Reynolds Number Dependence Research Articles

Nonuniversality and Finite Dissipation in Decaying Magnetohydrodynamic Turbulence.

A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to Cϵ=Cϵ,∞+C/R-+O(1/R-(2)), where R- is a generalized Reynolds number. The constant Cϵ,∞ describes the total energy transfer flux. This flux depends on magnetic and cross helicities, because these affect the nonlinear transfer of energy, suggesting that the value of Cϵ,∞ is not universal. Direct numerical simulations were conducted on up to 2048(3) grid points, showing good agreement between data and the model. The model suggests that the magnitude of cosmological-scale magnetic fields is controlled by the values of the vector field correlations. The ideas introduced here can be used to derive similar model equations for other turbulent systems.

Level-crossing statistics and production in low Reynolds number wall turbulence

Statistical properties at velocity level crossings are analysed in a low Reynolds number fully developed turbulent channel flow. Emphasis is placed on local production statistics conditioned by fixed amplitudes of the streamwise u and wall-normal v velocity components. Direct numerical simulations performed in large computational domains are used for this purpose. The Reynolds number based on the channel half width and the shear velocity varies from 180 to 1100. Particular attention is paid to correctly determine the conditional quantities at level crossings of u and v velocity fluctuations, to prevent biasing effects. Level crossings along the longitudinal x and spanwise z directions in homogeneous planes are introduced together with different characterisations, such as directional and contour crossings. The frequency of events detected at fixed thresholds follows a Gaussian model acceptably well. There is more level-crossing activity in the spanwise direction than in the streamwise. The mean conditional production distributions are dissymmetrical with respect to the level-crossing thresholds in the low buffer and viscous sublayers. These statistics differ significantly from a statistical model that assumes joint normality between u and v. There is a clear but relatively mild Reynolds number dependence of the conditional expected means of u and v that do not scale with inner, outer or mixed variables. The Reynolds number sensitivity of these statistics increases towards the edge of the wall layer.

High-fidelity simulations of the lobe-and-cleft structures and the deposition map in particle-driven gravity currents

The evolution of a mono-disperse gravity current in the lock-exchange configuration is investigated by means of direct numerical simulations for various Reynolds numbers and settling velocities for the deposition. We limit our investigations to gravity currents over a flat bed in which density differences are small enough for the Boussinesq approximation to be valid. The concentration of particles is described in an Eulerian fashion by using a transport equation combined with the incompressible Navier-Stokes equations. The most interesting results can be summarized as follows: (i) the settling velocity is affecting the streamwise vortices at the head of the current with a substantial reduction of their size when the settling velocity is increased; (ii) when the Reynolds number is increased the lobe-and-cleft structures are merging more frequently and earlier in time, suggesting a strong Reynolds number dependence for the spatio-temporal evolution of the head of the current; (iii) the temporal imprint of the lobe-and-cleft structures can be recovered from the deposition map, suggesting that the deposition pattern is defined purely and exclusively by the structures at the front of the current.

The Reynolds number dependency of the steady and unsteady loading on a slightly rough circular cylinder: From subcritical up to high transcritical flow state

Simultaneous measurements of the spanwise-integrated unsteady aerodynamic forces and time-averaged local surface pressures on a 2D slightly rough circular cylinder were carried out over a wide range of Reynolds numbers in the high-pressure wind tunnel in Göttingen. The Reynolds numbers of 15×103≤Re≤12×106 spanned the known flow state regimes from subcritical up to high transcritical. The surface of the cylinder had a mean relative roughness of ks/D=1.2×10−3. The results demonstrated that especially in the critical flow regime the spanwise flow was strongly three-dimensional. In this regime two discontinuities at two closely spaced Reynolds numbers were observed, coupled with critical fluctuations in the lift force and the formation of a separation bubble at each side of the cylinder. The narrowing of the wake led to a sharp decrease of the drag coefficient and a steep increase of the values for the minimum pressure coefficients and the base pressure coefficient. In the upper transition state the boundary layer separation wandered upstream, resulting in an increase of the drag coefficient and a decrease of the base pressure coefficient and the Strouhal number. All measured flow field properties reached intermediate steady plateaus in the transcritical state for Re≥1.3×106. It was also shown that the surface roughness had a strong effect on the cylinder flow; in particular the disappearance of the supercritical regime and the subsequent strong recovery of the drag coefficient in the upper transition.

