Time-averaged Streamwise Velocity Research Articles

Large-eddy simulation of turbulent flow past wind turbines/farms: the Virtual Wind Simulator (VWiS)

A large-eddy simulation framework, dubbed as the Virtual Wind Simulator (VWiS), for simulating turbulent flow over wind turbines and wind farms in complex terrain is developed and validated. The wind turbines are parameterized using the actuator line model. The complex terrain is represented by the curvilinear immersed boundary method. The predictive capability of the present method is evaluated by simulating two available wind tunnel experimental cases: the flow over a stand-alone turbine and an aligned wind turbine array. Systematic grid refinement studies are carried out, for both single turbine and multi-turbine array cases, and the accuracy of the computed results is assessed through detailed comparisons with wind tunnel experiments. The model is further applied to simulate the flow over an operational utility-scale wind farm. The inflow velocities for this case are interpolated from a mesoscale simulation using a Weather Research and Forecasting (WRF) model with and without adding synthetic turbulence to the WRF-computed velocity fields. Improvements on power predictions are obtained when synthetic turbulence is added at the inlet. Finally the VWiS is applied to simulate a yet undeveloped wind farm at a complex terrain site where wind resource measurements have already been obtained. Good agreement with field measurements is obtained in terms of the time-averaged streamwise velocity profiles. To demonstrate the ability of the model to simulate the interactions of terrain-induced turbulence with wind turbines, eight hypothetical turbines are placed in this area. The computed extracted power underscores the significant effect of site-specific topography on turbine performance. Copyright © 2014 John Wiley & Sons, Ltd.

Influence of relative submergence on spatial variance and form-induced stress of gravel-bed flows

[1] Spatial flow variance has a strong control on sediment transport, sediment-water interface exchange mechanisms, and the distribution and behavior of aquatic organisms in rivers. Thus, being able to quantify spatial flow variance, and how it varies with different water levels, is important for understanding how fluvial processes change during periods of time varying flow. In this paper, laboratory flume measurements of near-bed flow velocity were used to quantify spatial flow variance and form-induced stress, and their variation with flow submergence, within and above the surface of porous, gravel beds with differing grain roughness. The analysis revealed spatial flow variance was usually four or five times higher within the roughness layer than above. A rise in relative submergence resulted typically in a decrease in spatial variance—relative to bed shear velocity—in streamwise form-induced intensity, streamwise turbulence intensity, and form-induced momentum flux, both within and above the roughness layer. Flow submergence had no consistent influence on spatial variance in the vertical flow direction and in Reynolds stress. Form-induced stress was significant within the roughness layer, more so at shallow depths. The greater significance was driven primarily by higher spatial flow variance in time-averaged streamwise velocity at these depths. The implication is the relative role of momentum transfer mechanisms within the roughness layer, and thus, sediment-water interface exchange processes in rivers will change during periods of time varying flows.

Time-Average Velocity and Turbulence Measurement Using Wireless Bend Sensors in an Open Channel with a Rough Bed

This paper is motivated by the need to develop low cost, wireless velocity sensors for hydraulic research and application in streams. A velocity bend sensor (VBS) is a flexible plastic polyimide substrate sheet with an electronic resistor connected to a voltage divider. Drag of a moving fluid bends the sensor, changes the electronic resistance, and produces a voltage drop that can be related to the time-averaged freestream velocity of the fluid. VBSs were tested in a recirculating hydraulic flume with a gravel bed. The VBSs show transition from rigid to elastic bending with increasing freestream velocity, which can be described using dimensionless fluid and beam- bending properties. The relationship between stream velocity and voltage drop across the circuit is nonlinear. A semitheoretical approach to estimate time-averaged streamwise velocity from the voltage drop based on fluid drag, elastic member bending, and circuit principles is applied and shows good agreement with experimentally derived calibration curves. The triple decomposition theorem and spectral analysis are performed on VBS and acoustic Doppler velocimeter (ADV) time series. Results show that the VBS captures low-frequency character- istics of macroturblence present within the turbulent open channel flow but is unable to measure smaller-scale characteristics of eddy shed- ding for these hydraulic conditions. Turbulent intensity calculated using VBS data is 12% of that from the ADV attributed to the lack of detection of shedding-sized eddies. But, the linear fit between turbulent intensity from the VBS and ADV suggests that the VBS can be used as a proxy for more detailed turbulent measurements when applied in streams. DOI: 10.1061/(ASCE)HY.1943-7900.0000725. © 2013 American Society of Civil Engineers. CE Database subject headings: Probe instruments; Decomposition; Spectral analysis; Turbulence; Open channels; Velocity; Flow measurement.

