Flow In Straight Pipe Research Articles

Liquid metal flow through a thin walled elbow in a plane perpendicular to a uniform magnetic field

This paper presents analytical solutions for the liquid-metal flow through two straight pipes connected by a smooth elbow with the same inside radius. The pipes and the elbow lie in a plane which is perpendicular to a uniform, applied magnetic field. The strength of the magnetic field is assumed to be sufficiently strong that inertial and viscous effects are negligible. This assumption is appropriate for the liquid-lithium flow in the blanket of a magnetic confinement fusion reactor, such as a tokamak. The pipes and the elbow have thin metal walls. The flow tends toward the inside surface of the elbow, approaching a vortex about the center of curvature of the elbow. This flow migration away from the uniform fully developed flow in the pipes leads to voltage variations along the pipes. These voltage variations drive four electric current circulations in planes perpendicular to the magnetic field. These current circulations produce significant pressure variations in the cross sections of the pipes and elbow. A long length of pipe is required on both sides of the elbow for the completion of the circuits for these electric current circulations and for the decay of the disturbances to the fully developed flow in the straight pipes. All pressure drops and rises due to the three-dimensional electric current circulations cancel. The total pressure drop is the same as that for fully developed flow in a single straight pipe with the same length. While the analysis treats pipes and elbows with circular cross sections, the absence of a pressure drop in addition to that for fully developed flow is true for any smooth elbow.

Flow of Dilute Polymer Solutions Through Curved Pipes : 2nd Report, Pressure Loss in 360°Bends

Experiments on flows of water and dilute aqueous solutions of polyethylene oxide are carried out in the Reynolds number range of 103 to 5× 104. Concentration of polymer solutions is varied from 1ppm to 100ppm. The ratios of curvature radius to pipe radius, R/a, are 18.7, 34.3 and 47.3. Measured pressure distributions along a bend axis are classified in three types by their patterns. Flow property of each pattern is clarified by using the method of flow visualization. Drag reduction in a bend flow is smaller than that in a straight pipe flow. Pressure loss coefficients are correlated with the Reynolds number, the ratio of radius R/a and the Weissenberg number. The empirical formulas presented for the bend loss coefficient are useful from an engineering viewpoint.

Flow of dilute polymer solutions through curved pipes. 2nd report. Pressure loss in 360.DEG. bends.

Experiments on flows of water and dilute aqueous solution of polyethylene oxide are carried out over the Reynolds number range of 103 to 5×104. Concentration of polymer solutions is varried from 1 ppm to 100 ppm. The ratios of curvature radius to pipe radius R/a are 18.7, 34.3 and 47.3. Measured pressure distributions along a bend axis are classified in three types by their patterns. Flow property of each pattern is clarified by using the method of flow visualization. Drag reduction in bend flow is smaller than that in straight pipe flow. Pressure loss coefficients are correlated with the Reynolds number, the ratio of radius R/a, and the Wissenberg number. The empirical formulas presented for the bend loss coefficient are useful from an enginnering viewpoint.

Axi-Asymmetric Character of Turbulent Swirling Flow in Straight Pipe

Axi-Asymmetric Character of Turbulent Swirling Flow in Straight Pipe

Determination of two-stroke engine exhaust noise by the method of characteristics

A computational technique was developed for the method of characteristics solution of a one-dimensional compressible, unsteady flow in a duct as applied to the wave action in an engine exhaust system. By using the method it was possible to compute the detailed flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two-stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operating engine has been achieved in the calculation of both the third-octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of non-linear behaviour which results in wave steepening and shock wave formation. The calculation method developed differs from those of others, principally that of Blair and that of Karnopp, Dwyer and Margolis. Its essential feature is the computation of the precise paths on the x-t plane of a finite number of C+, C- and p characteristics, to provide high accuracy in determining the tailpipe outlet velocity and hence radiated noise. (Author/TRRL)

管内流れの予知─今と昔 : 直管内の流れを中心として

管内流れの予知─今と昔 : 直管内の流れを中心として

Determination of two‐stroke engine exhaust noise by the method of characteristics

A unique computational technique was developed for the method of characteristics solution of a one‐dimensional flow in a duct as applied to the wave action in an engine exhaust system. By using the method it was possible to compute the detailed unsteady flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two‐stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operating engine has been achieved in the calculation of both the third‐octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of nonlinear behavior which results in wave steepening and shock wave formation. The calculation method developed differs from those of others, principally that of Blair and that of Karnopp, Dwyer, and Margolis. The method computes the precise paths on the x−t plane of a finite number of C+, C−, and P characteristics, thereby obtaining high accuracy in determining the tailpipe outlet velocity and hence radiated noise.

