Equivalent Hydraulic Diameter Research Articles

Experimental Study of Differences in Single-Phase Forced-Convection Heat Transfer Characteristics between Upflow and Downflow for Narrow Rectangular Channel

The differences in the single-phase forced-convection heat transfer characteristics between upflow and downflow were investigated experimentally with a narrow vertical rectangular channel. The objectives of the experiment were to investigate in both laminar and turbulent flow regions the applicability of existing correlations to and the effects of buoyant force on the heat transfer characteristics in the narrow vertical rectangular channel, which is simulating a subchannel of 2.25 mm in gap and 750 mm in length in the fuel element of the research reactor, JRR-3 to be upgraded at 20 MWt. As the results, it was revealed that (1) by use of equivalent hydraulic diameter, existing correlations are applicable to a channel as narrow as 2.25 mm in gap for turbulent flow though the precision and critical Reynolds number are different among the correlations, and (2) in the laminar flow, the difference in heat transfer characteristics arises between upflow and downflow with Reynolds number less than about 700 and Grashof number larger than about 1,000, giving smaller Nusselt number for down-flow than for upflow as the effect of buoyant force. New heat transfer correlations for channel heated from both sides are proposed as lower limits for upflow and downflow, respectively, in the laminar flow.

Frictional Pressure Losses for Annular Flow of Drilling Mud and Mud-Gas Mixtures

The calculation of single-phase and two-phase flowing pressure gradients in a well annulus is generally based on an extension of empirical correlations developed for Newtonian fluids in circular pipes. Various techniques for extending pipe flow correlations to an annular geometry have been presented in the literature which involve the representation of the annular well geometry with an equivalent circular diameter and the representation of non-Newtonian fluid behavior with an apparent Newtonian viscosity. Unfortunately, little experimental data have been available which would allow a comparison of the relative accuracy of the various proposed techniques. In this study, experimental pressure gradient data have been taken in two 6000-ft wells. Frictional pressure losses for single-phase flow (mud only) in two annuli were compared to values predicted by the Bingham plastic and power law models. These calculations utilized the equivalent diameters defined by the Crittendon criteria, the hydraulic diameter, and the slot approximation. Also, total pressure difference for two-phase flow was measured for one annular geometry. This data was compared to that predicted by the Poettmann and Carpenter, Hagedorn and Brown, Orkiszewski, and Beggs and Brill correlations. Comparison of experimental data with the various prediction techniques was favorable, each having advantage in certain situations. For the data investigated, the Crittendon criteria using a Bingham plastic model gave the best results. The two-phase flow data was best predicted by the Hagedorn and Brown correlation utilizing an equivalent hydraulic diameter.

Experimental study of differences in single-phase forced-convection heat transfer characteristics between upflow and downflow for narrow rectangular channel.

The differences in the single-phase forced-convection heat transfer characteristics between upflow and downflow were investigated experimentally with a narrow vertical rectangular channel. The objectives of the experiment were to investigate in both laminar and turbulent flow regions the applicability of existing correlations to and the effects of buoyant force on the heat transfer characteristics in the narrow vertical rectangular channel, which is simulating a subchannel of 2.25 mm in gap and 750 mm in length in the fuel element of the research reactor, JRR-3 to be upgraded at 20 MWt. As the results, it was revealed that (1) by use of equivalent hydraulic diameter, existing correlations are applicable to a channel as narrow as 2.25 mm in gap for turbulent flow though the precision and critical Reynolds number are different among the correlations, and (2) in the laminar flow, the difference in heat transfer characteristics arises between upflow and downflow with Reynolds number less than about 700 and Grashof number larger than about 1,000, giving smaller Nusselt number for down-flow than for upflow as the effect of buoyant force. New heat transfer correlations for channel heated from both sides are proposed as lower limits for upflow and downflow, respectively, in the laminar flow.

