Reynolds Number Dependence Research Articles

Experimental study of drag loads on open and closed low-aspect-ratio circular cylinders in steady current

We investigate the drag load on low-aspect ratio circular cylinders, submerged as in infinite fluid and subjected to steady current. A series of experiments are carried out in a circulating water tunnel with three different types of models; open and closed cylinders, and open with a splitter plate inside the middle of the cylinders. The length-to-draft ratio of the models, L/D, varies from 0.15 to 0.6. The Reynolds number, based on the cylinder diameter, varies from 40000 to 105000. The experiments show small Reynolds number dependency. The drag coefficient, CD, varies substantially for the open cylinder case; being around 2 for the lowest aspect ratios L/D≤0.2, while 0.65-0.8 for L/D>0.25. There is an abrupt change of flow pattern for L/D=0.25: for L/D≤0.2 the flow which is separated from the front half of the cylinder goes through the cylinder, producing a wide von Karman type vortex street, while for L/D≥0.25 the flow does not go through the models and, as a consequence, produces a significantly more narrow wake. The wide wake regime is suppressed when the splitter plate is added, with drag coefficients CD=0.6−0.8. The drag coefficients for the closed cylinders are lower than the ones with splitter plate, and also consistent with published data on low-aspect ratio closed cylinders. A rational drag load model is proposed for the high-drag regime, with reasonable results. Tests where the cylinder with splitter plate is sectioned into a front and a rear half are presented, revealing a very small contribution of the drag from the rear half. This is discussed in view of existing studies on two-dimensional flat plates in tandem.

Validation of computational fluid dynamics simulations for determining pressure loss coefficients of ventilation components

Ventilation systems include a variety of components for which necessary pressure loss data is often unavailable. Computational fluid dynamics simulations could substitute for expensive measurements, but validation simulations with suitable data are crucial to assess model uncertainties. Existing CFD validation studies either did not focus specifically on pressure losses, only covered few components, or did not include recent developments in turbulence modelling. In the present work, 33 bends, 4 gates and 2 tees were simulated using a consistent approach. Computational fluid dynamics simulations were validated with published data: rectangular high-edge and wide-edge bends from the experimental dataset of Sprenger, gates and diverging tees from the SMACMA guide. The considered flows cover important basic flow phenomena: deflection, splitting and flow separation. The 39 components were simulated with three turbulence models at 14 Reynolds numbers. The simulations predicted pressure loss coefficients accurately for various components. Cases with strong flow separation regions were most challenging. The model prediction uncertainty was assessed by carrying out simulations with three selected turbulence models. As in the experimental data from Sprenger, the simulations showed a distinct dependence of pressure loss coefficients on the Reynolds number for bends. In contrast, for abrupt deflections and flow separation at sharp edges, the Reynolds number dependency was minor. Technical pressure loss data of ductwork components is needed for the dimensioning, optimisation, and energy assessment of ventilation systems. The present validation study assesses the present state of the art of CFD simulations to determine pressure loss coefficients and the resulting prediction uncertainties.

Optimization of twisted-tape element static mixers for industrially relevant setups

Static mixer studies in literature have often been reported for idealized systems with a concentric injected flow. These do not account for real-world mixing scenarios where the additive comes in through an injector. Depending on the injector geometry, the injected flow, and pipe Reynolds number, the injected flow may end up off-centered. This impacts the static mixer performance as the first few elements are unable to provide efficient mixing. This paper discusses a parametric study of twisted-tape mixers to numerically ascertain their performance for Newtonian flows. It focuses on industrially relevant mixers which operate with some inexactness, e.g., off-center flow of the additive. Effect on mixing of angle of twist and aspect ratio of the individual element along with Reynolds number are studied; and the Reynolds number dependency of mixer geometry for optimal performance is established. This is done without using some oft-used approximations/assumptions in previous literature like zero-thickness mixer walls, 2d analysis, periodic boundary conditions etc. Two non-dimensional quantities, i.e., Coefficient of Variation (CoV) and Z-factor, are used to assess and quantify the operation of the mixers. For idealized systems, increasing the number of elements by reducing the aspect ratio and/or the twist angle is seen to improve mixing for all Reynolds numbers tested (1−100). However, for a real-world mixer constrained by its total length/pressure drop, mixing is proven to be an optimization problem between increasing the number of flow-splits by introducing a greater number of elements and mitigating the anomalous flow (uneven split) caused due to it. For Re≤ 10, reduction of twist angle from 180∘ to 140∘ improves mixing for only aspect ratios greater than approximately 0.9. For Reynolds number of 100, the 140∘ twist angle outperforms the 180∘ twist angle for all aspect ratios studied. In summary, there is no combination of twist angle and aspect ratio that is a universally optimal solution and these parameters must be decided subjectively based on multiple other input parameters for a given system.

