Pipe Of Circular Cross-section Research Articles

Energy dissipation of the liquid in systems with a hydrophobic surface

The work is divided into theoretical and experimental parts. In the theoretical part the viscous forces performance for both laminar as well as turbulent flow of compressible fluids are defined. It is split into the viscous forces useful power and the power corresponding to mechanical losses. This part is expressed by the dissipation function. It is shown that the dissipation function considering hydrophobic surfaces cannot be determined from the pressure difference. It is necessary to take into account the slip of the liquid over the hydrophobic surface which depends on the value of surface energy. The values of surface energy for different types of hydrophobic surfaces, obtained by experiment, are shown within this work. The new definition of the dissipation function for hydrophobic surfaces is presented depending on the adhesion coefficient, also determined by an experiment. The theoretical part of the work is complemented by experiment. The experiment is aimed at the differential pressure measurement in a circular cross section pipe. The results are processed for both laminar and turbulent stationary flow in relation to the flow. Both hydrophilic and hydrophobic surfaces and their mutual correlation are taken into consideration. On the basis of the new mathematical model for hydrophobic surfaces the value of dissipation function is determined depending on the slip velocity of the liquid along the hydrophobic surface.

Radiation Heat Transfer in the Molten Salt FLiNaK

The molten fluoride salt eutectic LiF-NaF-KF (FLiNaK) has been proposed as a coolant for use in Generation IV reactors designed to operate at temperatures at which radiation heat transfer (RHT) may be significant. Little research has been performed into the absorption coefficient of FLiNaK as it pertains to thermal RHT. An estimate of the spectral absorption coefficient for FLiNaK has been generated using informed assumptions and existing data for the constituent salts. The effect of heat transfer, as it pertains to flowing salt in circular cross-section pipes with heated walls, has been investigated for laminar flow using a mathematical model. The combined energy equation, in various geometries, was solved for laminar flow, with the radiative heat flux calculated using the differential approximation. The percentage of energy transferred by radiation to the salt was found to be primarily a function of pipe diameter, wall temperature, and the salt absorption coefficient. A map of temperatures and pipe diameters has been generated, which indicates where RHT is significant. A correlation has been proposed, based on the mathematical model, to account for increase in Nusselt number due to radiation. Additional discussion is included on the effects of wall emissivity and high Reynolds flows.

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.

Numerical investigation of flow and heat transfer performances of horizontal spiral-coil pipes

The flow and heat transfer performances of horizontal spiral-coil pipes of circular and elliptical cross-sections are studied. The numerical results are compared with the experimental data, to verify the numerical method. The effects of the inlet water mass flow rate, the structural parameters, the helical pitch and the radius ratio on the heat transfer performances are investigated. Performances of the secondary fluid flow with different radius ratios are also investigated. Numerical results demonstrate that the heat transfer coefficient and the Nusselt number increase with the increase of the water mass flow rate or the helical pitch. The maximum heat transfer coefficient and the maximum Nusselt number are obtained when the radius ratio is equal to 1.00. In addition, the fluid particle moves spirally along the pipe and the velocity changes periodically. The particle flow intensity and the spiral movement frequency decrease significantly with the increase of the radius ratio. Besides, the secondary flow profile in the horizontal spiral-coil pipe contains two oppositely rotating eddies, and the eddy intensity decreases significantly along the pipe owing to the change of curvature. The decreasing tendency of the eddy intensity along the pipe increases with the increase of the radius ratio.

On the drag reduction effect and shear stability of improved acrylamide copolymers for enhanced hydraulic fracturing

Polymeric drag reducers, such as partially hydrolysed polyacrylamide (PHPAAm), are important chemical additives in hydraulic fracturing fluids as they can significantly decrease the frictional pressure drop in the casing (by up to 80%), resulting in an increase of the injection rate that can be delivered to the fracturing point. The incorporation of sodium 2-acrylamido-2-methylpropane sulphonic acid (NaAMPS) moieties into polyacrylamide (PAAm) can further improve the performance of fracturing fluids by addressing some compatibility issues related to the use of PHPAAm, e.g., the sensitivity to water salinity. In this study, three types of poly(acrylamide-co-NaAMPS) and pure PHPAAm were investigated with respect to polymer induced drag reduction and mechanical polymer degradation in turbulent pipe flow in a pressure-driven pipe flow facility. The test section comprised a horizontal 1" bore circular cross-section pipe. The facility was modified in order to allow long time/length experiments by automatically recirculating the polymer solution in a closed-loop through the test section. The presence of NaAMPS groups in the copolymer backbone is found to increase the ability of PHPAAm to reduce frictional drag while the vulnerability to mechanical degradation remains unaffected. The drag reduction of NaAMPS copolymer solutions can be described by a modified version of Virk׳s correlation (1967), extended to include the effect of Reynolds number. Polymer mechanical degradation is found to proceed until the friction reducer is almost ineffective in reducing drag. This phenomenon is in contrast with the most common correlation for polymer degradation, which predicts the existence of an asymptotic (but finite) limit to the reduced drag reduction.

