Reynolds Number Correction Research Articles

Corrections to long wavelength approximation of peristalsis viscous fluid flow within a wavy channel

This research paper delves into the pumping phenomenon of peristaltic motion within a wavy, straight channel. Our aim is to provide analytical solutions for the well-established long wavelength and small Reynolds number approximation. To achieve this, we derive third-order corrections to the ideal leading-order solutions. These closed-form solutions encompass the axial and transverse velocity components, pressure rise and axial pressure gradients, and drag force along the wavy channel. Additionally, we elucidate the trapping phenomena of viscous flowing boluses through stream function contours. Notably, these exact solutions enable the analysis of peristalsis with finite wave numbers and moderate Reynolds numbers, eliminating the need for numerical simulations of the full Navier–Stokes equations at such physical parameters. Our simulations reveal that the pumping region is significantly influenced by short wavelength and moderate Reynolds number corrections. Further, the corrections enhance the drag force, and cell divisions within the boluses are observed at higher Reynolds numbers. The analytical derivations provided save researchers from the need for full simulations of the complex equations to acquire the key insights and contributions to capture the essence of the physical peristalsis mechanism inside wavy channels.

Wind Tunnel Tests of an Aeroelastic Model of a Long-Span Transmission Tower

The modal analysis of a long-span transmission tower was carried out using a finite element method, and then its aeroelastic model was established by the discrete stiffness method for wind tunnel tests. The displacement and acceleration of the aeroelastic model were measured by a vision-based displacement measuring instrument and accelerometer, respectively. Also, the wind-induced responses of the tower were conducted by finite element calculation, with which the results of the wind tunnel tests are compared. The gust response factor was calculated and compared with those from the specifications and other studies. The results show that the vision-based displacement instrument can record well the vibration of the model tower in the wind tunnel. The acceleration of the tower is dominated by the first-order resonant response, whereas the displacement is dominated by the background response. The displacement and acceleration in the longitudinal and transversal directions are almost equal, indicating that the crosswind and along-wind responses are of the same magnitude. The displacement atop the tower obtained from the test after considering the Reynolds number correction almost coincided with that from the numerical simulation. The gust response factor of the tower obtained via wind tunnel tests is smaller than that of the codes and close to that found via finite element calculations.

Multiphase Flow Through Chokes - An Evaluation of Frozen, Equilibrium, and Nonequilibrium Flow Models

This work has evaluated the most common published mechanistic multiphase choke models and compared them with a newly developed model. A typical assumption for most of the models is that the flow through the choke is adiabatic because it is argued that there is limited amount of time for heat and mass transfer. Such models are often referred to as “frozen flow” models and are widely used in the industry. The new model deviates from the frozen flow concept because it includes phase transfer. The depressurization through the choke is fast; hence, thermodynamic equilibrium will not be established and a nonequilibrium coefficient will account for this intermediate state. The goal was to investigate whether frozen flow and adiabatic expansion through the choke is a reasonable simplification or whether the concept of nonequilibrium flow could provide higher predictive ability.The predicted mass rates from all models have been calculated for two experimental multiphase datasets, and the mean relative error, mean absolute percentage error, root-mean-square deviation, and standard deviation have been calculated to compare the performances. The new model seems to be more robust and performs better than the more common frozen flow models. It has better overall predictive potential with a mean absolute percentage error of 2.6% and 5.2% for the multiphase datasets.The new model is generic and can be used with any given thermodynamic process, e.g., equilibrium flow, nonequilibrium flow, or frozen flow. For frozen flow, both adiabatic and polytropic gas expansion can be used, and the model performance will then be similar to previously published frozen flow models such as Al-Safran and Kelkar or Mwalyepelo.Further, a methodology for highly viscous flow has been proposed. All the present models originally assume frictionless flow, and high viscous flow is therefore not accounted for. A Reynolds number correction has been incorporated by adjusting the choke discharge coefficient. The correction is based on a study of highly viscous flow through safety valves.