Numerical simulation of two-phase flow in a microchannel for evaluating liquid film thickness and its Reynolds number dependency

Numerical simulation of two-phase flow in a microchannel for evaluating liquid film thickness and its Reynolds number dependency

LES and PIV Investigation of the Flow Past a Cactus-Shaped Cylinder with Four Ribs

The flow past a cactus-shaped cylinder with four ribs is investigated numerically using large eddy simulations (LES) at Reynolds number of 20,000 and experimentally using particle image velocimetry (PIV) at Reynolds number of 50,000. In both approaches, the full range of angle of attack is covered. LES results show a good qualitative and quantitative match of the aerodynamic properties to previous experimental data, although the value of the critical angle of attack is slightly lower. The results confirm that there is no Reynolds number dependency within the investigated range allowing a comparison of the flow fields from the present LES and PIV. Significant variations of the flow patterns with the angle of attack are found and quantified using the recirculation length and wake width. Overall, the observed angle of attack dependence resembles the behaviour of the square cylinder. However, the studied cylinder has a narrower wake at all angular orientations. Proper orthogonal decomposition is used to identify large coherent structures in the flow. At all angles of attack the first two modes remain dominant making it possible to reconstruct the periodic vortex shedding process using a low-order model.

Reynolds number dependence of particle transport in a 90° bend with electrostatic effects

In this work, particle transport in a fully developed turbulent 90° bend flow at the “electrostatic equilibrium” state is simulated using large eddy simulation coupled with Lagrangian particle tracking technique. The flow Reynolds numbers (based on bulk velocity) considered is from 34000 to 58000. Three particle size 5, 10 and 50 μm are considered and their corresponding St number are from 2.2 to 547. Simulation results of the bend flow agree well with experimental data. The electrostatic field formed in the bend is symmetric in the spanwise direction but asymmetric in the vertical direction and radial direction, which is independent of Reynolds number. The minimum electrostatic field strength occurs at r/ra = 0.25 near the inner wall of the bend. Particles transported in a bend gradually accumulate near the wall due to turbophoresis, such trend is improved by electrostatics. In addition, under the effect of electrostatics, the plume pattern of particle distribution disappeared. Particle concentration at the inner wall of the bend is higher than that at the outer wall, which depends on the combined effect of electrostatics and Dean vortices in the bend.

Models for Estimation of Lift and Drag Coefficients for Low-Reynolds-Number Cambered Plates

Empirical models capable of predicting the lift and drag coefficients of circular-arc cambered plate blades are presented, together with the detailed documentation of the related wind-tunnel technique and data evaluation. The blade profiles are equipped with rounded leading and trailing edges. The empirical models offer an easy-to-use tool for preliminary design of low-solidity low-speed blade cascades. By means of the models, the lift-coefficient range of 0–1.3 is covered, associated with the drag coefficient varying between 0.02 and 0.14. The validity ranges of the empirical models are as follows: Reynolds-number between and , relative camber ranging from 0 to 8%, and angle of attack between 0 and 8 deg. The force coefficients are expressed as a function of relative camber, angle of attack, and Reynolds-number. The models assume linear relationships between the Reynolds-number and the force coefficients, as inspired by the literature and justified by statistical means. The dependence of the force coefficients on the angle of attack and the relative camber is expressed by incorporating second-order polynomials. The trends of force changes with Reynolds-number are analyzed. The cases of apparently extraordinary trends in the Reynolds-number dependence (i.e., increasing drag and decreasing lift with increasing Reynolds-number) are discussed in detail. A method for the determination of the confidence intervals related to the models is presented, and a detailed uncertainty analysis is provided. On this basis, the relative errors of the force coefficients can be quantified in a case-specific, empirical manner.

