Study of the equilibrium free surface of a capillary liquid in a toroidal vessel

2021 ◽  
Author(s):  
Y. Zhaokai ◽  
A.N. Temnov
Keyword(s):  
Free Surface ◽  
Liquid Fuel ◽  
Solid Wall ◽  
Intermolecular Forces ◽  
Bond Number ◽  
Space Technology ◽  
Stationary Potential ◽  
Microgravity Conditions ◽  
Two Phases ◽  
Capillary Liquid

The paper considers an axisymmetric problem of determining the forms of equilibrium of liquid in spacecraft toroidal tanks under conditions close to weightlessness. In the absence of significant mass gravitational forces, the behavior of liquid fuel in tanks begins to be determined by surface tension forces, which are intermolecular forces at the interface of two phases. Relying on the principle of stationary potential, we obtained the conditions of equilibrium of the closed system "liquid - gas - solid wall" under microgravity conditions. The study introduces a system of differential equations that determines the form of equilibrium of a liquid in toroidal tanks, the Young — Dupre equation, the condition for the contact of a free surface with a solid wall, and the condition for the conservation of the volume of the liquid. Furthermore, we quantified the influence of various parameters, such as the contact angle α_0, the Bond number B_0, the ratio of the radii of the circles δ=R_0⁄r_0 and the relative filling volume of liquids V_0, on the form of the equilibrium of the capillary liquid. The study of the forms of equilibrium of liquid fuel makes it possible to develop recommendations for the design of intake devices for fuel tanks in rocket and space technology. Findings of research show that the obtained equilibrium surface is also the unperturbed boundary of the region occupied by liquid fuel, which gives necessary information for further investigation of the spacecraft dynamics.

Equilibrium and oscillations of liquid fuel free surface in coaxial-cylindrical vessels under microgravity conditions

2021 ◽  
Author(s):  
Y. Zhaokai ◽  
A.N. Temnov
Keyword(s):  
Contact Angle ◽  
Free Surface ◽  
Liquid Fuel ◽  
Outer Space ◽  
Surface Displacement ◽  
Ideal Liquid ◽  
Intermolecular Forces ◽  
Hydrodynamic Characteristics ◽  
Free Surface Displacement ◽  
Microgravity Conditions

In the absence of significant mass forces, the behavior of liquid fuel under microgravity conditions is determined by surface tension forces, which are intermolecular forces at the interface of two phases. The paper posed and solved the problem of equilibrium and small oscillations of an ideal liquid under microgravity conditions, and also quantified the influence of various parameters: the contact angle α0, the Bond number, the ratio of the radii of the inner and outer walls of the vessel and the depth of the liquid. For the coaxial-cylindrical vessels, there were obtained expressions in the form of a Bessel series for the potential of the fluid velocities and the free surface displacement field. The study relies on the analytical and experimental data available in the literature and proves the reliability of the developed numerical algorithm. Findings of research show that for and r, with the physical state of the wetted surface being unchanged, the shape of the free surface tends to be flat and the contact angle has little effect on the intrinsic vibration frequency of the free surface of the liquid. The results obtained can be used to solve problems of determining the hydrodynamic characteristics of the movement of liquid fuel in outer space.

Molecular Dynamic Simulation of Surface Roughness Effects on Nanoscale Flows

2009 ◽  
Author(s):  
Ali Kharazmi ◽  
Reza Kamali
Keyword(s):  
Surface Roughness ◽  
Solid Wall ◽  
Intermolecular Forces ◽  
Intermolecular Potential ◽  
Roughness Effects ◽  
Time Step ◽  
Restoring Force ◽  
Rapid Sampling ◽  
Micro Channels ◽  
Fifth Order

In the present study, a molecular based scheme has been developed for simulating flows in nano- and micro-channels with roughness. In micro channel flow, there is some difference on the flow friction between roughness and cavitations which is not well studied. The presented approach is based on the molecular dynamics (namely MD) in which different ensemble has been used. For modeling the simulation the classical Newtonian particles are allowed to obey Newtonian mechanics and intermolecular forces are founded by integrating intermolecular potential. Lennard-Jones potential is used to model the interactions between particles. Particles equation of motion is integrated using fifth order Gear predictor-corrector. To ensure rapid sampling of phase space, the time step is made as large as possible. Periodic boundary condition is implemented via minimum image convention. Each atom of the solid wall is anchored at its lattice site by a harmonic restoring force and its temperature has been controlled by utilizing Nose-Hoover thermostat. The roughness is implemented on the lower channel wall. To make a comparison between the effect of roughness and cavitation, the same dimension is used for both for different aspect ratio. To allow comparison with previous results the same fluid density has been used. The effects of surface roughness and cavitation on velocity distribution of hydrophobic and hydrophilic wall undergoing Poiseuille flow are presented.

