Pressure Equation Research Articles

Non-isochoric stable granular models taking into account fluidisation by pore gas pressure

In this paper, we study non-isochoric models for mixtures of solid particles, at high volume concentration, and a gas. One of the motivations for this work concerns geophysics and more particularly the pyroclastic density currents, whose dense basal parts are precisely mixtures of pyroclasts and lithic fragments and air. They are extremely destructive phenomena, capable of devastating urbanised areas, and are known to propagate over long distances, even over almost flat topography. Fluidisation of these dense granular flows by pore gas pressure is one response that could explain this behaviour and must therefore be taken into account in the models. Starting from a solid–gas mixing model and invoking the compressibility of the gas through a law of state, we rewrite the conservation of mass equation of the gas phase into an equation of the pore gas pressure whose net effect is to reduce the friction between the particles. The momentum equation of the solid phase is completed by generic constitutive laws, specified as in Schaeffer et al. (J. Fluid Mech., vol. 874, 2019, pp. 926–951) by a yield function and a dilatancy function. Therefore, the divergence of the velocity field, which reflects the ability of the granular flow to expand or compress, depends on the volume fraction, pressure, strain rate and inertial number. In addition, we require the dilatancy function to describe the rate of volume change of the granular material near an isochoric equilibrium state, i.e. at constant volume. This property ensures that the volume fraction, which is the solution to the conservation of mass equation, is positive and finite at all times. We also require that the non-isochoric fluidised model be linearly stable and dissipate energy (over time). In this theoretical framework, we derive the dilatancy models corresponding to classical rheologies such as Drucker–Prager and $\mu (I)$ (with or without expansion effects). The main result of this work is to show that it is possible to obtain non-isochoric and fluidised granular models satisfying all the properties necessary to correctly account for the physics of granular flows and which are well posed, at least linearly stable.

A unified stiffness model of rolling lobe air spring with nonlinear structural parameters and air pressure dependence of rubber bellows

The structural parameters of the rolling lobe air spring and the mechanical characteristic of rubber bellows are the key factors affecting the stiffness and mechanical characteristic of the rolling lobe air spring. Aiming at the prediction difficulties of structural parameters of the rolling lobe air spring with the composite curved contour piston and the modeling complexity of the hysteretic mechanical characteristic of rubber bellows under variable pressure conditions, the geometrical method is applied to derive the structural parameters models of the rolling lobe air spring with the composite curved contour piston. A new pressure factor is introduced and the Coulomb frictional pressure perturbation model and the fractional derivative Kelvin-Voigt pressure perturbation model are reconstructed to accurately describe the hysteretic mechanical characteristic of rubber bellows under variable pressure conditions. A unified pressure equation is constructed to characterize the evolution of model parameters under variable pressure conditions. Furthermore, a hysteretic mechanical characteristic pressure perturbation model (abbreviated as HMCPP model) of rubber bellows under variable pressure conditions is put forward. Finally, a unified stiffness model of the rolling lobe air spring including prediction models of nonlinear structural parameters and a HMCPP model of rubber bellows is built. Taking a certain type of rolling lobe air spring as the test sample A, the structural parameters tests and static/dynamic characteristic tests of sample A are carried out based on the MTS852.05 test bench, which verified the accuracy of the unified stiffness model of the rolling lobe air spring. The research results provide theoretical support for the mechanical characteristic matching and air pressure precise control of the rolling lobe air spring under variable pressure conditions.

Smooth criteria for two kinds of equations in pressure

Smooth criteria for two kinds of equations in pressure

No change in 24-h sodium intake estimated from spot urine in Norwegian adults from 2006 to 2019: the population-based Trøndelag Health Study (HUNT).

