Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Modeling overcontact binaries. I. The effect of tidal deformation

Abstract: Context. In the realm of massive stars, strong binary interactions are commonplace. One extreme case is that of over- contact systems, which are expected to be part of the evolution of all stars evolving towards a merger and hypothesized as playing a role in the formation of binary black holes. However, important simplifications are made to model the evolution of overcontact binaries. The deformation from tidal forces is almost always put aside, and even rotation is frequently ignored in such models. Yet, both observations and theory have shown that overcontact stars are tidally deformed to a great extent, leaving a potentially important effect on the outer layers unaccounted for in models. Fur-thermore, in eclipsing binaries where radii can be determined to high precision, the question of how large the effect of tidal deformation is on the inferred properties of stellar models is still uncertain. Aims. We aim to consistently model overcontact binary stars in a one-dimensional (1D) stellar evolution code. To that end, we developed the required methodology to represent tidally distorted stars in 1D evolution codes. Methods. Using numerical methods, we computed the structure correction factors to the 1D spherical stellar structure equations of hydrostatic equilibrium and radiative energy transfer due to the binary Roche potential. We then compared them to existing results and the structure corrections of single, rotating stars. We implemented the new structure correction factors in the stellar evolution code MESA and explored several case studies. We compared the differences between our simulations: when no rotation is included, when we treat rotation using single star corrections (only accounting for centrifugal deformation), or when we use tidal deformation. Results. We find that ignoring rotation in deformed detached eclipsing binaries can produce a radius discrepancy of up to 5%. The difference between tidal and single star centrifugal distortion models is more benign at 1%, showing that single rotating star models are a suitable approximation of tidally deformed stars in a binary system. In overcontact configurations, we find a similar 5% variation in surface properties as a result of tidal distortion with respect to non-rotating models, showing that it is inappropriate to model binary stars filling their Roche lobe significantly as non-rotating.

Wave-by-wave control in irregular waves for a wave energy converter with approximate parameters

Abstract: This paper investigates wave-by-wave control of a single-mode wave energy converter driven to operate such that the oscillation velocity closely matches the hydrodynamically optimum velocity for best power absorption. Such control typically requires prediction of the incident wave profile, which, for realistic wave spectra may be obtained using up-wave measurements over a duration and at a distance based on a deterministic propagation model and the device dynamics. This work investigates how such control may be attempted when the device inertia, viscous damping, hydrostatic stiffness, frequency-dependent hydrodynamic coefficients, and exciting force are quantified approximately. In particular, this paper studies an implementation of adaptive trajectory-tracking control using on-line estimation of the mechanical and hydrodynamic parameters (i.e. inertia, viscous damping, hydrostatic stiffness, frequency-dependent added mass, frequency-dependent radiation damping, and the exciting force), where a hydrodynamically optimum velocity variation based on approximate parameter estimates provides the reference trajectory. In this study, the rest mass, infinite-frequency added mass, hydrostatic stiffness, a linearized viscous damping coefficient, and two parameters representing the uncertainties in the radiation impulse-response function and the exciting force impulse-response function are estimated on line. The present method relies on feedback and feedforward forces derived using a Lyapunov function comprised of a system Hamiltonian that combines the mechanical and information exergy functions. Energy capture results under oscillation constraints show that, while the present implementation leaves significant room for improvement relative to near-optimal wave-by-wave control with exact parameters, considerable improvement is still observed relative to resistive control with exact parameters.

A compressible two-layer model for transient gas–liquid flows in pipes

Abstract: This work is dedicated to the modeling of gas-liquid flows in pipes. As a first step, a new two-layer model is proposed to deal with the stratified regime. The starting point is the isentropic Euler set of equations for each phase where the classical hydrostatic assumption is made for the liquid. The main difference with the models issued from the classical literature is that the liquid as well as the gas are assumed compressible. In that framework, an averaging process results in a five-equation system where the hydrostatic constraint has been used to define the interfacial pressure. Closure laws for the interfacial velocity and source terms such as mass and momentum transfer are provided following an entropy inequality. The resulting model is hyperbolic with non conservative terms. Therefore, regarding the homogeneous part of the system, the definition and uniqueness of jump conditions is studied carefully and acquired. The nature of characteristic fields and the corresponding Riemann invariants are also detailed. Thus, one may build analytical solutions for the Riemann problem. In addition, positivity is obtained for heights and densities. The overall derivation deals with gas-liquid flows through rectangular channels, circular pipes with variable cross-section and includes vapor-liquid flows.

Oscillations of a self-gravitating fluid spheroid with a prevalent magnetic field.

Abstract: The Kelvin modes of oscillation of a selfgravitating, homogeneous fluid spheroid in hydrostatic equilibrium with a poloidal magnetic field inside and a dipole type field outside, are studied, using a variational principle. On the assumption that the eccentricitye of the spheroid is small, the frequencies of oscillation are calculated to the first order ine2.

Process for utilization of hydrostatic energy and gravity and resulting equipment

Abstract: The present patent of invention refers to a process for utilization of hydrostatic energy and gravity and the resulting equipment for generation of mechanical or electrical energy, through the utilization of a liquid storage tank ( 1 ) in a static form, with the use of thrust for the raising of the propellers ( 2 ), endowed with a set of bodies ( 2 -A) linked to each other by belts or chains ( 3 ) inside the tank ( 1 ) and with the use of the force of gravity for the falling of the propellers ( 2 ) outside the tank ( 1 ), forming a thrust-gravity-power generation rotary cycle, bringing a clean, ecological and economic new option in energy generation, with a good cost-benefit relation.