Showing papers on "Reynolds number published in 2013"

On the logarithmic region in wall turbulence

Abstract: Considerable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally 2 × 104 < Reτ < 6 × 105 for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall. © 2013 Cambridge University Press.

One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to δ+ ≈ 2000

Abstract: One-point statistics are presented for new direct simulations of the zero-pressure-gradient turbulent boundary layer in the range Reθ = 2780–6680, matching channels and pipes at δ+ ≈ 1000–2000. For tripped boundary layers, it is found that the eddy-turnover length is a better criterion than the Reynolds number for the recovery of the largest flow scales after an artificial inflow. Beyond that limit, the integral parameters, mean velocities, Reynolds stresses, and pressure fluctuations of the new simulations agree very well with the available numerical and experimental data, but show clear differences with internal flows when expressed in wall units at the same wall distance and Reynolds number. Those differences are largest in the outer layer, independent of the Reynolds number, and apply to the three velocity components. The logarithmic increase with the Reynolds number of the maximum of the streamwise velocity and pressure fluctuations is confirmed to apply to experimental and numerical internal and ext...

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model.

Abstract: Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/√a. Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.

Direct Numerical Simulation of Turbulent Pipe Flow at Moderately High Reynolds Numbers

Abstract: Fully resolved direct numerical simulations (DNSs) have been performed with a high-order spectral element method to study the flow of an incompressible viscous fluid in a smooth circular pipe of radius R and axial length 25R in the turbulent flow regime at four different friction Reynolds numbers Reτ = 180, 360, 550 and \(1\text{,}000\). The new set of data is put into perspective with other simulation data sets, obtained in pipe, channel and boundary layer geometry. In particular, differences between different pipe DNS are highlighted. It turns out that the pressure is the variable which differs the most between pipes, channels and boundary layers, leading to significantly different mean and pressure fluctuations, potentially linked to a stronger wake region. In the buffer layer, the variation with Reynolds number of the inner peak of axial velocity fluctuation intensity is similar between channel and boundary layer flows, but lower for the pipe, while the inner peak of the pressure fluctuations show negligible differences between pipe and channel flows but is clearly lower than that for the boundary layer, which is the same behaviour as for the fluctuating wall shear stress. Finally, turbulent kinetic energy budgets are almost indistinguishable between the canonical flows close to the wall (up to y + ≈ 100), while substantial differences are observed in production and dissipation in the outer layer. A clear Reynolds number dependency is documented for the three flow configurations.

Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability

Abstract: The flow around the three-dimensional blunt geometry presented in the work of Ahmed, Ramm & Faitin (Tech. Rep., 1984) is investigated experimentally at (where is free-stream velocity, the height of the body and viscosity). The very large recirculation on the base responsible for the dominant part of the drag is characterized. The analyses of the coherent dynamics of the wake reveal the presence of two very distinctive time scales. At long time scales , the recirculation region shifts between two preferred reflectional-symmetry-breaking positions leading to a statistically symmetric wake; the sequence of these asymmetric states is random. This bi-stable behaviour is independent of the Reynolds number but occurs only above a critical value of ground clearance. At short time scales , the wake presents weak coherent oscillations in the vertical and lateral directions. They are respectively associated with the interaction of the top/bottom and lateral shear layers; when normalized by the height and width of the body, the Strouhal numbers are close to 0.17. These results suggest an alternate shedding associated with the vertical oscillation and a one-sided vortex shedding in the lateral direction with an orientation linked to the current asymmetric position. Finally, the impact of these coherent wake motions on the base pressure is discussed to motivate further drag reduction strategies.

Wavepackets in the velocity field of turbulent jets

Abstract: We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10 %, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow–acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers 0.3 ≤ St ≤ 0.9 and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.

The unifying theory of scaling in thermal convection: the updated prefactors

Abstract: The unifying theory of scaling in thermal convection (Grossmann & Lohse, J. Fluid. Mech., vol. 407, 2000, pp. 27–56; henceforth the GL theory) suggests that there are no pure power laws for the Nusselt and Reynolds numbers as function of the Rayleigh and Prandtl numbers in the experimentally accessible parameter regime. In Grossmann & Lohse (Phys. Rev. Lett., vol. 86, 2001, pp. 3316–3319) the dimensionless parameters of the theory were fitted to 155 experimental data points by Ahlers & Xu (Phys. Rev. Lett., vol. 86, 2001, pp. 3320–3323) in the regime 3×107≤Ra≤3×109 and 4≤Pr≤34 and Grossmann & Lohse (Phys. Rev. E, vol. 66, 2002, p. 016305) used the experimental data point from Qiu & Tong (Phys. Rev. E, vol. 64, 2001, p. 036304) and the fact that Nu(Ra,Pr) is independent of the parameter a, which relates the dimensionless kinetic boundary thickness with the square root of the wind Reynolds number, to fix the Reynolds number dependence. Meanwhile the theory is, on the one hand, well-confirmed through various new experiments and numerical simulations; on the other hand, these new data points provide the basis for an updated fit in a much larger parameter space. Here we pick four well-established (and sufficiently distant) Nu(Ra,Pr) data points and show that the resulting Nu(Ra,Pr) function is in agreement with almost all established experimental and numerical data up to the ultimate regime of thermal convection, whose onset also follows from the theory. One extra Re(Ra,Pr) data point is used to fix Re(Ra,Pr). As Re can depend on the definition and the aspect ratio, the transformation properties of the GL equations are discussed in order to show how the GL coefficients can easily be adapted to new Reynolds number data while keeping Nu(Ra,Pr) unchanged

