Singular Pressure Research Articles

Pressure Loss Modeling for Multi-Stage Obstacles in Pressurized Ducts

Estimating singular pressure losses for multi-stage obstacles in pressurized hydraulic ducts is a challenging task. An experimental study was conducted in a closed-loop hydrodynamic tunnel to characterize the pressure losses of a system consisting of a porous fibrous foam placed in front of a bar rack. The pressure losses of different foam–rack configurations were measured over a range of inlet velocities in order to highlight the mutual influence of their characteristics on the flow. The interdependence between the two stages has been evidenced by both the experimental results and additional numerical simulations using RANS (Reynolds-Averaged Navier–Stokes Equations) simulations with a k-ω SST turbulent closure model. The pressure losses were first modeled using two approaches based on the assumption of either independence or full dependence between the stages. The respective advantages and limitations of these approaches led to an improved analytical formula that considers the transition of the flow from the porous foam to the bar rack. By taking into account an empirical transition factor, the proposed model improves the head loss prediction for all tested configurations, with an average relative error between the formula and experimental results less than that of the two simpler approaches. This study improves our understanding of global pressure losses in multi-stage systems that include a porous foam or other filtering or clogging media in front of bar racks.

Fast solution of incompressible flow problems with two-level pressure approximation

This paper develops efficient preconditioned iterative solvers for incompressible flow problems discretised by an enriched Taylor–Hood mixed approximation, in which the usual pressure space is augmented by a piecewise constant pressure to ensure local mass conservation. This enrichment process causes over-specification of the pressure when the pressure space is defined by the union of standard Taylor–Hood basis functions and piecewise constant pressure basis functions, which complicates the design and implementation of efficient solvers for the resulting linear systems. We first describe the impact of this choice of pressure space specification on the matrices involved. Next, we show how to recover effective solvers for Stokes problems, with preconditioners based on the singular pressure mass matrix, and for Oseen systems arising from linearised Navier–Stokes equations, by using a two-stage pressure convection–diffusion strategy. The codes used to generate the numerical results are available online.

Inflation Driven by Nonlinear Electrodynamics in Anisotropic Spacetime

The well-known Big Bang theory has explained how the universe came into being. This extraordinary event caused the later universe to be accelerated by a scale factor a(t). However, standard Big Bang theory has had some problems that can’t be explained, such as monopoles, horizons, and flatness. To solve this problem, a model of inflation in the early universe is required. Recent studies show that nonlinear electrodynamics coupled with general relativity can describe the inflation of the universe. In this work, we consider a model of nonlinear electrodynamics in anisotropic spacetime. We derive the dynamical equation from Einstein’s field equation and the law of conservation of energy-momentum tensor. Then, we use the perturbation method to solve the dynamical equation of the universe and obtain the evolution of the non-singular scale factor with anisotropy parameter ϵ. Using a phase-space analysis of the inflationary model, we obtain a phase portrait in the presence of fixed points. Our result shows that in the model of nonlinear electrodynamics coupled to gravity in anisotropic spacetime, the universe can undergo an inflationary mechanism if ϵ < 1. We also show the absence of singularity in density and pressure using this model.

Universe inflation and nonlinear electrodynamics

We analyse the inflation of the universe when the source of gravity is electromagnetic fields obeying nonlinear electrodynamics, with two parameters and without singularities. The cosmology of the universe with stochastic magnetic fields is considered, and the condition for universe inflation is obtained. It is demonstrated that singularities of energy density and pressure are absent as the scale factor approaches zero. When the scale factor goes to infinity, we have the equation of state for the ultra-relativistic case. The curvature invariants do not possess singularities. The evolution of the universe shows that at large time scales, the scale factor corresponds to the radiation era. The duration of universe inflation is also analysed. We study the classical stability and causality by computing the speed of sound. Cosmological parameters including the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r, and the running of the spectral index αs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _s$$\\end{document} are evaluated.

