Hydrostatic equilibrium

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

The Effect of Varying Damage History in Crystalline Rocks on the P- and S-Wave Velocity under Hydrostatic Confining Pressure

Abstract: Cracks play a very important role in many geotechnical issues and in a number of processes in the Earth’s crust. Elastic waves can be used as a remote sensing tool for determining crack density. The effect of varying crack density in crystalline rock on the P- and S-wave velocity and dynamic elastic properties under confining pressure has been quantified. The evolution of P- and S-wave velocity were monitored as a suite of dry Westerly granite samples were taken to 60, 70, 80 and 90 % of the unconfined uniaxial strength of the sample. The damaged samples were then subjected to hydrostatic confining pressure from 2 MPa to 200 MPa to quantify the effect of varying crack density on the P- and S-wave velocity and elastic properties under confining pressure. The opening and propagation of microcracks predominantly parallel to the loading direction during uniaxial loading caused a 0.5 and 6.3 % decrease in the P- and S-wave velocity, respectively. During hydrostatic loading, microcracks are closed at 130 MPa confining pressure. At lower pressures the amount of crack damage in the samples has a small but measureable effect. We observed a systematic 6 and 4 % reduction in P- and S-wave velocity, respectively, due to an increase in the fracture density at 2 MPa confining pressure. The overall reduction in the P- and S-wave velocity decreased to 2 and 1 %, respectively, at 50 MPa. The elastic wave velocities of samples that have a greater amount of microcrack damage are more sensitive to pressure. Effective medium modelling was used to invert elastic wave velocities and infer crack density evolution. Comparing the crack density results with experimental data on Westerly granite samples shows that the effective medium modelling used gave interpretable and reasonable results. Changes in crack density can be interpreted as closure or opening of cracks and crack growth.

Stiffness and Efficiency Optimization of a Hydrostatic Laser Surface Textured Gas Seal

Abstract: Microdimples generated by laser surface texturing (LST) can be used to enhance performance in hydrostatic gas-lubricated mechanical seals. This is achieved by applying microdimples with high area density over a certain portion of the sealing dam width adjacent to the high-pressure side, leaving the remaining portion untextured. The textured portion provides an equivalent larger gap that results in converging clearance in the direction of pressure drop and hence, hydrostatic pressure buildup, similar to that of a radial step seal. A mathematical model based on the solution of the Reynolds equation for compressible Newtonian fluid in a narrow gap between two nominally parallel stationary surfaces is developed. A detailed dimensionless analysis of the texturing parameters is performed to achieve maximum gas film stiffness with minimum gas leakage. DOI: 10.1115/1.2540120

Constructing and characterising solar structure models for computational helioseismology

Abstract: In local helioseismology, numerical simulations of wave propagation are useful to model the interaction of solar waves with perturbations to a background solar model. However, the solution to the linearised equations of motion include convective modes that can swamp the helioseismic waves that we are interested in. In this article, we construct background solar models that are stable against convection, by modifying the vertical pressure gradient of Model S (Christensen-Dalsgaard et al., 1996, Science272, 1286) relinquishing hydrostatic equilibrium. However, the stabilisation affects the eigenmodes that we wish to remain as close to Model S as possible. In a bid to recover the Model S eigenmodes, we choose to make additional corrections to the sound speed of Model S before stabilisation. No stabilised model can be perfectly solar-like, so we present three stabilised models with slightly different eigenmodes. The models are appropriate to study the f and p1 to p4 modes with spherical harmonic degrees in the range from 400 to 900. Background model CSM has a modified pressure gradient for stabilisation and has eigenfrequencies within 2% of Model S. Model CSM_A has an additional 10% increase in sound speed in the top 1 Mm resulting in eigenfrequencies within 2% of Model S and eigenfunctions that are, in comparison with CSM, closest to those of Model S. Model CSM_B has a 3% decrease in sound speed in the top 5 Mm resulting in eigenfrequencies within 1% of Model S and eigenfunctions that are only marginally adversely affected. These models are useful to study the interaction of solar waves with embedded three-dimensional heterogeneities, such as convective flows and model sunspots. We have also calculated the response of the stabilised models to excitation by random near-surface sources, using simulations of the propagation of linear waves. We find that the simulated power spectra of wave motion are in good agreement with an observed SOHO/MDI power spectrum. Overall, our convectively stabilised background models provide a good basis for quantitative numerical local helioseismology. The models are available for download from http://www.mps.mpg.de/projects/seismo/NA4/.

A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution

Abstract: In this work we present a multilayer approach to the solution of non-stationary 3D Navier–Stokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal velocity and a linear (in z) vertical velocity in each layer, possibly discontinuous across layer interfaces. The multilayer approach is deduced by using the variational formulation and by considering a reduced family of test functions. The procedure naturally provides the mass and momentum interfaces conditions. The mass and momentum conservation across interfaces is formulated via normal flux jump conditions. The jump conditions associated to momentum conservation are formulated by means of an approximation of the vertical derivative of the velocity that appears in the stress tensor. We approximate the multilayer model for hydrostatic pressure, by using a polynomial viscosity matrix finite volume scheme and we present some numerical tests that show the main advantages of the model: it improves the approximation of the vertical velocity, provides good predictions for viscous effects and simulates re-circulations behind solid obstacles.