The minimum flow rate of electrosprays in the cone-jet mode

2019 ◽  
Vol 876 ◽  
pp. 553-572 ◽  
Author(s):  
Manuel Gamero-Castaño ◽  
M. Magnani
Keyword(s):  
Dielectric Constant ◽  
Reynolds Number ◽  
Flow Rate ◽  
Numerical Solutions ◽  
Viscous Stress ◽  
Flow Rates ◽  
Minimum Flow ◽  
Electric Stress ◽  
Work Done ◽  
Minimum Flow Rate

Stable electrospraying in the cone-jet mode is restricted to flow rates above a minimum, and understanding the physics of this constraint is important to improve this atomization technique. We study this problem by measuring the minimum flow rate of electrosprays of tributyl phosphate and propylene carbonate at varying electrical conductivity $K$ (all other physical properties such as the density $\unicode[STIX]{x1D70C}$, surface tension $\unicode[STIX]{x1D6FE}$ and viscosity $\unicode[STIX]{x1D707}$ are kept constant and equal to those of the pure liquids), and through the analysis of numerical solutions. The experiments show that the dimensionless minimum flow rate is a function of both the dielectric constant $\unicode[STIX]{x1D700}$ of the liquid and its Reynolds number, $Re=(\unicode[STIX]{x1D70C}\unicode[STIX]{x1D700}_{o}\unicode[STIX]{x1D6FE}^{2}/\unicode[STIX]{x1D707}^{3}K)^{1/3}$. This result is unexpected in the light of existing theories which, for the conditions investigated, predict a minimum flow rate that depends only on $\unicode[STIX]{x1D700}$ and/or is marginally affected by $Re$. The experimental dependency on the Reynolds number requires the viscous stress to be a factor in the determination of the minimum flow rate. However, the numerical solutions suggest that a balance of opposing forces including the fixing viscous stress, which at decreasing flow rates may lower the acceleration of the flow to the point of making it unstable, is unlikely to be the cause. An alternative mechanism is the significant viscous dissipation taking place in the transition from cone to jet, and which at low flow rates cannot be supplied by the work done by the tangential electric stress in the same area. Instead, mechanical energy injected into the system farther downstream must be transferred upstream where dissipation predominantly takes place. This mechanism is supported by the balance between the energy dissipated and the work done by the electric stress in the transition from cone to jet, which yields a relationship between the minimum flow rate, the Reynolds number and the dielectric constant that compares well with experiments.

scholarly journals Net-exergetic, hydraulic and thermal optimization of coaxial heat exchangers using fixed flow conditions instead of fixed flow rates

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Tobias Blanke ◽  
Markus Hagenkamp ◽  
Bernd Döring ◽  
Joachim Göttsche ◽  
Vitali Reger ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Mass Flow ◽  
Flow Rate ◽  
Heat Exchangers ◽  
Circular Ring ◽  
Flow Conditions ◽  
Flow Rates ◽  
Mass Flow Rates ◽  
Pipe Radius

AbstractPrevious studies optimized the dimensions of coaxial heat exchangers using constant mass flow rates as a boundary condition. They show a thermal optimal circular ring width of nearly zero. Hydraulically optimal is an inner to outer pipe radius ratio of 0.65 for turbulent and 0.68 for laminar flow types. In contrast, in this study, flow conditions in the circular ring are kept constant (a set of fixed Reynolds numbers) during optimization. This approach ensures fixed flow conditions and prevents inappropriately high or low mass flow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic effort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass flow rate but not the Reynolds number of the circular ring. The thermal calculations base on Hellström’s borehole resistance and the hydraulic optimization on individually calculated linear loss of head coefficients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy difference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy flux and hydraulic effort. The Reynolds number in the circular ring is instead of the mass flow rate constant during all optimizations. The result from a thermal perspective is an optimal width of the circular ring of nearly zero. The hydraulically optimal inner pipe radius is 54% of the outer pipe radius for laminar flow and 60% for turbulent flow scenarios. Net-exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the flow type. Conclusively, coaxial geothermal probes’ design should focus on the hydraulic optimum and take the thermal optimum as a secondary criterion due to the dominating hydraulics.