Energy transfer and dissipation in forced isotropic turbulence.

A model for the Reynolds-number dependence of the dimensionless dissipation rate C(ɛ) was derived from the dimensionless Kármán-Howarth equation, resulting in C(ɛ)=C(ɛ,∞)+C/R(L)+O(1/R(L)(2)), where R(L) is the integral scale Reynolds number. The coefficients C and C(ɛ,∞) arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to R(L)=5875 (R(λ)=435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law R(L)(n) with exponent value n=-1.000±0.009 and that this decay of C(ɛ) was actually due to the increase in the Taylor surrogate U(3)/L. The model equation was fitted to data from the DNS, which resulted in the value C=18.9±1.3 and in an asymptotic value for C(ɛ) in the infinite Reynolds-number limit of C(ɛ,∞)=0.468±0.006.

Spectral behaviour of the turbulence-driven power fluctuations of wind turbines

Field and laboratory experiments were performed to unravel the structure of the power output fluctuations of horizontal-axis wind turbines based on incoming flow turbulence. The study considers the power data of three wind turbines of rotor sizes 0.12, 3.2, and 96 m, with rated power spanning six decades from the order of 100 to 106 W. The 0.12 m wind turbine was tested in a wind tunnel while the 3.2 and 96 m wind turbines were operated in open fields under approximately neutrally stratified thermal conditions. Incoming flow turbulence was characterised by hotwire and sonic anemometers for the wind tunnel and field set-ups. While previous works have observed a filtering behaviour in wind turbine power output, this exact behaviour has not, to date, been properly characterised. Based on the spectral structure of the incoming flow turbulence at hub height, and the mechanical and structural properties of the turbines, a physical basis for the behaviour of temporal power fluctuations and their spectral structure is found with potential applications in turbine control and numerical simulations. Consistent results are observed across the geometrical scales of the wind turbines investigated, suggesting no Reynolds number dependence in the tested range.

Modeling average gas–solid heat transfer using particle-resolved direct numerical simulation

The purpose of this work is to develop gas–solid heat transfer models using Particle-resolved Direct Numerical Simulations (PR-DNS). Gas–solid heat transfer in steady flow through a homogeneous fixed assembly of monodisperse spherical particles is simulated using the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). PR-DNS results are obtained over a range of mean slip Reynolds number (1–100) and solid volume fraction (0.1–0.5). Fluid heating is important in gas–solid heat transfer, especially in dense low-speed flows, and the PUReIBM formulation accounts for this through a heat ratio which appears in the thermal self-similarity boundary condition that ensures thermally fully-developed flow. The average volumetric interphase heat transfer rate (average gas–solid heat transfer) that appears in the average fluid temperature evolution equation is quantified and modeled using PR-DNS results. The Nusselt number corresponding to average gas–solid heat transfer is obtained from PR-DNS data, and compared with Gunn’s Nusselt number correlation (Gunn, 1978). A new Nusselt number correlation is proposed that fits the PR-DNS data more closely and also captures the Reynolds number dependence more accurately. It is shown that the use of Nusselt number correlations based on the average bulk fluid temperature in the standard two-fluid model for gas–solid heat transfer is inconsistent, and results in up to 35% error in prediction of the average gas–solid heat transfer. Using PR-DNS data, a consistent two-fluid model is proposed that improves the predicted average gas–solid heat transfer.