Aeroelastic Simulation of Stall Flutter Undergoing High ‎and Low Amplitude Limit Cycle Oscillations

The aeroelastic behaviour of an airfoil oscillating in large and small pitch amplitudes due to nonlinearity ‎in aerodynamics is examined. The phenomenon of stall flutter resulted in the limit cycle oscillations of ‎NACA 0012 at low to intermediate Reynolds number is investigated numerically through the unsteady ‎two-dimensional aeroelastic simulation. The simulations employed unsteady Reynolds Average Navier ‎Stokes shear stress transport k-ω turbulent model with the low Reynolds number correction. The ‎simulations of the fluid-structure interaction were performed by coupling the structural equation of ‎motion with a fluid solver through the user-defined function utility. Numerical simulations were executed ‎at three different elastic axis positions; the leading-edge, 18% and 36% of the airfoil chord length. The ‎airfoil chord measures 0.156 m. The simulations were executed at the free stream velocity ranging from ‎‎5.0 m/s to 13 m/s corresponding to the Reynolds number between 51618 and 134207. Two types of ‎oscillation amplitudes were observed at each elastic axis position. At the leading-edge and 18% case, ‎small amplitude oscillations were observed while at 36%, the system underwent high amplitude ‎oscillations. The analysis revealed the cause for small oscillation amplitude is due to the separation of the ‎laminar boundary layer on the suction side of the airfoil starting at the trailing edge. High amplitude ‎oscillations occurred due to the existence of the dynamic stall phenomenon beginning at the leading-edge. ‎Small amplitude LCOs only occurred within a limited range of airspeed before it disappeared due to ‎increasing airspeed‎‎.

Numerical and Experimental Investigation of Soot Suppression by Acoustic Oscillated Combustion.

The soot suppression by acoustic oscillations for acetylene diffusion flames was investigated combining numerical and experimental studies. The combustion and soot formation were predicted by the finite-rate detailed chemistry model and modified Moss-Brookes model, respectively, while the turbulence was predicted by the detached eddy simulation (DES) with a low Reynolds number correction. Experimental results showed that the soot rate almost decreased linearly with the amplitude of acoustic oscillation, and the pinch-off of the flame occurred at a large acoustic oscillation. Numerical results showed that the flame structure was well predicted, while the soot rate was over-predicted at large acoustic oscillations; the consumption of O2 increased obviously with the acoustic oscillation. The soot suppression was mainly caused by the decrease of the surface growth rate when the air was pushed toward the flame.

The Effect of Turbulence Model and Nanofluid on Fluid Flow and Heat Transfer in a Narrow Rectangular Duct

The effect of turbulence model and nanofluid on the heat transfer and fluid flow in a horizontal narrow rectangular duct is numerically studied under constant wall heat flux boundary condition. Numerical study is carried out using ANSYS Fluent 17.0 software. Examined parameters are the type of turbulence model, the type of nanofluid, the volume fraction of nanofluid, and the Reynolds number. Three different k-e and four different k-w turbulence models are employed. Aluminum oxide Al2O3-water and copper oxide CuO-water are used as nanofluids. Volume fractions of nanoparticles used are 0%, 0.1%, 0.5%, 1%, 2% and 4%. Reynolds number changes from 3×103 to 50×103. Results showed that k-ω standard turbulence model with low Reynolds number correction gives better result. It is seen that both the type and volume fraction of nanofluid affect heat transfer and pressure drop. Using Al2O3 and CuO nanoparticles in water increases thermal performance. It is found that the performance of CuO-water nanofluid is better than that of Al2O3-water nanofluid. It is seen that using turbulent fully developed correlations derived for circular ducts may end up with incorrect results for the flow in a two dimensional rectangular duct.

Large-Eddy Simulation of a Laminar Separation Bubble

Large-eddy simulation of a laminar separation bubble on a flat plate has been performed and compared with the data in the literature. Suitability of different subgrid-scale models has been examined for simulation of transition. Comparison of various parameters and three-dimensional visualization of instantaneous flow fields indicate that standard Smagorinsky model, being too dissipative, is not suitable for this kind of problem and fails to properly resolve transition. With the application of low Reynolds number correction and a reduced model constant, a good agreement with the dynamic model is obtained at a lower computational cost. Of the three SGS models investigated, dynamic model gives the most physically accurate description of transition. The simulations illustrate that the appearance of Λ-vortices, vortex stretching and break down of longitudinal streaks characterize the transition process. Low values of reverse flow make it clear that a convective instability is involved. It is concluded that the initial amplification of disturbances is due to Tollmien -Schlichting mechanism while the roll-up of the shear layer takes place due to Kelvin-Helmholtz instability. It is observed that the universal log-law profile is not reached by the velocity profiles even far downstream.