Heat Transfer From Air-Cooled Contrarotating Disks

1997 ◽  
Vol 119 (1) ◽  
pp. 61-67 ◽  
Author(s):  
J.-X. Chen ◽  
X. Gan ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flow Rate ◽  
Reynolds Numbers ◽  
The Other ◽  
Reynolds Analogy ◽  
Flow Rates ◽  
Nusselt Numbers ◽  
Radial Outflow ◽  
Equivalent Conditions

A superposed radial outflow of air is used to cool two disks that are rotating at equal and opposite speeds at rotational Reynolds numbers up to 1.2 × 106. One disk, which is heated up to 100°C, is instrumented with thermocouples and fluxmeters; the other disk, which is unheated, is made from transparent polycarbonate to allow the measurement of velocity using an LDA system. Measured Nusselt numbers and velocities are compared with computations made using an axisymmetric elliptic solver with a low-Reynolds-number k–ε turbulence model. Over the range of flow rates and rotational speeds tested, agreement between the computations and measurements is mainly good. As suggested by the Reynolds analogy, the Nusselt numbers for contrarotating disks increase strongly with rotational speed and weakly with flow rate; they are lower than the values obtained under equivalent conditions in a rotor–stator system.

A Mechanistic Study on Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells

2012 ◽  
Vol 30 (2) ◽  
pp. 122-132 ◽  
Author(s):  
W. Zhibin ◽  
L. Yingchuan ◽  
L. Zhongneng ◽  
Z. Haiquan ◽  
L. Yonghui
Keyword(s):  
Flow Rate ◽  
Mechanistic Study ◽  
Gas Wells ◽  
Minimum Flow ◽  
Minimum Flow Rate

Numerical and asymptotic methods for certain viscous free-surface flows

1992 ◽  
Vol 340 (1656) ◽  
pp. 1-45 ◽  
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Lubrication Approximation ◽  
Navier Stokes Equations ◽  
Flow Rates

This paper concerns the two-dimensional motion of a viscous liquid down a perturbed inclined plane under the influence of gravity, and the main goal is the prediction of the surface height as the fluid flows over the perturbations. The specific perturbations chosen for the present study were two humps stretching laterally across an otherwise uniform plane, with the flow being confined in the lateral direction by the walls of a channel. Theoretical predictions of the flow have been obtained by finite-element approximations to the Navier-Stokes equations and also by a variety of lubrication approximations. The predictions from the various models are compared with experimental measurements of the free-surface profiles. The principal aim of this study is the establishment and assessment of certain numerical and asymptotic models for the description of a class of free-surface flows, exemplified by the particular case of flow over a perturbed inclined plane. The laboratory experiments were made over a range of flow rates such that the Reynolds number, based on the volume flux per unit width and the kinematical viscosity of the fluid, ranged between 0.369 and 36.6. It was found that, at the smaller Reynolds numbers, a standard lubrication approximation provided a very good representation of the experimental measurements but, as the flow rate was increased, the standard model did not capture several important features of the flow. On the other hand, a lubrication approximation allowing for surface tension and inertial effects expanded the range of applicability of the basic theory by almost an order of magnitude, up to Reynolds numbers approaching 10. At larger flow rates, numerical solutions to the full equations of motion provided a description of the experimental results to within about 4% , up to a Reynolds number of 25, beyond which we were unable to obtain numerical solutions. It is not known why numerical solutions were not possible at larger flow rates, but it is possible that there is a bifurcation of the Navier-Stokes equations to a branch of unsteady motions near a Reynolds number of 25.

