Experiments on the pressure drop created by a sphere settling in a viscous liquid. Part 2. Reynolds numbers from 0·2 to 21,000

1968 ◽  
Vol 32 (4) ◽  
pp. 705-720 ◽  
Author(s):  
Guili A. Feldman ◽  
Howard Brenner
Keyword(s):  
Pressure Drop ◽  
Large Diameter ◽  
Reynolds Numbers ◽  
Cross Sectional ◽  
Number Range ◽  
Liquid Part ◽  
Small Spherical Particle ◽  
Quiescent Liquid ◽  
Limiting Value ◽  
Unbounded Fluid

The pressure drop ΔP created by the motion of a ‘small’ spherical particle settling along the axis of a large-diameter circular cylinder filled with a quiescent liquid was measured in the particle Reynolds number range (based on diameter) from Re = 0·2 to 21,000. For Re < 125 it was found that ΔPA/D = 2·0 (A = cylinder cross-sectional area; D = particle drag), in agreement with existing theory in the Stokes and Oseen regimes. Beyond Re = 125 a fairly abrupt transition occurs, the ΔPA/D ratio decreasing asymptotically towards 1·0, the limiting value predicted by elementary momentum principles for an ‘unbounded’ fluid, with increasing Re. At Re ≈ 6000 the transition is essentially complete.

Heat Transfer And Pressure Drop Of An Angled Discrete Turbulator At Elevated Reynolds Numbers Up To 900,000

2021 ◽  
pp. 1-29
Author(s):  
Sam Ghazi-Hesami ◽  
Dylan Wise ◽  
Keith Taylor ◽  
Peter Ireland ◽  
Étienne Robert
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Enhance Heat Transfer ◽  
Near Surface ◽  
Number Range ◽  
Smooth Channel

Abstract Turbulators are a promising avenue to enhance heat transfer in a wide variety of applications. An experimental and numerical investigation of heat transfer and pressure drop of a broken V (chevron) turbulator is presented at Reynolds numbers ranging from approximately 300,000 to 900,000 in a rectangular channel with an aspect ratio (width/height) of 1.29. The rib height is 3% of the channel hydraulic diameter while the rib spacing to rib height ratio is fixed at 10. Heat transfer measurements are performed on the flat surface between ribs using transient liquid crystal thermography. The experimental results reveal a significant increase of the heat transfer and friction factor of the ribbed surface compared to a smooth channel. Both parameters increase with Reynolds number, with a heat transfer enhancement ratio of up to 2.15 (relative to a smooth channel) and a friction factor ratio of up to 6.32 over the investigated Reynolds number range. Complementary CFD RANS (Reynolds-Averaged Navier-Stokes) simulations are performed with the κ-ω SST turbulence model in ANSYS Fluent® 17.1, and the numerical estimates are compared against the experimental data. The results reveal that the discrepancy between the experimentally measured area averaged Nusselt number and the numerical estimates increases from approximately 3% to 13% with increasing Reynolds number from 339,000 to 917,000. The numerical estimates indicate turbulators enhance heat transfer by interrupting the boundary layer as well as increasing near surface turbulent kinetic energy and mixing.

Steady Flow Through a Double Converging-Diverging Tube Model for Mild Coronary Stenoses

1989 ◽  
Vol 111 (3) ◽  
pp. 212-221 ◽  
Author(s):  
S. C. van Dreumel ◽  
G. D. C. Kuiken
Keyword(s):  
Pressure Drop ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Tube Model ◽  
Mean Flow ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
In Series ◽  
Coronary Stenoses ◽  
Converging Angle

Velocity profiles and the pressure drop across two mild (62 percent) coronary stenoses in series have been investigated numerically and experimentally in a perspex-tube model. The mean flow rate was varied to correspond to a Reynolds number range of 50–400. The pressure drop across two identical (62 percent) stenoses show that for low Reynolds numbers the total effect of two stenoses equals that of two single stenoses. A reduction of 10 percent is found for the higher Reynolds numbers investigated. Numerical and experimental results obtained for the velocity profiles agree very well. The effect of varying the converging angle of a single mild (62 percent) coronary stenosis on the fluid flow has been determined numerically using a finite element method. Pressure-flow relation, especially with respect to relative short stenoses, is discussed.

