Mean Flow Reynolds Number Research Articles

Evaluating the effects of stream power on rill flow resistance

AbstractLimited information is currently available on how sediment transport affects rill flow resistance and the influence of hydraulic variables, as stream power, on sediment transport capacity for rill flows. In this paper, the available measurements of hydraulic variables (flow depth, channel slope, mean flow velocity, Reynolds number, Froude number, and Darcy–Weisbach friction factor) carried out by Ban et al. (Measurement of rill and ephemeral gully flow velocities and their model expression affected by flow rate and slope gradient. Journal of Hydrology, 589, 125172) and Ban (Measurements and estimation of flow velocity in mobile bed rills. International Journal of Sediment Research, 38(1), 97–104) for fixed and mobile bed rills are used to test the applicability of a theoretically deduced rill flow resistance equation based on a power‐velocity profile. The results allowed for stating that (i) the theoretical flow resistance approach can predict Darcy–Weisbach friction factor for flows over fixed and mobile beds, (ii) the stream power, dependent on flow discharge and slope, determines different flow behaviour, and (iii) the data are supportive of the slope independence hypothesis of rill velocity, for the mobile bed condition, only for the highest investigated discharge values (greater than 0.133 L s−1).

Effect of different underlying surfaces on hydraulic parameters of overland flow

The estimation of hydraulic parameters is the basis for establishing soil erosion models. However, the underlying surfaces greatly influence the hydraulic parameters of the overland flow. Since sediment flow and slope surface resistance interact, exploring the mechanism of overland flow movement in relation to different underlying surfaces is essential. A potential relationship between hydrodynamic parameters and slope gradient and flow discharge was investigated by carrying out overland flow experiments, which used four types of non-erosion slope surfaces (stem cover, brown soil, frozen soil, and organic glass), four slope gradients (3°, 6°, 9°, and 12°), and four flow discharges (0.35, 0.45, 0.55, and 0.65 L s–1). The results showed that the hydraulic parameters (i.e., mean flow velocity, flow depth, Froude number, Reynolds number, shear stress, drag coefficient, stream power, and unit stream power) differed with the increased slope gradients and flow discharges. The mean flow velocity of the stem cover slope was lower than that of the frozen soil slope, brown soil slope, and organic glass slope by 33%, 40%, and 50%, respectively. The stem cover slope drag coefficient was higher than the frozen soil slope, brown soil slope, and organic glass slope by 201%, 323%, and 630%, respectively. The critical flow states of the underlying surface were different under different slope gradients and flow discharge conditions. The flow on frozen soil slopes was mainly laminar and transitional, while the other three were transitional. These results help us understand the hydrodynamic mechanisms of the sediment transport process during overland flow. The results of the study provide a scientific basis for understanding the hydrodynamic mechanism of the dynamic changes of the sediment transport on the slope, deepening the understanding of the soil erosion mechanism and improving the prediction accuracy of the soil erosion process model.

Deep learning methods for predicting fluid forces in dense particle suspensions

Two deep learning methods, Multi-Layer Perceptron (MLP) network and Convolution Neural Network (CNN) are evaluated to predict drag forces in dense suspensions of ellipsoidal particles using data from Particle Resolved Simulations (PRS). The MLP is trained on the mean flow Reynolds number, solid fraction of the suspension, the aspect ratio of the particle, and orientation to flow direction. The CNN is given an additional 3D spatial map of the particle of interest and its immediate neighborhood via a distance function. The prediction capability of the trained networks is tested at different levels of complexity: on an unseen particle arrangement (Level 1), to all arrangements of an unseen numerical experiment (Level 2), and finally to all experiments of an unseen Reynolds number, solid fraction or aspect ratio (Level 3). The CNN is shown to perform better than the MLP for all testing levels except when testing on an unseen aspect ratio.

Determination of the flow regime using the experimental hydrodynamic stand

The article describes the approach to determining the flow regime using the experimental hydrodynamic stand for researching the cavitation processes. A series of experiments with technical tap water was performed, which allowed to confirm the reliability of the results obtained by comparing them with theoretical values. The researched values include mean flow rate, Reynolds number and cavitation numbers. Conclusions about the type of cavitation flow was made.

