Maximum Spread of Droplet on Solid Surface: Low Reynolds and Weber Numbers

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Ri Li ◽  
Nasser Ashgriz ◽  
Sanjeev Chandra
Keyword(s):  
Kinetic Energy ◽  
Viscous Dissipation ◽  
Theoretical Study ◽  
Control Volume ◽  
Reynolds Numbers ◽  
Solid Surfaces ◽  
Initial Kinetic Energy ◽  
Spherical Cap ◽  
Fundamental Physics ◽  
Single Droplets

This theoretical study proposes an analytical model to predict the maximum spread of single droplets on solid surfaces with zero or low Weber and Reynolds numbers. The spreading droplet is assumed as a spherical cap considering low impact velocities. Three spreading states are considered, which include equilibrium spread, maximum spontaneous spread, and maximum spread. Energy conservation is applied to the droplet as a control volume. The model equation contains two viscous dissipation terms, each of which has a defined coefficient. One term is for viscous dissipation in spontaneous spreading and the other one is for viscous dissipation of the initial kinetic energy of the droplet. The new model satisfies the fundamental physics of drop-surface interaction and can be used for droplets impacting on solid surfaces with or without initial kinetic energy.

Determination of the Drop Size During Air-Blast Atomization

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
T.-W. Lee ◽  
J. E. Park
Keyword(s):  
Kinetic Energy ◽  
Viscous Dissipation ◽  
High Speed ◽  
Drop Size ◽  
Integral Form ◽  
Initial Kinetic Energy ◽  
Air Blast ◽  
Dissipation Term ◽  
Wide Range ◽  
Drop Size Distributions

We have used the integral form of the conservation equations, to find a cubic formula for the drop size during in liquid sprays in coflow of air (air-blast atomization). Similar to our previous work, the energy balance dictates that the initial kinetic energy of the gas and injected liquid will be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation. Using this approach, the drop size can be determined based on the basic injection and fluid parameters for “air-blast” atomization, where the injected liquid is atomized by high-speed coflow of air. The viscous dissipation term is estimated using appropriate velocity and length scales of liquid–air coflow breakup. The mass and energy balances for the spray flows render to an expression that relates the drop size to all of the relevant parameters, including the gas- and liquid-phase velocities and fluid properties. The results agree well with experimental data and correlations for the drop size. The solution also provides for drop size–velocity cross-correlation, leading to computed drop size distributions based on the gas-phase velocity distribution. This approach can be used in the estimation of the drop size for practical sprays and also as a primary atomization module in computational simulations of air-blast atomization over a wide range of injection and fluid conditions, the only caveat being that a parameter to account for the viscous dissipation needs to be calibrated with a minimal set of observational data.

scholarly journals Hydrodynamic constraints on the energy efficiency of droplet electricity generators

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Antoine Riaud ◽  
Cui Wang ◽  
Jia Zhou ◽  
Wanghuai Xu ◽  
Zuankai Wang
Keyword(s):  
Energy Efficiency ◽  
Kinetic Energy ◽  
Total Energy ◽  
Viscous Dissipation ◽  
Shear Force ◽  
Mechanical Energy ◽  
Electric Energy ◽  
The Past ◽  
Viscous Shear ◽  
Impingement Velocity

AbstractElectric energy generation from falling droplets has seen a hundred-fold rise in efficiency over the past few years. However, even these newest devices can only extract a small portion of the droplet energy. In this paper, we theoretically investigate the contributions of hydrodynamic and electric losses in limiting the efficiency of droplet electricity generators (DEG). We restrict our analysis to cases where the droplet contacts the electrode at maximum spread, which was observed to maximize the DEG efficiency. Herein, the electro-mechanical energy conversion occurs during the recoil that immediately follows droplet impact. We then identify three limits on existing droplet electric generators: (i) the impingement velocity is limited in order to maintain the droplet integrity; (ii) much of droplet mechanical energy is squandered in overcoming viscous shear force with the substrate; (iii) insufficient electrical charge of the substrate. Of all these effects, we found that up to 83% of the total energy available was lost by viscous dissipation during spreading. Minimizing this loss by using cascaded DEG devices to reduce the droplet kinetic energy may increase future devices efficiency beyond 10%.

