Flow In Circular Pipe Research Articles

Electron Spin-Vorticity Coupling in Pipe Flows at Low and High Reynolds Number

Spin-hydrodynamic coupling is a recently discovered method to directly generate electricity from an electrically conducting fluid flow in the absence of Lorentz forces. This method relies on a collective coupling of electron spins---the internal quantum-mechanical angular momentum of the electrons---with the local vorticity of a fluid flow. In this work, we experimentally investigate the spin-hydrodynamic coupling in circular- and noncircular-capillary pipe flows and extend a previously obtained range of Reynolds numbers to smaller and larger values, $20<\mathrm{Re}<21\phantom{\rule{0.1em}{0ex}}500$, using the conducting liquid-metal alloy ($\mathrm{Ga}$,$\mathrm{In}$)$\mathrm{Sn}$ as the working liquid. In particular, we provide experimental evidence for the linear dependence of the generated electric voltage with respect to the bulk-flow velocity in the laminar regime of the circular pipe flow as predicted by Matsuo et al. [Phys. Rev. B. 96, 020401 (2017)]. Moreover, we show analytically that this behavior is universal in the laminar regime regardless of the cross-sectional shape of the pipe. Finally, the proposed scaling law by Takahashi et al. [Nat. Phys. 12, 52 (2016)] for the generated voltage in turbulent circular pipe flows is experimentally evaluated at Reynolds numbers higher than in previous studies. Our results verify the reliability of the proposed scaling law for Reynolds numbers up to $\mathrm{Re}=21\phantom{\rule{0.1em}{0ex}}500$ for which the flow is in a fully developed turbulent state.

Analytical Solutions for Unsteady Pipe Flows with Slip Boundary Condition

In this paper analytical expressions for time-dependent velocity profiles and pressure gradient are obtained for fully-developed laminar flows with given volume flow-rate conditions in circular pipe flows with slip boundary conditions. The governing equations are solved analytically using the traditional Laplace transform method together with Mellin’s inversion formula. The evolution of velocity profiles and pressure gradient for starting and pulsatile flow with slip boundary conditions are analyzed. New simplified expressions and perspectives on velocity and pressure gradient for no-slip and slip flows are obtained from the analytical results. New scalings in starting and pulsatile flows are proposed for pipe flows with no-slip and slip boundary conditions using non-dimensional numbers. Special attention is paid to the effect of slip factor and pulsatile flow frequency on the time-dependent skin-friction factor. Finally, by using the starting and pulsating flow results, analytical expressions of velocity and pressure for arbitrary inflow are obtained by approximating the arbitrary volume flow-rate by a Fourier series

Criteria of sinkhole formation in soils from physical models

This study addresses mechanical models of sinkhole formation and their criteria obtained via simulation test. Sinkholes are a common geohazard and are widely distributed throughout the world. Previous studies suggest that sinkhole formation is the result of complex interactions among geological conditions, with one or more factors triggering occurrence of sinkholes. We suggest that the existence of a void caused by soil loss is the premise of this issue. Therefore, we present soil loss is the mechanism of sinkhole formation in soils in this paper. Soil loss is caused by the interaction between groundwater and soils in nature. This interaction includes the groundwater condition and the characteristics of soils. In this study, we considered three types of groundwater conditions and two types of soils to discuss the mechanical model of sinkholes. There are three models of sinkhole formation in soils: the disintegration model in vadose zone, the seepage erosion model in unconfined aquifer, and the hydraulic fissures model in confined aquifer. A disintegration apparatus was designed to simulate the disintegration process and to obtain the criteria parameters of water content. Circular pipe flow equipment was designed to simulate the seepage erosion process to obtain the criteria parameter of groundwater velocity. The mechanical model of sinkholes in the confined aquifer was the hydraulic fissures model. The hydraulic equipment was designed to simulate the hydraulic fissure process to measure the criteria parameter of water pressure.

Investigation of granular dispersion in turbulent pipe flows with electrostatic effect

The electrostatic effect on granular dispersion in circular pipe flows at Reb = 44,000 was investigated using Large Eddy Simulation (LES) in one-way coupling Lagrangian granule tracking method. Granule motion equation is governed by drag force, gravity and electrostatic force. LES results obtained for single phase flow agree well with experimental data and DNS results. Three granule sizes (dp = 20, 80, 200 μm) were considered in this work. It is found that in the absence of electrostatic effect granular dispersion near the wall mainly depends on local flow characteristics. Electrostatic effect was found to change the effect of turbulent flows on granular dispersion particularly near the pipe wall. Granules were found to accumulate in the near-wall region (y/R > 0.95) but well distribute in most pipe (0 < y/R < 0.95). In the near-wall region, it is electrostatic force that dominates granular concentration, which is independent of granule size. In addition, the electrostatic force is found to be obviously larger than drag force and gravity for all sized granules in this region. In most pipe region (y/R < 0.95) electrostatic effect tends to decrease granular concentration and it becomes more significant with granule size.

