Showing papers on "Pipe flow published in 1973"

On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug

Abstract: Conditionally sampled hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence. The pipe was smooth and carefully aligned so that turbulent slugs appeared naturally at Re > 5 × 104. Transition could be initiated at lower Re by introducing disturbances into the inlet. For smooth or only slightly disturbed inlets, transition occurs as a result of instabilities in the boundary layer long before the flow becomes fully developed in the pipe. This type of transition gives rise to turbulent slugs which occupy the entire cross-section of the pipe, and they grow in length as they proceed downstream. The leading and trailing ‘fronts’ of a turbulent slug are clearly defined. A unique relation seems to exist between the velocity of the interface and the velocity of the fluid by which relaminarization of turbulent fluid is prevented. The length of slugs is of the same order of magnitude as the length of the pipe, although the lengths of individual slugs differ at the same flow conditions. The structure of the flow in the interior of a slug is identical to that in a fully developed turbulent pipe flow. Near the interfaces, where the mean motion changes from a laminar to a turbulent state, the velocity profiles develop inflexions. The total turbulent intensity near the interfaces is very high and it may reach 15% of the velocity at the centre of the pipe. A turbulent energy balance was made for the flow near the interfaces. All of the terms contributing to the energy balance must vanish identically somewhere on the interface if that portion of the interface does not entrain non-turbulent fluid. It appears that diffusion which also includes pressure transport is the most likely mechanism by which turbulent energy can be transferred to non-turbulent fluid. The dissipation term at the interface is negligible and increases with increasing turbulent energy towards the interior of the slug.Mixed laminar and turbulent flows were observed far downstream for \[ 2000 < Re < 2700 \] when a large disturbance was introduced into the inlet. The flow in the vicinity of the inlet, however, was turbulent at much lower Re. The turbulent regions which are convected downstream at a velocity which is slightly smaller than the average velocity in the pipe we shall henceforth call puffs. The leading front of a puff does not have a clearly defined interface and the trailing front is clearly defined only in the vicinity of the centre-line. The length and structure of the puff is independent of the character of the obstruction which created it, provided that the latter is big enough to produce turbulent flow at the inlet. The puff will be discussed in more detail later.

The origin of secondary flow in turbulent flow along a corner

Abstract: The mechanisms which initiate secondary flow in developing turbulent flow along a corner are examined on the basis of both energy and vorticity considerations. This is done by experimentally evaluating the terms of an energy balance and vorticity balance applied to the mean motion along a corner bisector. The results show that a transverse flow is initiated and directed towards the corner as a direct result of turbulent shear stress gradients normal to the bisector. The results further indicate that anisotropy of the turbulent normal stresses does not play a major role in the generation of secondary flow. Possible extensions of the present results to other related flow situations are ahstrated and discussed.

Experimental investigation on secondary currents in the turbulent flow through a straight conduit

Abstract: In continuation to an earlier publication, experiments have been made in the turbulent flow through a conduit of rectangular cross-section with large aspect ratio. One of the long walls has been made rough, except for a strip, located centrally. As shown in the earlier paper, secondary currents will occur in the regions of transition from smooth to rough wall-condition. The main purpose of the investigation was to check the admissibility of the simplifying assumptions made to the mechanical-energy balance equation. The results of the measurements indeed justified the neglect of unimportant terms of this equation, leading to the following rule. When in a localized region the production is much greater (smaller) than the viscous dissipation, there must be a secondary current that transports turbulence-poor fluid into (outwards) this region and turbulence-rich fluid outwards (into) the region.

Parametric analysis of turbulent wall jets in still air.

Abstract: An examination has been made of all the data available on incompressible (nominally) plane wall jets in still air, supplementing these when necessary with some additional measurements. For a wall jet in still air, the chief mean flow qualities of interest are the maximum velocity, the inner length scale, and a total thickness, in addition to the wall stress. On the basis of the analysis, a (nominally) plane wall jet flow can be divided into an initial region, a fully developed flow region, and a confined wall jet flow region.