MHD formulations for the liquid metal flow in a curved pipe of circular cross section

The laminar fully developed magnetohydrodynamic (MHD) flow of a liquid metal into a curved pipe of circular cross section, subjected to a transverse external magnetic field, is studied. Three different formulations are used for the implementation of the electromagnetic variables. The extended Continuity Vorticity Pressure (CVP) numerical variational method for MHD flows is used for the coupling of the momentum and the continuity equation. Results are obtained for different values of the curvature (0–0.2) and of the Hartmann number (0–1000). The magnitude of the axial velocity is determined by the balance of the centrifugal and the electromagnetic forces. The results reveal the limits of applicability of the used electromagnetic models as the Hartmann number increases.

AN OVERVIEW ON PULSATILE FLOW DYNAMICS

Pulsatile flow dynamics in reference to the relevant experimental research on the manner between the time periods of 1997- 2015 is presented in this paper. The flow field under discussion is generated through a rigid circular cross-sectional pipe as an axial slightly- compressible and sinusoidal one in a controlled range of the oscillation parameters. Laminar and turbulent flow regimes are considered with a particular emphasis devoted to the transitional characteristics of laminar pulsatile flow into turbulence. The definitions of the flow characteristics, the methodology of the experimental studies and the results on the physical nature of the field are described. The departure of pulsatile flow from a steady one is presented in reference to the velocity field and frictional field analyse sunder the influence of oscillation frequency and amplitude. In this context, the critical magnitudes of Womersley number, time-averaged Reynolds number and oscillation amplitude to estimate the ranges of pulsatile flow field are proposed

Viscous dissipation effect on the flow of a thermodependent Herschel-Bulkley fluid

The present study concerns the numerical analysis of both hydrodynamic and thermal properties of a Herschel-Bulkley fluid flow in a pipe. The flow, which involves forced heat transfer convection, is steady and takes place within a pipe of circular cross section with uniform wall temperature. The Herschel-Bulkley model with the Papanastasiou regularization is used and flow index values of 1 and 1.5 are considered. The study focuses on the effect of neglecting both viscous dissipation and temperature dependence of the fluid consistency on its hydrodynamic and thermal properties. For that purpose, we investigate both wall heating (Br<0) and wall cooling (Br>0) as well as the exponential temperature dependence of the consistency. The results show that neglecting both of these parameters results in more than a 50% underestimation of the heat transfer due to the viscous nature of this kind of fluid.

A Numerical Study of MHD Laminar Flow in a Rotating Curved Pipe with Circular Cross Section

The incompressible viscous steady flow through a rotating curved pipe of circular cross-section with magnetic field is investigated numerically to examine the combined effects of rotation (Coriolis force), magnetic field and curvature (centrifugal force) on the flow. The curvature of the pipe has been assumed to be small, that is, the radius of the circle in which the central line of the pipe is coiled is large in comparison with the radius of the cross section. Spectral method is applied as a main tool for the numerical technique, where Fourier series, Chebyshev polynomials, Collocation methods, and Iteration method are used as secondary tools. The flow depends on the Taylor number (Tr), Dean Number (Dn), Magnetic Parameter (M) and the dimensionless curvature of the pipe δ. When Tr > 0, the rotation is in the direction so that the Coriolis force enforces the curvature effect. When Tr < 0, the rotation is in the direction so that the Coriolis force exhibits an opposite effect to that of the curvature. The calculations are carried out for −1500 ≤ Tr ≤ 1500, Dn ≥ 1000 (large Dean number), M ≥ 0 and δ = 0.01. Due to high magnetic field four-vortex solution is observed in a rotating curved pipe system. Visualization is attained with MAPLE software.

Exact Solutions of Electro-Osmotic Flow of Generalized Second-Grade Fluid with Fractional Derivative in a Straight Pipe of Circular Cross Section

Abstract The transient electro-osmotic flow of generalized second-grade fluid with fractional derivative in a narrow capillary tube is examined. With the help of the integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson-Boltzmann equation and the Navier-Stokes equation. It was shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The effects of retardation time, fractional derivative parameter, and the Debye-Hückel parameter on the generation of flow are shown graphically.

Study of Under Pressure Viscous Fluid Pulsating Flow in Cylindrical Pipe of Circular Cross-Section

Often due to the pressure gradient change in pressure systems the stationary flow pattern is disturbed initiating respective time-dependent change of hydraumechanical parameters at the cross-section. As a consequence of the pressure gradient change under the influence of varying friction and inertia forces unstable flow of fluid occurs. The study of this phenomenon presents important practical and theoretical interest.