Re-examining log law velocity profile in smooth open channel flows

A comprehensive investigation of velocity distribution is presented, and the log law is re-examined using experimental data from a smooth uniform open channel flow. It is widely reported that the coefficients of the log law in channel flows deviate from those obtained from circular pipe flows by Nikuradse (Laws of flow in rough pipes, 1933), but the mechanism is not clear and no theoretical formulae are available to express these deviations. A Laser Doppler Velocimetry system was used to measure velocity profiles at the centre of the channel. The data obtained support previous conclusions that the additive constant B of the log law in channel flows can no longer be considered to be 5.5. Interestingly, the experimental data also support Tracy and Lester’s discovery that the shear velocities on both sides of the log law are different. Better agreement can be achieved if the global shear velocity (U*1) is used to normalize the measured velocity, and the local shear velocity (U*2) is used to normalize the distance from the wall. Other researchers’ data in the literature also validates this new relationship. Based on this new relationship, a theoretical value of B is obtained, which agrees well with the observed B, thus a new form of log law for channel flow is suggested. The new relationship developed was verified with present experimental and past literature data suggesting its universality irrespective of wide or narrow open channels, or subcritical or super critical flow conditions. By using the developed relationship the large scatter associated with the additive constant B associated with the log law has been explained. It is found that the additive constant B in the log law is a function of channel aspect ratio. The developed relationship for B is validated from a wide range of data from the literature to confirm its universality.

Oscillating Flows in Circular Pipes

Pulsation flows in pipes heated externally produces oscillating temperature field. This type of unsteady flow happens in heat exchangers. Simulating this type of flows is complex in engineering. In this present study the field variables like velocity and temperature are calculated by numerical control volume scheme. Velocity pulsation is applied at inlet of pipe to produce oscillations. Simulation variables like lengths, diameter and thickness of the pipe are considered as parameters for this study. Also additionsl structural constraints has been added to see how it influences effective thermal stresses.

Simulations of axisymmetric, inviscid swirling flows in circular pipes with various geometries

The numerical simulations of the dynamics of high Reynolds number ($$Re>100{,}000$$) swirling flows in pipes with varying geometries of engineering applications continues to be a challenging computational problem, specifically when vortex-breakdown zones or wall-separation regions naturally evolve in the flows. To tackle this challenge, the present paper describes a simulation scheme of the evolution of inviscid, axisymmetric and incompressible swirling flows in expanding or contracting pipes. The integration in time of the circulation together with azimuthal vorticity uses an explicit, first-order accurate finite-difference scheme with a second-order accurate upwind difference formulation in the axial and radial directions. The Poisson solver for advancing in time the spatial distribution of the stream function as a function of azimuthal vorticity uses a second-order accurate over-relaxation difference scheme. No additional numerical steps are needed for computing the natural evolution of flows including the dynamics to states with slow-speed recirculation zones along the pipe centerline or attached to pipe wall. This numerical method shows convergence of the computed results with mesh refinement for various swirl levels and pipe geometry variations. The computed results of time-asymptotic states also present agreement with available theoretical predictions of steady vortex flows in diverging or contracting pipes. In addition, comparison with available experimental data demonstrates that the present algorithm accurately predicts instability processes and long-term mean-flow dynamics of vortex flows in pipes at high Re. The inviscid-flow simulation results support the theoretical predictions and clarify the nature of high-Re flow evolution.

Experimental investigation on heat transfer in laminar, transitional and turbulent circular pipe flow with respect to flow regime boundaries

The empirical prediction methods for heat transfer coefficients in the transition regime between laminar and fully turbulent flow are still subject to changes. This situation reflects a lack of reliable experimental data, which are consistently determined over a wide range of relevant Reynolds and Prandtl numbers. This contribution presents new measurement data, in particular 164 data points for heat transfer coefficients, consistently determined over a wide range of Reynolds and Prandtl numbers, ranging from 13 < Pr < 70 and 375 < Re < 13100. In addition, the widely accepted prediction method for heat transfer in circular pipes according to Gnielinski is tested with the present data and other relevant data from literature. This method relies on a linear interpolation between the heat transfer coefficients at the onset of the transition regime and that of the fully turbulent regime. Consequently, working on a consensus about the values of these onset points is an important issue. In this contribution, the transitional flow regime has been found to start at Recr = 2300, and the fully turbulent flow regime to start in the range of 4100 < Ret < 5400. Those findings support the latest version of Gnielinski’s method, published in 2013, as well as other recent work on the topic, particularly that of Everts and Meyer.