Numerical Study of a Compact Wavy Heat Exchanger

2011 ◽  
Author(s):  
Riccardo Mereu ◽  
Emanuela Colombo ◽  
Fabio Inzoli
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Nusselt Number ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Temperature Fields ◽  
Mean Velocity ◽  
Qualitative Comparison ◽  
Cross Sectional ◽  
Number Range

The present work deals with the design of compact wavy heat exchangers, where high values of heat transfer area per unit volume are looked for in order to reduce size and increase efficiency. A numerical investigation of a rectangular cross-sectional shape geometry, with duct aspect ratio of 7.3, and a corrugation angle of 145° is here proposed. The Reynolds numbers (based on the duct hydraulic diameter) range from 300 to 5000. The numerical analysis is performed by means of a finite volume commercial CFD code. Laminar and Unsteady Reynolds Averaged Navier-Stokes (U-RANS) approaches are applied to a three-dimensional fluid domain over a single module with periodic conditions, respectively for, lower (<1000) and higher (≥1000) Reynolds numbers. Mean velocity and temperature fields are obtained. The average values of Fanning friction factor and Nusselt number are compared with experimental data from literature for the same geometry operating at the same Reynolds number range. For the evaluation of heat transfer quantities obtained in the numerical study the analogy between Sherwood and Nusselt number is used. The numerical results agree with experimental data, by showing the capability of laminar and U-RANS two-equation approach, via RNG model, to capture the mean fluid flow including the Taylor-Gortler instability that appear at low Reynolds numbers. The qualitative comparison of heat results shows an agreement between experimental and numerical data, whereas the extension to quantitative comparison is limited by some deficiencies in experimental correlation for mass/heat transfer analogy.

Augmented Heat Transfer in a Recovery Passage Downstream From a Grooved Section: An Example of Uncoupled Heat/Momentum Transport

1995 ◽  
Vol 117 (2) ◽  
pp. 303-308 ◽  
Author(s):  
M. Greiner ◽  
R.-F. Chen ◽  
R. A. Wirtz
Keyword(s):  
Heat Transfer ◽  
Reynolds Numbers ◽  
Pumping Power ◽  
Power Performance ◽  
Velocity Measurements ◽  
Cross Sectional ◽  
Number Range ◽  
Transverse Grooves ◽  
Pressure And Velocity Measurements ◽  
The Heat Transfer Coefficient

Earlier experiments have shown that cutting transverse grooves into one surface of a rectangular cross-sectional passage stimulates flow instabilities that greatly enhance heat transfer/pumping power performance of air flows in the Reynolds number range 1000 < Re < 5000. In the current work, heat transfer, pressure, and velocity measurements in a flat passage downstream from a grooved region are used to study how the flow recovers once it is disturbed. The time-averaged and unsteady velocity profiles, as well as the heat transfer coefficient, are dramatically affected for up to 20 hydraulic diameters past the end of the grooved section. The recovery lengths for shear stress and pressure gradient are significantly shorter and decrease rapidly for Reynolds numbers greater than Re = 3000. As a result, a 5.4-hydraulic-diameter-long recovery region requires 44 percent less pumping power for a given heat transfer level than if grooving continued.

The Steady Expiratory Pressure-Flow Relation in a Model Pulmonary Bifurcation

1993 ◽  
Vol 115 (3) ◽  
pp. 299-305 ◽  
Author(s):  
J. M. Collins ◽  
A. H. Shapiro ◽  
E. Kimmel ◽  
R. D. Kamm
Keyword(s):  
Pressure Drop ◽  
Reynolds Numbers ◽  
Generation Model ◽  
Cross Sectional ◽  
Pressure Flow ◽  
Frictional Pressure Drop ◽  
Curved Tube ◽  
Equivalent Length ◽  
Dye Visualization ◽  
Sectional Shape

Experiments were conducted over a range of Reynolds numbers from 50 to 8000 to study the pressure-flow relationship for a single bifurcation in a multi-generation model during steady expiratory flow. Using the energy equation, the measured static pressure drop was decomposed into separate components due to fluid acceleration and viscous energy dissipation. The frictional pressure drop was found to closely approximate that for an equivalent length of curved tube with the same curvature ratio as in the model bifurcation. The sensitivity of these results to changes in airway cross-sectional shape, non-planar configuration, and flow regime (laminar-turbulent) was investigated. In separate experiments using dye visualization and hot-wire anemometry, a transition to turbulent flow was observed at Reynolds numbers between 1000 and 1500. Transition had very little effect on the pressure-flow relation.