Flow in Rotating Straight Pipes of Circular Cross Section

The friction factor for fully developed flow in smooth wall straight pipes of circular cross section rotating at a constant angular velocity about an axis perpendicular to its own has been measured in the Reynolds number range from 20 to 60,000. Empirical equations for friction factors for small values of RΩ/R were presented for both laminar and turbulent flow. In the case of laminar flow, an approximate analysis based on the assumption that the flow consists of a frictionless central core surrounded by a boundary layer was presented. The results were in good qualitative agreement with experimental results in regard to the friction factor, velocity distribution in the plane of symmetry and pressure distribution along the circumferential wall of the pipe.

Junction Losses in Laminar and Transitional Flows

Analytical and experimental studies were carried out to develop additional data on energy losses at a junction for systems operating in the Reynolds number range of between 10 and 10,000. The test pipe fittings were short-radius, galvanized screwed tees operated so as to produce both a combination and division of flow. The fittings were mounted in a 3/4-in. standard black iron pipeline with SAE No. 10 cylinder oil being circulated by a gear pump driven by a variable speed motor. The analytical phase of the program yielded fitting loss coefficients which can be used to estimate the energy loss due to the fitting over and above that due to straight pipe friction. It was concluded from an analysis of the results that the relationship between the loss coefficients and Reynolds number for pipe fittings can be represented by a family of curves similar in format to those of the Moody diagram for flow in straight pipes without fittings.

Solution of Problems Involving Grease Flow in Straight Pipe or Tubing

A SIMPLE method for solving problems involving steady flow of grease in pipes or tubing is being developed by the NLGI Subcommittee on Grease Dispensing in Central Systems. The method, based largely on a 1964 NLGI Annual Meeting paper, uses a graphical presentation of the Poiseuille equation for laminar flow. For this purpose, the Subcommittee has prepared charts that are direct reading in pressure drop and flow rate for pipe and tubing sizes commonly used in centralised systems and in transfer of grease from one point to another. The user of the charts must know the apparent viscosity characteristics of the particular grease of interest to him. When these data are plotted on the proposed NLGI chart as lines of shear stress vs. shear rate at constant temperature, various types of flow problems can be solved by drawing a few straight lines on the chart. Since the apparent viscosity is equal to the shear stress divided by the shear rate, the shear stress is found by multiplying each apparent viscosity value by its corresponding shear rate.

Laminar dispersion in capillaries: Part IV. The slug stimulus

AbstractAn exact analytical theory of the local behavior of finite slugs which are dispersed in three‐dimensional velocity fields is developed. It is shown that the dispersion coefficient enters the problem as an eigenvalue. For the important special case of fully developed straight pipe flow, considered first by Taylor and later generalized by Aris, the dispersion coefficient can be found very easily by the present method, which also provides the basis for studying a large class of more complicated problems.A detailed numerical analysis is carried out to determine the limits of applicability of the analytical theory. Fortunately, it is found that dispersion of slug stimuli in fully developed laminar tube flow is described by Equation (15) when τ exceeds certain minimum values which depend only weakly on Peclet number and are independent of slug length in the region considered here. Since peak mean concentrations are predicated accurately by Equation (19) for X > 0.1, this is a convenient quantity to use to determine dispersion coefficients experimentally.On comparing the numerical and analytical results for local point concentrations, good agreement is found, provided the average concentration is predicted accurately by Equation (15). This is significant because it implies that a broad class of difficult transient heat and mass transfer problems, with aperiodic inlet disturbances, can be solved by using superposition in conjunction with the present approach.

Study on forced convective heat transfer in curved pipes: (1st report, laminar region)

The theoretical study of fully developed laminar flow in a curved pipe gives a satisfactory result for resistance coefficient and heat-transfer coefficient in fully developed temperature field under the condition of uniform heat flux at large Dean numbers [= Re√( a/ R)]. The ratio of the Nusselt number for a curved pipe flow to that for a straight pipe flow is obtained as a function of Dean number and Prandtl number. As Dean number and Prandtl number increase, the effect of curvature on flow resistance and heat transfer increases, but the Nusselt number ratio approaches to the asymptotic value with the increasing Prandtl number. Experimental study is carried out for air flow in a curved pipe. The velocity and temperature distributions are measured and the Nusselt number ratio obtained by the experiments is shown to be in good agreement with that of the theoretical analysis.