The effect of source Reynolds number on the rise height of a fountain

The focus of this paper is to establish the effect of source Reynolds number, Re0, on the mean rise heights of Boussinesq miscible fountains and thereby the range of Re0 for which rise heights are independent of Re0. We present results from experiments on aqueous-saline fountains spanning source Reynolds numbers of 15 ≤ Re0 ≤ 4000 and source Froude numbers of 0.3 ≤ Fr0 ≤ 40. We provide threshold values for the source Reynolds number, i.e., values above which fountain rise height may be regarded as independent of Re0. For Reynolds numbers immediately beneath these threshold values, the fountain rise height increases as Re0 decreases—in agreement with Lin and Armfield [“The Reynolds and Prandtl number dependence of weak fountains,” Comput. Mech. 31, 379–389 (2003)]. At even lower Re0, we show that the rise heights reach a maximum and that further decreases in Re0 decrease the rise height attained—in agreement with Phillipe et al., [“Penetration of a negatively buoyant jet in a miscible liquid,” Phys. Fluids 17, 053601 (2005)]. As such, we resolve an apparent inconsistency within the existing fountain literature.

Water slip flow in superhydrophobic microtubes within laminar flow region

The fabrication of superhydrophobic surfaces and the studies on water flow characteristics therein are of great significance to many industrial areas as well as to science and technology development. Experiments were carried out to investigate slip characteristics of water flowing in circular superhydrophobic microtubes within laminar flow region. The superhydrophobic microtubes of stainless steel were fabricated with chemical etching–fluorination treatment. An experimental setup was designed to measure the pressure drop as function of water flow rate. For comparison, superhydrophilic tubes were also tested. Poiseuille number Po was found to be smaller for the superhydrophobic microtubes than that for superhydrophilic ones. The pressure drop reduction ranges from 8% to 31%. It decreases with increasing Reynolds number when Re<900, owing to the transition from Cassie state to Wenzel state. However, it is almost unchanged with further increasing Re after Re>900. The slip length in superhydrophobic microtubes also exhibits a Reynolds number dependence similarly to the pressure drop reduction. The relation between slip length and Darcy friction factor is theoretically analyzed with consideration of surface roughness effect, which was testified with the experimental results.

S0510202 低レイノルズ数円形噴流乱流の低解像度二次元PIV測定

In this study, we carried out a low resolution 2D-PIV(Particle Image Velocimetry) measurement of low Reynolds number turbulent round jet. The spatial resolution was of the order of Taylor micro-scale and under-estimates the turbulence energy. Mean velocity statistics coincided with the standard reference. Second and third order statistics qualitatively in good agreement with the previous studies. The difference between the results is due to a loss of turbulence energy and the Reynolds number dependence. Nevertheless, the results showed the self-preserving property in far field region.

Drag Reduction of a Turbulent Boundary Layer over an Oscillating Wall and Its Variation with Reynolds Number

Spanwise oscillation applied on the wall under a spatially developing turbulent boundary layer flow is investigated using direct numerical simulation. The temporal wall forcing produces a considerable drag reduction over the region where oscillation occurs. Downstream development of drag reduction is investigated from Reynolds number dependency perspective. An alternative to the previously suggested power-law relation between Reynolds number and peak drag reduction values, which is valid for channel flow as well, is proposed. Considerable deviation in the variation of drag reduction with Reynolds number between different previous investigations of channel flow is found. The shift in velocity profile, which has been used in the past for explaining the diminishing drag reduction at higher Reynolds number for riblets, is investigated. A new predictive formula is derived, replacing the ones found in the literature. Furthermore, unlike for the case of riblets, the shift is varying downstream in the case of wall oscillations, which is a manifestation of the fact that the boundary layer has not reached a new equilibrium over the limited downstream distance in the simulations. Taking this into account, the predictive model agrees well with DNS data. On the other hand, the growth of the boundary layer does not influence the drag reduction prediction.