Identification of viscosity and solid fraction in slurry pipeline transportation based on the inverse heat transfer theory

A method based on the inverse heat transfer theory for identifying the viscosity coefficient and solid volume fraction of slurries is proposed in this study. An inverse heat convection problem for non-Newtonian fluid is solved in a fully developed laminar circular pipe flow based on temperature measurements obtained at several radial locations in the stream. An optimal estimation of the apparent viscosity of slurries is obtained by the relationship between temperature profile and apparent viscosity. The solid volume fraction in the pipe can be eventually determined through the applicable relation between solid loading and viscosity. Several experiments were conducted to verify the accuracy of the method. Coal-water slurry and coal-slime slurry were considered for the validation. Comparisons between the estimated values and experimental data showed that this method was reliable for predicting viscosity coefficient and solid fraction in slurry fluid. It is expected to be useful in detecting the rheological properties for determining operation mode of slurry pipelines.

Analytical solutions of incompressible laminar channel and pipe flows driven by in-plane wall oscillations

Emerging flow control strategies have been proposed to tackle long-lasting problems, for instance, precise mixing of chemicals and turbulent drag reduction. Employing actuators imposing in-plane wall oscillations are particularly popular. This paper investigates incompressible laminar rectangular channel and circular pipe flows driven by uniform and traveling wave in-plane wall oscillations. A comprehensive set of exact analytical solutions are presented describing parallel and concentric flows. Dimensionless groups are identified, and it is described how they characterize the one- and two-dimensional time-dependent velocity and pressure fields. The solutions enable to compute the oscillating boundary layer thickness. It is demonstrated that the dimensionless groups and the boundary layer thickness narrows the region of interest within the parameter space. In particular, the oscillating boundary layer thickness obtained from these laminar flows estimates a “radius of action” within which flow features can be altered to boost mixing or reduce turbulent friction drag. The results are suitable for software validation and verification, may open the way to promising complex wall oscillations, and ease the optimization task that delays the industrial application of flow controls.

Experimental study on interfacial and wall friction factors under counter-current flow limitation in vertical pipes with sharp-edged lower ends

Experiments on air-water counter-current annular flows in circular vertical pipes of 20 and 40 mm in diameter were carried out to obtain databases of the interfacial and wall friction factors. The pipes were made of transparent acrylic resin to observe counter-current flow limitation (CCFL) in the pipe. The vertical pipe was connected to an upper and a lower tank. The liquid and gas phases were supplied to the upper and lower tanks, respectively. The liquid volume flow rate, the pressure gradient and the liquid volume fraction were measured to evaluate the friction factors. The flows in the pipe were observed using a high-speed video camera and the flow pattern under CCFL was identified using the time-strip visualization technique. The main conclusions obtained under the present experimental conditions are as follows: (1) the flows under CCFL condition can be classified into four regimes, i.e. the smooth film, the transition from smooth film to rough film regimes, the rough film with large amplitude disturbance waves forming at the lower pipe end, and the rough film with simultaneous onsets of disturbance waves inside the pipe, (2) the slope of the CCFL diagram depends on the flow regimes, (3) the flow structure strongly affects the friction factors, and therefore, available correlations of friction factors not accounting for their dependences on the flow regimes cannot give good evaluations, (4) the wall friction factor can be correlated in terms only of the liquid Reynolds number, (5) the interfacial friction factor in the rough film regimes can be well correlated in terms of the gas Wallis parameter (Froude number) since the interface structure strongly depends on the Wallis parameter, and (6) the CCFL model derived using the present empirical correlations of friction factors agrees well with the CCFL characteristics data.