The effects of oyygen on acclimatized men at high altitude

1954 ◽  
Vol 143 (910) ◽  
pp. 14-17 ◽  
Keyword(s):  
Experimental Data ◽  
Flow Rate ◽  
Experimental Work ◽  
Lung Ventilation ◽  
Open Circuit ◽  
Work Rate ◽  
Flow Rates ◽  
The Times ◽  
Extra Weight ◽  
Work Done

Knowledge of the effects of oxygen on acclimatized men at altitudes above 22 000 ft. depends entirely on the experience of mountaineers on Everest. Experimental data are, however, available up to 20000 ft. from work done on the Cho Oyu expedition in 1952, and up to 21000 ft. from work done on Everest the following year. The results of this experimental work are presented here, followed by the empirical findings of the Everest climbers in 1953. On Cho Oyu in 1952 we studied the effect of breathing different concentrations of oxygen on work rate and lung ventilation. Work rates were compared by timing men ascending a 300 ft. snow slope on a prepared track. Runs were done using open circuit equipment at flow rates of 4 and 10 l. O 2 /min. The equipment, which was carried on the back, weighed 22 lb. Control runs were done ( a ) breathing air and not carrying the equipment, ( b ) carrying the equipment with the supply of oxygen turned off. The effect of the extra weight of the equipment was to increase the times by approximately 25%. The effect of breathing extra oxygen was to shorten the times by approximately 10 %. The 10 l. flow rate was somewhat more effective than the 4 l. flow rate but the differences were small.

Effect of Low Reynolds Number Mixed Convection on Channel Flows Structure

2012 ◽  
Author(s):  
Ahmed Elatar ◽  
Kamran Siddiqui
Keyword(s):  
Reynolds Number ◽  
Flow Rate ◽  
Wall Temperature ◽  
Heated Wall ◽  
Mean Velocity ◽  
Number Range ◽  
Flow Rates ◽  
Wall Heating ◽  
The Mean ◽  
Low Reynolds

The effect of wall heating on low Reynolds numbers channel flow has been investigated experimentally. The experiments were conducted at heated bottom wall temperatures from 30 °C to 50 °C for two flow rates 0.0210 and 0.0525 kg/s, corresponding to the Reynolds number range of 150 and 750 (in the absence of heating). The results showed that the initially laminar flow became turbulent due to wall heating, and that wall heating has a significant influence on both the mean and turbulent velocity fields. The mean velocity profiles were altered by the convective currents. The magnitude of mean streamwise velocity near the heated wall increased with an increase in the wall temperature. A back flow near the upper channel wall was also observed primarily at the lower flow rate which diminished for the high flow rate. The magnitude of backflow increased with an increase in the wall temperature. The turbulent intensities were found to increase with an increase in the wall temperature for both flow rates. The result also showed the presence of strong vortices originating from the heated wall and advecting towards the central core of the channel.

Secondary Flows in Centrifugal Pump Impellers: PIV Measurements and CFD Computations

2009 ◽  
Author(s):  
R. W. Westra ◽  
L. Broersma ◽  
K. van Andel ◽  
N. P. Kruyt
Keyword(s):  
Reynolds Number ◽  
Centrifugal Pump ◽  
Flow Rate ◽  
Stokes Equations ◽  
Suction Side ◽  
Velocity Profiles ◽  
Secondary Flows ◽  
Design Flow ◽  
Low Velocity ◽  
Flow Rates

Two-dimensional Particle Image Velocimetry measurements and three-dimensional Computational Fluid Dynamics (CFD) analyses have been performed of the flow field inside the impeller of a low specific-speed centrifugal pump operating with a vaneless diffuser. Flow rates ranging from 80% to 120% of the design flow rate are considered in detail. It is observed from the velocity measurements that secondary flows occur. These flows result in the formation of regions of low velocity near the intersection of blade suction side and shroud. The extent of this jet-wake structure decreases with increasing flow rate. Velocity profiles have also been computed from Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model, using a commercial CFD-code. For the considered flow rates the qualitative agreement between measured and computed velocity profiles is very good. Overall, the average relative difference between these velocity profiles is around 7%. Additional CFD computations have been performed to assess the influence of Reynolds number and shape of the inlet velocity profile on the computed velocity profiles. It is found that the influence of Reynolds number is mild. The shape of the inlet profile only has a weak effect at the shroud.

Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells

1969 ◽  
Vol 21 (11) ◽  
pp. 1475-1482 ◽  
Author(s):  
R.G. Turner ◽  
M.G. Hubbard ◽  
A.E. Dukler
Keyword(s):  
Flow Rate ◽  
Gas Wells ◽  
Minimum Flow ◽  
Minimum Flow Rate
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