Design, manufacture, and test of a prototype for a parabolic trough collector for industrial process heat

The manufacture of low-cost parabolic trough collectors (PTCs) for industrial process heat applications ranging from 70 to 250 °C is crucial for the widespread availability of this solar technology. Thus, we present a prototype of a PTC with a 90° rim angle and a small concentration ratio of 9.25 built in fiberglass and extruded polystyrene, called UNIVPM.01. Fiberglass is used as the external shell and extruded polystyrene as the inside fill component. The receiver is an aluminum pipe of circular cross-section, contained within a low-iron glass envelope. The tracking system is based on a solar-position computer program. The main features of this prototype are its cost-effectiveness, low weight, high mechanical resistance, and ease of manufacture. First, we show the design and manufacturing process in detail. Then, we describe the test bench used to evaluate the collector thermal efficiency. Tests were performed following the directives of ASHRAE Standard 93-2010 and using demineralized water for temperatures up to 85 °C. Results show that the equation for thermal efficiency is comparable to that of other similar collectors available in the literature: the intercept is 0.658 and the slope is −0.683.

Transient electro-osmotic flow of generalized Maxwell fluids in a straight pipe of circular cross section

Abstract The transient electro-osmotic flow of a generalized Maxwell fluid with fractional derivative in a narrow capillary tube is examined. With the help of an integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson-Boltzmann equation and the Navier-Stokes equation. It was shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The effects of relaxation time, fractional derivative parameter, and the Debye-Hückel parameter on the generation of flow are shown graphically and analyzed numerically. The velocity overshoot and oscillation are observed and discussed.

Numerical modeling for stratified gas–liquid flow and heat transfer in pipeline

A numerical three-dimensional non-isothermal hydrodynamic and thermal modeling based on the unidirectional flow analysis of stratified flow in the circular cross section pipe is developed and tested by experimental data. The model could solve the steady axial momentum equation and heat transfer equation with a low Reynolds number k∼ε model of turbulence for the eddy viscosity. Due to irregular geometry of stratified pipe flow, the equations of the problem are based on a bipolar coordinate system. Grid refinement near the interface and pipe wall is respectively used for an accurate solution near the boundaries. The model is capable of determining pressure drop and liquid height. In addition, wall and interface shear stress, flow field and temperature field for both phases could be predicted successfully. The predicted data of pressure drop, liquid holdup and velocity profile by the model fit well with some available experiment data and one-dimensional model. And the energy equation is solved, and temperature distribution is gained over the flow and compared well with experimental results. In conclusion, the model could have a practical application for estimation of hydrodynamics and thermodynamics in a pipeline.

DOMINANT CONTRIBUTION OF DIPOLES IN THE TURBULENCE-GENERATED NOISE

A problem of noise generation by a compact region of turbulence in an infinite straight immovable rigid-walled pipe of circular cross-section is solved by the Green’s function technique and the normal mode method. A turbulence region is modeled by quadrupoles and dipoles. The cases of homogeneous and non-homogeneous turbulence are considered. The generated noise power is shown to be a sum of powers of the pipe acoustic modes. The acoustic mode power consists of the three parts. The first part is the power generated by the quadrupoles, the second one results from the dipoles, and the third one is due to interaction of the quadrupoles and dipoles. Also, a particular case of the problem is considered. In this case the situation is studied when the generated noise field is dominated by the contribution made by surface dipoles. Those flows and shapes of the local pipe narrowing are of concern, that result in large or small eddies distributed uniformly in the turbulence region behind the narrowing. The corresponding simplified expressions for the generated noise power are obtained in the considered cases. Also, estimates of these expressions are carried out for the characteristic scales in the turbulence region. ых диполей. При этом интерес представляют такие потоки и формы локальных сужений труб, при которых регион турбулизированного сужением течения занимают равномерно распределенные большие или малые вихри. Для этих случаев получены соответствующие упрощенные выражения для мощности сгенерированного шума и проведены их оценки для характерных масштабов в области турбулентности.

Transient electro-osmotic flow of Oldroyd-B fluids in a straight pipe of circular cross section

The transient electro-osmotic flow of viscoelastic fluids in a narrow capillary tube is examined. With the help of integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson–Boltzmann equation and the Navier–Stokes equation. It is shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The results of classical fluid, i.e., Newtonian fluid and those of Maxwell fluid and the second grade fluid can be obtained as the special cases of the results in present study. The effects of relaxation time and retardation time on the velocity profiles are analyzed numerically. It is pointed out that the electro-osmotic flow of viscoelastic fluids is more difficult to achieve the steady state.

