Published by the American Physical Society 2024

Experimental Investigation of Snow Accumulations on Two-Span Single-Pitched Roofs Based on a New Similarity Criterion

Uneven snow distribution plays a main role in the collapse of two-span single-pitched roofs because of the intensified snow accumulation in the valleys and eaves. The roof pitches, wind velocities, and wind directions are the main reasons that cause unbalanced snowdrifts as they drastically affect the flow fields around the roofs. This research investigates the snow distribution characteristics on two-span single-pitched roofs based on the snow-wind combined experiment facility and new similarity criteria. Firstly, the setup of the experiment facility is introduced, and the wind fans matrix and snowfall simulator are calibrated, respectively. Then, a new Froude number similarity, based on the modification of friction velocity ratio, is proposed, and its reliability as a criterion is verified. Finally, experiments on two-span single-pitched roofs are conducted using the new similarity criteria to study the snowdrifts patterns under different conditions. The mechanism of snow accumulations on roofs is explained with the help of CFD calculation. The results show that the valley and eave on the second windward roof bear a larger snow load.

Wave- and current-dominated combined orthogonal flows over fixed rough beds

Orthogonal wave-current interaction often occurs in coastal regions, when waves approach the shoreline near-orthogonally and longshore currents are present. Notwithstanding its wide relevance, this phenomenon is far from being understood to a full extent, especially in the presence of bed roughness. Indeed the effects on the apparent roughness due to the combination of steady currents and surface waves propagating at right angles are still a matter of debate, both in the current and in the wave dominated cases.To this aim, the hydrodynamic effects of an orthogonal regular wave on a current propagating over a rough bed were investigated; two different rough beds, one sandy and one made of gravel, were considered. Both surface elevation and velocity profiles were acquired by means of an array of wave gauges and Micro Acoustic Doppler Velocimeters positioned within the tank. Here the range of the investigated parameters was significantly enlarged with respect to the existing literature studies.The present paper focuses on the analysis of the mean velocity profiles. More specifically, observation of velocity profiles shows that the current to wave velocity ratio and the bed roughness play an important role, by impacting the value of the apparent roughness. Indeed it was found that as far as the flow is current dominated the addition of waves on the current increases the flow resistance. The opposite happens when the flow is wave dominated, irrespective of the bed roughness type. In particular, the apparent roughness increases as far as the wave plus current to current only friction velocity ratio increases. The increase is more rapid if the wave plus current prevails on the current only friction velocity.

Air–Sea Interaction in the Southern Ocean: Exploring the Height of the Wave Boundary Layer at the Air–Sea Interface

We investigate the momentum and energy exchange across the wave boundary layer (WBL). Directly at the air–sea interface, we test three wave-growth parametrizations by comparing estimates of the wave-induced momentum flux derived from wave spectra with direct covariance estimates of the momentum flux. An exponential decay is used to describe the vertical structure of the wave-induced momentum in the atmospheric WBL through use of a decay rate, a function of the dimensionless decay rate and wavenumber (A = α k). The decay rate is varied to minimize the difference between the energy extracted from the WBL and the energy flux computed from wave spectra using our preferred wave-growth parametrization. For wave ages (i.e. the peak phase speed to atmospheric friction velocity ratio) in the range $$ 15 < c_{p}/u_{*} < 35 $$ we are able to balance these two estimates to within 10%. The decay rate is used to approximate the WBL height as the height to which the wave-induced flux is 0.1 of its surface value and the WBL height determined this way is found to be between 1–3 m. Finally, we define an effective phase speed with which to parametrize the energy flux for comparison with earlier work, which we ultimately attempt to parametrize as a function of wind forcing.

On extraction of time-varying mean wind speed from wind record based on stationarity index

We have proposed in a previous study a non-stationary wind model to represent the typhoon record as a summation of a time-varying mean wind speed (TVM) and a stationary turbulence. This note further suggests a quantitative scheme, rather than the previous qualitative method, to find the best TVM for any given wind record. Trial TVMs are first extracted from the wind record by a data-processing technique named empirical mode decomposition. For each TVM, its corresponding turbulent component is computed by removing the TVM from the original wind record, and the degree of stationarity of the turbulence component is checked. The best TVM is taken as the one that leads to the maximum degree of stationarity. The degree of stationarity of turbulence is quantified by two indicators: β the ratio of horizontal wind variability and wind speed; and γ the ratio of friction velocity at different Reynolds averaging periods. The applicability of the suggested scheme is validated with 550 typhoon and 3300 monsoon records of 10 minute duration and at different measurement heights. Threshold values for the two stationary indicators β and γ are determined using field measurements and their sensitivities to the Reynolds averaging periods are discussed. Observations in this study demonstrate that the suggested scheme is proper for finding the TVM of a wind record. For a stationarity quantification of 10 minute duration record, the γ indicator with 30 second Reynolds averaging period is recommended.