Combined Experimental and Computational Investigation of Unsteady Structure of Sheet/Cloud Cavitation

Abstract: The objective of this paper is to apply combined experimental and computational modeling to investigate unsteady sheet/cloud cavitating flows. In the numerical simulations, a filter-based density corrected model (FBDCM) is introduced to regulate the turbulent eddy viscosity in both the cavitation regions on the foil and in the wake, which is shown to be critical in accurately capturing the unsteady cavity shedding process, and the corresponding velocity and vorticity dynamics. In the experiments, high-speed video and particle image velocimetry (PIV) technique are used to measure the flow velocity and vorticity fields, as well as cavitation patterns. Results are presented for a Clark-Y hydrofoil fixed at an angle of attack of a ¼8deg at a moderate Reynolds number, Re ¼7 � 10 5 , for both subcavitating and sheet/cloud cavitating conditions. The results show that for the unsteady sheet/cloud cavitating case, the formation, breakup, shedding, and collapse of the sheet/cloud cavity lead to substantial increase in turbulent velocity fluctuations in the cavitating region around the foil and in the wake, and significantly modified the wake patterns. The turbulent boundary layer thickness is found to be much thicker, and the turbulent intensities are much higher in the sheet/cloud cavitating case. Compared to the wetted case, the wake region becomes much broader and is directed toward the suction side instead of the pressure side for the sheet/cloud cavitation case. The periodic formation, breakup, shedding, and collapse of the sheet/cloud cavities, and the associated baroclinic and viscoclinic torques, are shown to be important mechanisms for vorticity production and modification. [DOI: 10.1115/1.4023650]

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

Abstract: The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier-Stokes equation

Abstract: We generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier–Stokes equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term – contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier–Stokes constraints, e.g. Reynolds equations, can be achieved in straightforward variation of the presented results.

Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms

Abstract: Previous studies investigating the effect of aspect ratio ( ) for insect-like regimes have reported seemingly different trends in aerodynamic forces, however no detailed flow observations have been made. In this study, the effect of and Reynolds number on the flow structures over insect-like wings is explored using a numerical model of an altered fruit fly wing revolving at a constant angular velocity. Increasing the Reynolds number for an of 2.91 resulted in the development of a dual leading-edge vortex (LEV) structure, however increasing at a fixed Reynolds number generated the same flow structures. This result shows that the effects of Reynolds number and are linked. We present an alternative scaling using wing span as the characteristic length to decouple the effects of Reynolds number from those of . This results in a span-based Reynolds number, which can be used to independently describe the development of the LEV. Indeed, universal behaviour was found for various parameters using this scaling. The effect of on the vortex structures and aerodynamic forces was then assessed at different span-based Reynolds numbers. Scaling the flow using the wing span was found to apply when a strong spanwise velocity is present on the leeward side of the wing and therefore may prove to be useful for similar studies involving flapping or rotating wings at high angles of attack.

Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field

Abstract: In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge–Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al2O3) and titanium oxide (TiO2) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.

Particle Focusing in Curved Microfluidic Channels

Abstract: The decoupled effects of Reynolds and Dean numbers are examined in inertial focusing flows. In doing so, a complex set of inertial focusing behavioral regimes is discovered within curved microfluidic channels over a range of channel Reynolds numbers, curvature ratios and particle confinement ratios. These regimes are characterized by particle migration either towards or away from the center of curvature as the channel Reynolds number is increased. The transition between these two regimes is shown to be a set of conditions where single-point equilibrium position focusing of particles of different sizes is achieved. A mechanism describing the observed motion of particles in such flows is hypothesized incorporating the redistribution of the main flow velocities caused by Dean flow and its effect on the balance forces on suspended particles.

Nonlinear elastic instability in channel flows at low Reynolds numbers.

