Straight Pipe Of Circular Cross Section Research Articles

An explicit representation for mean profiles and fluxes in forced passive scalar convection

We derive explicit formulae for the mean profiles of passive scalars (either temperature or concentration of a diffusing substance), and their respective wall fluxes (either heat or mass fluxes), in forced turbulent convection, as a function of the Reynolds and Prandtl numbers. Direct numerical simulation data for turbulent flow within a smooth straight pipe of circular cross-section, at friction Reynolds number ${{Re}}_{\tau }=1140$ , in the range of Prandtl numbers from ${{Pr}}=0.00625$ to ${{Pr}}=16$ , are used to infer the proper analytical form of the eddy diffusivity. This is leveraged to derive accurate predictive formulae for the mean passive scalar profiles, and for the corresponding logarithmic offset function. Asymptotic scaling laws result for the thickness of the conductive (diffusive) layer, and for the Nusselt number, which significantly extend the predictive envelope of classical formulae.

Prandtl number effects on passive scalars in turbulent pipe flow

We study the statistics of passive scalars (either temperature or concentration of a diffusing substance) at friction Reynolds number ${Re}_{\tau }=1140$ , for turbulent flow within a smooth straight pipe of circular cross-section, in the range of Prandtl numbers from ${Pr}=0.00625$ , to ${Pr}=16$ , using direct numerical simulations (DNS) of the Navier–Stokes equations. Whereas the organization of passive scalars is similar to the axial velocity field at ${Pr} = O(1)$ , similarity is impaired at low Prandtl number, at which the buffer-layer dynamics is filtered out, and at high Prandtl number, at which the passive scalar fluctuations become confined to the near-wall layer. The mean scalar profiles at ${Pr} \gtrsim 0.0125$ are found to exhibit logarithmic overlap layers, and universal parabolic distributions in the core part of the flow. Near-universality of the eddy diffusivity is exploited to derive accurate predictive formulas for the mean scalar profiles, and for the corresponding logarithmic offset function. Asymptotic scaling formulas are derived for the thickness of the conductive (diffusive) layer, for the peak scalar variance, and its production rate. The DNS data are leveraged to synthesize a modified form of the classical predictive formula of Kader & Yaglom (Intl J. Heat Mass Transfer, vol. 15, 1972, pp. 2329–2351), which is capable of accounting accurately for the dependence on both Reynolds and Prandtl numbers, for ${Pr} \gtrsim 0.25$ .

One-point statistics for turbulent pipe flow up to

We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$ , which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$ , which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$ , as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

Low-Reynolds-number effects derived from direct numerical simulations of turbulent pipe flow

Fully developed, statistically steady and non-swirling turbulent flow through straight pipes of circular cross-section is investigated by means of direct numerical simulation. A finite-volume scheme of second-order accuracy and a semi-implicit time integration scheme of the same order of accuracy are used to integrate the incompressible Navier–Stokes equations on staggered grids. Significant low-Reynolds- number effects are observed in the mean axial velocity, the components of the Reynolds stress tensor, the pressure and vorticity fluctuations, the turbulent kinetic energy budget and two-point velocity correlations. It is confirmed that turbulence data obtained in the near-wall region do not scale on wall variables. Within the range of Reynolds numbers investigated, the non-dimensional streak spacing increases slightly with Re τ .

Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics

The nonlinear, three-dimensional Euler equations can be reduced to a simple linear equation when the flow has helical symmetry and when the flow consists of a rigidly rotating basic part plus a Beltrami disturbance part (with vorticity proportional to velocity or a slight generalization of this). Solutions to this linear equation represent steadily rotating, non-axisymmetric waves of arbitrary amplitude. Exact solutions can be constructed in the case of flow in a straight pipe of circular cross-section. Analogous results are obtained for the incompressible, non-dissipative equations of magnetohydrodynamics. In addition to a rigidly rotating basic flow, there may exist a toroidal magnetic field varying linearly with radius.

The flow of dilute aqueous solutions of macromolecules in various geometries: VI. Properties of the solutions

For pt.V see ibid., vol.9, p.1967 (1976). The flow of dilute aqueous solutions of polyacrylamide (PAM-P250), of polyethylene oxide (PEO-WSR301), and of 'Kelzan' has been studied in straight pipes of circular cross-section, in bent pipes, between concentric rotating cylinders, and in porous beds. Results and their various speculative interpretations are collated and discussed. Viscosities as determined in an Ostwald viscometer, at 15-35 degrees C, were used to characterise the solutions. Values are consistent with views that PAM and PEO occupy flexible spherical shapes between 15 and 35 degrees C, whereas Kelzan is a semi-rigid elongated molecule which is becoming more flexible as temperature increases. Shear thickening of PAM solutions occurs as the Deborah number approaches unity. Values of the material constants of the second-order and third-order fluids are obtained from the stability of Couette flow and from draft reductions in bent pipes. Molecular processes are discussed.

The flow of dilute aqueous solutions of macromolecules in various geometries. II. Straight pipes of circular cross-section

For pt.I see ibid., vol.9, no.5, p.721 (1976). The effect of traces of macromolecular additives on the stability of laminar flow has been studied in pipes of radii 0.85, 0.88, 1.60, 2.00, 2.20, 2.70, and 3.00 mm at temperatures ranging from 15-35 degrees C. Drag reduction in fully-developed turbulence and pressure fluctuations during the transition from laminar to turbulent flow have also been studied. Most experiments have been done with 250 ppm polyacrylamide solutions. Drag reduction occurred whether or not the stability was affected, the amount increasing the decreasing pipe diameter. Both the amount of destabilization (or stabilization as the case may be) and the amount of drag reduction decreased as the temperature was increased. It might be concluded that the factors affecting drag also affected the stability. Pressure fluctuations were least in the solution when the flow was destabilized and most when it was stabilized. A phenomenological theory involving known molecular properties is put forward to account for the results.