Input-output analysis of stochastic base flow uncertainty

We adopt an input-output approach to analyze the effect of persistent white-in-time structured stochastic base flow perturbations on the mean-square properties of the linearized Navier-Stokes equations. Such base flow variations enter the linearized dynamics as multiplicative sources of uncertainty that can alter the stability of the linearized dynamics and their receptivity to exogenous excitations. Our approach does not rely on costly stochastic simulations or adjoint-based sensitivity analysis. We provide verifiable conditions for mean-square stability and study the frequency response of the flow subject to additive and multiplicative sources of uncertainty using the solution to the generalized Lyapunov equation. For small-amplitude base flow perturbations, we bypass the need to solve large generalized Lyapunov equations by adopting a perturbation analysis. We use our framework to study the destabilizing effects of stochastic base flow variations in transitional parallel flows, and the reliability of numerically estimated mean velocity profiles in turbulent channel flows. We uncover the Reynolds number scaling of critically destabilizing perturbation variances and demonstrate how the wall-normal shape of base flow modulations can influence the amplification of various length scales. Furthermore, we explain the robust amplification of streamwise streaks in the presence of streamwise base flow variations by analyzing the dynamical structure of the governing equations as well as the Reynolds number dependence of the energy spectrum.

Analytical Study on Intricacies of Axial Conduction in Microchannel Heat Sinks

Abstract Microchannel heat sinks are potential devices that remove heat flux from high power density miniaturized electronic components. While the large surface-area-to-volume ratio and high heat transfer coefficient are the key features rendering benefits, the small flow rate and short channel lengths alongside high solid cross section to fluid free flow area make them susceptible to intense axial conduction loss. The conventional models for macrodevices based on the one-dimensional energy equation are often inappropriate in the microdomain. A novel multidimensional analytical model (capable of capturing axial heat transfer in microchannel heat sinks) has been used to study the thermal performance over a varied range of geometric and flow parameters. The effect of axial conduction has been seen in the solid–fluid temperature profiles, interfacial flux distribution and the average amount of heat transferred axially. The results indicate a skewed flux distribution at the fluid–solid interface leading to nonlinear temperature variation when axial conduction is dominant. Moreover, it has been shown that nonlinearity in the fluid temperature introduces significant errors in experimental data reduction, leading to apparently very low Nusselt number estimation. Moreover, this erroneous data interpretation is also linked to the prediction of a strong Reynolds number dependency of the average Nusselt number in the laminar flow regime.

Extreme events in transitional turbulence.

Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier-Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Mach and Reynolds number dependency of the unsteady shock-induced drag force on a sphere

Shock–particle interaction is an important phenomenon in a wide range of technological applications and natural phenomena, and the development of accurate models for this interaction is therefore of interest. This study investigates the transient forces during shock–particle interaction at particle Reynolds numbers between 100 and 1000, and incident shock wave Mach numbers between 1.22 and 2.51. This is achieved with the aid of particle-resolved large-eddy simulations. The simulation results show that shock–particle interaction differs qualitatively for subcritical and supercritical incident flow conditions. By decomposing the total force, the inviscid and viscous unsteady forces are estimated. The inviscid unsteady component is significantly larger than the viscous contribution, but the magnitude of the viscous component is comparable to steady-state drag. The predictions of current state of the art force models are compared to the computed particle forces. For subcritical flows, the models are quite successful in predicting the drag. For these conditions, the magnitudes of both the inviscid and viscous unsteady force models agree well with the simulation results, but the transient nature of the viscous unsteady force history is not well captured. For supercritical flows, the inviscid unsteady force model is not able to capture the force dynamics. This highlights the need for the development of unsteady force models for supercritical flow conditions.

Reynolds number dependence of inner peak turbulence intensity in pipe flow

Streamwise turbulence statistics in the range from Reτ = 990 to Reτ = 20 750 at the High Reynolds Number Actual Flow Facility at the National Metrology Institute of Japan are presented, specifically focusing on the Reynolds number dependence of the inner peak turbulence intensity. Velocity measurements are conducted using laser Doppler velocimetry (LDV), taking account of problems specific to this method, with the aim of providing reliable experimental results. The control volume and the fringe pattern of LDV, both of which influence turbulence statistics, are directly measured using a rotary wire device, and they are used to correct the measured turbulence intensity using methods developed in this study. The present results for mean velocity and turbulence intensity profiles agree well with direct numerical simulation data. The inner peak turbulence intensity in this pipe experiment increases with the increasing Reynolds number. It is found that the Reynolds number dependence of the inner peak up to Reτ = 20 750 is very similar to that in a turbulent boundary layer (TBL). The slope of the outer logarithmic region in the turbulence intensity profile is twice the slope obtained from the relation between the inner peak and the Reynolds number. This relation is also consistent with that for TBL flow.