Heat Transfer and Pressure Loss in a Two-Pass, Rectangular Channel Featuring a Reduced Cross-Sectional Area After the 180-Degree Tip Turn With Different Turning Vane Configurations

2020 ◽  
Author(s):  
Sulaiman M. Alsaleem ◽  
Lesley M. Wright ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Aspect Ratio ◽  
Cross Section ◽  
Pressure Loss ◽  
Circular Cross Section ◽  
Sectional Area ◽  
Cross Sectional ◽  
Number Range

Abstract Serpentine, varying aspect ratio cooling passages, are typically used in cooling advanced gas turbine blades. These passages are usually connected by sharp, 180-deg bends. In the open literature, most of the internal cooling studies use a fixed cross-sectional area for multi-pass channels. Studies that use varying aspect ratio channels, along with a guide (turn) vane to direct the flow with turning, are scarce. In general, studies show that the incorporation of turning vanes in the bend region of a multi-pass channel keeps the heat transfer rate high while reducing pressure loss. Therefore, the current study investigates the effect of using different guide (turn) vane designs on both the detailed heat transfer distribution and pressure loss in a multi-pass channel with an aspect ratio of (4:1) in the entry passage and (2:1) in the second passage downstream of the vane (s). The first vane configuration is one solid-vane with a semi-circular cross-section connecting the two flow passages. The second configuration has three broken-vanes with a quarter-circular cross-section; two broken vanes are located downstream in the first passage (entering the turn), and one broken vane is upstream in the second passage (exiting the turn). For a Reynolds number range 15,000 to 45,000, detailed heat transfer distributions were obtained on all surfaces within the flow passages by using a transient liquid crystal method. The results show that the turning vane configurations have large effects on the heat transfer, in the turning bend and second passage, and the overall pressure drop. Results show that including the semi-circular vane in the turning region of a multi-pass channel enhanced the overall heat transfer by around 29% with a reduction in pressure loss by around 20%. Moreover, results show that the quarter-circular vane design provides higher overall averaged heat transfer enhancement than the semi-circular vane design by around 9% with penalty of higher pressure drop by 6%, which yields higher thermal performance by 7%, over the Reynolds number range.

Experiments on the pressure drop created by a sphere settling in a viscous liquid

1963 ◽  
Vol 17 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Irwin Pliskin ◽  
Howard Brenner
Keyword(s):  
Pressure Drop ◽  
Viscous Liquid ◽  
Pressure Difference ◽  
Circular Tube ◽  
Reynolds Numbers ◽  
Experimental Measurements ◽  
Sectional Area ◽  
Small Sphere ◽  
Cross Sectional ◽  
The Difference

Experimental measurements were made of the difference in pressure at large distances on either side of a spherical particle settling slowly along the axis of a long circular tube filled with viscous liquid. At low particle Reynolds numbers and for small sphere-cylinder diameter ratios, it was found that the product of the pressure difference and the cross-sectional area of the tube is equal to twice the drag on the particle, in accord with theory.

Improved Reverse Electro-Dialysis Using Membranes With Integrated Spacers

2011 ◽  
Author(s):  
O. Burheim ◽  
David A. Vermaas ◽  
Kitty Nijmeijer ◽  
J. G. Pharoah
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Large Scale ◽  
Surface Membrane ◽  
Ionic Current ◽  
Parallel Plates ◽  
Cross Sectional ◽  
Membrane Area ◽  
Number Range ◽  
Power Extraction