Wall-pressure fluctuations of separated and reattaching flow over blunt plate with chord-to-thickness ratio c/d = 9.0

The separated and reattaching turbulent flow over a finite blunt plate with the chord-to-thickness ratio c/d=9.0 was experimentally studied; the Reynolds number based on the plate’s thickness (d) was Red=1.58×104. Wall-pressure fluctuations on the plate surface were taken into extensive consideration, which are closely related to unsteady flow behaviors buried in the separated and reattaching flow and the unsteady wake. Toward this end, synchronized measurements of wall-pressure fluctuations and velocity fluctuations were performed by using a microphone array and a split-fiber film probe, respectively. Characteristics of the separated and reattaching flow were discussed in terms of time-averaged streamwise velocity and its fluctuation intensity, reverse-flow intermittency, wall-pressure fluctuation coefficient, cross-correlation and coherence of wall pressure and velocity. The results showed that the peaked wall-pressure fluctuation coefficient (x/d=4.25) appears 1d behind the time-mean reattachment point (x/d=3.25), which is due to the intensified impingement fluid induced by the growing large-scale vortical structures in the reattachment zone. Two characteristic frequencies fd/U0=0.118 and 0.162 were determined, which correspond to the shedding large-scale vortical structures and the unsteady wake, respectively. Cross-correlation of the wall-pressure field demonstrated rapid decay of the large-scale vortical structures beyond the reattachment zone (x/d>4.75), which might be due to strong interference with the unsteady wake at higher frequency fd/U0=0.162. The wall-pressure auto-spectra showed that wall-pressure fluctuations near the trailing edge are overwhelmingly dominated by the unsteady wake at fd/U0=0.162. Coherence of the wall-pressure field and the streamwise velocity at x/d⩾7.75 elucidated that unsteady behaviors of the redeveloping boundary layer at both frequencies fd/U0=0.118 and 0.162 play important role in wall-pressure fluctuations in large upstream area of the surface.

Characteristics of turbulent flow in the near wake of a stack

The characteristics of the Reynolds stress field in the wake of a stack were experimentally studied in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was ReD=2.3×104, and the jet-to-crossflow velocity ratio (R) was varied from zero to three. The stack was partially immersed in a turbulent flat-plate boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. In general, the time-averaged velocities and Reynolds stresses were both found to be strongly influenced by the velocity ratio. For example, the vertical profile of the Reynolds shear stress in the wake was strongly influenced by the local velocity gradients, especially for lower values of R in the stack wake, and for higher values of R in the jet wake. The spanwise characteristics of the time-averaged streamwise and wall-normal velocities also varied along the stack height (z/H) and with the value of R. The behaviour of the shear correlation coefficient indicated that there is more turbulent mixing in the vicinity of the free end of the stack than at mid-height.

Instability Theory of Sand Ripples Formed by Turbulent Shear Flows

AbstractA theory of turbulent shear flow over a sand bed is developed, addressing the instability principle of the fluid-granular bed interface leading to the formation of ripples. The Reynolds-averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation are analyzed using a 1/7-power law of the time-averaged streamwise velocity and treating the curvilinear streamlines by the Boussinesq approximation. The integration of the RANS equations leads to a governing dynamical equation of flow over a mobile bed. A near-bed flow layer of 3.5 times the ripple height is considered being affected by the ripples. The dynamical equation of the mobile sand bed is based on the Exner’s sediment continuity equation in conjunction with the Meyer-Peter and Muller bed-load transport formula as modified to account for the effect of local bed slope attributable to bed forms. The coupled dynamical equations are then analyzed to estimate the parameters for the instability that results in the formation of ripp...

Direct Numerical Simulation of Naturally Evolving Free Circular Jet

Direct numerical simulation (DNS) of incompressible, spatially developing circular jets at a moderate Reynolds number of 1030 is performed to understand the details of the evolution of the flow field. The axisymmetric shear layer rolls up in the near field of the jet forming vortex rings. The rings tilt as they convect downstream before becoming turbulent in the far field. The evolution of vortical structures reveals the presence of a helical structure in the flow field along with the occurrence of vortex pairing. The time-averaged streamwise velocity distribution shows self-similarity in the far field. The cross-streamwise distribution of the Reynolds stresses also shows weak self-similarity downstream as the flow is not fully developed within the streamwise length of the computational domain. A detailed comparison with experiments is carried out and the computed time-averaged as well as statistical data shows excellent match with the experimental results. Numerical simulation also reveals various transitions during flow evolution in the streamwise direction.

