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.

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.

Nonlinear Helmholtz oscillations in harbours and coupled basins

1981 ◽  
Vol 104 ◽  
pp. 407-418 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Free Surface ◽  
Additional Assumption ◽  
Phase Plane ◽  
Surface Displacement ◽  
Elliptic Functions ◽  
Forced Oscillations ◽  
Amplitude Parameter ◽  
Spatial Uniformity ◽  
Open Sea ◽  
Free Surface Displacement

Free and forced oscillations in a basin that is connected through a narrow canal to either the open sea or a second basin are considered on the assumption that the spatial variation of the free-surface displacement is negligible. The free-surface displacement in the canal is allowed to be finite, subject only to the restriction (in addition to that implicit in the approximation of spatial uniformity) that the canal does not run dry. The resulting model yields a Hamiltonian pair of phase-plane equations for the free oscillations, which are integrated in terms of elliptic functions on the additional assumption that the kinetic energy of the motion in the basin(s) is negligible compared with that in the canal or otherwise through an expansion in an amplitude parameter. The corresponding model for forced oscillations that are limited by radiation damping yields a generalization of Duffing's equation for an oscillator with a soft spring, the solution of which is obtained as an expansion in the amplitude of the fundamental term in a Fourier expansion. Equivalent circuits are developed for the various models.

Oscillatory Free Surface Displacement of Finite Amplitude in a Small Orifice

2004 ◽  
Vol 126 (5) ◽  
pp. 818-826
Author(s):  
Brian J. Daniels ◽  
James A. Liburdy
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Surface Displacement ◽  
Experimental Results ◽  
Significant Shift ◽  
Curvature Effect ◽  
Modal Frequency ◽  
Large Curvature ◽  
Curvature Effects ◽  
Free Surface Displacement

The oscillatory free-surface displacement in an orifice periodically driven at the inlet is studied. The predictions based on a potential flow analysis are investigated in light of viscous and large curvature effects. Viscous effects near the wall are estimated, as are surface viscous energy loss rates. The curvature effect on the modal frequency is shown to become large at the higher modal surface shapes. Experimental results are obtained using water for two orifice diameters, 794 and 1180 μm. Results of surface shapes and modal frequencies are compared to the predictions. Although modal shapes seem to be well predicted by the theory, the experimental results show a significant shift of the associated modal frequencies. A higher-order approximation of the surface curvature is presented, which shows that the modal frequency should, in fact, be reduced from potential flow predictions as is consistent with the large curvature effect. To account for the effect of finite surface displacements an empirical correlation for the modal frequencies is presented.

scholarly journals Three dimensional numerical simulations for non-breaking solitary wave interacting with a group of slender vertical cylinders

2009 ◽  
Vol 1 (1) ◽  
Author(s):  
Weihua Mo ◽  
Philip L.-F. Liu
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Dynamic Pressure ◽  
Laboratory Data ◽  
Three Dimensional ◽  
Time History ◽  
Surface Displacement ◽  
Numerical Results ◽  
Finite Volume Scheme ◽  
Free Surface Displacement

AbstractIn this paper we validate a numerical model for-structure interaction by comparing numerical results with laboratory data. The numerical model is based on the Navier-Stokes(N-S) equations for an incompressible fluid. The N-S equations are solved by two-step projection finite volume scheme and the free surface displacements are tracked by the slender vertical piles. Numerical results are compared with the laboratory data and very good agreement is observed for the time history of free surface displacement, fluid particle velocity and force. The agreement for dynamic pressure on the cylinder is less satisfactory, which is primarily caused by instrument errors.

On free-surface oscillations in a rotating paraboloid

1963 ◽  
Vol 17 (2) ◽  
pp. 257-266 ◽  
Author(s):  
John W. Miles ◽  
F. K. Ball
Keyword(s):  
Free Surface ◽  
Second Harmonic ◽  
Harmonic Component ◽  
Surface Displacement ◽  
Wave Number ◽  
Rigid Displacement ◽  
Axisymmetric Solution ◽  
Axisymmetric Mode ◽  
Azimuthal Wave ◽  
Free Surface Displacement