CFD study of sand erosion in pipeline

Pipeline erosion remain a major headache for petroleum industry with its underlying safety threats and financial integrity. The main objective of this research paper is to investigate sand erosion behaviour in 76.2 mm diameter with Computational Fluid Dynamics (CFD). According to literature, simulation erosion by fine sand particles (<50 μm) tend overpredict the erosion result; transportation of sand particles in elbow are under the influence of fluid particles; slight altered geometries produce significantly different erosion results. Thus, CFD analysis with Eulerian-Lagrangian approach is utilised to solve continuous phase with Navier-Stokes equations, while secondary phase with particle force balance. Reynolds Stress Model along with low Reynolds number correction is used to model the turbulence behaviour of continuous fluid phase to address viscous boundary effect at near wall region and secondary flows in elbow for more accurate results. Validation results of this study shown that assumption of constant size for every sand particle led to more than 10% overprediction of maximum erosion rate. Overprediction had been successfully reduced to less than 5% by fitting actual size distribution of particle into Rosin Rammler equation to model the particle size. In addition, effect of sand size, flow orientation, elbow bending angle and fluid type were investigated. The following conclusion had been made: power law relationship observed between erosion rate and sand size; 30 μm particle produced a local maximum erosion at the trendline due to combination effect of sliding and direct collision; horizontal oriented flow shown asymmetric erosion behaviour due to effect of gravity; erosion with increasing elbow angle from 30° to 90° showed increasing erosion rate; water sand erosion was focused at the side of the elbow rather than the outer radius indicated erosion was highly dependent on carrier fluid properties.

A delayed detached eddy simulation model with low Reynolds number correction for transitional swirling flow in a multi-inlet vortex nanoprecipitation reactor

The objective of the presented work is to verify a delayed detached eddy simulation (DDES) model for simulating transitional swirling flow in a micro-scale multi-inlet vortex reactor (MIVR). The DDES model is a k-ω based turbulence model with a low Reynolds number correction applied to the standard k-ω model such that the Reynolds-averaged Navier-Stokes (RANS) component of the DDES model is able to account for low Reynolds number flow. By limiting the dissipation rate in the k-equation, the large-eddy simulation (LES) part of the DDES model behaves similarly to a one-equation sub-grid model. The turbulent Reynolds number is redefined to represent both modeled and resolved turbulence level so that underestimation of the RANS length scale in the LES range can be reduced. Applying the DDES model to simulate both laminar and transitional flow in the micro-scale MIVR produces an accurate prediction of mean velocity and turbulent intensity compared with experimental data. It is demonstrated that the proposed DDES model is capable of simulating transitional flow in the complex geometry of the micro-scale MIVR. These simulation results also help to understand the flow and mixing patterns in the micro-scale MIVR and provide guidances to optimize the reactor for the application of producing functional nanoparticles.

A direct comparison of particle-resolved and point-particle methods in decaying turbulence

We use particle-resolved direct numerical simulation (PR-DNS) as a model-free physics-based numerical approach to validate particle acceleration modelling in gas-solid suspensions. To isolate the effect of the particle acceleration model, we focus on point-particle direct numerical simulation (PP-DNS) of a collision-free dilute suspension with solid-phase volume fraction$\unicode[STIX]{x1D719}=0.001$in a decaying isotropic turbulent particle-laden flow. The particle diameter$d_{p}$in the suspension is chosen to be the same as the initial Kolmogorov length scale$\unicode[STIX]{x1D702}_{0}$($d_{p}/\unicode[STIX]{x1D702}_{0}=1$) in order to overlap with the regime where PP-DNS is valid. We assess the point-particle acceleration model for two different particle Stokes numbers,$St_{\unicode[STIX]{x1D702}}=1$and 100. For the high Stokes number case, the Stokes drag model for particle acceleration under-predicts the true particle acceleration. In addition, second moment quantities which play key roles in the physical evolution of the gas–solid suspension are not correctly captured. Considering finite Reynolds number corrections to the acceleration model improves the prediction of the particle acceleration probability density function and second moment statistics of the point-particle model compared with the particle-resolved simulation. We also find that accounting for the undisturbed fluid velocity in the acceleration model can be of greater importance than using the most appropriate acceleration model for a given physical problem.