scholarly journals Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers

2021 ◽  
Vol 6 (4) ◽  
Author(s):  
Petr Hellinger ◽  
Andrea Verdini ◽  
Simone Landi ◽  
Emanuele Papini ◽  
Luca Franci ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Reynolds Numbers ◽  
Scale Dependence ◽  
Hydrodynamic Turbulence

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

The Aerodynamics of Trailing-Edge-Cooled Transonic Turbine Blades: Part 2 — Theoretical and Computational Approach

1997 ◽  
Author(s):  
Mathias Deckers ◽  
John D. Denton
Keyword(s):  
Transonic Flow ◽  
Theoretical Study ◽  
Computational Study ◽  
Control Volume ◽  
Turbine Blades ◽  
Computational Approach ◽  
Trailing Edge ◽  
Time Marching ◽  
Transonic Turbine ◽  
Volume Method

A theoretical and computational study into the aerodynamics of trailing-edge-cooled transonic turbine blades is described in this part of the paper. The theoretical study shows that, for unstaggered blades with coolant ejection, the base pressure and overall loss can be determined exactly by a simple control volume analysis. This theory suggests that a thick, cooled trailing edge with a wide slot can be more efficient than a thin, solid trailing edge. An existing time-marching finite volume method is adapted to calculate the transonic flow with trailing edge coolant ejection on a structured, quasi-orthogonal mesh. Good overall agreement between the present method, inviscid and viscous, and experimental evidence is obtained.

Large-scale modes of turbulent channel flow: transport and structure

2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Upstream Region ◽  
Two Dimensional ◽  
Normal Plane

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

scholarly journals The influence of moderate angle-of-attack variation on disturbances evolution and transition to turbulence in supersonic boundary layer on swept wing

2019 ◽  
Vol 234 (1) ◽  
pp. 96-101
Author(s):  
Alexander Kosinov ◽  
Nikolai Semionov ◽  
Yury Yermolaev ◽  
Boris Smorodsky ◽  
Gleb Kolosov ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Theoretical Study ◽  
Angle Of Attack ◽  
Reynolds Numbers ◽  
Supersonic Boundary Layer ◽  
Linear Stability Theory ◽  
Transition To Turbulence ◽  
Computational Results ◽  
Swept Wing ◽  
Turbulent Transition

The paper is devoted to an experimental and theoretical study of effect of moderate angle-of-attack variation on disturbances evolution and laminar-turbulent transition in a supersonic boundary layer on swept wing at Mach 2. Monotonous growth of the transition Reynolds numbers with angle of attack increasing from −2° to 2.7° is confirmed. For the same conditions, calculations based on linear stability theory are performed. The experimental and computational results show a favourable comparison.

Highly Resolved Large Eddy Simulation Study of Gap Size Effect on Low-Pressure Turbine Stage

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
R. Pichler ◽  
V. Michelassi ◽  
R. Sandberg ◽  
J. Ong
Keyword(s):  
Kinetic Energy ◽  
Cross Sections ◽  
Control Volume ◽  
Leading Edge ◽  
Suction Side ◽  
Low Pressure ◽  
Small Time ◽  
Gap Size ◽  
Low Pressure Turbine ◽  
Large Eddy

Blade-to-blade interactions in a low-pressure turbine (LPT) were investigated using highly resolved compressible large eddy simulations (LESs). For a realistic setup, a stator and rotor configuration with profiles typical of LPTs was used. Simulations were conducted with an in-house solver varying the gap size between stator and rotor from 21.5% to 43% rotor chord. To investigate the effect of the gap size on the prevailing loss mechanisms, a loss breakdown was conducted. It was found that in the large gap (LG) size case, the turbulence kinetic energy (TKE) levels of the stator wake close to the rotor leading edge were only one third of those in the small gap (SG) case, due to the longer distance of constant area mixing. The small time-averaged suction side separation on the blade, found in the LG case, disappeared in the SG calculations, confirming how stronger wakes can keep the boundary layer attached. The higher intensity wake impinging on the blade, however, did not affect the time-averaged losses calculated using the control volume approach of Denton. On the other hand, losses computed by taking cross sections upstream and downstream of the blade revealed a greater distortion loss generated by the stator wakes in the SG case. Despite the suction side separation suppression, the SG case gave higher losses overall due to the incoming wake turbulent kinetic energy amplification along the blade passage.

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