The statistical behaviour of attached eddies

Townsend’s attached eddy hypothesis forms the basis of an established model of the logarithmic layer in wall-bounded turbulent flows in which this inertially dominated region is characterised by a hierarchy of geometrically self-similar eddying motions that scale with their distance to the wall. The hypothesis has gained considerable support from high Reynolds number measurements of the second-order moments of the fluctuating velocities. Recently, Meneveau and Marusic [“Generalized logarithmic law for high-order moments in turbulent boundary layers,” J. Fluid Mech. 719, R1 (2013)] presented experimental evidence that all even-ordered moments of the streamwise velocity will exhibit a logarithmic dependence on the distance from the wall. They demonstrated that this was consistent with the attached eddy hypothesis, so long as the velocity distribution is assumed to be Gaussian (which allows the use of the central limit theorem). In this paper, we derive this result from the attached eddy model without assuming a Gaussian velocity distribution, and find that such logarithmic behaviours are valid in the large Reynolds number limit. We also revisit the physical and mathematical basis of the attached eddy hypothesis, in order to increase rigour and minimise the assumptions required to apply the hypothesis. To this end, we have extended the proof of Campbell’s theorem to apply to the velocity field corresponding to a forest of variously sized eddies that are randomly placed on the wall. This enables us to derive all moments of the velocity in the logarithmic region, including cross-correlations between different components of the velocity. By contrast, previous studies of the attached eddy hypothesis have considered only the mean velocity and its second order moments. From this, we obtain qualitatively correct skewnesses and flatnesses for the spanwise and wall-normal fluctuations. The issue of the Reynolds number dependence of von Kármán’s constant is also addressed.

Effects of forcing time scale on the simulated turbulent flows and turbulent collision statistics of inertial particles

In this paper, we study systematically the effects of forcing time scale in the large-scale stochastic forcing scheme of Eswaran and Pope [“An examination of forcing in direct numerical simulations of turbulence,” Comput. Fluids 16, 257 (1988)] on the simulated flow structures and statistics of forced turbulence. Using direct numerical simulations, we find that the forcing time scale affects the flow dissipation rate and flow Reynolds number. Other flow statistics can be predicted using the altered flow dissipation rate and flow Reynolds number, except when the forcing time scale is made unrealistically large to yield a Taylor microscale flow Reynolds number of 30 and less. We then study the effects of forcing time scale on the kinematic collision statistics of inertial particles. We show that the radial distribution function and the radial relative velocity may depend on the forcing time scale when it becomes comparable to the eddy turnover time. This dependence, however, can be largely explained in terms of altered flow Reynolds number and the changing range of flow length scales present in the turbulent flow. We argue that removing this dependence is important when studying the Reynolds number dependence of the turbulent collision statistics. The results are also compared to those based on a deterministic forcing scheme to better understand the role of large-scale forcing, relative to that of the small-scale turbulence, on turbulent collision of inertial particles. To further elucidate the correlation between the altered flow structures and dynamics of inertial particles, a conditional analysis has been performed, showing that the regions of higher collision rate of inertial particles are well correlated with the regions of lower vorticity. Regions of higher concentration of pairs at contact are found to be highly correlated with the region of high energy dissipation rate.

J0550301 Taylor-Couette流の平均トルク遷移レイノルズ数域における乱流渦構造

It is known that Taylor-Couette flow shows a transition in the Reynolds number dependency of the mean torque near Re 〜 10000. To investigate the turbulent vortical structures in the transition state, direct numerical simulations of Taylor-Couette flow with fixed outer cylinder have been conducted in the different Reynolds numbers from Re = 8000 to 25000. As the Reynolds number increases, the fine scale eddies are more populated in a large part of the domain and they tend to take more various angles. The joint probability functions of the tilting angles of eddies with respect to the tangential direction and their radial positions exhibit preferential distributions, which is due to the shear layer between the large scale Taylor vortex motions. The present results suggest that the distribution and the orientation of the fine scale eddies in this Reynolds number range are greatly affected by the Taylor vortex structure.

Heat transfer in turbulent planar offset attaching jets with small initial offset distances

Measurements of the mean heat transfer coefficient from the wall below turbulent offset wall attaching planar jets were performed for jets with Reynolds numbers (Rej) of 21,800–54,500. The jets were initially offset 0.2–1 times the initial jet height (Hj) above the wall. The Reynolds number dependence of the maximum Nusselt number varied with offset distance from Rej0.64 for the flows with an offset distance of 0.2Hj to Rej0.77 for flows with initial offset distances of Hj. The distance from the jet exit to the location of the maximum heat transfer coefficient also increased with Reynolds number for the jets with smaller offset distances. The maximum heat transfer coefficient for the different offset jets could be correlated by hXm/ka=c(UjXm/ν)0.74 where Xm is the distance to the maximum heat transfer location and the parameter c varies with the initial offset distance from 0.08 to 0.1. The profiles of the Nusselt number approach the results for a wall jet downstream of x/Hj≈8 and collapsed when scaled by Rej0.77 in all cases.