Monitoring time trends in salt consumption is important for evaluating the impact of salt reduction initiatives on public health outcomes. There has so far not been available data to indicate if salt consumption in Norway has changed during the previous decade. We aimed to assess whether average 24-h salt intake estimated from spot urine samples in the adult population of mid-Norway changed from 2006-2008 to 2017-2019 and to describe variations by sex, age and educational level. Repeated cross-sectional studies. The population-based Trøndelag Health Study (HUNT). In each of two consecutive waves (HUNT3: 2006-2008 and HUNT4: 2017-2019), spot urine samples were collected from 500 men and women aged 25-64 years, in addition to 250 men and women aged 70-79 years in HUNT4. Based on spot urine concentrations of Na, K and creatinine and age, sex and BMI, we estimated 24-h Na intake using the International Cooperative Study on Salt and Blood Pressure (INTERSALT) equation for the Northern European region. Mean (95 % CI) estimated 24-h salt intakes in men were 11·1 (95 % CI 10·8, 11·3) g in HUNT3 and 10·9 (95 % CI 10·6, 11·1) g in HUNT4, P = 0·25. Corresponding values in women were 7·7 (95 % CI 7·5, 7·9) g and 7·7 (95 % CI 7·5, 7·9) g, P = 0·88. Mean estimated salt intake in HUNT4 decreased with increasing age in women, but not in men, and it did not differ significantly across educational level in either sex. Estimated 24-h salt intake in adult men and women in mid-Norway did not change from 2006-2008 to 2017-2019.

Hybrid Mimetic Finite Difference and Streamline Methods for Numerical Simulation of Two-phase Flow in Fractured Reservoirs

In this work, we present a novel numerical formulation for efficiently modeling two-phase flow in fractured reservoirs. The novel formulation is developed by hybridizing mimetic finite difference and streamline (MFD-SL) methods, in which mimetic finite difference (MFD) is employed to discretize the pressure equation, and the streamline (SL) method is adopted to solve the saturation equation along 1D streamlines. The hybrid formulation is implemented on discrete fracture model (DFM) and is operated in an IMPES-like manner. A simple and practical streamline tracing method is developed on 2D triangular and 3D tetrahedral grids that are commonly implemented in the DFM framework. We benchmark the hybrid MFD-SL formulation with others using various cases with different complexity. Results show the proposed approach could achieve promising results yet with lower computation costs compared to other classical formulations. These achievements benefit from utilizing streamline tracing, which significantly alleviates the numerical diffusion error and improves the computation efficiency. This work, for the first time, incorporates hybrid MFD-SL formulation into DFM in case of triangular and tetrahedral grids and has great potential to be deployed on reservoir-scale simulation workflow.

DETERMINATION OF THE DEGREE OF INFLUENCE OF HYDRODYNAMIC PRESSURE DROP AND CAPILLARY PRESSURE ON THE DEPTH OF THE ZONE OF PENETRATION OF FILTRATE OF WASHING FLUID INTO THE FORMATION

When mud filtrate is introduced into the formation, its rate of advancement is determined by hydrodynamic and capillary forces. Hydrodynamic forces act at a distance between points of different pressures. Unlike hydrodynamic forces, capillary pressure acts locally, at the interface. In some cases, when hydrodynamic filtration in the formation is not carried out, the entry of washing fluid is due to capillary penetration. The ratio of forces depends on changes in pressure, water supply, interfacial tension, radius of porous channels and a number of other factors. The calculation method proposed in the article allows to determine the values of the radius of the pore channels and the distance from the well at which the equality of hydrodynamic and capillary forces will be observed. A plot of the dependence of the hydrodynamic force difference and capillary pressure equation on the radius of the porosity channels determined by the distance of the radius from the well is described.