Abstract: It is presently believed that flows of viscoelastic polymer solutions in geometries such as a straight pipe or channel are linearly stable. Here we present experimental evidence that such flows can be nonlinearly unstable and can exhibit a subcritical bifurcation. Velocimetry measurements are performed in a long, straight microchannel; flow disturbances are introduced at the entrance of the channel system by placing a variable number of obstacles. Above a critical flow rate and a critical size of the perturbation, a sudden onset of large velocity fluctuations indicates the presence of a nonlinear subcritical instability. Together with the previous observations of hydrodynamic instabilities in curved geometries, our results suggest that any flow of polymer solutions becomes unstable at sufficiently high flow rates.

Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers

Abstract: The onset and development of turbulence from controlled disturbances in compressible ( ), flat-plate boundary layers is studied by direct numerical simulation. We have validated the initial disturbance development, confirmed that H- and K-regime transitions were reproduced and, from these starting points, we carried these simulations beyond breakdown, past the skin-friction maximum and to higher Reynolds numbers than investigated before to evaluate how these two flow regimes converge towards turbulence and what transitional flow structures embody the statistics and mean dynamics of developed turbulence. We show that H- and K-type breakdowns both relax toward the same statistical structure typical of developed turbulence at high Reynolds number immediately after the skin-friction maximum. This threshold marks the onset of self-sustaining mechanisms of near-wall turbulence. At this point, computed power spectra exhibit a decade of Kolmogorov inertial subrange; this is further evidence of convergence to equilibrium turbulence at the late stage of transition. Here, visualization of the instantaneous flow structure shows numerous, tightly packed hairpin vortices (Adrian, Phys. Fluids, vol. 19, 2007, 041301). Strongly organized coherent hairpin structures are less perceptible farther downstream (at higher Reynolds numbers), but the flow statistics and near-wall dynamics are the same. These structurally simple hairpin-packet solutions found in the very late stages of H- and K-type transitions obey the statistical measurements of higher-Reynolds-number turbulence. Comparison with the bypass transition of Wu & Moin (Phys. Fluids, vol. 22, 2010, pp. 85–105) extends these observations to a wider class of transitional flows. In contrast to bypass transition, the (time- and spanwise-averaged) skin-friction maximum in both H- and K-type transitions overshoots the turbulent correlation. Downstream of these friction maxima, all three skin-friction profiles collapse when plotted versus the momentum-thickness Reynolds number, . Mean velocities, turbulence intensities and integral parameters collapse generally beyond in each transition scenario. Skin-friction maxima, organized hairpin vortices and the onset of self-sustaining turbulence found in controlled H- and K-type transitions are, in many dynamically important respects, similar to development of turbulent spots seen by Park et al. (Phys. Fluids, vol. 24, 2012, 035105). A detailed statistical comparison demonstrates that each of these different transition scenarios evolve into a unique force balance characteristic of higher-Reynolds-number turbulence (Klewicki, Ebner & Wu, J. Fluid Mech., vol. 682, 2011, pp. 617–651). We postulate that these dynamics of late-stage transition as manifested by hairpin packets can serve as a reduced-order model of high-Reynolds-number turbulent boundary layers.

Fluid flow in rock fractures: From the Navier-Stokes equations to the cubic law

Abstract: The mathematical analysis of the flow of a single-phase Newtonian fluid through a rough-walled rock fracture is reviewed, starting with the Navier-Stokes equations. By a combination of order-of-magnitude analysis, appeal to available analytical solutions, and reanalysis of some data from the literature, it is shown that the Navier-Stokes equations can be linearized if the Reynolds number is less than about 10. Further analysis shows that the linear Stokes equations can be replaced by the simpler Reynolds lubrication equation if the wavelength of the dominant aperture variations is about three times greater than the mean aperture. However, this criterion does not seem to be strongly obeyed by all fractures. The Reynolds equation (i.e., the local cubic law) may therefore suffice in estimating fracture permeabilities to within a factor of about 2, but more accurate estimates will require solution of the Stokes equations. Similarly, estimates of mean aperture based on inverting transmissivity data may have errors of a factor of two if any version of the local cubic law is used to relate transmissivity to mean aperture.

Generalized logarithmic law for high-order moments in turbulent boundary layers

Abstract: High-Reynolds-number data in turbulent boundary layers are analysed to examine statistical moments of streamwise velocity fluctuations . Prior work has shown that the variance of exhibits logarithmic behaviour with distance to the surface, within an inertial sublayer. Here we extend these observations to even-order moments. We show that the -order moments, raised to the power also follow logarithmic behaviour according to , where is the velocity fluctuation normalized by the friction velocity, is an outer length scale and are non-universal constants. The slopes in the logarithmic region appear quite insensitive to Reynolds number, consistent with universal behaviour for wall-bounded flows. The slopes differ from predictions that assume Gaussian statistics, and instead are consistent with sub-Gaussian behaviour.