Heat transfer and pressure drop investigation through pipe with different shapes using different types of nanofluids

In the present study, the heat transfer and hydrodynamic analysis of flow through single-pipe heat exchangers of circular and square cross-sectional configurations were performed. The experimental and numerical investigations were conducted to evaluate the performance of two metallic oxides (Al2O3 and SiO2) and two carbon-based nanostructured nanofluids (KRG and GNP) in comparison with the distilled water (DW). The data obtained from the experimental runs with DW as a working fluid in both test sections were used to validate the 3-D numerical models for the square and circular pipe heat exchangers. The flow in both test sections is considered as a fully developed turbulent flow with the Reynolds number range of 6000–11,000, and both the test sections were subjected to a uniform heat flux at their outer surfaces. The concentrations of all nanofluids used in the present study were in the range of (0.025–0.1 mass%). The test rig was firstly validated during the water run by using different empirical correlations for the evaluation of pressure drop and Nusselt number and showing a very good agreement, and then, the numerical models were validated with the data obtained experimentally and the errors were less than 10% for both models. For the square tube flow, the average errors between the numerical and experimental findings of Nusselt number and pressure drop were 6.8% and 2.49%, respectively, and for the circular pipe flow, the evaluated errors were 9.34% and 5.92% for Nusselt number and pressure drop, respectively. The performance index for all the nanofluids was calculated to obtain the convective heat transfer coefficients and friction losses of the fluids in both the tubes. The results showed that the non-covalent graphene–DW is not suitable for heat transfer applications due to its higher viscosity. The results also showed a different enhancement of heat transfer for the same nanofluid in circular and square tube flows, whereas the performance index of the same nanofluid appears nearly the same for flow through both the cross sections.

Three-Dimensional Velocity Distribution in Straight Smooth Channels Modeled by Modified Log-Law

Time-average velocity distribution in steady and uniform channel flows is important for fundamental research and practical application as it is always three-dimensional (3D), regardless of channel geometry. However, its determination has predominantly been carried out by using complex numerical software, even for the simplest geometry such as rectangular channels. The log-law was developed initially for circular pipe flows, where a single shear velocity is used to normalize the velocity (u+) and its distance (y+). Tracy and Lester found that the performance of the log-law can be extended to express velocity profiles in rectangular channels when the global shear velocities (gRS)0.5 and (ghS)0.5 are used to normalize the measured velocity u and its distance y. This study extends this discovery from the channel central line to the corner regions, and its general form of log-law was found to be valid even in trapezoidal or triangular open channels or closed ducts. This modified log-law can produce good agreement with the measured velocity with an average error of less than 5%. Therefore, this study provides a simple and reliable tool for engineers and researchers to estimate the velocity contours in straight and smooth channel flows.

The elements of fluid mechanics of bile flow through biliary drainage catheters

Obstructive jaundice in the biliary tract can infect blood and result in mortality with a high rate. Percutaneous transhepatic biliary drainage (PTBD) with catheters is a useful solution discharging the obstructive jaundice. However, the elements of fluid mechanics showing clinical performance of a PTBD catheter have been documented little so far. In the article, empirical relationships between bile flow rate and pressure gradient in PTBD catheters were studied in terms of equivalent friction factor for the first time. Firstly, an equivalent friction factor in a catheter was raised and determined based on existing in vitro experimental data of bile flow through the catheters with different materials, various inner diameters and lengths under various pressure differences. Then, an empirical correlation of bile flow rate through a catheter was established based on pressure gradient, inner diameter and bile viscosity. The correlation was used to identify effects of catheter inner diameter and bile viscosity on the bile flow rate under the physiological bile pressure difference across obstructed common bile ducts. The feature of minor hydraulic losses in the catheters was clarified, too. The proposed equivalent friction factor was proportional to Reynolds number in a power of -0.654 in comparison with a power of -1 for the fully developed laminar flow in circular pipes. The bile flow rate through a catheter was proportional to inner diameter, kinematic viscosity, and pressure gradient in the powers of 3.2, -0.5 and 0.74, respectively. The minor hydraulic losses could be significant when Reynolds number was greater than 100.