Reverse Electro-Dialysis, RED, utilises the energy of mixing between two solutions of different salinity by allowing ionic current to pass through the membranes and the two solutions such that cations are transport to the cathode and anions to the anode. [1–4.] The ionic current is converted to electronic current by red-ox reactions at the cathode and the anode. The membranes applied in this process are ionic selective, traditionally of uniform thickness and separated by a non-conductive spacer [5, 6]. Traditionally, non-conductive spacers have been deployed as eddy promoters and membrane spacers in salinity difference power extraction systems, such as Pressure Retarded Osmosis (PRO) and Reverse Electro-Dialysis (RED). For RED, traditional spacers inhibit parts of the ionic current paths in the fluid compartments and magnify the pressure drop imposed by the fluid flow between the membranes. [6] In a strive to lower the pressure drop in the fluid flow compartment and to increase the conductive region between the membranes, it is suggested to manufacture membranes with new shapes and profiles. [6] By modeling transport of mass and momentum in different geometries, spacing, mixing and active membrane area can be optimised with respect to increasing the power extraction. Such work has previously been done for traditional, i.e. non-electrochemical, flow in spacer separated membrane systems. A classical, approach has been to study submerged and non-submerged non-conductive spacer rods in fluid flow between two parallel plates (membranes) for Reynolds numbers (Re) from 50 and upwards. [7–17] This work discusses how spacers united with the reactant surface (membrane) will affect the mixing and the pressure drops of RED systems with Re numbers between 1 and 100, the expected operational Re number range for RED [6, 18, 19]. This is essential for the power production of RED. For a process converting renewable energy present in nature, such as RED, optimising these parameters is detrimental for the exergy yield. In going from a laboratory scale with a 10 × 10 cm2 cross sectional membrane to a large scale of 100 × 100 cm2, the Reynolds number (Re) increases from 10 to 100 simply because the volume flow is proportional to the flow length. Since it is within this range that eddies starts to get promoted by spacers, different mixing properties is expected exist when comparing laboratory and industrial scaled RED systems.

scholarly journals Parametric optimization of a stamped longitudinal vortex generator inside a circular tube of a solar water heater at low Reynolds numbers

2021 ◽  
Vol 3 (8) ◽  
Author(s):  
Felipe A. S. Silva ◽  
Luis Júnior ◽  
José Silva ◽  
Sandilya Kambampati ◽  
Leandro Salviano
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Reynolds Numbers ◽  
Geometric Parameters ◽  
Vortex Generators ◽  
Longitudinal Vortex ◽  
Solar Water Heater ◽  
Water Heater ◽  
Solar Water

AbstractSolar Water Heater (SWH) has low efficiency and the performance of this type of device needs to be improved to provide useful and ecological sources of energy. The passive techniques of augmentation heat transfer are an effective strategy to increase the convective heat transfer coefficient without external equipment. In this way, recent investigations have been done to study the potential applications of different inserts including wire coils, vortex generators, and twisted tapes for several solar thermal applications. However, few researchers have investigated inserts in SWH which is useful in many sectors where the working fluid operates at moderate temperatures. The longitudinal vortex generators (LVG) have been applied to promote heat transfer enhancement with a low/moderate pressure drop penalty. Therefore, the present work investigated optimal geometric parameters of LVG to enhance the heat transfer for a SWH at low Reynolds number and laminar flow, using a 3D periodical numerical simulation based on the Finite Volume Method coupled to the Genetic Algorithm optimization method (NSGA-II). The LVG was stamped over a flat plate inserted inside a smooth tube operating under a typical residential application corresponding to Reynolds numbers of 300, 600, and 900. The geometric parameters of LGV were submitted to the optimization procedure which can find traditional LVG such as rectangular-winglet and delta-winglet or a mix of them. The results showed that the application of LGVs to enhance heat transfer is an effective passive technique. The different optimal shapes of the LVG for all Reynolds numbers evaluated improved more than 50% of heat transfer. The highest augmentation heat transfer of 62% is found for the Reynolds number 900. However, the best thermo-hydraulic efficiency value is found for the Reynolds number of 600 in which the heat transfer intensification represents 55% of the pressure drop penalty.

Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Henrique Stel ◽  
Rigoberto E. M. Morales ◽  
Admilson T. Franco ◽  
Silvio L. M. Junqueira ◽  
Raul H. Erthal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Velocity Magnitude ◽  
Geometric Configurations ◽  
Corrugated Surfaces ◽  
Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

Sign in / Sign up

Export Citation Format

Share Document