Near-Bed Turbulence Characteristics at the Entrainment Threshold of Sediment Beds

This experimental study is devoted to quantification of the near-bed turbulence characteristics at an entrainment threshold of noncohesive sediments. Near the bed, the departure in the distributions of the observed time-averaged streamwise velocity from the logarithmic law is more for immobile beds than for entrainment-threshold beds. In the Reynolds shear stress distributions, a damping that occurs near the bed for sediment entrainment is higher than that for immobile beds. Quadrant analysis reveals that in the near-bed flow zone, ejections and sweeps on immobile beds cancel each other, giving rise to the outward interactions, whereas sweeps are the dominant mechanism toward sediment entrainment. The bursting duration for entrainment-threshold beds is smaller than that for immobile beds. On the other hand, the bursting frequency for entrainment-threshold beds is larger than that for immobile beds. The third-order correlations indicate that during sediment entrainment, a streamwise acceleration associated with a downward flux and advection of streamwise Reynolds normal stress is prevalent. The streamwise and the downward vertical fluxes of turbulent kinetic energy (TKE) increase with sediment entrainment. The TKE budget proves that for sediment entrainment, the pressure energy diffusion changes drastically to a negative magnitude, indicating a gain in turbulence production.

Flow Characteristics of Synthetic Jet Induced by Plasma Actuator

The flowfield induced by a plasma synthetic jet actuator was investigated by solving Reynolds-averaged Navier- Stokes equations, augmented with a phenomenological model representing the plasma-induced body force imparted by a plasma actuator on the fluid. Flow characteristics of an unsteady plasma synthetic jet in quiescent air were presented. The results indicate that the time-averaged flowfield is quite similar to the steady plasma synthetic jet, the traditional blowing synthetic jet, and the plane jet. The time-averaged streamwise velocity is a little smaller than that of the steady case, but the jet half-width is much larger. This makes the volume and momentum flux of an unsteady plasma synthetic jet larger. With unsteady actuation, a plasma synthetic jet does not exhibit the suction effect of the cavity during the second half-period, as does the traditional blowing synthetic jet. The vortex pair, formed from the wall jets that are produced by plasma actuators, has a strong unsteady effect on the plasma synthetic jet close to the wall. In the far field, the vortex pair coalesces and eventually develops to a continuous jet.

Non-universality of von Kármán's κ in fluvial streams

A distinguished universal aspect of wall-bounded turbulent flows is Theodore von Kármán's universal logarithmic law (log-law) of the wall, describing the time-averaged streamwise velocity variation with distance from the wall. The log-law has a universal von Kármán constant κ governing the velocity gradient. There remain a number of cases of the non-universality of κ in fluvial streams. In particular, it behaves as a variable in flows with low submergence, or if there is bed- and suspended-load transport. This research focuses on the non-universality of κ raising various issues and inviting future research directions.

Experimental studies of the influence of parameters on axisymmetric synthetic jets

This paper studies the influences of two dimensionless parameters, the Reynolds number and dimensionless stroke, on an axisymmetric synthetic jet by using flow visualization and particle image velocimetry (PIV) techniques. The flow visualization results and the relevant analyses, such as the formation and state of the vortex ring, the time-averaged streamwise velocity and kinetic energy of the fluctuating motion, etc., are provided. It was found that the Reynolds number does not influence the formation location of vortex rings; however, with increasing Reynolds number, the vortex rings go through the laminar–turbulent transition and tend to lose stability, leading to breakdown. In addition, the similarity of the jet kinetic energy distribution of fluctuating motion can be reached in a short distance downstream from the orifice, and the characteristics of conventional turbulent jets also appear as the Reynolds number is increased to a certain value. The dimensionless stroke strongly influences the formation and development of vortex rings. Furthermore, the experimental investigations on an axisymmetric synthetic jet actuated by a novel actuator signal, proposed by Zhang and Wang [16], are implemented in the present paper, and the ‘actual efficient stroke’ concept is introduced.