The Confinement Effects on Jet Kinetic Momentum Flux Quantified by Measuring the Reaction Force

A turbulent jet is the most important flow element in mechanical ventilation. Mixing ventilation is based on the properties of turbulent jets. By entrainment into the jet the ambient air is set into motion. For a jet supplied within a room the enclosure may affect the jet in several ways, through:Coanda effect which is the tendency of a fluid to be attracted to a nearby surface. A free jet is turned into a wall jet and the momentum flux of the jet decreases by friction against the room surfaces.The jet collides with the opposing wall and the jet is transformed into a wall jet.The size of the cross sectional area relative to the supply opening will affect the flow pattern within the enclosure. One can expect the direction of the inflow (entrainment) to the jet to be affected.Location of supply and extract. The location of the supply is a factor that influences the pressure gradient within the room.This paper considers the items b), c) and d).The main characteristic of a jet is its momentum flux, but determining the momentum flux is not an easy task and has lead to contradicting results. Standard methods require velocity field measurements which have their restrictions and uncertainties. To overcome these problems a direct and more reliable method was used by recording the flow force, caused by an impinging jet, with a digital balance. The tests were carried out both for unenclosed (free jet) and enclosed cases. In the latter case tests were conducted with supply and extract both located on the same wall and located on opposite walls. Detailed pressure measurements were conducted to describe the details of the reaction force. There was a clear effect of the confinement on the reaction force and a Reynolds number dependence.

Reynolds number dependency of an insect-based flapping wing

SummaryAerodynamic characteristics depending on Reynolds number (Re) ranges were studied to investigate the suitable design parameters of an insect-based micro air vehicle (MAV). The tests centered on the wing rotation timing and Re ranges, and were conducted to understand the lift augmentations and unsteady effects. A dynamically scaled-up flapping wing controlled by a pair of servos was installed underwater with a micro force/torque sensor. A high-speed camera and a laser sheet were also put in front of the water tank for the time-resolved digital particle image velocimetry (DPIV). The lift augmentations clearly appeared at low Re and were well reflected on the insect’s flight range. In the case of the high Re, however, the peak standing for the wing–wake interaction was delayed, and the pitching-up rotation was not able to lead to another lift enhancement, i.e., rotational lift. In such Re, the mean CL and the L/D of the advanced rotation were substantially decreased from those of the other rotations. The DPIV results at high Re well described turbulent characteristics such as the irregular, unstable, and high-intensity vortex structures with a short temporal delay. In the advanced rotation, the LEV in the rotational phase could not maintain the attachment. Thus, the rotational lift was not able to work. On the contrary, the temporal response delay benefitted the wing in the delayed rotation. Therefore, the wing in the delayed rotation had both a similar level of the mean CL and a higher marked L/D than those of the advanced rotation. Such results indicate that the high Re could interrupt lift augmentation mechanisms, and these augmentations would not be suitable for a heavier MAV. In conclusion, using adequate wing kinematics to acquire estimations of the weight and range of the Re is highly recommended at the aerodynamic design step.

Reynolds number effects in the near-field of a turbulent square jet

High-resolution particle image velocimetry (PIV) was used to study the flow characteristics in the near-field of a turbulent square water jet issuing from a smooth contraction nozzle. Mean velocity and turbulence statistics are investigated over a range of jet Reynolds number ReD (based on jet exit velocity and equivalent nozzle diameter) varying from 10,000 to 41,400. The influence of ReD on the shear layer formation in terms of momentum thickness, Taylor length scale and the evolution of the turbulent/non-turbulent interface are also studied. The velocity measurements reveal that the jet in the near-field is dependent on Reynolds number at the lower end of the range (ReD=10,000) despite the fact that all exit jet profiles closely approximate a “top-hat” shape. It is shown that the jet shear layer grows faster at lower Reynolds number which, combined with an increase of the spanwise turbulence component (vrms) along the jet centerline, suggest rapid axis switching. Much weaker Reynolds number dependence of the mean velocity, turbulence intensities, momentum thickness and jet centerline anisotropy (urms/vrms) was found for square jets at ReD>104. The Taylor length scale calculated along the jet centerline decreases with increasing Reynolds number and asymptotes to a constant value for X/D>4. The turbulent/non-turbulent (T/NT) regions of the jet have been identified using the velocity criteria proposed in the literature. Evolution of the T/NT interface and the effect of ReD on the conditionally averaged streamwise velocity and vorticity are also investigated in the near-field of the jet. No jump of the conditionally averaged streamwise velocity and vorticity profiles was noted in the near-field of the square jet.

