Pipe Reynolds Number Research Articles

Microscale Flow Field Analysis and Flow Prediction Model Exploration of Dry Gas Seal

The characteristics of high speed, high pressure, microscale, and rotating flow fields result in very complicated flow between the dynamic and static rings of a dry gas seal. In particular, the existence of a groove, dam, and weir further contribute to the uncertainty of a microscale flow field. Classically, the flow regime of pipe flow is determined based on the critical Reynolds number (Pipe model) while the rotating flow field is sometimes determined by the flow factor (Oval model). In this study, a new method was developed that can be used for prediction of flow regime of a dry gas seal rotating flow field based on a three-dimensional velocity component (Ellipsoid model). The aim was to make the given model reflect the flow regime more realistically based on the consideration of the axial velocity component. When modeling dry gas seal rotating flow fields, we showed that compared to the one-dimensional Pipe model and the two-dimensional Oval model, the three-dimensional Ellipsoid model proposed in this paper can produce more accurate results.

A universal velocity profile for smooth wall pipe flow

The most important unanswered questions in turbulence regard the nature of turbulent flow in the limit of infinite Reynolds number. The Princeton superpipe (PSP) data comprise 26 velocity profiles that cover three orders of magnitude in the Reynolds number from $Re=19\,639$, to $Re=20\,088\,000$ based on pipe radius and pipe centreline velocity. In this paper classical mixing length theory is combined with a new mixing length model of the turbulent shear stress to solve the streamwise momentum equation and the solution is used to approximate the PSP velocity profiles. The model velocity profile is uniformly valid from the wall to the pipe centreline and comprises five free parameters that are selected through a minimization process to provide an accurate approximation to each of the 26 profiles. The model profile is grounded in the momentum equation and allows the velocity derivative, Reynolds shear stress and turbulent kinetic energy production to be studied. The results support the conclusion that logarithmic velocity behaviour near the wall is not present in the data below a pipe Reynolds number somewhere between $Re=59\,872$, and $Re=87\,150$. Above $Re=87\,150$, the data show a very clear, nearly logarithmic, region. But even at the highest Reynolds numbers there is still a weak algebraic dependence of the intermediate portion of the velocity profile on both the near-wall and outer flow length scales. One of the five parameters in the model profile is equivalent to the well-known Kármán constant, $k$. The parameter $k$ increases almost monotonically from $k=0.4034$ at $Re=87\,150$ to $k=0.4190$ at $Re=20\,088\,000$, with an average value, $k=0.4092$. The variation of the remaining four model parameters is relatively small and, with all five parameters fixed at average values, the model profile reproduces the entire velocity data set and the wall friction reasonably well. With optimal values of the parameters used for each model profile, the fit to the PSP survey data is very good. Transforming the model velocity profile using the group, $u/u_{0}\rightarrow ku/u_{0}$, $y^{+}\rightarrow ky^{+}$ and $R_{\unicode[STIX]{x1D70F}}\rightarrow kR_{\unicode[STIX]{x1D70F}}$ where $R_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, leads to a reduced expression for the velocity profile. When the reduced profile is cast in outer variables, the physical velocity profile is expressed in terms of $\ln (y/\unicode[STIX]{x1D6FF})$ and a new shape function $\unicode[STIX]{x1D719}(y/\unicode[STIX]{x1D6FF})$. In the limit of infinite Reynolds number, the velocity profile asymptotes to plug flow with a vanishingly thin viscous wall layer and a continuous derivative everywhere. The shape function evaluated at the pipe centreline is used to produce a new friction law with an additive constant that depends on the Kármán constant and a wall damping length scale.

Experiment and simulation analysis of the suspension behavior of large (5–30 mm) nonspherical particles in vertical pneumatic conveying

The particle suspension velocity has a strong practical impact on pneumatic conveying systems. The barycenter and centroid of large nonspherical particles are not in the same point, and the particles rotate under the action of torque when the particles are subjected to an unbalanced force in the flow field. This rotation causes the vortexes or turbulence near the particles. The stirring effect of large particle is especially obvious and directly affects the particle suspension behavior. To investigate the suspension behavior of large (5–30 mm) nonspherical particles in vertical pneumatic conveying, the CFD-DEM coupling method is adopted to realize the coupling between the solid phase and the gas phase and establish the coupling simulation model between the nonspherical particles and flow field. The suspension velocity relations of three flow drag zones are calculated on the basis of the particle-size method and the relationships between the pipe diameter, particle shape, Reynolds number and fluid drag coefficient. It will help in designing and operation of pneumatic conveying systems. The dynamic characteristics of large nonspherical particles in the vertical flow field are analyzed according to the particle suspension experiment and simulation results. The experiment and simulation results show that the nonspherical particles rotate in the vertical flow field, which can reduce the required flow velocity of large nonspherical particles in vertical pneumatic conveying.