Interpretation of moment measures derived from water‐lain sediments

ABSTRACT Although mean size provides a useful value for characterizing sediments, it is an inadequate expression of the interaction between sediments and hydraulic regimes and many authors have explored the significance of other statistical moment measures in different parts of the particle size spectrum. Few publications, however, have described such relationships over a very wide range of particle sizes. Using a combined data base (of marine and lacustrine sediments) we have been able to demonstrate the following:The distributions of standard deviation (and entropy) values are repeated in similar form on either side of the sand size class, describing mixtures between sands and gravel and sands and clay.Skewness is modified by the hydraulic response of the sediment and a skewness divide is present at about 2.7 φ, where it coincides with the minimum shear velocity required to initiate particle motion. This divide may be used to distinguish between high and low energy regimes.Kurtosis, like standard deviation, is a measure of the mixing of end member populations but it is more sensitive to changes in the tails of distribution curves. The maximum positive peak of kurtosis, at about 2.5 φ, lies close to the skewness divide (in our data).By using skewness/kurtosis plots it is possible to define separate field distribution for sediments which, to a greater or lesser degree, appear to conform to hydraulic equilibrium.By using sediments which are close to equilibrium (and lie at or close to our skewness/kurtosis boundary curves, it should be possible to define hydraulic shear velocities, at the time of formation. Values may be established by empirical relationships or by defining the break‐point (traction and intermittent suspension) between linear components of individual sample φ size/probability distribution plots. Such relationships should be enhanced by using hydraulic equivalent diameters instead of sieve diameters.In fine sediments, the use of fractional (silt: clay) ratios offers sensitivity at a level comparable to that of skewness/kurtosis plots and may be more easily computed.

Measurements and predictions of fully developed turbulent flow in a simulated rod bundle

Fully developed air flow has been investigated over a Reynolds-number range of 82800-346700 in a duct that simulates two interconnected subchannels of a rod bundle with a pitchldiameter ratio of 1.20. Based on equivalent hydraulic diameter, friction factors were found to be 2% lower than for pipe flow. Detailed measurements were made at a Reynolds number of 200000 of axial velocities, secondary velocities, and the Reynolds stresses. The distribution of axial velocity near the walls (normalized with the local friction velocity) could be expressed by an inner law of the wall for y+ up to 1500. Distributions of the normal Reynolds stresses and the mean turbulence kinetic energy were similar to those observed in a number of pipe and two-dimensional channel flows and could be correlated using the axial-velocity fluct,uations normalized with the local friction velocity. Maximum secondary velocities were about 1.5 % of the bulk axial velocity. The ‘k-ε’ turbulence model and an algebraic vorticity source for generating secondary velocities enabled the computation of axial velocities, secondary velocities, and mean turbulence kinetic energies that are in satisfactory agreement with those measured.

Flow regime boundaries for an interior subchannel of a horizontal 37‐element bundle

AbstractA needle contact probe system has been constructed and used to determine flow regime transitions for an interior subchannel in the upper half of a 37‐element horizontal bundle (to include the effect of gravity separation) for adiabatic air‐water flow. For the experimental range considered (up to ˜15.5 K*s−1, 50% quality), five distinct flow regimes were identified. Using the equivalent hydraulic diameter concept and cross‐sectional average superficial velocities, air quality and total mass flux, flow regime maps were constructed. These maps are shown to deviate from pipe flow regime maps. The stratified smooth flow regime was never observed at the lowest flow rate considered due to the periodical disturbance of the flow by the bundle end plates and mid‐plane spacers.

Measurements and prediction of fully developed turbulent flow in an equilateral triangular duct

Fully developed air-flows through an equilateral triangular duct of 12·7 cm sides were investigated over a Reynolds number range of 53 000 to 107 000. Based on equivalent hydraulic diameter, friction factors were found to be about 6% lower than for pipe flow. Mean axial velocity distributions near the wall were describable by the inner law of the wall (when based on local wall shear stress) but the constants differ slightly from those for pipe flow. As expected, the secondary flow pattern was found to consist of six counter-rotating cells bounded by the corner bisectors. Maximum secondary velocities of about 1 ½% of the bulk velocity were observed. The effects of secondary currents were evident in the cross-sectional distributions of mean axial velocity, wall shear stress and Reynolds stresses, and very prominent in the turbulent kinetic energy distribution. For the flow prediction, the vorticity production terms were expressed by modelling the Reynolds stresses in the plane of the cross-section in terms of gradients in the mean axial velocity and a geometrically calculated turbulence length scale. The experimental and predicted characteristics of the flow are shown to be in good agreement.