Finite Reynolds number corrections of the 4/5 law for decaying turbulence

We examine finite Reynolds number contributions to the inertial range solution of the third order structure functions D3,0 and D1,2 stemming from the unsteady and viscous terms. Under the assumption that the second order correlations f and g are self-similar under a coordinate change, we are able to rewrite the exact second order equations as a function of a normalized scale r̃ only. We close the resulting system of equations using a power law and an eddy-viscosity ansatz. If we further assume K41 scaling, we find the same Reynolds number dependence as previously in the literature. We proceed to extrapolate towards higher Reynolds numbers to examine the unsteady and viscous terms in more detail. We find that the intersection between the two terms, where their contribution to the solution of the structure function equations is relatively small, scales with the Taylor scale λ.2 MoreReceived 29 February 2016DOI:https://doi.org/10.1103/PhysRevFluids.1.064403Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasTurbulenceFluid Dynamics

Model Deformation Corrections of NASA Common Research Model Using Computational Fluid Dynamics

Computational fluid dynamics-aided wind-tunnel data corrections for the static model deformation effect of the NASA-Common Research Model are performed for wind-tunnel data obtained at the Transonic Wind Tunnel of Japan Aerospace Exploration Agency, the National Transonic Facility, and the European Transonic Wind Tunnel. Although it is important to use the same configuration when comparing wind-tunnel data obtained at various facilities, this has not yet been performed with an appropriate validation. In this paper, the model deformation effects are estimated from the difference between the computational fluid dynamics results for a designed configuration and that for a deformed configuration considering support systems. Initially, the techniques for the model deformation correction are validated with two sets of National Transonic Facility wind-tunnel data at a Reynolds number of with different dynamic pressures. Then, the validated model deformation corrections are performed on the wind-tunnel data obtained at the Transonic Wind Tunnel, National Transonic Facility, and European Transonic Wind Tunnel. Differences in the drag coefficients among the three sets of wind-tunnel data fall within about 10 drag counts for the model deformation corrections and the Reynolds number corrections applied to the Transonic Wind Tunnel data to align the Reynolds number to .

Screening and Correlating Data on Heat Transfer to Fluids at Supercritical Pressure

A simple criterion for screening experimental data on turbulent heat transfer in vertical tubes to identify those not significantly influenced by buoyancy was proposed by the author many years ago and found to work quite well for water and air at normal pressures. However, it was recognized even then that the ideas on which the criterion was based were too simplistic to be suitable for use in the case of fluids at supercritical pressure. With the passage of time and tremendous advancement in data processing capability using present-day computers, it is now possible to contemplate adopting a refined approach specifically designed to be suitable for such fluids. The present paper describes a semi-empirical model of buoyancy-influenced heat transfer to fluids at supercritical pressure, which takes careful account of nonuniformity of fluid properties. It provides a criterion for determining the conditions under which buoyancy influences are negligibly small. Thus, the extensive databases now available on heat transfer to fluids at supercritical pressure can be reliably screened to eliminate those affected by such influences. Then, the many correlation equations that have been proposed for forced convection heat transfer can be evaluated in a reliable manner. These equations mostly relate Nusselt number to Reynolds number, Prandtl number, and simple property ratio correction terms. Thus, they should be evaluated using only experimental data that are definitely not influenced by buoyancy. A further outcome of the present paper is that it might now prove possible to correlate the buoyancy-influenced data in such databases and fit the equation for mixed convection heat transfer yielded by the model to the correlated data. If this can be done, it will represent a major advancement in terms of providing thermal analysts with a valuable new tool.