Investigation of Optimum Heat Flux Profile Based on the Boiling Safety Factor

An experimental study is conducted to investigate the effect of heat flux distribution on the boiling safety factor of its cooling channel. The water is allowed to flow in a horizontal circular pipe whose outlet surface is subjected to different heat flux profiles. Four types of heat flux distribution profiles are used during experiments: (constant distribution profile, type a, triangle distribution profile with its maximum in channel center, type b, triangle distribution profile with its maximum in the channel inlet, type c, and triangle distribution profile with its maximum in the channel outlet, type d). The study is conducted using heat sources of (1000 and 2665W), water flow rates of (5, 7 and 9 lit/min). The water temperature at cooling channel inlet is kept constant at (25°C). Copper test section of (0.6 m) length (0.025m) inner diameter is used during the experiments. The electrical heater used for water heating is wrapped around the copper pipe covering (50 cm) of its length. Calibrated thermocouples are distributed along pipe surface at distances (0.1, 0.2, 0.3, 0.4 and 0.5 m) from pipe inlet to measure pipe surface temperature. The results shows that the heat source with heat flux profile of type (c) is the most reliable one from thermo-hydraulic safety point of view for both types of heat sources, as it ensures a maximum boiling safety factor (K) of (1.6, 1.7, 2) at water flow rates of (5, 7 and 9 lit/min) respectively based on maximum heat capacity of (2665 w), while the heat source with heat flux profile of type (d) which posses minimum boiling safety factors of (1, 1.2, 1.3) at water flow rates of (5, 7 and 9 lit/min) respectively based on same heat capacity value is the worst one from same point of view.&#x0D;

Spreadsheet Solutions for Rheological Properties and Viscoplastic Fluid Flow in Circular Pipes and in Parallel-plates

Spreadsheet Solutions for Rheological Properties and Viscoplastic Fluid Flow in Circular Pipes and in Parallel-plates

Effect of Reynolds Number and Concentration of Biopolymer (Gum Arabic) on Drag Reduction of Turbulent Flow in Circular Pipe

Effect of Reynolds Number and Concentration of Biopolymer (Gum Arabic) on Drag Reduction of Turbulent Flow in Circular Pipe

Laminar-turbulent transition in channel flow: wall effects and critical Reynolds number

This article describes a possible cause of natural laminar-turbulent transition in channel flow, and the minimum critical Reynolds number Rc,min is determined. It is assumed that the mechanism of transition is the same for both circular pipe flow and channel flow since each flow has its own minimum critical Reynolds number. Our starting points are that under natural disturbance conditions, transition appears to take place only in the developing entrance region and that the critical Reynolds number Rc becomes Rc,min when using a sharp-edged uniform channel. In our previous studies of circular pipe flow, we have developed a model for transition and obtained Rc,min=1910 and 1950 in two mesh systems. In this study, for channel flow, the above transition model is verified by obtaining Rc,min=1190 and 1260 in two mesh systems.

On an analytic solution for general unsteady/transient turbulent pipe flow and starting turbulent flow

Abstract The literature already offers analytic solutions for steady-state laminar (Hagen–Poiseuille), transient laminar (Szymanski) and steady-state turbulent (Pai) incompressible pipe flows. However, no reference could be found for the most general case that encompasses all of them: the unsteady turbulent incompressible pipe flow. This study presents a General Analytic Solution (GAS) for the Reynolds–averaged Navier–Stokes equations corresponding to unsteady turbulent incompressible circular pipe flow, which is composed of the transient response of the initial mean velocity field to external interactions, the unsteady response to time-dependent pressure gradient, and the unsteady component due to the turbulence’s Reynolds stress. The particular cases of laminar, turbulent, steady-state and transient incompressible pipe flows emanate directly from such solution. A general method is proposed to obtain an analytical solution for any particular pipe flow problem for which some relevant function could be provided. That general method is exemplified in a test case, a much simplified version of the starting flow initiated in a circular pipe, after suddenly applying a constant pressure gradient. The time evolution for such starting flow, with a growing stage and a shrinking stage, is presented graphically and discussed.

Second Law Analysis of Flow in a Circular Pipe With Uniform Suction and Magnetic Field Effects

The present paper investigates analytically the two-dimensional heat transfer and entropy generation characteristics of axisymmetric, incompressible viscous fluid flow in a horizontal circular pipe. The flow is subjected to an externally applied uniform suction across the wall in the normal direction and a constant magnetic field. Constant wall temperature is considered as the thermal boundary condition. The reduced Navier–Stokes equations in a cylindrical coordinate system are solved to obtain the velocity and temperature distributions. The velocity distributions are expressed in terms of stream function and the solution is obtained using the homotopy analysis method (HAM). Validation with earlier nonmagnetic solutions in the literature is incorporated. The effects of various parameters on axial and radial velocities, temperature, axial and radial entropy generation numbers, and axial and radial Bejan numbers are presented graphically and interpreted at length. Streamlines, isotherms, pressure, entropy generation number, and Bejan number contours are also visualized. Increasing magnetic body force parameter shifts the peak of the velocity curve near to the axis, whereas it accelerates the radial flow. The study is relevant to thermodynamic optimization of magnetic blood flows and electromagnetic industrial flows featuring heat transfer.