Analysis of shift in discharge coefficient for contaminated multihole orifice flow meter

The aim of this paper is to provide a comprehensive numerical study of influence of contamination and multi-hole orifice (MHO) flow meter geometry on shift in discharge coefficient. In this research, authors analyzed steady, three-dimensional, turbulent flow of dry air through MHO flow meter with 3 different β parameters. Shift in discharge coefficient was calculated for 29 different combinations of contamination parameters for 7 contamination angles, 3 different Reynolds numbers and 3 β parameters. Numerical method that was used was finite volume method with SIMPLE algorithm and standard k-ε turbulence model. Grid sensitivity study was performed on four systematically refined numerical grids for MHO with contamination for all values of Reynolds number, all values of β parameters and 3 values of contamination angle. Obtained results were grid independent. Numerical results for MHO without contamination were compared with the experimental results found in the literature. It was found that contamination angle has most influence on shift in discharge coefficient. Also it was found that the contamination has influence on the change of pressure drop values, which directly affects the change of other parameters. Pressure drop and singular pressure loss coefficient of the orifice with contamination are smaller compared to the values for a pure orifice, whereby the measurement accuracy was reduced. It was found that the multi-hole orifice meter was less sensitive to the pressure drop changes due to the increasing of contamination angle in regards to the single-hole orifice meters.

Optimal decay rates for the viscous two-phase model without constraints on transition to single-phase flow

In this paper, we study a free-boundary problem of the liquid-gas two-phase drift-flux model with constant viscosity, where the initial liquid and gas masses are assumed to be connected with vacuum continuously, and the pressure function takes a singular form. We utilize the flow map to reformulate the problem and prove the global existence and decay rates of strong solutions with general initial data that involve transition to pure single-phase points or regions. In particular, both the optimal decay rates of the mass functions and the decay estimates of the velocity towards its asymptotic profile as time goes to infinity are studied. As far as we are concerned, this is the first result on the global existence of strong solutions to the two-phase drift-flux model with singular pressure function and with general initial data that allow for transition to single-phase flow. It is also worth noting that our method in recovering the non-weighted estimates of the solution by utilizing the Poincaré type inequality can apply to the single-phase problem studied in Zeng (2015) [37], so as to derive the decay estimates for the velocity and relax the constraints on the initial data.

An adhesive detachment paradox: Does the substrate thickness matter?

A normal adhesive contact between a flat-ended cylindrical punch with elliptical cross-section and the surface of an elastic substrate, which can be regarded as an elastic layer of finite thickness, is considered. The experimental evidence published elsewhere indicates that the initiation of detachment can occur at the ends of the minor axis of the elliptical contact area, which eventually comes into contradiction with the surface energy theory developed so far. This paradox of adhesive detachment is examined in the framework of the JKR-type model formulated in terms of the stress intensity factor (SIF) of the contact normal stress. Based on the asymptotic model for a relatively thick elastic layer, the contact SIFs at the ends of the minor axis are shown to grow with decreasing the relative layer thickness faster than those at the ends of the major axis of the initial contact area. A plausible explanation for the observed inconsistency between experiment and state-of-the-art theory is found in the effect of the nonuniform elastic deformations on the square root singularity of the contact pressure at the punch edge.

Surface acoustic wave induced instability and pattern formation in a liquid polymer film

Recently, standing surface acoustic waves (SAWs) have been demonstrated to stimulate wrinkles on polymer films. Here, we theoretically investigate the underlying mechanism of the acoustic-induced micro-structures on a thin liquid film. The standing SAWs leak into the liquid polymer and generate radiation potential gradients. The strong potential gradients produce acoustic radiation pressure and induce an instability that features the wrinkling structure. Surface stability of the liquid film is firstly investigated by a linear instability analysis and the critical conditions of instability are analytically derived. Theoretical prediction of the film thickness that is favorable for surface instability well agrees with the optimal value found in previous experiments. Balance between the radiation and gravity-capillary pressure at the fluid surface forms the equilibrium equation of the surface profiles. Analytic solution reveals that the component of radiation pressure varying spatially makes the wavelength of the generated surface patterns equal to half of the SAW wavelength, while the constant component of radiation pressure absorbs the film onto the substrate. The interplay between the acoustic waves and the surface morphology is also investigated. Effects of the surface deformation on the radiation pressure is negligible except for that the mean thickness of the liquid approaches the resonance mode where singularity of the radiation pressure occurs.