Turbulent kinetic energy transport in a corner formed by a solid wall and a free surface

2000 ◽  
Vol 410 ◽  
pp. 343-366 ◽  
Author(s):  
T. Y. HSU ◽  
L. M. GREGA ◽  
R. I. LEIGHTON ◽  
T. WEI
Keyword(s):  
Free Surface ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Transport ◽  
Solid Wall

Transport of passive scalar in turbulent shear flow under a clean or surfactant-contaminated free surface

2011 ◽  
Vol 670 ◽  
pp. 527-557 ◽  
Author(s):  
HAMID R. KHAKPOUR ◽  
LIAN SHEN ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Solid Wall ◽  
Surface Flux ◽  
Scalar Fields ◽  
Transport Processes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Scalar Flux ◽  
Conditional Averaging

Direct numerical simulation is performed to study the turbulent transport of passive scalars near clean and surfactant-contaminated free surfaces. As a canonical problem, a turbulent shear flow interacting with a flat free surface is considered, with a focus on the effect of splats and anti-splats on the scalar transport processes. Using conditional averaging of strong surface flux events, it is shown that these are associated with coherent hairpin vortex structures emerging from the shear flow. The upwelling at the splat side of the oblique hairpin vortices greatly enhances the scalar surface flux. In the presence of surfactants, the splats at the surface are suppressed by the surface tension gradients caused by spatial variation of surfactant concentration; as a result, scalar flux is reduced. Conditional averaging of weak surface flux events shows that these are caused by anti-splats with which surface-connected vortices are often associated. When surfactants are present, the downdraught transport at the surface-connected vortices is weakened. Turbulence statistics of the velocity and scalar fields are performed in terms of mean and fluctuation profiles, scalar flux, turbulent diffusivity and scalar variance budget. Using surface layer quantification based on an analytical similarity solution of the mean shear flow, it is shown that the depth of the scalar statistics variation is scaled on the basis of the Schmidt number. In the presence of surfactants, the scalar statistics have the characteristics of those near a solid wall in contrast to those near a clean surface, which leads to thickened scalar boundary layer and reduced surface flux.

The Consistent Second-Order Wave Theory and Its Application to a Submerged Spheroid

1970 ◽  
Vol 14 (01) ◽  
pp. 23-50
Author(s):  
Young H. Chey
Keyword(s):  
Free Surface ◽  
Solid Wall ◽  
Three Dimensional ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Resistance ◽  
Second Order ◽  
Surface Phenomena ◽  
First Order ◽  
Theoretical Results

Because of the recognized inadequacy of first-order linearized surface-wave theory, the author has developed, for a three-dimensional body, a new second-order theory which provides a better description of free-surface phenomena. The new theory more accurately satisfies the kinematic boundary condition on the solid wall, and takes into account the nonlinearity of the condition at the free surface. The author applies the new theory to a submerged spheroid, to calculate wave resistance. Experiments were conducted to verify the theory, and their results are compared with the theoretical results. The comparison indicates that the use of the new theory leads to more accurate prediction of wave resistance.

Thermocapillary and oscillatory-shear instabilities in a layer of liquid with a deformable surface

1998 ◽  
Vol 360 ◽  
pp. 21-39 ◽  
Author(s):  
A. C. OR ◽  
R. E. KELLY
Keyword(s):  
Free Surface ◽  
Marangoni Number ◽  
Thermocapillary Convection ◽  
Oscillatory Shear ◽  
Heated Layer ◽  
Long Wavelength ◽  
Deformable Surface ◽  
Microgravity Conditions ◽  
Shear Instabilities ◽  
Oscillating Plate

The thermocapillary and shear-induced instabilities of a thin heated layer of liquid bounded from the top by a deformable free surface and at the bottom by a horizontally oscillating plate are studied for both Earth-bound and microgravity conditions. Finite-wavelength thermocapillary convection can be stabilized very significantly by the oscillatory shear, whereas shear-induced instabilities are greatly stabilized if the Marangoni number is negative. For long-wavelength thermocapillary convection, oscillatory shear can stabilize or destabilize the basic state, depending primarily on the imposed forcing frequency. With microgravity, significant stabilization of the dominant long-wavelength convection can be achieved by carefully selecting the imposed frequency.

scholarly journals Dissipation of shear-free turbulence near boundaries

2000 ◽  
Vol 422 ◽  
pp. 167-191 ◽  
Author(s):  
M. A. C. TEIXEIRA ◽  
S. E. BELCHER
Keyword(s):  
Numerical Simulation ◽  
Boundary Condition ◽  
Free Surface ◽  
Direct Numerical Simulation ◽  
Dissipation Rate ◽  
Solid Wall ◽  
Tangential Velocity ◽  
Main Role ◽  
Nonlinear Processes ◽  
Viscous Layer

The rapid-distortion model of Hunt & Graham (1978) for the initial distortion of turbulence by a flat boundary is extended to account fully for viscous processes. Two types of boundary are considered: a solid wall and a free surface. The model is shown to be formally valid provided two conditions are satisfied. The first condition is that time is short compared with the decorrelation time of the energy-containing eddies, so that nonlinear processes can be neglected. The second condition is that the viscous layer near the boundary, where tangential motions adjust to the boundary condition, is thin compared with the scales of the smallest eddies. The viscous layer can then be treated using thin-boundary-layer methods. Given these conditions, the distorted turbulence near the boundary is related to the undistorted turbulence, and thence profiles of turbulence dissipation rate near the two types of boundary are calculated and shown to agree extremely well with profiles obtained by Perot & Moin (1993) by direct numerical simulation. The dissipation rates are higher near a solid wall than in the bulk of the flow because the no-slip boundary condition leads to large velocity gradients across the viscous layer. In contrast, the weaker constraint of no stress at a free surface leads to the dissipation rate close to a free surface actually being smaller than in the bulk of the flow. This explains why tangential velocity fluctuations parallel to a free surface are so large. In addition we show that it is the adjustment of the large energy-containing eddies across the viscous layer that controls the dissipation rate, which explains why rapid-distortion theory can give quantitatively accurate values for the dissipation rate. We also find that the dissipation rate obtained from the model evaluated at the time when the model is expected to fail actually yields useful estimates of the dissipation obtained from the direct numerical simulation at times when the nonlinear processes are significant. We conclude that the main role of nonlinear processes is to arrest growth by linear processes of the viscous layer after about one large-eddy turnover time.

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