Simulated time-dependent data to estimate uncertainty in fluid flow measurements

Abstract Positron Emission Particle Tracking (PEPT) is an emerging measurement technique for Lagrangian data collection in experimental fluid flows. The nature of the measurement extends the study of turbulent flows to applications lacking optical access. A simulated pipe flow PEPT measurement is used in this work to verify reconstruction algorithm and identify novel sources of uncertainty. Simulated measurement occurs in a 38 mm diameter pipe with 0.55 m/s mean flow velocity and Reynolds number equal 21,000. Flow is simulated using computational fluid dynamics (CFD), generating 1000 time-dependent trajectories of tracers from CFD to prescribe movements of 40 µCi, fluorine-18-point sources. Geant4 Application for Tomographic Emission (GATE) simulates the response of the Inveon Pre-Clinical scanner model and produces an array of coincidence lines for the prescribed sources. The array is provided to a multiple PEPT (mPEPT) code reconstructing the position of simulated tracers and assigns positions to coherent trajectories. The mPEPT reconstructed trajectories are compared to prescribed positions. Reconstruction of 754 trajectories is achieved with measurement bias centered at 0.0 mm in all directions and standard deviation of 0.29 mm, 0.29 mm, and 0.30 mm in the x, y, and z component respectively using 2.0 ms time-steps. Two instances of position misassignments induced by the close-approach of two tracers in measurement volume are identified. This is a novel reconstruction error to PEPT measurements, unable to be identified without prior knowledge of tracer trajectories provided by these simulation tools.

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016

Phase-Change Materials for Transient Cooling of a Heater Array in a High Aspect Ratio Channel in the Presence of Mean Flow

This paper explores the effectiveness of phase-change material (PCM) for cooling of a discrete array of heat sources in low form factor channels in the presence of mean flow. The alkane n-Eicosane was chosen as the material for this work. A parametric experimental study was conducted on an array of heaters that simulate the heat dissipating components in a low form factor portable electronic device. The effects of the clearance at the top of the devices, thickness/volume of the PCM, as well as the mean flow velocity were studied under uniform and nonuniform patterns. It was found that the cooling effect of the PCM in the time frame considered reduces with increase in the mean flow Reynolds number due to its delayed melting. Thus, the cooling effect in a natural convection environment is higher compared to one with mean flow. The thickness of the PCM increases its effectiveness for a certain threshold value beyond which we reach a region of diminishing returns. The results are presented as design curves in terms of nondimensional parameters. The use of thin spreader inside the PCM pack improves its cooling effectiveness due to better lateral spreading. However, the cooling time for the n-Eicosane is not negligible and can be a potential challenge under repeated cyclic loads.

An analysis on the pressure loss through perforated plates at moderate Reynolds numbers in turbulent flow regime

Perforated plates are widely used in order to reduce flow nonuniformities, to retard onset of turbulence and to attenuate cavitation. There are some studies carried out for investigation of effects of geometrical parameters of perforated plates and flow parameters on pressure loss coefficient. However the related studies were performed at high Reynolds numbers in the order of 105. This work aims to research pressure loss through a variety of perforated plates having different geometrical aspects in a mean flow Reynolds number range of 2500≤Rem≤9500 and a porosity range of 0.064≤β≤0.331 for different numbers of holes ranging in 5≤nh≤26. The dependency of the pressure loss upon the Reynolds number, the porosity of the perforated plates, the number and the distribution of the holes is investigated under no cavitating conditions. An expression, Eu=0.67β−2.24, describing the relationship between the pressure loss coefficient and the porosity of perforated plate is proposed with a mean deviation of 12% for easy estimation of pressure loss coefficient at moderate Reynolds numbers of turbulent flow regime as a practical solution.

A scaling law for form drag coefficients in incompressible turbulent flows

We present a similarity law for form drag coefficients, which is obtained by a judicious utilization of an energy dissipation equation due to eddy viscosity for incompressible turbulent flow, the steady-state κ–ω turbulence model, and the Kolmogorov turbulence dissipation length scales. It is shown that the form drag coefficients of three geometrically similar vessels subjected to turbulent flows are scaled according to C¯p={c1+c2Re¯−1/3+c3Re¯−1} where (C¯p,Re¯,ci(i=1,2,3)) are the form drag coefficient ratio, the mean flow Reynolds number ratio, and ci are closure coefficients to be determined from existing geometrically similar vessels, respectively. The present theoretical form factor methodology is applied to predict the full scale form factor from the scaled towing tank experiment based on three simulation results, which show improved correlations compared to the empirical least-squares prediction methods.