Reynolds averaged theory of turbulent shear flows over undulating beds and formation of sand waves

Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation, a theory of turbulent shear flow over an undulating sand bed is developed addressing the instability criterion of plane sand beds in free-surface flows leading to the formation of sand waves. In the analysis, the integration of RANS equations leads to generalized Saint Venant equations, in which the time-averaged streamwise velocity is characterized by a power law obtained from turbulence closure, treating the curvilinear streamlines by the Boussinesq approximation. As a consequence, the modified pressure distribution has a departure from the traditionally linear hydrostatic pressure distribution. The instability analysis of a plane sand bed yields the curves of the Froude number versus nondimensional wave number, determining an instability zone for which at lower Froude numbers (less than 0.8), the plane bed becomes unstable with the formation of dunes; whereas at higher Froude numbers, the plane bed becomes unstable with the formation of standing waves and antidunes. For higher Froude numbers, the experimental data for antidunes lie within the unstable zone; while for lower Froude numbers, the same is found for dunes with some experimental scatter.

Water‐worked gravel beds in laboratory flumes – a natural analogue?

AbstractAn investigation has been conducted to identify the key parameters that are likely to scale laboratory sediment deposits to the field scale. Two types of bed formation were examined: one where sediment is manually placed and screeded and the second where sediment is fed into a running flume. This later technique created deposits through sequential cycles of sediment transport and deposition. Detailed bed surface topography measurements have been made over a screeded bed and three fed beds. In addition, bulk subsurface porosity and hydraulic conductivity have been measured. By comparing the four beds, results revealed that certain physical properties of the screeded bed were clearly different from those of the fed beds. The screeded bed had a random organization of grains on both the surface and within the subsurface. The fed beds exhibited greater surface and subsurface organization and complexity, and had a number of properties that closely resembled those found for water‐worked gravel beds. The surfaces were water‐worked and armoured and there was preferential particle orientation and direction of imbrication in the subsurface. This suggested that fed beds are able to simulate, in a simplified manner, both the surface and subsurface properties of established gravel‐bed river deposits. The near‐bed flow properties were also compared. It revealed that the use of a screeded bed will typically cause an underestimation in the degree of temporal variability in the flow. Furthermore, time‐averaged streamwise velocities were found to be randomly organized over the screeded bed but were organized into long streamwise flow structures over the fed beds. It clearly showed that caution should be taken when comparing velocity measurements over screeded beds with water‐worked beds, and that the formation of fed beds offers an improved way of investigating intragravel flow and sediment–water interface exchange processes in gravel‐bed rivers at a laboratory scale. Copyright © 2008 John Wiley & Sons, Ltd.

Momentum and heat transport in a finite-length cylinder wake

This paper reports an experimental study of turbulent momentum and heat transport in the wake of a wall-mounted finite-length square cylinder, with its length-to-width ratio L/d = 3–7. The cylinder was slightly heated so that heat produced could be considered as a passive scalar. A moveable three-wire probe (a combination of an X-wire and a cold wire) was used to measure velocity and temperature fluctuations at a Reynolds number of 7,300 based on d and the free-stream velocity. Measurements were performed at 10 and 20d downstream of the cylinder at various spanwise locations. Results indicate that L/d has a pronounced effect on Reynolds stresses, temperature variance and heat fluxes. The downwash flow from the free end of the cylinder acts to suppress spanwise vortices and, along with the upwash flow from the cylinder base, makes the finite-length cylinder wake highly three-dimensional. Reynolds stresses, especially the lateral normal stress, are significantly reduced as a result of suppressed spanwise vortices at a small L/d. The downwash flow acts to separate the two rows of spanwise vortices further apart from the wake centerline, resulting in a twin-peak distribution in temperature variance. While the downwash flow entrains high-speed fluid into the wake, responsible for a small deficit in the time-averaged streamwise velocity near the free end, it does not alter appreciably the distribution of time-averaged temperature. It has been found that the downwash flow gives rise to a counter-gradient transport of momentum about the central region of the wake near the free end of the cylinder, though such a counter-gradient transport does not occur for heat transport.

Simultaneous Measurement of Velocity and Pressure in a Wing-Tip Vortex

Simultaneous measurements of fluctuating velocity and pressure have been conducted in the near field of a wing-tip vortex trailing from a NACA0012 half wing. In the vortex core, the time-averaged streamwise velocity shows a wake-like profile which exhibits a deficit by approximately 25% of free stream velocity. The meandering of the vortex is evident from both velocity and pressure measurements: The power spectral density (PSD) of the transverse velocity fluctuation increases in the lower frequency range, and the distribution of the pressure fluctuation exhibits an elongated shape in the z direction as well as two peaks slightly off from the vortex center. The distribution of the measured velocity-pressure correlation varies significantly near the center of the vortex especially in downstream locations.