The Calculation of Compressible Fluid Flow by the Use of a Generalized Entropy Chart

Calculations of the flow of gases in pipes or ducts of varying cross-sections are important in the design of turbines and compressors, nozzles for various applications, exhaust or radiator ducts, thrust augmenting devices, etc. Provided certain simplifying assumptions are made, there is no difficulty in writing down the basic equations, but when the velocities are comparable to that of sound and compressibility effects cannot therefore be neglected, the solution of the transcendental equations present difficulties which hinder a clear discussion of the physical phenomena. Here the problem is solved by the use of a generalized entropy chart, off which results may be directly read. For example, if the conditions in the reservoir from which the gas is assumed to be discharged are known, the complete conditions at any given cross-section may be read off when two parameters at the section considered are specified. The parameters may include the velocity, pressure, density, temperature, local Mach number, local velocity of sound, area of cross-section, mass flow per unit area, momentum per second, etc. The method is not confined to isentropic flows and may be applied to such problems as the flow in straight pipes or convergent and divergent nozzles including losses by either friction or condensation shocks. The co-ordinates of the chart are: dimensionless entropy σ = ( s— s0) J/R and dimensionless enthalpy ι = h/h0 = T/T0 where the meaning of the symbols is given later. All other variables are expressed in terms of these two co-ordinates and tables for several values of the ratio of specific heats are included to facilitate the drawing of such charts. The method does not aim at presenting new facts, but its usefulness lies in the provision of a comprehensive graphical means of calculating one-dimensional flow of compressible fluids. The charts lend themselves to the construction of a mechanical device for simplifying their use, such as a portable scale with sliding curves.

Concerning secondary flow in straight pipes

In this paper the condition for the existence of a secondary flow in a straight non-circular pipe is determined according to the modified vorticity transfer theory, with Goldstein's assumed form for the tensorIt is shown that a secondary motion arises if the mixture length is not constant on the curves along which | gradu| is constant,ubeing the velocity parallel to the pipe axis.In problems of turbulent flow treated by means of the modified vorticity transfer theory, the quantitywhereis the mean value of the square of the velocity fluctuation andpthe mean pressure, plays a part analogous to the pressure in laminar flow. In two-dimensional flow through a channel the theory shows the existence of a gradient ofacross the channel from the central plane to each wall. Qualitative arguments such as are used to explain the existence of a secondary flow for laminar motion in a curved pipe are applied here to show that a secondary flow is to be expected near the short sides in the turbulent flow through a straight rectangular pipe of large length/breadth ratio.The equations to determine the secondary flow through an almost circular elliptic pipe are discussed, the mixture length being assumed constant on ellipses similar to and concentric with the pipe section. For a first approximation the problem is reduced to the numerical solution of three simultaneous ordinary linear differential equations.

Experiments on stream-line motion in curved pipes

Author's previous Experiments .—In the paper read by the author on the “Flow of Water in Curved Pipes,” before the Royal Society on June 2, 1910, it was shown that even a small curvature in the length of a cylindrical pipe affected the quantity of flow of water through the pipe. The effect at velocities below the critical velocity for a straight pipe was most remarkable, inasmuch as the experiments showed that in coiled pipes there was apparently no critical velocity region, whilst in less pronounced curves, where the critical velocity is not entirely absent, a very slight sinuosity of the pipe lessened the flow. This was shown by the increase in the value of the index n in the formula, s = K v n / m from n = 1, for perfectly straight pipes, to n = 1·1 to 1·2 for pipes slightly curved or sinuous. Here s or h / l is the hydraulic gradient, v is the velocity of flow, m is the hydraulic mean radius, and K is a constant. In an attempt to discover the cause of this departure from the law of flow in straight pipes, the author had tried Prof. Osborne Reynolds’ colour-band test in a coiled glass tube, but the arrangements were of a primitive character and the results obtained were not decisive. At the suggestion of Sir Joseph Larmor the colour tests have been repeated with specially made glass tubes, in which the stream motion could be traced by the introduction of coloured water through capillary nozzles.