Influence of Microscale Turbulent Droplet Clustering on Radar Cloud Observations

Abstract This study investigates the influence of microscale turbulent clustering of cloud droplets on the radar reflectivity factor and proposes a new parameterization to account for it. A three-dimensional direct numerical simulation of particle-laden isotropic turbulence is performed to obtain turbulent clustering data. The clustering data are then used to calculate the power spectra of droplet number density fluctuations, which show a dependence on the Taylor microscale-based Reynolds number (Reλ) and the Stokes number (St). First, the Reynolds number dependency of the turbulent clustering influence is investigated for 127 &amp;lt; Reλ &amp;lt; 531. The spectra for this wide range of Reλ values reveal that Reλ = 204 is sufficiently large to be representative of the whole wavenumber range relevant for radar observations of atmospheric clouds. The authors then investigate the Stokes number dependency for Reλ = 204 and propose an empirical model for the turbulent clustering influence assuming power laws for the number density spectrum. For Stokes numbers less than 2, the proposed model can estimate the influence of turbulence on the spectrum with an RMS error less than 1 dB when calculated over the wavenumber range relevant for radar observations. For larger Stokes number droplets, the model estimate has larger errors, but the influence of turbulence is likely negligible in typical clouds. Applications of the proposed model to two idealized cloud observing scenarios reveal that microscale turbulent clustering can cause a significant error in estimating cloud droplet amounts from radar observations with microwave frequencies less than 13.8 GHz.

DNS of hydrodynamically interacting droplets in turbulent clouds: Parallel implementation and scalability analysis using 2D domain decomposition

The study of turbulent collision of cloud droplets requires simultaneous considerations of the transport by background air turbulence (i.e., geometric collision rate) and influence of droplet disturbance flows (i.e., collision efficiency). In recent years, this multiscale problem has been addressed through a hybrid direct numerical simulation (HDNS) approach (Ayala et al., 2007). This approach, while currently is the only viable tool to quantify the effects of air turbulence on collision statistics, is computationally expensive. In order to extend the HDNS approach to higher flow Reynolds numbers, here we developed a highly scalable implementation of the approach using 2D domain decomposition. The scalability of the parallel implementation was studied using several parallel computers, at 5123 and 10243 grid resolutions with O(106)–O(107) droplets. It was found that the execution time scaled with number of processors almost linearly until it saturates and deteriorates due to communication latency issues.To better understand the scalability, we developed a complexity analysis by partitioning the execution tasks into computation, communication, and data copy. Using this complexity analysis, we were able to predict the scalability performance of our parallel code. Furthermore, the theory was used to estimate the maximum number of processors below which the approximately linear scalability is sustained. We theoretically showed that we could efficiently solved problems of up to 81923 with O(100,000) processors. The complexity analysis revealed that the pseudo-spectral simulation of background turbulent flow for a dilute droplet suspension typical of cloud conditions typically takes about 80% of the total execution time, except when the droplets are small (less than 5 μm in a flow with energy dissipation rate of 400 cm2/s3 and liquid water content of 1 g/m3), for which case the particle–particle hydrodynamic interactions become the bottleneck. The complexity analysis was also used to explore some alternative methods to handle FFT calculations within the flow simulation and to advance droplets less than 5 μm in radius, for better computational efficiency. Finally, preliminary results are reported to shed light on the Reynolds number-dependence of collision kernel of non-interacting droplets.