Laminar Flow In Circular Pipe Research Articles

Pressure–flow rate relationship and its polynomial expansion for laminar flow in a circular pipe based on exponential viscosity-pressure characteristics: An extension of classical Poiseuille's law

Laminar flow in circular pipes is widespread in various fields. Poiseuille's law is the classical equation describing the pressure–flow rate relationship for laminar flow in circular pipes. However, the fluid viscosity is treated as a constant in Poiseuille's law. Therefore, Poiseuille's law cannot be used to accurately analyze fluids that have viscosities that vary exponentially with pressure, such as hydraulic oils and lubricating oils. In this study, with the exponential viscosity-pressure characteristics, a total of four simple and explicit equations are given for calculating the flow rate or pressure difference of the pipe, and corresponding polynomial expansions are derived based on the Taylor series. Experimental tests and computational fluid dynamics simulations are carried out to verify the correctness of the theoretical equations, with error of less than 6% and 2%, respectively. An error analysis of the theoretical equations for different numbers of polynomial terms is also performed. The results show that the proposed theoretical equations all degenerate to the classical Poiseuille's law when the number of polynomial terms is taken to be 1, and the relative errors are less than ±5% for viscosity changes less than 10%. When the number of terms is 2, the relative error is less than ±5% for viscosity changes less than 40%. In the calculation of connection pipelines of a deep-sea hydraulic actuator, the difference in pressure loss calculated with or without viscosity change is 31.47% and reaches up to 5.7202 MPa, which shows the practical value of this research in piping systems.

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.

Enhanced mixing by optimized streamwise and angular positioning of longitudinal vorticity

Streamwise vortices can be readily generated to enhance the mass and momentum transfer in continuous static mixers. The topology of these vortices is related to the shape and dimensions of the vortex generator (VG). It is essential to design the VG in such a way that the mass and momentum transfer are obtained for relatively small power dissipation. In the present paper, a streamwise and angular optimization study is performed for the passive scalar mixing enhancement downstream from rectangular wings inserted in a laminar circular pipe flow. The rectangular wing generates streamwise vortices which size is of the same order of the pipe radius. The optimal distance between two successive VGs is determined by analyzing the streamwise intensity of segregation and the pressure drop. The angular positioning of the vortices is also determined via local analysis of the scalar intensity of segregation. Such a study may be applied for other configurations of VGs where streamwise vorticity is used to enhance the mixing process in circular pipe flows.

Studying nanoparticle distribution in nanofluids considering the effective factors on particle migration and determination of phenomenological constants by Eulerian–Lagrangian simulation

In this study, concentration distribution was obtained for nanofluid laminar flow in circular pipe. The effects of viscosity gradient, shear rate and Brownian diffusion on particle migration were considered. One needs to determine the phenomenological constants in order to find the diffusion fluxes. The two-phase Euler–Lagrange method was used to find these constants, where gravity, drag, Saffman’s lift, Brownian and thermophoretic forces were considered. The constants are not much dependent on the concentration, but they change significantly by varying Peclet number. They increase with increasing Peclet number, which shows that at higher Peclet numbers, the effects of shear rate and viscosity gradient are intensified on particle migration. Meanwhile, by raising Peclet number, the role of shear rate becomes more pronounced in comparison with the viscosity gradient. At lower Peclet numbers with intensified effect of the Brownian diffusion, a more uniform concentration distribution was achieved. Moreover, the particles enlargement considerably intensifies the non-uniformity in concentration distribution. Furthermore, particle migration causes non-uniformity in the properties distribution and consequently reduces the thermal conductivity and viscosity adjacent to the wall due to lower concentration there. Thus, smaller pressure drop and heat transfer coefficient were obtained in comparison with the case of applying uniform properties.

A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids

In this work, we propose an approximate methodology to estimate the Nusselt number and friction factor in fully developed non-Newtonian laminar flow in circular pipes for a constant wall heat flux. The methodology was tested using several constitutive equations, including generalized Newtonian fluids and viscoelastic models such as the simplified Phan-Thien–Tanner (sPTT), Herschel–Bulkley, Bingham, Casson, and Carreau–Yasuda constitutive equations. The error of the approximate methodology was found to be smaller than 3.2%, except for the fluids with yield stress for which the maximum error increased to about 8% for the cases analyzed, which cover a wide range of shear viscosity curves.

Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles

Considering the non-uniformity of the flow velocity distribution in fluid-conveying pipes caused by the viscosity of real fluids, the centrifugal force term in the equation of motion of the pipe is modified for laminar and turbulent flow profiles. The flow-profile-modification factors are found to be 1.333, 1.015–1.040 and 1.035–1.055 for laminar flow in circular pipes, turbulent flow in smooth-wall circular pipes and turbulent flow in rough-wall circular pipes, respectively. The critical flow velocities for divergence in the above-mentioned three cases are found to be 13.4%, 0.74–1.9% and 1.7–2.6%, respectively, lower than that with plug flow, while those for flutter are even lower, which could reach 36% for the laminar flow profile. By introducing two new concepts of equivalent flow velocity and equivalent mass, fluid-conveying pipe problems with different flow profiles can be solved with the equation of motion for plug flow.

Estimation of Unknown Boundary Heat Flux in Laminar Circular Pipe Flow Using Functional Optimization Approach: Effects of Reynolds Number

An inverse forced convection problem was studied in this paper. The unknown space-dependent heat flux at the outer boundary of a circular pipe was identified from the temperature measurements within the flow using the algorithm based on an improved conjugate gradient method, which is a combination of the modified inverse algorithm proposed by Ozisik et al. (Huang and Ozisik, 1992, “Inverse Problem of Determining Unknown Wall Heat Flux in Laminar Flow Through a Parallel Plate Duct,” Numer. Heat Transfer, Part A 21, pp. 2615–2618) and the general inverse algorithm based on the conjugate gradient method. The effects of the convection intensity, the number of thermocouples, the location of the thermocouples, and the measurement error on the performance of the modified inverse algorithm method and the improved inverse algorithm were studied thoroughly through three examples. It is shown that the improved inverse algorithm can greatly improve the solution accuracy in the entire computation domain. The accuracy and stability of both the modified inverse algorithm method and the improved inverse algorithm are strongly influenced by the Reynolds number and the shape of the unknown heat flux. Those functions, which contain more high-frequency components of Fourier series, are more sensitive to the increase in the Reynolds number.

Instantaneous Liquid Flow Rate Measurement Utilizing the Dynamics of Laminar Pipe Flow

This paper deals with the utilization of the dynamic characteristics of laminar flow in circular pipes for the indirect measurement of flow rates. A discrete-time state space realization of the transmission line dynamics is computed via inverse Laplace transform and an identification and model reduction method based on the singular value decomposition. This dynamic system is used for the computation of the flow rate at one end of a pipe section. Special attention is paid to the identification of the speed of sound and the dimensionless dissipation number of the pipe section, since exact knowledge of these parameters is crucial for the reliability of the measurement results. First, experimental validation results are given in a limited range of operating frequencies between 100 Hz and 2000 Hz. Flow rate variations within ±1.2 l/min have been measured with an uncertainty of ±0.07 l/min at the 95% confidence level. The test fluid was mineral oil.

Effects of Velocity Distribution of Dialysate on Mass Transfer in the Shell Side of a Hollow-Fiber Dialyzer

The relation between mass transfer and flow characteristics in the shell side of a hollow-fiber dialyzer has not been investigated sufficiently because of the tangled flow path. In this paper, the effects of velocity distribution of dialysate on mass transfer in the shell side were investigated experimentally. In order to measure the velocity at various radial and axial positions of a dialyzer, cut dialyzers of various lengths were used. The velocity distributions over the section of the cut dialyzers were measured by means of the electro-chemical method. In addition, the concentration distribution at the cross section of the outlet of lumens of the hollow-fibers was measured when the deionized water and aqueous solution of potassium chloride were fed into a dialyzer countercurrently. Potassium chloride was taken up as a model of low molecular weight species in blood. The velocity was not constant over cross sections of the shell side and the concentration was distributed over the cross section of the outlet of the lumens of the hollow-fibers. These results showed that the mass transfer coefficient in the shell side was varied over the dialyzer. It was considered that the mass transfer coefficient at the local radial position should be discussed in order to make the transport process in the shell side clear. The correlation between the Sherwood number and the Reynolds number based on the velocity and the mass transfer coefficient at local radial positions of the shell side was made. The result of the correlation suggested that the transport process in the center region of the shell side was similar to that in a laminar circular pipe flow.