Ice accretion measurements of Jet A-1 in aircraft fuel lines

Ice accretion and blockages in aircraft fuel systems continue to be of interest as a result of their influence on system design and alternative fuel synthesis as well as their role in aviation incidents and accidents. Ice accumulation tests are performed in a recirculating fuel system with Jet A-1 fuel. Removable stainless steel test pipes and variable flow rates allow for the examination of ice accretion with variation of pipe diameter and Reynolds number in a repeatable manner. The flow loop is installed in an altitude chamber capable of −50 °C and the experiments involve full-scale flow components. Temperature of the flow loop is controlled with an initial −11 °C/h cooling rate followed by a constant temperature test time. Instantaneous measurements of pressure drop along the test pipe are used to characterize ice accretion. Additionally, end-view imaging of the test pipes is performed to characterize the size and quality of the accreted ice. Normalized pressure drop is seen to increase nearly linearly with time for the range of Reynolds numbers and temperatures tested. Approximate ice accretion rates are extracted from the time varying pressure drops assuming the ice accumulation changes the pipe surface roughness. Accreted ice layer growth rates as high as 0.91±0.12 mm/hr are seen at low flow rate conditions (Re∼4000, −10.5 °C) and decrease with increasing Reynolds number. Growth rates at −7 °C and −19 °C are ∼25% and ∼1.5% of the −10.5 °C growth rate, respectively, and follow the same Reynolds number trend.

Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows

Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baarset al.(J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of$7:1:1$in the streamwise, spanwise and wall-normal directions, respectively.

The Effect of the Pipe Bending Angle on the Pressure Losses Vane Elbow Pipes

Pressure loss is one of the significant parameters in designing pipe bends. In this paper, the pressure distribution and pressure losses induced by turbulent flows in a circular cross-sectioned piping elbow with or without guide vane were simulated. The flow distribution in the piping elbow was simulated by the k- model using control volume method. The main objective of this study is to characterize the effect of changing the angle of pipe bend and Reynolds number on the flow separation of single-phase turbulent flow through numerical simulation. Results were validated by other experimental results and then loss coefficient was calculated in different angles from 45 to 135-degree pipe bend in various radius ratios with or without guide vane. Despite the fact that increasing pipe angle increased the pipe bend loss coefficient, using guide vane in the pipe elbow decreased this coefficient. In the radius ratio 1.5 with one guide vane, the loss coefficient of the pipe bends decreased by 50 percent in all degrees. Results revealed that the use of two vanes in pipe bend is more effective on the reduction of elbow pressure losses. Moreover, two guide vanes can decrease loss coefficient more than 50 percent. Also, the results indicated that loss coefficient decreased by increasing Reynolds number.

A relation between membrane permeability and flow rate at low Reynolds number in circular pipe

A relation between membrane permeability to a pure solvent and flow rate is derived in a circular pipe driven by a constant pressure difference across the pipe length. Membrane is assumed to be non-deformable and zero thickness, and the permeate flux of pure solvent due to pressure discontinuity across the flat membrane is coupled with the governing equations for incompressible Newtonian fluid in the Stokes regime. The permeation flow rate (normalised by that of the Hagen-Poiseuille flow for the no-membrane case or with a membrane of infinite permeability) is represented as a function of a non-dimensional permeability including the aspect ratio of the pipe geometry. The relation is established through comparison with a fully-validated numerical simulation result: the numerical discretisation is based on our original discrete-forcing immersed boundary method, which guarantees (i) conservations of mass and momentum even in the immediate vicinity of the membrane surface and (ii) consistency between incompressible velocity and pressure fields. Inverse analysis of the above formula yields the permeability as function of the flow rate through the pipe, comprising three equations covering the entire permeability ranges. The established permeability formulae are expected to be useful for identifying effective permeabilities of membrane to single-component fluid or pure solvent in practical applications.