Cross-flow aerodynamics of bridge cables with wire meshes

Adverse weather conditions in the northern regions during winter might lead to accumulation of ice or snow on bridge cables and consequently trigger ice shedding. The falling ice poses a risk for the traffic and pedestrians below, which often results in bridge closures and/or insurance claims. A passive surface-modifying device in the form of a steel wire mesh tautened on the surface of a cable sheath was previously found to substantially reduce the risk associated with falling ice through improved ice retention. In this paper, the cross-flow aerodynamic behaviour of bridge cables fitted with steel wire meshes is investigated in detail. The wire mesh generally resulted in higher levels of aerodynamic drag when compared with a plain cable sheath, although the Reynolds number dependence was highly reduced. Several angles of attack were investigated and no instability issues with respect to the across-wind vibrations were observed for any of the tested wire mesh configurations based on the quasi-steady theory. Even though vortex shedding was still present in all cases, the intensity of the fluctuating lift forces was much lower than that of the plain cable. To investigate basic aspects of the flow structure produced by the wire mesh, two flow visualisation techniques, combined with streamwise wind speed measurements in the near wake, were further used and are discussed.

Numerical Studies on Turbulent Flow Field in a 90 deg Pipe Bend

Abstract This paper deals with the modeling of turbulent flow through a 90 deg pipe bend using an unsteady Reynolds-averaged Navier–Stokes (U-RANS) approach where k–ε model is used for turbulence closure. While limitations in solving complex flows of the k–ε model have been reported in the literature, this study demonstrates that for pipe flows with curvature, the k–ε model performs reasonably well. Investigations have been carried out to find out the influence of Reynolds number (Re) and bend curvature ratio (Rc/D) on turbulent flow parameters, namely, instantaneous axial velocity, turbulent kinetic energy, turbulent intensity, and wall shear stress. Bend curvature is found to strongly influence the turbulent flow characteristics, while no such high Reynolds number dependency is observed in this study range. In general, this paper presents a computationally cost-effective numerical study on the time averaged turbulent flow field in a 90 deg pipe bend, which may be used for the design and development of 90 deg pipe bends at a high Reynolds number regime.

Ridge-type roughness: from turbulent channel flow to internal combustion engine

While existing engineering tools enable us to predict how homogeneous surface roughness alters drag and heat transfer of near-wall turbulent flows to a certain extent, these tools cannot be reliably applied for heterogeneous rough surfaces. Nevertheless, heterogeneous roughness is a key feature of many applications. In the present work we focus on spanwise heterogeneous roughness, which is known to introduce large-scale secondary motions that can strongly alter the near-wall turbulent flow. While these secondary motions are mostly investigated in canonical turbulent shear flows, we show that ridge-type roughness—one of the two widely investigated types of spanwise heterogeneous roughness—also induces secondary motions in the turbulent flow inside a combustion engine. This indicates that large scale secondary motions can also be found in technical flows, which neither represent classical turbulent equilibrium boundary layers nor are in a statistically steady state. In addition, as the first step towards improved drag predictions for heterogeneous rough surfaces, the Reynolds number dependency of the friction factor for ridge-type roughness is presented.Graphic abstract

From Substrate to Surface: A Turbulence‐Based Model for Gas Transfer Across Sediment‐Water‐Air Interfaces in Vegetated Streams

AbstractDissolved Oxygen (DO) fluxes across the air‐water and sediment‐water interface (AWI and SWI) are two major processes that govern the amount of oxygen available to living organisms in aquatic ecosystems. Aquatic vegetation generates different scales of turbulence that change the flow structure and affect gas transfer mechanisms at AWI and SWI. A series of laboratory experiments with rigid cylinder arrays to mimic vegetation was conducted in a recirculating race‐track flume with a lightweight sediment bed. 2D Planar Particle Image Velocimetry was used to characterize the flow field under different submergence ratios and array densities to access the effect of vegetation‐generated turbulence on gas transfer. Gas transfer rate across AWI was determined by DO re‐aeration curves. The effective diffusion coefficient for gas transfer flux across SWI was estimated by the difference between near‐bed and near‐surface DO concentrations. When sediment begins to mobilize, near‐bed suspended sediment provides a negative buoyancy term that increases the critical Reynolds number for the surface gas transfer process according to a modified Surface Renewal model for vegetated flows. A new Reynolds number dependence model using near‐bed turbulent kinetic energy as an indicator is proposed to provide a universal prediction for the interfacial flux across SWI in flows with aquatic vegetation. This study provides critical information and useful models for future studies on water quality management and ecosystem restoration in natural water environments such as lakes, rivers, and wetlands.