Optimising the quality of safe food: Computational modelling of a continuous sterilisation process

Continuous food sterilisation processes require that a given level of sterility is reached for minimal quality loss. Current designs are empirically based on ideas developed on batch systems, for processing at high temperature for short time (HTST). A computational model for continuous flow sterilisation has been used to test these assumptions. A model system for a laminar flow in circular pipes with uniform wall temperatures has been developed; both Newtonian and non-Newtonian viscosity models, (including temperature dependence) have been used. Temperature and velocity profiles have been modelled using a validated computational fluid dynamics (CFD) package. Results from the simulations have been used together with conventional food processing sterility and quality kinetics, adapted to the continuous flow case. Data from the model were used to study the efficiency of a continuous sterilisation process. Results have shown that the conservative approach used in the food industry can lead to significant overprocessing and thus unnecessary deterioration of the overall product quality. The conventional HTST assumption fails under some circumstances, for example when the fluid layer near the wall is overprocessed.

An analytical approach to fully developed heating of laminar flows in circular pipes

An analytical solution is proposed to predict the fully developed Nusselt number for laminar flow in circular pipes, as arising from exponential heating. The solution is obtained in terms of Confluent Hypergeometric Functions, characterized by fast convergence and easy implementation. Both positive and negative exponents are considered. The range of practical interest is discussed.

Reversal of laminar flow in a circular pipe

In the analysis of the loss of coolant accident (LOCA) in water reactors, the frictional resistance is treated in a one-dimensional sense using the quasi-steady state approximation for evaluation of the friction factor. The calculation has predicted one or more flow reversals. The present paper examines the limits of validity of the quasi-steady approximation by comparing with a new exact solution assuming no flow separation. Radial velocity distributions, mean flowrate and friction coefficients are compared for the specific case of a ramp change in pressure gradient including the limiting step. For low ramp rates with transient laminar flow in circular pipes the quasi-steady approximation is found valid; for high ramp rates the time to zero bulk flow is underestimated by 22.2%.

Heat transfer by magnetohydrodynamic laminar flow in circular pipe

This paper presents the influence of magnetic field on heat due to viscous and electrical dissipations for an incompressible, viscous, electrically conducting fluid through a circular pipe in the presence of an applied (transverse) uniform magnetic field. The walls of the pipe are assumed to be non-conducting and kept at uniform temperature gradient in one case and at a constant temperature gradient in another case. The heat equation governing the present problem is solved exactly in hypergeometric series. The temperature at the centre of the pipe Te, unweighted mean temperature Tm and weight mean temperature TM are calculated. The temperature profiles are shown graphically for different values of Hartmann number M, Brinkman number Br and a non-dimensional number S. Numerical calculations are made for the Nusselt number and are entered in the table.

Laminar Flow in Circular Pipes under the Effect of a Traveling Magnetic Field

The interaction between the flow of a conducting incompressible fluid in an infinitely extended circular pipe and the magnetic field created by an azimuthal traveling wave current sheet surrounding the pipe is studied. Only low magnetic Reynolds number flows are considered. Exact solutions for the magneticfield distribution are obtained. Closed form solutions for the laminar velocity profile are developed. The latter are used to examine the effect of the magnetic field on the friction coefficient and total energy balance. The solutions show that, for positive pressure gradients and strong magnetic fields, secondary flows appear. These flows have previously been observed experimentally. The solutions also show that the stabilizing effect of the magnetic field in general, depends on an equivalent Hartmann number—which is a function of the wavelength of the traveling wave—and on the difference between the wave velocity and the average fluid velocity.

On the Velocity Distribution and Pressure Gradient in the Inlet of a Circular Pipe

There are Schiller's and Boussinesq's solutions as mathematical solutions for the velocity distribution and pressure gradient in the inlet of a circular pipe for laminar flow. But they are not satisfactory solutions for over the total range of inlet length of laminar flow. We have operated, this calculation by the numerical solution which has often been used by Asawo. When this resultis compared with the Nikuradses experiment, these velocity distributions coincide over the total range except a particular part. Moreover we have got z/aK=0.24 as a inlet length of laminar flow in circular pipe, when we admit the error 1/200 as velocities and 1/100 as pressure gradients.