Finite Reynolds number properties of a turbulent channel flow similarity solution

Finite Reynolds number behaviors of the asymptotically logarithmic mean velocity profile in fully developed turbulent channel flow are investigated. The scaling patch method of Fife et al. [“Multiscaling in the presence of indeterminacy: Wall-induced turbulence,” Multiscale Model. Simul. 4, 936 (2005)] is used to reveal invariance properties admitted by the appropriately simplified form of the mean momentum equation. These properties underlie the existence of a similarity solution to this equation over an interior inertial domain. The classical logarithmic mean velocity profile equation emerges from this similarity solution as the Reynolds number becomes large. Originally demonstrated via numerical integration, it is now shown that the solution to the governing nonlinear equation can be found by straight-forward analytical integration. The resulting solution contains both linear and logarithmic terms, but with the coefficient on the linear term decaying to zero as the Reynolds number tends to infinity. In this way, the universality of the classical logarithmic law comports with the existence of an invariant form of the mean momentum equation and is accordingly described by the present similarity solution. Existing numerical simulation data are used to elucidate Reynolds number dependent properties of the finite Reynolds number form of the similarity solution. Correspondences between these properties and those indicated by finite Reynolds number corrections to the classical overlap layer formulation for the mean velocity profile are described and discussed.

A Performance Prediction Model for Low-Speed Centrifugal Fans

A generalized model for mapping the trend of the performance characteristics of a double-discharge centrifugal fan is developed based on the work by Casey and Robinson (C&amp;R), which formulated compressor performance maps for tip-speed Mach numbers ranging from 0.4 to 2 using test data obtained from turbochargers with vaneless diffusers. The current paper focuses on low-speed applications for Mach number below 0.4. The C&amp;R model uses four nondimensional parameters at the design condition including the flow coefficient, the work input coefficient, the tip-speed Mach number, and the polytropic efficiency, in developing a prediction model that requires limited geometrical knowledge of the centrifugal turbomachine. For the low-speed fan case, the C&amp;R formulas are further extended to a low-speed, incompressible analysis. The effort described in this paper begins by comparing generalized results using efficiency data obtained from a series of fan measurements to that using the C&amp;R model. For the efficiency map, the C&amp;R model is found to heavily depend on the ratio of the flow coefficient at peak efficiency to that at the choke flow condition. Since choke flow is generally not applicable in the low-speed centrifugal fan operational environment, an alternate, but accurate estimation method based on fan free delivery derived from the fan test data is presented. Using this new estimation procedure, the modified C&amp;R model predicts reasonably well using the double-discharge centrifugal fan data for high-flow coefficients, but fails to correlate with the data for low-flow coefficients. To address this undesirable characteristic, additional modifications to the C&amp;R model are also presented for the fan application at low flow conditions. A Reynolds number correction is implemented in the work input prediction of the C&amp;R model to account for low-speed test conditions. The new model provides reasonable prediction with the current fan data in both work input and pressure rise coefficients. Along with the developments for the efficiency and work input coefficient maps, the use of fan shut-off and free delivery conditions are also discussed for low-speed applications.

Cospectral budget of turbulence explains the bulk properties of smooth pipe flow.

Connections between the wall-normal turbulent velocity spectrum E(ww)(k) at wave number k and the mean velocity profile (MVP) are explored in pressure-driven flows confined within smooth walls at moderate to high bulk Reynolds numbers (Re). These connections are derived via a cospectral budget for the longitudinal (u') and wall-normal (w') velocity fluctuations, which include a production term due to mean shear interacting with E(ww)(k), viscous effects, and a decorrelation between u' and w' by pressure-strain effects [=π(k)]. The π(k) is modeled using a conventional Rotta-like return-to-isotropy closure but adjusted to include the effects of isotropization of the production term. The resulting cospectral budget yields a generalization of a previously proposed "spectral link" between the MVP and the spectrum of turbulence. The proposed cospectral budget is also shown to reproduce the measured MVP across the pipe with changing Re including the MVP shapes in the buffer and wake regions. Because of the links between E(ww)(k) and the MVP, the effects of intermittency corrections to inertial subrange scales and the so-called spectral bottleneck reported as k approaches viscous dissipation eddy sizes (η) on the MVP shapes are investigated and shown to be of minor importance. Inclusion of a local Reynolds number correction to a parameter associated with the spectral exponential cutoff as kη→1 appears to be more significant to the MVP shape in the buffer region. While the bulk shape of the MVP is reasonably reproduced in all regions of the pipe, the solution to the cospectral budget systematically underestimates the negative curvature of the MVP within the buffer layer.