Shear-driven Hall-magnetohydrodynamic dynamos

Nonlinear Hall-magnetohydrodynamic dynamos associated with coherent structures in subcritical shear flows are investigated by using unstable invariant solutions. The dynamo solution found has a relatively simple structure, but it captures the features of the typical nonlinear structures seen in simulations, such as current sheets. As is well known, the Hall effect destroys the symmetry of the magnetohydrodynamic equations and thus modifies the structure of the current sheet and mean field of the solution. Depending on the strength of the Hall effect, the generation of the magnetic field changes in a complex manner. However, a too strong Hall effect always acts to suppress the magnetic field generation. The hydrodynamic/magnetic Reynolds number dependence of the critical ion skin depth at which the dynamos start to feel the Hall effect is of interest from an astrophysical point of view. An important consequence of the matched asymptotic expansion analysis of the solution is that the higher the Reynolds number, the smaller the Hall current affects the flow. We also briefly discuss how the above results for a relatively simple shear flow can be extended to more general flows such as infinite homogeneous shear flows and boundary layer flows. The analysis of the latter flows suggests that interestingly a strong induction of the generated magnetic field might occur when there is a background shear layer.

Investigation of internal intermittency by way of higher-order spectral moments

The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive-scalar (temperature) fields. This study first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time Fourier-transform-based method is developed to estimate these higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence over the Reynolds-number range $35\leq R_{\lambda } \leq ~731$ . Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (Mech. Syst. Signal Pr., vol. 20 (2), 2006, pp. 282–307), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds (Péclet) number dependence of the internal intermittency of velocity and passive-scalar fields. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Finally, the relative levels of internal intermittency of the velocity and passive-scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed, whereas a similar level of internal intermittency is observed for the velocity and passive-scalar fields for the high-Reynolds-number cases as the Kolmogorov length scale is approached.

State-Space Modeling of Viscous Unsteady Aerodynamic Loads

In this paper, we summarize our recently developed viscous unsteady theory, which couples potential flow with the triple-deck boundary-layer theory. This approach provides a viscous extension of potential-flow unsteady aerodynamics. As such, a Reynolds-number-dependent transfer function is determined for unsteady lift. We then use the Wiener–Hammerstein structure to develop a finite-dimensional approximation of such an infinite-dimensional theory, presenting it in a state-space model. This novel nonlinear state-space model of viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the classical Theodorsen’s model because it captures viscous effects (that is, Reynolds number dependence) as well as nonlinearity and additional lag in the lift dynamics; it also allows simulation of arbitrary time-varying airfoil motions (not necessarily harmonic). Moreover, being in a state-space form makes it quite convenient for simulation and coupling with structural dynamics to perform aeroelasticity, flight dynamics analysis, and control design. We then develop a linearization of such a model, which enables analytical results. Subsequently, we derive an analytical representation of the viscous lift frequency response function: an explicit function of both the frequency and Reynolds number. We also develop a state-space model of the linearized response. We finally simulate the nonlinear and linear models to a nonharmonic small-amplitude pitching maneuver at a Reynolds number of 100,000 and compare the resulting lift and pitching moment with those obtained from potential flow; this is in reference to relatively higher-fidelity computations of the unsteady Reynolds-averaged Navier–Stokes equations.

On the method of determining instantaneous wall shear stress from near-wall velocity measurements in wall turbulence

The determination of the instantaneous wall shear stress (WSS) from near-wall velocity measurements has received considerable attention. However, the most appropriate procedure and the achievable accuracy remain open topics. The present work uses direct numerical simulation datasets of channel flow to investigate the influences of the wall-normal distribution of instantaneous velocity, the method for estimating the velocity gradient, and the wall-normal position of velocity vectors on the accuracy of the instantaneous WSS determined from near-wall velocity measurements. In general, the method of dividing instantaneous velocity vectors by their wall-normal positions performs better than the method of linearly fitting instantaneous velocity profiles for estimating the wall velocity gradients when the wall position is correctly determined. However, the nonlinear instantaneous velocity distribution within the viscous layer means that all methods introduce a negative mean bias error and non-negligible root mean square error for the instantaneous WSS and its statistics. The magnitudes of these errors increase with the wall-normal position of the velocity vectors. An empirical method for correcting the instantaneous WSS statistics is proposed based on the negligible Reynolds number dependence of the bias error of all statistics. The influence of the wall-normal position of the velocity vectors on the WSS statistics and the correction method are verified using experimental data from open channel flows. The verification results show that the correction method significantly improves the accuracy of the statistics of instantaneous WSS determined from near-wall velocity measurements under canonical wall turbulence.