Surface Orientation Effect on Local Heat Transfer by Round Water Jet Impingement

This paper describes local heat transfer for a round water jet on upward-facing and downward-facing static plates. Impinging liquid jets have high heat transfer rates. One of the technological issues in the steel making process is uniformity in cooling between the top and bottom sides of a plate. The objective of this study is to investigate the surface orientation effect on transient heat transfer experimentally. Experiments were conducted for a range of water flow rate, surface orientation. Both surface orientations were conducted on the same apparatus. The heat transfer plate was stainless steel to deal with both supercritical flow and subcritical flow regions. The plate length was wide for laboratory scale. Initial plate temperature was 800 degrees Celsius. Pipe Reynolds numbers were laminar flow regime. Inverse solution was employed to estimate transient local surface temperature and heat flux. Heat transfers between upward-facing and downward-facing surfaces are the same in the order of magnitude at downward-facing surface flow rate from 1.2 times to twice that of upward-facing surface. Local downward-facing surface temperature is higher than that of upward-facing temperature at the same flow rate. The following points can be given as reasons. Downward-flowing impinging jet velocity is larger than that of upward-flowing jet at the same flow rate due to gravity direction. Heat transfer is affected by a geometric arrangement relation of radial spreading liquid film, vapor and hot plate.

Laminar-turbulent transition in the near field of the jet at the instability regime of the jet source

The paper presents the results of an experimental study of the hydrodynamics of jets flowing from long tubes at low Reynolds numbers. The main attention in the research is given to the mechanism of interaction between pipe and jet instability, which results in a vortical motion in several spatial regions. In the experiments we used Hilbert-visualization, high-speed visualization, and measurements with a hot-wire anemometer. The subsonic gas jet flows into the air space from a long tube with a diameter of 2, 3.2, and 5 mm within the Reynolds number range of 200-6700. Air and Freon-22 were used as the working gases. The critical pipe Reynolds numbers are characterized by the mechanism of a two-stage instability caused by the formation of turbulent spots (puff) inside the tube and generation of vortex structures in the jet mixing layer. These organized structures (puff) exert a strong influence on the free jet flow destroying the laminar flow part. The obtained data make it possible to consider in detail the evolution of turbulent spots along the distance downstream, while the spots are generated in a cylindrical tube due to the laminar-turbulent transition.

Numerical Study on Turbulent Separation Reattachment Flow in Pipe Bends with Different Small Curvature Ratio

A turbulent separation flow is one of the most complex flows in existence. Flow separation and reattachment phenomena take place on the lower curved wall under high-pressure gradient for high Reynolds number in different pipe bends. The present study deals with the numerical simulation of the turbulent separation reattachment flow under high Reynolds number in different curvature ratios. Through making use of k–e turbulence model, the turbulent single-phase flow via a 90-degree bend pipe is studied numerically. A more precise research has been conducted to discover the impact of Reynolds number (Re) as well as curvature ratio (Rc/D) on the reattachment and separation of flow inside the pipe bend. The separation region and the separation–reattachment points are reported here. Additionally, mean statistics of the primary and secondary velocity field flows in diverse sections and the occurrence of Dean vortices have been shown. It has been observed that bends with low curvature ratio enable flow separation to be clearly visualized. Distribution of velocity depicted that the secondary motion is clearly encouraged by the progress of fluid from the inner to the outer wall region of the bend resulting in the separation of flow. In general, this numerical study analyses the flow separation phenomenon and predicts the separation and reattachment locations in 90° bend pipe for different Reynolds numbers and bend curvatures.

Fluid-mechanic interactions between a pipe flow having circumferential pressure variations and a piezometer ring

PurposeThis paper aims to investigate and understand the fluid mechanics of piezometer rings, a device frequently encountered in engineering practice.Design/methodology/approachThe investigation, implemented by numerical simulation, is based on turbulent flow in a pipe with a 90-degree bend. The pipe Reynolds numbers ranged from approximately 50,000 to 200,000. Two rings, with different dimensions, were investigated. Each ring consisted of four radially deployed straight segments of tubing which connect the pipe to a surrounding circular ring. The interconnections between the pipe and the ring were situated at 90-degree intervals around the circumference of the pipe.FindingsThe focus was directed to optimal circumferential locations of the radial connections, the optimal circumferential locations for accurate pressure measurements and the pressure drop penalty incurred by the use of a piezometer ring. For both of the investigated piezometer ring configurations, it was found that measurement locations situated just beyond the points of intermediate circumferential pressure variations were suitable for determining accurate values. The pressure drop was seen to increase because of the presence of the ring. For the smaller ring configuration, the increase in relative pressure drop was on the order 15 per cent, whereas the larger ring configuration lead to a 10 per cent increase.Originality/valueThis is the first attempt known to the authors to investigate and understand the fluid mechanics of piezometer rings.