Experimental study of turbulence and vertical temperature profile in the urban boundary layer

We observed the turbulence and vertical profile of temperature in and above the roughness sublayer (RS) using a tower, a tethered balloon and a Doppler sodar in Himeji City. A 3-D ultrasonic anemometer-thermometer was sited at a height of 54 m on the tower. The present results showed that in the RS, the ratio of friction velocity to wind speed, u*/u, observed under unstable conditions of − 4.2 < z′/L < −0.5 were close to those under neutral conditions, where z´ = z – d; the displacement height d = 2 m; L is the Monin-Obkhov stability length. In addition, σw/u* were lower than the universal function presented by Panofsky et al. (1977). The cross correlation coefficients for u′w′ and T′w′ under neutral and unstable conditions were also studied.

Investigation of the Level of Action on Wall Shear Stress and the Law of the Wall for Rough Wall Turbulent Boundary Layer

The discussion on the law of the wall has been performed for turbulent boundary layer over rough surface under a zero pressure gradient. The wall shear stress was directly measured with a drag balance of a floating element device. The center of the wall shear stress, which is calculated from the moment of the pressure drag acting on a roughness element, is well consistent with the vertical origin estimated with the assumption of the log law profile. The distance from the crest of the roughness element to the center of the wall shear stress normalized with the roughness height increases with increasing roughness density λs. The value approaches to zero less than λs=0.5 and tends to 0.5 in the limit of λs=1. The roughness function is formulated as function of Reynolds number based on the distance from the crest to the center of the wall shear stress and the friction parameter, which is the ratio of friction velocity to the free stream velocity, for the equilibrium boundary layer over the rough surface. Experimental data collapses on the formula in the case of the constant friction parameter.

建物近傍の雪吹きだまりの風洞相似則に関する考察

This paper presents the requirements in order to simulate drifting snow around buildings in a wind tunnel. The threshold friction velocity ratio and the angle of the repose of the particles should match in both the wind tunnel model and the prototype situations. The real snow particles and the large particles with artificial snow in the wind tunnel did not follow the flow around the building model. Stokes parameter in the wind tunnel should be less than one in order to follow the flow around the building model. If the model particles were very fine, the terminal velocity ratio was not necessarily matched for both the model and prototype. By the large turbulence generated by buildings, particles were easy to transit from the saltation motion to the suspension motion at a low wind speed of 5-6m/s. As a result, the saltation motion was not the principal mechanism of the particle transport process near buildings. The Froude number requirement was then relaxed from the wind tunnel similarity pa-rameter.

A Simple Model for Pollution Dispersion in a Convective Boundary Layer

Abstract A simplified model for dispersion in a convective boundary layer is presented and is used to diagnose crosswind-integrated concentrations, ground-level concentrations, and vertical plume spread over flat terrain for various release heights. The model parameterizes the long-wavelength oscillation of the time-averaged plume centerline versus downwind distance under unstable conditions, using a simple sine wave. This wave is phase shifted to account for the influence of source height and is damped toward the mid–mixed layer to account for the well-mixed end state of convective dispersion. This model represents an improvement over a previous model in two ways. First, vertical dispersion about the oscillating time-averaged centerline is parameterized using a lognormal distribution instead of a Gaussian distribution so as to give better ground-level concentration. Second, to account for the addition of surface-layer shear-generated turbulence to a convective boundary layer, the wavelength of the time-averaged oscillation is stretched as a function of the ratio of friction velocity to the Deardorff convective velocity scale. Results are tested against published laboratory, large-eddy simulation, and field data and are compared with the dispersion scheme used in the AERMOD regulatory dispersion model. In general, the simplified convective dispersion model provides close agreement with the observations and simulations. The utility of a buoyancy velocity to serve as a convection scale is also demonstrated.