Energy Losses at 90° Pipe Junctions

Abstract: The loss coefficients and the power-loss coefficients for four smooth tees with diameter ratio of unity were determined experimentally for each of all configurations of flow through tees. Throughout the test the Reynolds number before the division or after the combination of flow was within the range of 10\u5–2x10\u5. The radius of curvature of the wall at the joining edge ranged from zero up to half the diameter of the straight pipe. Empirical formulas for loss coefficients and those for power-loss coefficients which are in good agreement with experiments were presented for each configuration of flow. Empirical formulas for loss coefficients for dead end tees were also given. The comparison of the proposed formulas with the experimental results of the previous investigations showed that the proposed formulas can be used to reliably estimate the energy losses at tees.

Experiments on swirling turbulent flows. Part 1. Similarity in swirling flows

Abstract: The effects of swirl on internal turbulent flows are studied by conducting experiments on turbulent pipe flow with variable initial swirl. This first part of the study is primarily concerned with similarity laws. The mean velocity profiles, both away from and close to the wall, are found to admit similarity representations at sufficiently large Reynolds numbers, provided that flow reversal does not take place near the entrance. While the wall law is not sensibly dependent on swirl, the velocity defect law in its extended form is sensitive to swirl. Further, a logarithmic skin-friction law is obtained in which only the additive coefficient depends on swirl. This coefficient is found to vary linearly with the swirl angle in the range of the present experiments.

Friction Factor and Reynolds Number in Porous Media Flow

Abstract: The concept of hydraulic radius of pore space is used to substantiate that the square root of the permeability is the important length parameter in defining the friction factor and Reynolds number in flow through porous media. Hydraulic radius was defined by applying the Kozeny-Carman theory of hydraulic radius of pore space. It was found that various porous media had different relationships between friction factor and Reynolds number. Experimental results showed a similarity to the Moody diagram used for pipe flow, with a ratio of particle mean diameter to the mean hydraulic radius of pore spaces as the third parameter.

Spectral measurements of turbulent momentum transfer in fully developed pipe flow

Abstract: Measurements of the spectral components of turbulent momentum transfer for fully developed pipe flow are presented. The results indicate that near the wall (y+ < 15) two types of momentum transfer processes occur. A net positive transfer takes place in the higher frequency range of the energy-containing part of the turbulence spectrum whereas a net negative transfer returns low momentum to the wall region at the lower end of the spectrum. Examination of the turbulence at various y+ shows that the significant features of the turbulence spectra scale on frequency at any given Reynolds number, thus leading to an interpretation of the flow structure which is consistent with the hydrogen-bubble visualization data of Runstadler, Kline & Reynolds (1963). The results are consistent with a flow model in which disturbances extend from the sublayer to the core of the flow. Recent turbulent heat transfer measurements are also interpreted successfully by this model.

A model of flow separation at a free surface

Abstract: Study of flow separation which can be observed at the leading edge of a spilling breaker of 'white-cap', at the lower edge of a tidal bore or hydraulic jump and upstream of an obstacle abutting a steady free-surface flow. At the point of flow separation there is a discontinuity in the slope of the free surface. The flow upstream of this point is relatively smooth; the flow downstream of the discontinuity is turbulent. A local solution for the flow in the neighborhood of the discontinuity is derived. The turbulence is represented by a constant eddy viscosity, and the tangential stress across the interface between the laminar and turbulent zones is expressed in terms of a drag coefficient.

Cavitation and Size Scale Effects for Orifices

Abstract: Cavitation data are presented for circular sharp-edged orifices which identify incipient, critical, moderate, heavy, and choking cavitation. The experimental program included pipe sizes from 1 to 23.5 in. (25 to 597 mm), pressures from 20 to 200 psi (140 to 1,400 kn/m²), and orifice size ratios from β = 0.332 to 0.884. Incipient and critical cavitation are affected by pipe size but are independent of pressure and velocity. Choking cavitation is independent of pressure, velocity, and size. An accelerometer was used to evaluate incipient and critical limits. Moderate and heavy cavitation regions were selected by aural observations. Choking flow was identified as the flow condition where the discharge coefficient began to rapidly decrease.

Computer Programming for Flow over Side Weirs

Abstract: A procedure is presented for computing water surface profiles and discharge in an open channel with flow over side weirs. There is little restriction about the channel shape, variation of invert slope, convergence of the channel along the length of weir, etc. A criterion for determining whether flow will be subcritical or supercritical on a mild slope is also developed. The procedure is illustrated by some examples. Some deficiencies in available knowledge are noted.