Numerical Study of Laminar Flow and Mass Transfer for In-Line Spacer-Filled Passages

Performance calculations for laminar fluid flow and mass transfer are presented for a passage containing cylindrical spacers configured in an inline-square arrangement, typical of those employed in the process industries. Numerical calculations are performed for fully-developed flow, based on stream-wise periodic conditions for a unit cell and compared with those obtained for developing regime in a row of ten such units. The method is validated for an empty passage, i.e., a plane duct. Results are presented for the normalized mass transfer coefficient and driving force, as a function of mean flow Reynolds number, and also the wall mass flux, or blowing parameter. Both constant and variable wall velocities were considered, the latter being typical of those found in many practical membrane modules.

The effect of flow pulsation on drag and heat transfer in an array of heated square cylinders

Laminar 2-D pulsating flow through homogeneous linear arrays of heated square tubes is simulated for pulsation frequencies of 0–80 Hz for tube diameter-based Reynolds numbers from 50 to 200. The objective is to examine the effects of flow pulsation on drag and heat transfer in heat exchanger tube bundles. Cycle-averaged and maximum drag coefficients, as well as the instantaneous and cycle-averaged Nusselt numbers are reported for each of the ten rows of tubes in the simulated array. The results show that flow pulsations can enhance heat transfer in tube bundles, and the level of enhancement increases with pulsation frequency and mean flow Reynolds number. A wake interference effect has been observed which significantly amplifies the drag on the leading rows and reduces and instantaneously reverses the sign of the drag force on the tubes located in the wake region. Cycle-average drag coefficients decreased with increasing Reynolds number and porosity, and were only a weak function of pulsation frequency. Peak drag coefficients were found to decrease with increasing Reynolds number and porosity, but increase with frequency approximately linearly. Empirical correlations are presented for a tube bundle with 64% porosity that relate maximum and cycle-average drag coefficients as well as Nusselt numbers to the Reynolds number and frequency.

Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres

Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force F on solid volume fraction ϕ and the Reynolds number based on the mean slip velocity Re m . In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier–Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid–particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas–solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid–particle force F is obtained as a function of solid volume fraction ϕ (0.1 ⩽ ϕ ⩽ 0.5) and mean flow Reynolds number Re m (0.01 ⩽ Re m ⩽ 300) for random assemblies of monodisperse spheres. These results extend previously reported results of Hill et al. (2001a,b) to a wider range of ϕ, Re m , and are more accurate than those reported by Beetstra et al. (2007). Differences between the drag values obtained from PUReIBM and the drag correlation of Beetstra et al. (2007) are as high as 30% for Re m in the range 100–300. We take advantage of PUReIBM’s ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid–particle force, which is useful in developing drag correlations. Using a scaling argument, Hill et al. (2001b) proposed that the viscous contribution is independent of Re m but the pressure contribution is linear in Re m (for Re m > 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re m in accord with the analysis of Hill et al. (2001b). An improved correlation for F in terms of ϕ and Re m is proposed that corrects the existing correlations in Re m range 100–300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas–solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.

Laminar flow control via utilization of pipe entrance inserts (a comment on entrance length concept)