Large-eddy simulations of convective shear flows

Abstract The structure of the instantaneous flow fields and turbulence statistics in oceanic convection affected by wind-induced shear are analysed using a large-eddy simulation (LES) data set. A modified subgrid-scale (SGS) model has been developed in order to overcome known deficiencies of the Smagorinsky SGS model in near-wall flows. The SGS model has been formulated as a second-order moment approach. Three distinct convective flows driven by surface cooling are generated. One is the convectively mixed layer with negligible surface shear corresponding to calm wind conditions. The other two are convectively mixed layers affected by enlarged wind-generated shear stresses corresponding to a wind speed of 7 and 14 m s - 1 , respectively. The heat flux was held constant in order to provide equal thermal forcing. Surface gravity waves are excluded. Instantaneous flow fields reveal the ability of the mean shear to order temperature fluctuations into convective roll-like structures under severe wind conditions, whereas under calm to moderate wind conditions convective cells are formed. The ratio of friction velocity u * to Deardorff velocity w * controls the formation of either cell or roll structures. The well-known non-local effects due to turbulent and pressure transport of turbulent kinetic energy from the surface to the bulk of the convectively mixed layer are confirmed. The flows follow the “ 1 2 ” power law for the Nusselt–Rayleigh number relation (based on eddy viscosity and diffusivity) at high Rayleigh numbers. With increasing shear the heat flux decreases. Rotational effects clearly influence the flows despite the shallow mixed layer of only about 200 m depth. The unstable stratification significantly changes the volume transport of momentum compared to near-neutral stratified flows. Whereas for moderate wind conditions the transport is damped compared to the near-neutral case, the situation under strong wind conditions is completely different and volume transport of momentum is enhanced. As rotation as well as stratification tend to reduce the turbulent length scales, the role of the SGS model becomes more pronounced in the presence of rotation and/or stratification.

A regime diagram for classifying turbulent large eddies in the upper ocean

A large eddy simulation (LES) model is used to examine how buoyancy-driven thermal convection, wind-driven shear turbulence and wind/wave-driven Langmuir circulation compete to generate turbulence in the ocean surface mixed layer. The turbulent Langmuir number La t, a ratio of friction velocity to surface Stokes drift velocity, and the Hoenikker number Ho, a ratio of buoyancy forcing to wave forcing, are two controlling dimensionless parameters. We explore low-order turbulence statistics in the La t and Ho parameter space for a wide range of atmospheric forcing conditions and construct a regime diagram to differentiate buoyancy-, shear- and wave-driven turbulence. All three types of turbulent flows are anisotropic but show different orderings of turbulence intensities: vertical > (downwind, crosswind) in convective turbulence; downwind>crosswind>vertical in shear turbulence; crosswind ≈ vertical> downwind in Langmuir turbulence. These orderings of turbulence intensities can be explained by examining the turbulence energy production in three directions. Buoyancy production in the vertical direction dominates turbulence generation in convective turbulence, whereas shear production in the downwind direction dominates turbulence generation in shear-driven turbulence. In Langmuir turbulence, however, Stokes production due to surface waves generates turbulence energy in both crosswind and vertical directions. Turbulence in the wind-driven upper ocean shows a transition from shear to Langmuir turbulence as La t decreases. A fully-developed sea state corresponds to La t≈0.3 and lies within the Langmuir regime. Vertical turbulence intensity in Langmuir turbulence is about two times larger than that in shear turbulence and falls into the range observed in the upper ocean. Hence the wind-driven upper ocean will be dominated by Langmuir turbulence under typical sea state conditions. Transition from Langmuir to convective turbulence occurs around Ho = O ( 1 ) , which is much greater than Ho = O ( 0.01 ) obtained using typical heat fluxes and wind speeds.

Comparison of aerodynamically and model-derived roughness lengths ( zo) over diverse surfaces, central Mojave Desert, California, USA