The flow of dilute aqueous solutions of macromolecules in various geometries. I. Introduction

Aqueous solutions of polyacrylamide, polyethylene oxide and 'Kelzan' (Xanthan gum, a polysaccharide) have been studied in flow through straight pipes of circular cross-section, through bent pipes of circular cross-section, through porous media and in the annular gap between rotating concentric cylinders. The objectives of the work are described. A summary of the behaviour of macromolecules in solution and details of their structure are also given; these will be used in subsequent discussion to form phenomenological theories.

Unsteady elastico-viscous flow in a rotating pipe

An analysis is presented of incompressible flow in a straight pipe of circular cross-section, rotating about an axis perpendicular to its length, under the influence of a periodic pressure gradient. It is shown that the secondary axial velocity along the pipe is comprised of a steady part and an unsteady part oscillating at twice the frequency of the applied pressure gradient. Of particular interest is the steady component of velocity for which it is shown that, at high frequencies, a reversal of drift in certain regions can be induced.

Numerical solutions of some unsteady flows of elastico-viscous liquids

Consideration is given to the rectilinear flow of anOldroyd model fluid in a straight pipe of circular cross-section. A numerical solution of the full non-linear equations is obtained without the necessity for a perturbation analysis in terms of some small parameter. Results are presented for a number of different flow conditions.

Fluidic detection of large particles embedded in a confined turbulent flow field

Pressure changes in a straight pipe of circular cross-section caused by the existence of a spherical object have been investigated. The pressure drop can be predicted based on the Reynolds number for fully developed turbulent flow conditions and the diameter ratio of the spherical object and the pipe. Standard fluidic devices can be attached to the pipe for detection and monitoring purposes as the spherical objects pass.

Developing laminar flows with visco-elastic and non-Newtonian liquids

Developing laminar flows have been studied experimentally in straight pipes of circular cross-section. Velocity profiles have been measured and entry lengths determined for the transition from an initially flat profile to the equilibrium form: flow visualisation using fine tracer particles was the technique used. It has been found that non-Newtonian (pseudo-plastic) fluids have significantly longer development regions than those corresponding to dynamically similar Newtonian conditions. Viscoelastic liquids depart even more from the simple case. The experimental evidence seems to indicate that elastic effects influence the flow field at two differing time scales, not only where the process time is of the same order of magnitude as the natural (relaxation) time of the liquid but also in much slower processes.

Flow of Non-Newtonian Liquids under a Varying Pressure Gradient

IN papers presented at the 1968 autumn meeting of the British Society of Rheology and the Fifth International Congress on Rheology held at Kyoto, Japan, in 1968, we discussed the flow behaviour of non-Newtonian liquids in straight pipes of circular cross-section under the action of a pressure gradient P which varied sinusoidally about a non-zero mean. We considered a pressure gradient of the form where R denotes the “real part”. We were particularly interested in the relation between the mean pressure gradient and the mean flow-rate. In particular we showed theoretically that, for a fixed frequency n, one should expect an increase in mean flow-rate (for a given mean pressure p) for low mean pressures and a decrease in mean flow-rate at higher values of p. The theoretical predictions also indicated a “resonance” effect where quite large percentage increases in mean flow-rate could be expected in the low mean-pressure region.

Hydromagnetic Flow in a Rotating Straight Pipe

A theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight pipe of circular cross-section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it and also there is imposed a uniform magnetic field transverse to the motion. It is assumed for the purpose of mathematical analysis, the angular velocity about the axis of rotation, is small. A solution is developed by successive approximations in ascending powers of the Hartmann number, the first approximation corresponds to the non-magnetic case, formulated and discussed by Barua. The stream lines in the central plane and the projection of the stream lines on the cross-section of the pipe are compared with those in the non-magnetic case. An expression for the induced electric potential difference and sensitivity has been obtained.

Flow of elastico-viscous liquids in channels under the influence of a periodic pressure gradient, part 1

The flow of a non-Newtonian incompressible liquid in a straight pipe of circular cross-section under the influence of a periodic pressure gradient is investigated; the viscous and elastic properties of the liquid are defined in terms of a spectrum of relaxation times. Such a flow is of interest to the experimentalist, because the flow could be readily attained and controlled in practice. A solution is obtained which determines the variation in the mean-square velocity over the section of the pipe. In the numerical illustrations given, it is shown that the general nature of the flow is similar to that of a purely viscous liquid of constant viscosity, a high peak of average velocity occurring near the wall of the pipe. However, it is shown that elasticity of the type considered could strongly affect the value and position of this peak of the average velocity.

A note on the rectilinear flow of elastico-viscous liquids through straight pipes of circular cross-section

A note on the rectilinear flow of elastico-viscous liquids through straight pipes of circular cross-section

Secondary flow in a rotating straight pipe

When a straight pipe of circular cross-section through which liquid is flowing under a pressure gradient is rotated about an axis perpendicular to it, secondary motion is set up and the fluid particles move in spirals relative to the pipe. This secondary motion has been studied in detail and an expression for the consequent rise in the resistance coefficient has been obtained.

Stability of the Laminar Flow Through a Straight Pipe of Circular Cross-Section to Infinitesimal Disturbances Which are Symmetrical about the Axis of the Pipe

Stability of the Laminar Flow Through a Straight Pipe of Circular Cross-Section to Infinitesimal Disturbances Which are Symmetrical about the Axis of the Pipe

円管内の層流における熱傳達の理論に対する奇與(第1報)

円管内の層流における熱傳達の理論に対する奇與(第1報)

円管内の層流における熱傳達の理論に対する寄與(第2報)

円管内の層流における熱傳達の理論に対する寄與(第2報)