Wave and tidal current sorting of shelf sediments southwest of England

ABSTRACTThe relative roles of waves and tidal currents in transporting bottom sediment on the continental shelf off Lands End, southwest England, are evaluated by study of (a) sediment grain size in relation to boundary layer measurements in tidal currents, (b) regional variation in sediment parameters in relation to peak tidal and wave‐induced currents, and (c) visual observation of bedforms.(a) The sediments are mainly zoogenic sands. The average hydraulic equivalent median diameter is Mdφ=1.40φ (medium grade sand), and two‐thirds of the median grain sizes fall between 0.97φ and 1.83φ. The linear bottom current which will just move this range of sizes is exceeded only slightly by the highest tidal drag velocities Ū* measured in the area. Thus, sediment movement by tidal currents alone is restricted to areas of high bed roughness and strong peak tidal flows. In contrast, wave‐induced oscillatory currents at 100 m depth (typical of the area) attain sufficient speed to disturb the same particle sizes over 3% of the time. This includes storm periods when much greater velocities occur.(b) The average Mdφ of the sediment decreases southwest and northeast from south of the Lizard. This correlates well with the pattern of maximum tidal current speeds, suggesting that tidal currents control the areal distribution of sediment median grain size.Most sediments are well sorted (mean σi=0.48φ). Sorting improves at shallower depths but does not improve in areas of faster tidal currents, suggesting that wave‐induced currents exert the major control on sorting.Silt and clay proportions increase west of the Scilly Isles and are influenced by both wave and tidal currents.(c) Photographs and television pictures show that symmetrical bedforms due to wave action are dominant north and west of the western Channel. Asymmetric bedforms are more common in the western Channel itself, where tidal currents and bed roughness are both high.Results are used to construct a sediment transport model for the study area. Since medium grade well sorted sands occur in depths of over 100 m, many ancient, extensive, well sorted sand sheets may have been deposited at depths greater than previously suspected.

Airborne dust collections over the North Atlantic

Day-to-day airborne dust collections using the mesh technique on the bows of ships have been made across the temperate North Atlantic. In January 1969 the dust concentration (down to grain size of about 2-μ equivalent spherical diameter) was roughly constant at 0.003 μg/m3 air between Ireland and Newfoundland. In August 1969 the concentration was greater and varied between 0.003 at Ireland and 0.01–0.03 μg/m3 near Newfoundland. In the Bay of Maine the concentrations rise steeply, and off Cape Cod, if the exposure intersects a stream of black city pollution, it can rise to 4 μg/m3. All the dusts are gray to dark gray due to pollution by carbon and fly ash spherules. In the ≥3-μ size fraction, the spherules alone can be 60% of the sample when near the land; usually there are about 5% spherules in mid-ocean. The largest spherule seen (Bay of Maine) was 18 μ in diameter; in open ocean the spherules do not exceed 6 μ. Talc, especially abundant in the January collections, is noticeably present in the crystalline fraction of all samples. An estimation of air spreading across the ocean is attempted with the spherules used as tracers; a pollution stream increases its width fivefold in moving from Newfoundland to Ireland. Close to the West African coast, near Dakar, the concentration of red-brown dusts is 10 μg/m3 with grains ≥23 μ (hydraulic equivalent spherical diameter) contributing 0.1% of the total weight. At Barbados the corresponding size decreases to ≥11 μ with a marked fall in the percentage of quartz.

Friction Factors for Fully Developed Turbulent Flow in Ducts With and Without Heat Transfer

Tests were performed with water flowing vertically upward through a 0.087-in. × 1-in. × 27-in. long rectangular channel to determine friction factors with and without heat transfer. The following range of variables was covered: Mass velocities: 0.60 × 106 to 4.0 × 106 lbm/hr-ft2; Heat flux: 0 to 1.6 × 106 Btu/hr-ft2; Inlet temperature: 59 to 510 deg F; Pressures: 300 to 2000 psia. The isothermal data confirmed the use of the hydraulic equivalent diameter with the conventional circular tube friction factors for narrow rectangular channels at Reynolds numbers from 4 × 103 to 5 × 105. Using the results of the heated tests and the data existing in the literature, a general correlation was formulated which correlated the data for both water and air.

A General Correlation of Friction Factors for Various Types of Surfaces in Crossflow

Abstract This paper is the elaboration of an unpublished one by the late E. S. Davis and A. Y. Gunter, which was released only to the National Advisory Committee for Aeronautics. The present work, using the friction-factor correlation proposed for bare tubes by Davis and Gunter, demonstrates its merit as a general method for correlating on a single line, pure crossflow friction over both bare and extended surfaces. This result is made possible through the use of an equivalent volumetric hydraulic diameter Dv, in both the Reynolds number and the ordinate, plus configuration ratios of the form (Dv/ST)n and (SL/ST)n in the ordinate. Friction factors for bare tubes of diameters from 0.02 in. to 2 in. are included, with transverse and longitudinal pitches ranging from 1.25 to 5 diam. Extended-surface crossflow friction reported on herein covers external round and square cross fins, both meshed and unmeshed, finned cylinders, radiator core-type surface, and one sample of internal wire-mesh fins. It is shown that flat plates and core-type surface with turbulence promoters do not correlate well on the proposed curve.