Pressure and shear flow singularities: Fluid splitting and printing nip hydrodynamics

A numerical simulation of the fluid flow in the gravure printing nip, based on a discontinuous Galerkin algorithm, is used to study the fluid-splitting process and the transition between point and lamella splitting. We study the pressure and shear singularities at the contact point of the printing cylinder and substrate as a function of the variable microscopic residual gap and variations of the printing fluid quantities introduced to the nip. As the hydrodynamic boundary value problem is ill-defined by the nip singularity, we enhance the simulation using renormalization group and algebraic scaling techniques in order to obtain a numerically stable and physically meaningful prediction. Our simulations are compared to analytical results from lubrication theory and to experimental observations on a gravure press.

The non-uniqueness of admissible solutions to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint

We investigate the uniqueness of entropy solution to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint. The constraint is imposed with a singular pressure. Given initial data for which the standard self-similar solution consists of one shock or one shock and one rarefaction wave, it turns out that there exist infinitely many admissible weak solutions. This extends the result of Markfelder and Klingenberg in [S. Markfelder and C. Klingenberg, The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock, Arch. Ration. Mech. Anal. 227(3) (2018) 967–994] for classical Euler system to the case with maximum density constraint. Also some estimates on the density of these solutions are given to describe the behavior of solutions near congestion.

Numerical Study on the Evolution of Reservoir Pressure and CBM Concentration Considering Hydraulic Fractures

Based on the theories of mass conservation and coalbed methane (CBM) adsorption/desorption, this paper first establishes a novel reservoir pressure model for CBM production, following which, the CBM concentration and production models are also proposed. Then, these models are programmed and solved by means of the finite element method. Taking the Hunchun CBM field in Jilin province, China, as an example, the reservoir pressure, gas concentration, and production characteristics under different hydraulic fracture forms are simulated and investigated. In conclusion, the reservoir pressure decreases very rapidly in a small region near the fracture tip, which we called the “reservoir pressure singularity”. The existence of a hydraulic fracture greatly reduces the reservoir pressure in the process of CBM exploitation. The permeability sensitivity coefficient of reservoir pressure, Rpk, is defined to quantitatively describe the influence of coal seam permeability on the evolution of reservoir pressure. Rpk decreases logarithmically as the distance from the CBM extraction well increases. The reservoir pressure and CBM recovery rate characteristics in the presence of multiple hydraulic fractures are also investigated. We believe these results could contribute to the design of hydraulic fracturing wells and the evaluation of gas production in a CBM reservoir.

Analysis of Aluminium Filling in Cylindrical Pipe under High Pressure by Experiment and Mathematical Modelling

The preferred method for producing lightweight metal components, mainly from aluminum and magnesium alloys, is through high pressure die casting. This process involves rapidly and forcibly injecting liquid metal into a metal mold under high pressure. Our study aims to compare results obtained from the numerical modelling of the filling of aluminum under high pressure with the experimental results. Two different cylindrical pipes are used. The results indicate for imposed values of KE = 14 and KW = 60 for pipe 1(Dentry/Drp=40/40) and pipe 2 (Dentry/Drp=16/40) respectively, the mathematical model with the same initial conditions gives some results which are close to the experimental data. The results also indicate that pipe 2 is damped faster than pipe and this is due to the singular pressure loss at the entry.

Hard-congestion limit of the p-system in the BV setting

This note is concerned with the rigorous justification of the so-called hard congestion limit from a compressible system with singular pressure towards a mixed compressible-incompressible system modeling partially congested dynamics, for small data in the framework of BV solutions. We present a first convergence result for perturbations of a reference state represented by a single propagating large interface front, while the study of a more general framework where the reference state is constituted by multiple interface fronts is announced in the conclusion and will be the subject of a forthcoming paper. A key element of the proof is the use of a suitably weighted Glimm functional that allows to obtain precise estimates on the BV norm of the front-tracking approximation.