Friction--frequency dependence for oscillatory flows in circular pipe

Abstract: Measured data of velocity changes in oscillatory flows (0.16Hz-0.36Hz) are presented. The actual wall shear stresses obtained from the measurements are compared to calculated values based on steady flow relations and Zielke's model. A new model for the prediction of the wall shear stress as function of velocity and acceleration changes is introduced. The proposed model may be a suitable basis for the prediction of friction data for one-dimensional flow analysis under nonsteady conditions.

Characterization of drag reduction and degradation effects in the turbulent pipe flow of dilute polymer solutions

Abstract: Turbulent drag reduction data were obtained at Re = 9000 in a 0.62-cm-I.D. pipe for five Polyox compounds covering a wide range of molecular weights. The concentration dependence of drag reduction was shown to obey an improved form of Virk's drag reduction equation, which was previously applied only to flows in capillary tubes. The efficiency of the drag-reducing polymer additives on a unit concentration basis at infinite dilution was determined by using a characteristic parameter, DRm/[c], for each compound. A linear relationship was found to exist between this parameter and polymer molecular weight. The polymer degradation data were analyzed through use of a variable related to the dissipated energy in the wall region. The polymer molecular weight was found to decrease as a hyperbolic function of the dissipated energy function. By examining the change of molecular weight with respect to this function, a degradation index characteristic of the entire Polyox polymer family was established. This index may be of general application and provide a method by which the shear stability of various species of drag-reducing polymers may be meaningfully compared.

Base pressure in laminar supersonic flow.

Abstract: An asymptotic description is proposed for supersonic laminar flow over a wedge or a backward-facing step, for large Reynolds number and for a base or step height which is small compared with the boundary-layer length. The analysis is carried out for adiabatic wall conditions and a viscosity coefficient proportional to temperature. In a particular limit corresponding to a very thick boundary layer, a similarity law is obtained for the base pressure. For a thinner boundary layer an asymptotic form for the base pressure is obtained which shows the dependence on the parameters explicitly and which permits good agreement with experiment. This latter result is based on an inviscid-flow approximation for the corner expansion and for reattachment with viscous forces important primarily in a thin sublayer about the dividing streamline. A prediction of the pressure distribution at reattachment is given and the result is compared with experimental pressure distributions.

Method and apparatus of determining the density, velocity and viscosity of following fluids

Abstract: A method and apparatus for continuously and simultaneously determining the density, velocity and Fanning friction factor, and thus the viscosity, of a flowing fluid The fluid is caused to flow through a conduit having a curved portion Pressure transducers positioned in the curved portion of the conduit determine the difference in pressure between the fluid adjacent the inside and the outside of the curved portion of the conduit Additional pressure transducers are positioned in the conduit at selected, equal distances upstream and downstream of the transducers located in the curved portion of the conduit The differences in pressure in the fluid between these upstream and downstream locations and between the upstream and downstream locations and the curved portion of the conduit are determined These pressure determinations are utilized in equations according to this invention to determine the desired parameters of density, flow velocity and viscosity

Effect of subsonic inlet lip geometry on predicted surface and flow mach number distributions

Abstract: The effect of subsonic inlet lip geometry on predicted surface and flow Mach number distributions is illustrated. The theoretical results were obtained from incompressible potential flow calculations corrected for compressibility. The major emphasis of this investigation is on the low-speed (takeoff and landing) operating conditions. The low-speed results were obtained for a range of three geometric variables of interest: contraction ratio, defined as the ratio of highlight area to throat area; internal lip major - to minor-axis ratio; and internal lip shape. The low-speed results were obtained at both static conditions and a free-stream velocity of 42.6m/sec, with incidence angles ranging from 0 deg to 50 deg. The results indicate that of the three geometric variables considered, contraction ratio had the largest effect on the surface Mach number distributions. The effects of inlet diameter ratio and blunting of the external forebody on maximum external surface Mach numbers are illustrated at a cruise Mach number of 0.8.

Spiral flow in a porous pipe

Abstract: The equations developed by Prager for fully developed laminar flow with swirl in a porous pipe have been solved numerically. A complete description of the solutions is presented using graphs of the skin‐friction and the velocity profiles.