The spatial organisation of time-averaged streamwise velocity and its correlation with the surface topography of water-worked gravel beds

An examination was made into the spatial pattern of time-averaged streamwise velocity in the near-bed region over two water-worked gravel beds. Laboratory observations revealed that there is considerable spatial variability in velocity. It was organised into streamwise streaks of high-speed fluid which were overlain by spots of low-speed fluid. This spatial pattern was found to be consistently and heavily dependent on relative submergence. The spatial pattern of velocity was shown to have little linear coherence with bed surface topography at the grain-scale. It suggested that for flows above the two beds studied here, bed surface topography at the grain-scale exerted less of an influence on the spatial organisation of time-averaged streamwise velocities than relative submergence.

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

Abstract The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U0=0.03) and the flapping separation bubble (fH/U0=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were Uc=0.35U0 and 0.45U0, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.

Characteristics of Loose Rough Boundary Streams at Near-Threshold

Laboratory experimental results on the turbulent flow characteristics, measured by an acoustic Doppler velocimeter, over loose rough boundaries at the near-threshold of motion are reported. The primary endeavor was to investigate the response of the turbulent flow field, having zero-pressure gradient, to the uniform gravel beds at the near-threshold of motion with reasonably wide range of relative roughness ε∕h (0.02<ε∕h<0.15; where ε=Nikuradse’s equivalent roughness and h=flow depth). Five uniform gravel sizes, ranging from 4.1to14.25mm, were used in the experiments. The vertical distributions of time-averaged velocity, turbulence intensities and the Reynolds stress were measured and analyzed. The variation of the mixing-length is considerably linear with the depth within the inner layer, whose thickness is 0.23 times the boundary layer thickness δ, and the von Kármán constant is obtained as 0.35. The boundary shear stresses were determined by three independent methods, such as using the logarithmic law (the Clauser method), Reynolds stress profiles and bed slope. It is observed that in the inner layer, the logarithmic law of wall for the time-averaged streamwise velocity holds with the von Kármán constant 0.35 and a constant of integration 7.8; whereas in the outer layer, the law of the wake defines the velocity profiles with average value of the Coles’ wake parameter 0.11. Alternatively, velocity profiles based on 1∕nth power law are also put forward, where n is expressed as a function of ε∕δ. The equation of the friction factor f is obtained from the depth averaging of the velocity profile; and the collapse of the estimated f and the measured data (experimental and field) is reasonable. The turbulence intensities being non-isotropic can be defined by an exponential law; whereas the Reynolds stress varies almost linearly with the depth. The values of the Shields parameter for the threshold of gravel motion obtained experimentally correspond closely with the curve obtained from the modified model of Dey considering the present logarithmic law of velocity. For all the aforementioned parameters, thorough statistical and error analyses of the experimental data are done to ascertain the adequacy of the proposed equations.

G801 傾斜円管群を通過する流れの構造に関する研究(2)(GS8 管内流,ファン,一般セッション)

Flow structures passing through an inclined tube and inclined tube banks were investigared in the present study. Experiments were carried out using acrylic rectanglar water tunnel. Re is ranged from 2000 to 10000. Flow were visualized by minute particles and recorded by a high-speed video camera. The particle image velocimetry were carried out, and velocity fields are obtained. As a result, three typical regions of time-averaged streamwise velocity were observed in the wake region of an inclined tube. These velocity regions are considered to be caused by secondary flows that appeard in the wake region and both sides of the tube. Moreover, these secondary flows are considered to be caused by inclined vortex shedding.

A numerical study for the three-dimensional fluid flow past tube banks and comparison with piv experimental data

The analysis for the three-dimensional fluid flow past tube banks arranged in equilateral-triangular form at Remax=4,000 is carried out using a large eddy simulation technique. The governing equations for the mass and momentum conservation are discretized using the finite volume method. Parallel computational techniques using MPI (Message Passing Interface) are implemented in the present computer code. The computation time decreases linearly proportional to the number of used CPUs in the present parallel computation. We obtained the time-averaged streamwise and cross-streamwise velocities and turbulent intensities. The present numerical results are compared with the PIV experimental data and agree generally well with the experimental data.