Flow field measurements behind pipe entrance inserts called as flow conditioners in a mean flow Reynolds number range 547 ≤ Re ≤ 9000 are presented herein. A tube bundle, a Laws’ perforated plate and an etoile were located at the entrance of a smooth circular pipe of inner diameter, D = 26.6 mm . The covered ranges of open area ratio, β and non-dimensional length, L / D were 0.49 ≤ β ≤ 0.74 and 0.123 ≤ L / D ≤ 2 respectively. The cross-sectional axial velocity u = u ( r ) profiles at the downstream stations of X / D = 75 , X / D = 375 , X / D = 680 together with pressure losses Δ P are referred to determine the influence of utilized designs. The flow conditioners have a single performance characteristic expressed through a relationship of pressure loss coefficient K = K ( Re β ) which provides a practical method for the calculation of time-averaged pressure loss, Δ P ̄ in an average error margin of ±18%. The laminar flow inside the pipe without an insert in the range of Re < 2450 is not fully developed sensed with u = u ( r ) profiles having a ±20% deviation from the Blasius profile for the lengths X / D < 680 . Meanwhile flow conditioners provide a fully developed laminar flow independent of Re and X observed in terms of downstream u = u ( r ) profiles with a better fit to the Blasius profile in a mean error margin of ±10%. The laminar flow control via flow conditioners is analyzed through a discussion in terms of the introduced local non-dimensional velocity parameters. The used methodology is based on the definition of entrance length Reynolds Number; Re X = ( X / D ) Re . The proposed equations “ Re X β = C ” (where C is a constant) can be used for the estimation of settling distance of the flow conditioners and laminar entrance length. The experimental data are in conformity with the magnitudes of C = 2.87 × 10 4 and C = 3 × 10 5 with the corresponding error margins of ±4% and ±6% respectively.

Effect of Particle Clusters on Carrier Flow Turbulence: A Direct Numerical Simulation Study

Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas-phase turbulence, and to guide model development. The DNS approach is based on a discrete-time, direct-forcing immersed boundary method (IBM) that imposes no-slip and no-penetration boundary conditions on each particle’s surface. Results are reported for mean flow Reynolds number Rep = 50 and the ratio of the particle diameter dp to Kolmogorov scale is 5.5. The DNS confirm experimental observations that the clustered configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than the uniform configurations, and this increase is found to arise from a lower dissipation rate in the clustered particle configuration. The simulations also reveal that the particle-fluid interaction results in significantly anisotropic fluid-phase turbulence, the source of which is traced to the anisotropic nature of the interphase TKE transfer and dissipation tensors. This study indicates that when particles are larger than the Kolmogorov scale (dp > η), modeling the fluid-phase TKE alone may not be adequate to capture the underlying physics in multiphase turbulence because the Reynolds stress is anisotropic. It also shows that multiphase turbulence models should consider the effect of particle clustering in the dissipation model.

On steady rotational cyclonic flows: The viscous bidirectional vortex

This study is focused on the tangential boundary layers of a bidirectional vortex, specifically those forming at the core and the sidewall of a swirl-driven cyclonic chamber. Our analysis is based on the regularized, tangential momentum equation which is rescaled in a manner to capture the forced vortex near the chamber axis and the no slip requirement at the sidewall. After identifying the coordinate transformations needed to resolve the rapid changes in the regions of nonuniformity, two inner expansions are constructed. These expansions are then matched with the outer, free vortex solution that is sandwiched between the core and the hard wall. By combining inner and outer expansions, uniformly valid approximations are subsequently obtained for the swirl velocity, vorticity, and pressure. These are shown to be strongly influenced by a dimensionless grouping that we refer to as the vortex Reynolds number, V. This keystone parameter appears as a ratio of the mean flow Reynolds number and the product of the swirl number and the chamber aspect ratio. Based on V, several fundamental features of the bidirectional vortex are quantified. Among them are the thicknesses of the viscous core and sidewall boundary layers; these decrease with V1/2 and V, respectively. The converse may be said of the peak velocity which increases with V1/2. In the same vein, the angular speed of the rigid-body rotation of the forced vortex is found to be linearly proportional to V. Our laminar swirl velocity is reminiscent of Sullivan’s two-cell vortex except for its additional dependence on the aspect ratio of the chamber. For the purpose of verification, theoretical predictions are compared to particle image velocimetry measurements and Navier–Stokes simulations at high vortex Reynolds numbers. By properly accounting for the turbulent eddy viscosity in the analytical model, local agreement is obtained with both laboratory measurements and computer simulations.