Characterisation of textile shape and position upstream of a wastewater pump under different part load conditions

Accumulations of sanitary textile materials often lead to clogging of pumps in the wastewater system. Simulation of clogging phenomena may help to identify means of reducing the risk of clogging. In order to provide realistic initial conditions for clogging simulations, this study characterises textiles in artificial wastewater in the suction pipe to a dry-installed pump at nine different operating points. The textiles are recorded approximately 3.5 pipe diameters from the pump inlet and approximately three pipe diameters from the suction pipe bend at pipe Reynolds numbers in the range 300,000–900,000. Parameters of position, orientation, elongation and projected two-dimensional (2D) area are extracted using image analysis. The resulting parameters from the different operating points are compared using analysis of variance. The results show that the position, orientation and elongation do not change significantly with the operating point, while the projected 2D area decreases with an increased flow.

The Effect of Naturally Developing Roughness on the Mass Transfer in Pipes Under Different Reynolds Numbers

The local mass transfer over dissolving surfaces was measured at pipe Reynolds number of 50,000, 100,000, and 200,000. Tests were run at multiple time periods for each Reynolds number using 203 mm diameter test sections that had gypsum linings dissolving to water in a closed flow loop at a Schmidt number of 1200. The local mass transfer was calculated from the decrease in thickness of the gypsum lining that was measured using X-ray-computed tomography (CT) scans. The range of Sherwood numbers for the developing roughness in the pipe was in good agreement with the previous studies. The mass transfer enhancement (Sh/Shs) was dependent on both the height (ep−v) and spacing (λstr) of the roughness scallops. For the developing roughness, two periods of mass transfer were present: (i) an initial period of rapid increase in enhancement when the density of scallops increases till the surface is spatially saturated with the scallops and (ii) a slower period of increase in enhancement beyond this point, where the streamwise spacing is approximately constant, and the roughness height grows more rapidly. The mass transfer enhancement was found to correlate well with the parameter (ep−v/λstr)0.2, with a weak dependence on Reynolds number.

Performance of multiple fractured horizontal wells with consideration of pressure drop within wellbore

In this paper, we proposed a novel model for multiple fractured horizontal wells (MFHW) with consideration of pressure drop in the wellbore. To begin with, we proposed an analytical model incorporating with turbulent flow in wellbore, Darcy's flow in reservoir and hydraulic fractures, and effect of stress-sensitivity of permeability. Then, the model was solved by used mathematical methods of line source function, Pedrosa's substitution, and Newton-Raphson algorithm. After that, based on the solution, pressure transient behavior of the MFHW was obtained. Finally, model validation and sensitivity analysis were conducted.Results of validations show that there are good matches among our results, analytical results and numerical results. According to results of sensitivity analysis, we find that the pressure depletion decreases as fracture volume increases, and their effect on pressure depletion becomes weaker when increasing the pressure drops within wellbore. The pressure depletion increases with the increase of Reynolds number and relative pipe roughness; it decreases with the increase of reservoir-wellbore constant. The effects of Reynolds number, reservoir-wellbore constant, and relative pipe roughness on pressure behavior become stronger as fracture parameters increase, especially for fracture number. It is also found that the relative pipe roughness mainly affects the flow regimes at the early time, including bilinear flow and formation linear flow, while Reynolds number and reservoir-wellbore constant can influence all the flow regimes.This work provides some guidelines on understanding the effects of wellbore hydraulics on well performance in the tight gas reservoirs.

Experimental investigation of the solar FPC performance using graphene oxide nanofluid under forced circulation