Lamb's analysis of small-amplitude, shallow-water oscillations in a rotating paraboloid, interpreted by him in the inconsistent context of an approximately plane free surface, is re-interpreted to obtain results that are valid for $0 \le \omega^2l|2g \; \textless \;1$ (ω = rotational speed, l = latus rectum of paraboloid); no equilibrium is possible for ω2l/2g > 1. It is shown that the frequencies of the dominant modes for the azimuthal wave numbers 0 (axisymmetric motion) and 1 are independent of ω for an observer in a non-rotating reference frame and that the frequencies of all other axisymmetric modes are decreased by rotation (Lamb concluded that they would be increased). An axisymmetric mode of zero frequency, which was over-looked by Lamb, also is found.Exact solutions to the non-linear equations of motion, which reduce to the aforementioned dominant modes for small amplitudes, are determined. The axisymmetric solution is inferred from similarity considerations and is found to contain all harmonics of the fundamental frequency. The finite motion of azimuthal wave-number 1 is a quasi-rigid displacement of the liquid and is found to be simple harmonic except for a second-harmonic component of the free-surface displacement (but the horizontal velocity at a given point remains simple harmonic).

On an invariant property of water waves

1971 ◽  
Vol 49 (2) ◽  
pp. 385-389 ◽  
Author(s):  
T. Brooke Benjamin ◽  
J. J. Mahony
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Horizontal Plane ◽  
Wave Motion ◽  
Surface Displacement ◽  
Heavy Liquid ◽  
Invariant Property ◽  
Finite Region ◽  
Free Wave ◽  
Free Surface Displacement

The discussion concerns free wave motions generated from rest in a finite region of an ocean of heavy liquid lying on a horizontal plane. It is shown that the horizontal fist moment of the free-surface displacement varies linearly with time. Hence, if the total volume displaced is not zero and therefore the centroid of the displacement is definable, the centroid travels with a constant horizontal velocity as the wave motion evolves. This conclusion holds exactly for waves of any amplitude and even remains applicable subsequent to the breaking of waves.

scholarly journals Weak formulation of free-surface wave equations

2001 ◽  
Vol 5 (2) ◽  
pp. 75-85
Author(s):  
A. D. Sneyd
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Wave Equations ◽  
Evolution Equations ◽  
Surface Displacement ◽  
Wave Dispersion ◽  
The Body ◽  
Weak Formulation ◽  
Free Surface Displacement ◽  
Free Surface Wave

An alternative method for deriving water wave dispersion relations and evolution equations is to use a weak formulation. The free-surface displacement η is written as an eigenfunction expansion, η=∑n=1∞αn(t)En where the αn(t) are time-dependent coefficients. For a tank with vertical sides the En are eigenfunctions of the eigenvalue problem, ∇2+λ2E=0,  ∇E⋅n^=0 on the tank side walls. Evolution equations for the αn(t) can be obtained by taking inner products of the linearised equation of motion, ρ∂v∂t=−1ρ∇P+F with the normal irrotational wave modes. For unforced waves each evolution equation is a simple harmonic oscillator, but the method is most useful when the body force F is something more exotic than gravity. It can always be represented by a forcing term in the SHM evolution equation, and it is not necessary to assume F irrotational. Several applications are considered: the Faraday experiment, generation of surface waves by an unsteady magnetic field, and the metal-pad instability in aluminium reduction cells.

scholarly journals Simulation of Partially Filled Liquid in a Moving Tank

2020 ◽  
Vol 8 (6) ◽  
pp. 1941-1944
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Unsteady Flow ◽  
Numerical Simulations ◽  
Dynamic Pressure ◽  
Surface Displacement ◽  
Volume Of Fluid ◽  
Two Dimensional ◽  
Ansys Software ◽  
Free Surface Displacement

Numerical simulations have been carried out on a rectangular tank filled partially with liquid using volume of fluid technique. The tank has been given to and fro motion in one direction. Numerical simulation has been carried for a two dimensional case having laminar and unsteady flow. The changes in free surface displacement and dynamic pressure at different times has been observed using ANSYS software. The study was conducted for two sec. It was observed that free surface displacement of fluid increases with velocity. Also, with an increase in volume of liquid the sloshing effect decreases.

The Influence of a Free Surface on the Hydroelastic Stability of a Flat Panel

1972 ◽  
Vol 39 (1) ◽  
pp. 53-58 ◽  
Author(s):  
D. S. Weaver ◽  
T. E. Unny
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Two Dimensional ◽  
Flat Panel ◽  
Dimensional Solution ◽  
Dimensional Approximation ◽  
Free Surface Displacement

This paper examines the influence of a parallel free surface on the hydroelastic stability of a flat panel. A quasi-two-dimensional approximation is made for the free surface displacement and the results compared with the more general but cumbersome three-dimensional solution. This comparison shows that the former approach is quite reasonable as well as being considerably simpler and more instructive. It is found that the free surface has no effect for depth ratios greater than about one half and is stabilizing for smaller depth ratios.

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