Application of quadratic and cubic turbulence models on cavitating flows around submerged objects

Quadratic and cubic Non-Linear Eddy-Viscosity Models (NLEVMs) at low Reynolds number (Re) correction were introduced into the present Computational Fluid Dynamics (CFD) framework, to provide better numerical treatment about the anisotropic turbulence stress in cavitating flows, which have large density ratio and large-scaled swirling flow structures. The applications of these NLEVMs were carried out through a self-developed cavitation code, coupled with a cavitation model based on the transport equation of liquid phase. These NLEVMs were firstly validated by the benchmark of disk supercavity, and found able to obtain more accurate capture of the hydrodynamic properties than the linear models. One of such models was further applied on the cavitation problem of submerged vehicles. Ultimately, the supercavitating flows around an especially designed underwater vehicle were predicted using the cubic k – ɛ turbulence model, and its cavitation behaviors were studied.

Numerical investigation on flow and convective heat transfer of aviation kerosene at supercritical conditions

avier-Stokes equations were solved using RNG k-epsilon turbulence model with low Reynolds number correction. The thermophysical and transport properties of the China RP-3 kerosene were calculated with a 10-species surrogate and the extended corresponding state method (ECS) combined with Benedict-Webb-Rubin equation. The independence of grids was first studied and the numerical results were then compared with experimental data for validation. Under flow conditions given in the paper, the results show that deterioration of convective heat transfer occurs when the wall temperature is slightly higher than the pseudo-critical temperature of kerosene for cases with wall heat flux of 1.2 and 0.8 MW/m(2). The degree of the heat transfer deterioration is weakened as the heat flux decreases. The deterioration, however, does not happen when the heat flux on the pipe wall is reduced to 0.5 MW/m(2). Based on the analysis of the near-wall turbulent properties, it is found that the heat transfer deterioration and then the enhancement are attributed partly to the change in the turbulent kinetic energy in the vicinity of pipe wall. The conventional heat transfer relations such as Sieder-Tate and Gnielinski formulas can be used for the estimation of kerosene heat convection under subcritical conditions, but they are not capable of predicting the phenomenon of heat transfer deterioration. The modified Bae-Kim formula can describe the heat transfer deterioration. In addition, the frictional drag would increase dramatically when the fuel transforms to the supercritical state.

Direct numerical simulations of flow in realistic mouth–throat geometries

The flow in a set of four realistic mouth–throat geometries at a flow rate of 30L/min is studied in order to determine the effect of intrasubject and intersubject variations on the mean flow patterns and the turbulence fluctuations. Direct numerical simulations (DNS) are performed, which fully resolve all the scales in the flow, without requiring a turbulence model. An immersed boundary method is applied on curvilinear grids which simplifies the task of grid generation for the complex extrathoracic geometries and allows the use of a structured grid solver which increases the efficiency of the numerical scheme. Inspection of the mean, responsible for the convective transport of particles, and the fluctuating component of velocity, responsible for turbulent dispersion, allows us to explain in vitro deposition data in the literature obtained in the same mouth–throat models. The results provide insight as to how geometric variation affects aerosol deposition and explain the scatter in deposition data observed in the literature. Geometric variation is shown to have a large impact on both the mean velocity profiles and the turbulence intensities. Examination of the flow fields in the various mouth–throat geometries allows us to address the origin of the dependence of deposition on Reynolds number, and provide the physical significance of the empirical Reynolds number correction previously proposed in the literature.

Stirring by squirmers

We analyse a simple ‘Stokesian squirmer’ model for the enhanced mixing due to swimming micro-organisms. The model is based on a calculation of Thiffeault &amp; Childress (Phys. Lett. A, vol. 374, 2010, p. 3487), where fluid particle displacements due to inviscid swimmers are added to produce an effective diffusivity. Here we show that, for the viscous case, the swimmers cannot be assumed to swim an infinite distance, even though their total mass displacement is finite. Instead, the largest contributions to particle displacement, and hence to mixing, arise from random changes of direction of swimming and are dominated by the far-field stresslet term in our simple model. We validate the results by numerical simulation. We also calculate non-zero Reynolds number corrections to the effective diffusivity. Finally, we show that displacements due to randomly swimming squirmers exhibit probability distribution functions with exponential tails and a short-time superdiffusive regime, as found previously by several authors. In our case, the exponential tails are due to ‘sticking’ near the stagnation points on the squirmer's surface.