Experiments were conducted on a solar flat plate collector (FPC) with graphene oxide (GO) nanofluid as the working fluid, circulated forcibly with the aid of a pump. The FPC had a collector area of 2m2, a concentric tube heat exchanger (CTHX) and a storage tank. GO nanoparticles were synthesized from graphite by the modified Hummer’s method. The morphology of the GO was estimated by XRD, UV–vis spectrometry and SEM imaging. The GO nanofluid was prepared by ultrasonication of the GO nanoparticles with de-ionized (DI) water as the base fluid, without adding any surfactant. Homogeneous and stable GO nanofluid for three different mass concentrations, (φ)=0.005, 0.01 and 0.02, were prepared. The nanofluids were found to be stable for 60days without any sedimentation issues. The thermo-physical properties of the GO nanofluids, such as the thermal conductivity, viscosity, density and specific heat, were estimated. For the flow supplied by the pump, the maximum value of the FPC inlet pipe and fluid property-based Reynolds number was found to be 430. The FPC’s overall heat transfer co-efficient (h), friction factor and collector efficiency were investigated for GO nanofluids under laminar conditions. It was observed that for GO nanofluid with φ=0.02 and a flow rate of 0.0167kg/s, the enhancement in the collector efficiency was 7.3% over that of the base fluid (DI water). The collector efficiency was found to increase with increasing φ and flow rate. The increases in h for the GO nanofluid with φ=0.005, 0.01 and 0.02 were 8.03%, 10.93% and 11.5%, respectively.

Numerical study on flow separation in 90° pipe bend under high Reynolds number by k-ε modelling

The present paper makes an effort to find the flow separation characteristics under high Reynolds number in pipe bends. Single phase turbulent flow through pipe bends is investigated using k-ε turbulence model. After the validation of present model against existing experimental results, a detailed study has been performed to study the influence of Reynolds number on flow separation and reattachment. The separation region and the velocity field of the primary and the secondary flows in different sections have been illustrated. Numerical results show that flow separation can be clearly visualized for bend with low curvature ratio. Distributions of the velocity vector show the secondary motion clearly induced by the movement of fluid from inner to outer wall of the bend leading to flow separation. This paper provides numerical results to understand the flow characteristics of fluid flow in 90° bend pipe.

Turbulent boundary layer statistics at very high Reynolds number

Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from$\mathit{Re}_{{\it\tau}}=2600$to$\mathit{Re}_{{\it\tau}}=72\,500$($\mathit{Re}_{{\it\theta}}=8400{-}235\,000$). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For$\mathit{Re}_{{\it\tau}}\geqslant 20\,000$, both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.

On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows

Recent experiments in high Reynolds number pipe flow have shown the apparent obfuscation of the \(k_x^{-1}\) behaviour in spectra of streamwise velocity fluctuations (Rosenberg et al. in J Fluid Mech 731:46–63, 2013). These data are further analysed here from the perspective of the \(\log r\) behaviour in second-order structure functions, which have been suggested as a more robust diagnostic to assess scaling behaviour. A detailed comparison between pipe flows and boundary layers at friction Reynolds numbers of \({{Re}}_\tau \approx\) 5000–20,000 reveals subtle differences. In particular, the \(\log r\) slope of the pipe flow structure function decreases with increasing wall distance, departing from the expected \(2A_1\) slope in a manner that is different to boundary layers. Here, \(A_1 \approx 1.25\), the slope of the log law in the streamwise turbulence intensity profile at high Reynolds numbers. Nevertheless, the structure functions for both flows recover the \(2A_1\) slope in the log layer sufficiently close to the wall, provided the Reynolds number is also high enough to remain in the log layer. This universality is further confirmed in very high Reynolds number data from measurements in the neutrally stratified atmospheric surface layer. A simple model that accounts for the ‘crowding’ effect near the pipe axis is proposed in order to interpret the aforementioned differences.

Numerical analysis of friction factor for a fully developed turbulent flow using k–ε turbulence model with enhanced wall treatment

The aim of this study is to formulate a computational fluid dynamics (CFD) model that can illustrate the fully turbulent flow in a pipe at higher Reynolds number. The flow of fluids in a pipe network is an important and widely studied problem in any engineering industry. It is always significant to see the development of a fluid flow and pressure drop in a pipe at higher Reynolds number. A finite volume method (FVM) solver with k–ε turbulence model and enhanced wall treatment is used first time to investigate the flow of water at different velocities with higher Reynolds number in a 3D pipe. Numerical results have been presented to illustrate the effects of Reynolds number on turbulence intensity, average shear stress and friction factor. Friction factor is used to investigate the pressure drop along the length of the pipe. The contours of wall function are also presented to investigate the effect of enhanced wall treatment on a fluid flow. A maximum Reynolds number is also found for which the selected pipe length is sufficient to find a full developed turbulent flow at outlet. The results of CFD modeling are validated by comparing them with available data in literature. The model results have been shown good agreement with experimental and co-relation data.

Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Reλ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.