Prediction of turbulent particle-laden flow in horizontal smooth and rough pipes inducing secondary flow

The present paper is concerned with numerical simulations of pneumatic conveying in pipes of circular cross-section. Based on an Euler–Lagrange approach relying on the large-eddy simulation technique for the fluid flow and a particle tracking scheme accounting for all relevant elementary processes (particle rotation, transverse lift forces, inter-particle collisions, particle–wall collisions with smooth and rough walls, coupling between phases) several cases are analyzed in detail to elucidate the origin of secondary flow structures in the pipe cross-section. A smooth glass pipe and a rough steel pipe are taken into account at two different mass loadings considering a polydisperse size distribution with a number mean diameter of about 40μm mimicking the corresponding reference experiment. After a detailed validation of the single-phase as well as the two-phase flow based on experimental and DNS data, the secondary flow structures are analyzed qualitatively and quantitatively. That confirms recently published experimental results that the secondary flow observed is of second kind. Finally, to prove that for another particle size distribution numerically investigated in the literature the secondary flow is still of second kind, rather large monodisperse inertial particles (134μm) hitting the pipe walls with two different roughnesses are additionally simulated. The strength of the secondary flow is found to be strongly reduced for these cases compared with the polydisperse smaller particles, but the mechanism responsible for the secondary flow is the same.

Optimization of the heat exchanger in a flat plate indirect heating integrated collector storage solar water heating system

Due to the environmental impact of energy usage, consumers need to be encouraged to use renewable energy sources such as solar energy. The indirect heating flat plate integrated collector storage solar water heating system is one of the compact systems for domestic water heating. It incorporates the collection of a solar energy component and a hot water storage component in one unit. The objectives of this study were to investigate the effect of different parameters on the thermal performance of this system with the aim of reducing both the initial and the running costs. The outlet service water temperature was used as a measure of performance, because it is an indicator of the energy acquired from the solar radiation. The continuity, momentum and energy equations of the fluids involved in the system were numerically solved in a steady state condition, using FLUENT software. Three-D CFD models were developed and validated using previous experimental results. A standard k–ω turbulent model was used in the optimization of the heat exchanger because it produced good agreement with the experimental results. The surface-to-surface radiation model was included. The effect of single and double row heat exchangers with different lengths was investigated. Circular and elliptic cross-section pipes were also examined. Mass flow rates of 500 and 650 L/h were chosen. The results showed that the single row HX of 10.8 m length for both the elliptical and type B tube gave high service water outlet temperature (acceptable for heat exchanger design) and with low pumping power. This resulted in an increase in the thermal efficiency and a significant reduction in both the initial and the operating costs of the system.

GREEN'S FUNCTION OF THE CONVECTIVE WAVE EQUATION FOR THE RIGIDWALLED PIPE

Green’s function of the three-dimensional wave equation for an infinite straight rigid-walled pipe of circular cross-section with mean flow is found. This function is written in terms of the series of the pipe acoustic modes, and is periodic in the azimuthal coordinate and symmetric about the pipe axial section of the unit point impulse source location. Each term of the series is a sum of the direct and reverse waves propagating in the corresponding pipe mode downstream and upstream of the noted source. In the found Green’s function, the mean flow effects are reflected in the direct manner. The effects become more significant as the flow Mach number increases, causing, in particular, the appearance and further growth of the function asymmetry about the pipe cross-section of the source location. And vice versa, the decrease of the Mach number results in the decrease of the ef-fects and, in particular, the decrease of the indicated asymmetry of the function. In the case of mean flow absence the obtained Green’s function is symmetric about the indicated cross-section and coincides with the corresponding Green’s function for the investigated pipe, which is available in the scientific literature.

Graetz problem with non-linear viscoelastic fluids in non-circular tubes

A numerical investigation of the Graetz problem in straight pipes of circular and non-circular cross-sections is carried out to analyze the influence of the rheological parameters on the heat transfer enhancement with negligible axial heat conduction and viscous dissipation for a class of non-linear viscoelastic fluids constitutively represented by the simplified Phan-Thien–Tanner (SPPT) model. The analysis considers both constant wall heat flux and constant wall temperature thermal boundary conditions and concludes that the combined elastic and shear-thinning effects represented by the parameter ɛWe2 lead to heat transfer enhancement for low values of the parameter of order O(1) whereas values of the parameter ɛWe2 > O(10) lead to a decrease in the heat transfer rate in the case of constant wall heat flux. Nusselt number distributions in the entrance region of tubes of equilateral triangular, square and rectangular cross-sections as well as Nusselt numbers Nu = f(ɛWe2) for the fully developed flow in these non-circular tubes are reported for the first time for non-linear viscoelastic fluids of the SPPT type. It is concluded that for small values of elasticity (We), the computations based on the methods included in the Polyflow software are in full agreement with analytical results when available and that discrepancies exist for high values of We. Such limitations may not exist with pseudo-spectral methods.