Explicit Analytic Solutions for the Subsurface Stress Field in Single Plane Contacts of Elastically Similar Truncated Cylinders or Wedges

As has been pointed out recently, a possible solution strategy to the wear–fatigue dilemma in fretting, operating on the level of contact mechanics and profile geometries, can be the introduction of “soft” sharp edges to the contact profiles, for example, by truncating an originally smooth profile. In that regard, analysis of possible mechanical failure of a structure, due to the contact interaction, requires the knowledge of the full subsurface stress state resulting from the contact loading. In the present manuscript, a closed-form exact solution for the subsurface stress state is given for the frictional contact of elastically similar truncated cylinders or wedges, within the framework of the half-plane approximation and a local-global Amontons–Coulomb friction law. Moreover, a fast and robust semi-analytical method, based on the appropriate superposition of solutions for parabolic contact, is proposed for the determination of the subsurface stress fields in frictional plane contacts with more complex profile geometries, and compared with the exact solution. Based on the analytical solution, periodic tangential loading of a truncated cylinder is considered in detail, and important scalar characteristics of the stress state, like the von-Mises equivalent stress, maximum shear stress, and the largest principal stress, are determined. Positive (i.e., tensile) principal stresses only exist in the vicinity of the contact edge, away from the pressure singularity at the edge of the profile, and away from the maxima of the von-Mises equivalent stress, or the maximum shear stress. Therefore, the fretting contact should not be prone to fatigue crack initiation.

Probing Our Universe’s Past Using Earth’s Geological and Climatological History and Shadows of Galactic Black Holes

In this short review, we discuss how Earth’s climatological and geological history and also how the shadows of galactic black holes might reveal our Universe’s past evolution. Specifically we point out that a pressure singularity that occurred in our Universe’s past might have left its imprint on Earth’s geological and climatological history and on the shadows of cosmological black holes. Our approach is based on the fact that the H0 tension problem may be resolved if some sort of abrupt physics change occurred in our Universe 70–150 Myrs ago, an abrupt change that deeply affected the Cepheid parameters. We review how such an abrupt physics change might have been caused in our Universe by a smooth passage of it through a pressure finite-time singularity. Such finite-time singularities might occur in modified gravity and specifically in F(R) gravity, so we show how modified gravity might drive this type of evolution, without resorting to peculiar cosmic fluids or scalar fields. The presence of such a pressure singularity can distort the elliptic trajectories of bound objects in the Universe, causing possible geological and climatological changes on Earth, if its elliptic trajectory around the Sun might have changed. Also, such a pressure singularity affects directly the circular photon orbits around supermassive galactic black holes existing at cosmological redshift distances, thus the shadows of some cosmological black holes at redshifts z≤0.01, might look different in shape, compared with the SgrA* and M87* supermassive black holes. This feature however can be checked experimentally in the very far future.

Dissimilar donuts in the sky? Effects of a pressure singularity on the circular photon orbits and shadow of a cosmological black hole

The black hole observations obtained so far indicate one thing: similar “donuts” exist in the sky. But what if some of the observed black hole shadows that will be obtained in the future are different from the others? In this work the aim is to show that a difference in the shadow of some observed black holes in the future might explain the H 0-tension problem. In this letter we investigate the possible effects of a pressure cosmological singularity on the circular photon orbits and the shadow of galactic supermassive black holes at cosmological redshifts. Since the pressure singularity is a global event in the Universe, the effects of the pressure singularity will be imposed on supermassive black holes at a specific redshift. As we show, the pressure singularity affects the circular photon orbits around cosmological black holes described by the McVittie metric, and specifically, for some time before the time instance that the singularity occurs, the photon orbits do not exist. We discuss the possible effects of the absence of circular photon orbits on the shadow of these black holes. Our idea indicates that if a pressure singularity occurred in the near past, then this could have a direct imprint on the shadow of supermassive galactic black holes at the redshift corresponding to the time instance that the singularity occurred in the past. Thus, if a sample of shadows is observed in the future for redshifts , and for a specific redshift differences are found in the shadows, this could be an indication that a pressure singularity occurred, and this global event might resolve the H 0-tension as discussed in previous work. However, the observation of several shadows at redshifts is a rather far future task.