The vulnerability of dryland surfaces to wind erosion depends importantly on the absence or the presence and character of surface roughness elements, such as plants, clasts, and topographic irregularities that diminish wind speed near the surface. A model for the friction velocity ratio has been developed to account for wind sheltering by many different types of co-existing roughness elements. Such conditions typify a monitored area in the central Mojave Desert, California, that experiences frequent sand movement and dust emission. Two additional models are used to convert the friction velocity ratio to the surface roughness length ( z o) for momentum. To calculate roughness lengths from these models, measurements were made at 11 sites within the monitored area to characterize the surface roughness element. Measurements included (1) the number of roughness species (e.g., plants, small-scale topography, clasts), and their associated heights and widths, (2) spacing among species, and (3) vegetation porosity (a measurement of the spatial distribution of woody elements of a plant). Documented or estimated values of drag coefficients for different species were included in the modeling. At these sites, wind-speed profiles were measured during periods of neutral atmospheric stability using three 9-m towers with three or four calibrated anemometers on each. Modeled roughness lengths show a close correspondence (correlation coefficient, 0.84–0.86) to the aerodynamically determined values at the field sites. The geometric properties of the roughness elements in the model are amenable to measurement at much higher temporal and spatial resolutions using remote-sensing techniques than can be accomplished through laborious ground-based methods. A remote-sensing approach to acquire values of the modeled roughness length is particularly important for the development of linked surface/atmosphere wind-erosion models sensitive to climate variability and land-use changes in areas such as the southwestern United States, where surface roughness has large spatial and temporal variations.

Relations between aerodynamic and surface roughness in a hyper‐arid cold desert: McMurdo Dry Valleys, Antarctica

AbstractStudies of boundary‐layer winds and surface roughness characteristics of unvegetated rocky desert surfaces provide new insights into the relations between aerodynamic roughness and surface roughness, as described by the roughness density (λ). The description of non‐erodible roughness by the roughness density (λ) is shown to be valid for rocky surfaces as well as sparsely vegetated surfaces and simulated surfaces in a wind tunnel. There is a good relation (r2 = 0·71) between aerodynamic roughness and roughness density (λ), allowing use of the threshold friction velocity ratio to predict sediment transport rates on these surfaces. Copyright © 2004 John Wiley &amp; Sons, Ltd.

A linear stability analysis of tidally generated sand waves

A linear stability analysis is carried out to examine the initial stage of sand-wave growth under tidal flows and the occurrence of a preferred length scale. The fact that these bedforms typically have length scales small compared to the tidal excursion is exploited by adopting an asymptotic approach to solve the hydrodynamic part of the problem, i.e. to find the hydrodynamic response to an initially small bed perturbation. This method is shown to have important advantages over previously used methods, since it allows an exploration of the complete sand-wave regime (whereas other methods fail for short sand waves), and in general it is also more accurate. It is found that the selection of a preferred length scale depends mainly on only two parameters (the bed-slope coefficient, and the ratio of friction velocity to eddy viscosity), whereas there appears to be almost no dependence on the water depth.

Velocity and Concentration Profiles in Sheet-Flow Layer of Movable Bed

Sheet-flow layer of movable bed in steady currents has been investigated experimentally, using four kinds of sediment. Velocity and concentration profiles as well as flow resistance were measured inside and outside the sheet-flow layer. The range of fall-velocity–to–friction-velocity ratio ( w /U f) achieved in the study is 0.2 0.8–1). In the suspension-mode sheet flow, the flow resistance is found to depend not only on the Shields parameter but also on a parameter involving w . Measured velocity profiles are found to follow the logarithmic law near the bed, outside the sheet-flow layer, whereas inside the sheet-flow layer, they satisfy a power law. Measured concentration profiles, on the other hand, indicate a linear variation with the distance from the bed inside the sheet flow-layer near the bed, whereas away from the bed, the familiar Rouse distribution is sat...

The effect of roughness elements on wind erosion threshold

A theory is developed to describe the dependence upon roughness density of the threshold friction velocity ratio Rt, the ratio of the threshold friction velocity of an erodible surface without roughness to that of the surface with nonerodible roughness present. The roughness density is quantified by the frontal area index λ. The prediction is Rt = (1 − mσλ)−½(1 + mβλ)−½, where β is the ratio of the drag coefficient of an isolated roughness element on the surface to the drag coefficient of the substrate surface itself; σ is the basal‐to‐frontal area ratio of the roughness elements; and m (&lt; 1) is a parameter accounting for differences between the average substrate surface stress and the maximum stress on the surface at any one point. The prediction is well verified by four independent data sets.

Large-Eddy Simulation of Turbulent Sheared Convection

Abstract A series of large-eddy simulators of free and sheared convective flow between moving flat plates is presented. Results for free convection are compared with laboratory data. The ratio of friction velocity to the convective velocity sale,u*/w*,is identified as an important parameter in sheared convective flow determining the formation of longitudinal rolls. Rolls are found for u*/w* ≥ 0.35, with aspect ratio decreasing as this parameter increases. It is shown that, in this regime, two-dimensional simulations with a proper choice of roll orientation and turbulence length-scale can produce correct velocity variances and roll aspect ratio.