Numerical Modeling of Laminar Pulsating Flow in Porous Media

The laminar pulsating flow through porous media was numerically studied. Two-dimensional flows in systems composed of a number of unit cells of generic porous structures were simulated using a computational fluid mechanics tool, with sinusoidal variations in flow with time as the boundary condition. The porous media were periodic arrays of square cylinders. Detailed numerical data for the porosity ranging from 0.64 to 0.84, with flow pulsation frequencies of 20–64 Hz were obtained. Based on these numerical data, the instantaneous as well as the cycle-average permeability and Forchheimer coefficients, to be used in the standard unsteady volume-averaged momentum conservation equation for flow in porous media, were derived. It was found that the cycle-average permeability coefficients were nearly the same as those for steady flow, but the cycle-average Forchheimer coefficients were significantly larger than those for steady flow and were sensitive to the flow oscillation frequency. Significant phase lags were observed between the volume-averaged velocity and the pressure waves. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and the mean-flow Reynolds number.

Distortion of upstream disturbances in a Hiemenz boundary layer

A theoretical analysis of the distortion of unsteady three-dimensional disturbances in a Hiemenz boundary layer and its effect on the heat transfer enhancement is presented. It is shown that the disturbance length scale is a critical parameter in determining the amplification ratio of the incoming vorticity. For large disturbance length scales, the amplification ratio increases when the length scale decreases, and a maximum value occurs at a length scale close to five times the boundary-layer thickness. The unsteadiness of the disturbances is found to reduce the vorticity amplification, but the effect is second order when the frequency is low compared to the mean flow strain rate. The impinging disturbances induce large-amplitude vorticity of opposite sign at the wall whose magnitude controls the heat transfer enhancement. As an application of the present analysis, a new scaling correlation is derived for stagnation-point heat transfer in the presence of free-stream turbulence. The theoretical correlation, expressed in terms of turbulence intensity, integral length scale and mean flow Reynolds number, agrees reasonably well with recent experimental data.

The vibration of an artery-like tube conveying pulsatile fluid flow

A hybrid method for investigating pulsatile fluid flow in a long, thin, artery-like tube subjected to external excitations is presented. The non-linear partial differential equations governing the motion of the system, which incorporate the influence of circumferential strains, are solved by a combination of a finite element method, a finite difference method and a method of characteristics with interpolation. An initially axially stretched elastic tube conveying pulsating fluid, simply supported at both ends, is modelled to assess the effect of external harmonic excitation on the dynamic responses of the tube and the fluid flow. The results agree well with new experimental data. Comparison of the predicted results with those of a decoupled model demonstrates that it is necessary to consider the mechanism of fluid-structure interaction fully in the study of initially stretched cylindrical tubes conveying pulsatile fluid flow. An analysis of these coupling effects is presented for Womersley numbers alpha = 2.81 and 3.97 and a mean flow Reynolds number Re = 875.

Investigation of Anisotropy-Resolving Turbulence Models by Reference to Highly-Resolved LES Data for Separated Flow

The predictive properties of several non-linear eddy-viscosity models are investigated by reference to highly-resolved LES data obtained by the authors for an internal flow featuring massive separation from a curved surface. The test geometry is a periodic segment of a channel constricted by two-dimensional (2D) `hills' on the lower wall. The mean-flow Reynolds number is 21560. Periodic boundary conditions are applied in the streamwise and spanwise directions. This makes the statistical properties of the simulated flow genuinely 2D and independent from boundary conditions, except at the walls. The simulation was performed on a high-quality, 5M-node grid. The focus of the study is on the exploitation of the LES data for the mean-flow, Reynolds stresses and macro-length-scale. Model solutions are first compared with the LES data, and selected models are then subjected to a-priori studies designed to elucidate the role of specific model fragments in the non-linear stress-strain/vorticity relation and their contribution to observed defects in the mean-flow and turbulence fields. The role of the equation governing the length-scale, via different surrogate variables, is also investigated. It is shown that, while most non-linear models overestimate the separation region, due mainly to model defects that result in insufficient shear stress in the separated shear layer, model forms can be derived which provide a satisfactory representation of the flow. One such model is identified. This combines a particular quadratic constitutive relation with a wall-anisotropy term, a high-normal-strain correction and a new form of the equation for the specific dissipation ω = ∈/k.

On the low frequency linear instability of the Blasius flow

Considering the ratio of the mean flow Reynolds number to the wave Reynolds number, it is shown that for the low frequency instability the mean flow inertia is small in comparison to that of the disturbance. The mean flow gradient thus being small is neglected to obtain a truncated Orr-Sommerfeld equation. The numerical solutions of this equation show instability at lower Reynolds numbers.