Two-Phase Compressible/Incompressible Navier–Stokes System with Inflow-Outflow Boundary Conditions

We prove the existence of a weak solution to the compressible Navier–Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport equation. We then prove that the “stiff pressure” limit gives rise to the two-phase compressible/incompressible system with congestion constraint describing the free interface. We prescribe the velocity at the boundary and the value of density at the inflow part of the boundary of a general bounded \(C^2\) domain. For the positive velocity flux, there are no restrictions on the size of the boundary conditions, while for the zero flux, a certain smallness is required for the last limit passage.

A singularity analysis in Keer’s elastic indentation problem

A non-axisymmetric three-dimensional frictionless contact problem for an elastic half-space and a cylindrical indenter with the face in a wedge form is considered under the assumption of a circular region of contact. Explicit formulas are derived for the critical indenter displacement and contact force that are needed to ensure full contact over the entire contact region. It is shown that the contact pressure beneath the indenter maintains a logarithmic singularity, which is produced by the wedge edge and is similar to the singularity of the contact pressure in the corresponding two-dimensional contact problem for a wedge rigid indenter.

Did the Universe experience a pressure non-crushing type cosmological singularity in the recent past?

In the recent literature it has been shown that the H 0 tension may be eliminated if an abrupt physics transition changed the Cepheid parameters in the near past of the Universe, nearly 70–150 Myrs ago. In this letter we stress the possibility that this abrupt transition was caused by the smooth passage of our Universe through a pressure finite-time cosmological singularity. Being a non-crushing type singularity the pressure singularity can leave its imprints in the Universe, since it occurs globally and literally everywhere. We discuss how this scenario could easily be realized by F(R) gravity, with the strong energy conditions being satisfied without the need for a scalar field or specific matter fluids. We also stress the fact that the pressure singularity can affect the effective gravitational constant of F(R) gravity. Moreover, we stress the fact that pressure singularities can disrupt the trajectories of bound objects in the Universe, which is also pointed out in the literature, even in the context of general relativity. We also show numerically in a general relativistic framework that elliptic trajectories are distorted and changed to different elliptic trajectories when the Universe passes through the pressure singularity. Such a disruption of the trajectories could have tidal effects on the surface of the Earth, for example on sea waters and oceans, regarding the distortion of Moon's elliptic trajectory. Accordingly, the distortion of Earth's trajectory around the Sun could have affected climatologically the Earth 70–150 Myrs ago.

Multiparameter equation of state for classical and quantum fluids

A closed-form multi-parameter fluid equation of state (EoS) is proposed and tested with empirical pressure isotherms of water and hydrogen. The EoS is non-algebraic but elementary, applicable in the full temperature range above the melting point, and remains accurate at high pressure. The critical-point conditions (vanishing density-derivatives of pressure) are exactly implemented in the exponential attractive term of the EoS. The singular repulsive term is structured similar to the Carnahan-Starling EoS and depends on five substance-specific parameters, which can be regressed from the critical isotherm. The temperature evolution of the EoS above the critical temperature is regressed from supercritical isotherms. In the subcritical regime above the melting point, the temperature-dependent scale factors of the EoS are inferred from the empirical coexistence curve, which is fully implemented in the EoS. The pressure singularity occurs at a limit density that is noticeably higher than predicted by universal cubic EoSs such as the Peng-Robinson EoS. The parameters of the analytic and non-perturbative EoSs of water and hydrogen are derived from high-pressure data sets.