A novel streamline simulation method for fractured reservoirs with full-tensor permeability

In this work, we develop a novel streamline (SL) simulation method that integrates seamlessly within the embedded discrete fracture model (EDFM). The novel SL-based method is developed based on a hybrid of two-point flux approximation (TPFA) and mimetic finite difference (MFD) methods, which is applicable to a two-phase anisotropic flow in fractured reservoirs. We refer to this novel approach as EDFM-TPFA-MFD-SL. The approach is operated in an IMplicit Pressure Explicit Saturation (IMPES) manner. First, this work establishes a novel EDFM utilizing a hybrid TPFA-MFD scheme to solve the pressure equation for phase flux approximation. Subsequently, we introduce a practical streamline tracing workflow designed to derive the distribution of streamlines within the reservoir domain and the time-of-flight distribution along each individual streamline. This feature allows for the parallel computation of water saturation along the streamlines. Two numerical examples are presented to validate the superiority of the proposed EDFM-TPFA-MFD-SL method compared to the existing streamline-based EDFM on cases with full-tensor permeability. The results show that the proposed method could significantly mitigate the numerical dissipation and reduce the computation costs. Another numerical example demonstrates the effectiveness of the proposed method in dealing with complex fracture networks and providing rapid flow diagnostics, indicating its significant potential for real-world field applications.

Numerical analysis of double-diffusive natural convective flow of Ostwald-de Waele fluid in an irregular enclosure with a circular obstacle

PurposeThe current study aims to enhance the double diffusive natural convection in an Ostwald-de Waele fluid filled in a hexagonal enclosures using non-uniform magnetic field embedded with circular obstacle. The upper wall has maximum temperature Th∗ and concentration (Ch∗) whereas the lower wall is kept at minimum temperature Tc∗ and concentration Cc∗. The parameters that play a significant role in the heat and mass transfer are evaluated, including Hartmann number, power law index, Rayleigh number and buoyancy ratio. Design/Methodology/approachIn two-dimensions, the governing formulation is written as a set of balancing equations for velocities, pressures, energies and concentrations. The nonlinear governing PDEs are solved using numerical approach based on Finite Element Method (FEM). The discretization is performed using the stable finite element pair ℘2/℘1. Code validation and results are ensured by conducting a grid convergence and comparison test respectively. FindingsThe influence of flow on velocity, isotherms and iso-concentration field is examined by analyzing a broad variety of variables such as power-law index 0.7≤n≤1.2, Hartmann number 0≤Ha≤50, Rayleigh number 104≤Ra≤106, inclination angle 0°≤γ≤90° and buoyancy ratio -2≤N≤2. The findings are displayed graphically, including the flow, temperature and concentration fields. Heat and mass transfer rates are maximum for shear thinning fluids while for shear thickening fluids it reduces, whereas it is maximum for concentration dominated assistant flow and minimum for concentration dominant counter flow. ApplicationThe novel aspects of the research include its thorough examination of solar thermal power conversion and its inventive energy deficiency devices and a wide range of electrical design applications.

Hybrid mixed discontinuous Galerkin finite element method for incompressible miscible displacement problem

A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve the pressure and velocity equations, and a new hybrid mixed discontinuous Galerkin finite element procedure is constructed to solve the concentration equation with upwind technique. Compared with other traditional discontinuous Galerkin methods, the new method can reach a global system with less unknowns and sparser stencils. The consistency and conservation of the method are analyzed, the stability and optimal error estimates are also derived by the new technique. Meanwhile, numerical examples are provided to confirm the corresponding theoretical analysis.

Interaction model for horizontal dynamic response of monopile-friction wheel composite foundation in marine area

To ensure the expansion of offshore wind power market under economical investment, the monopile-friction wheel composite foundation is proposed by previous scholars. This paper develops a theoretical model to obtain the horizontal dynamic response of the composite foundation in marine environment. The soil reaction excited by the pile’s vibration is calculated based on the Novak’s thin layer model and Biot’s wave theory, and the shear force caused by the friction wheel can be obtained by use of the three-dimensional continuum mechanics theory. The dynamic equations of pile shaft and hydrodynamic pressure are described by Euler-Bernoulli beam theory and radiation wave theory, respectively. The correctness and accuracy of the analytical framework have been confirmed by comparing the similar results of existing literatures. Finally, the influences of the diameter and thickness of the friction wheel on the horizontal dynamic characteristics and displacement filed of seabed surface have been thoroughly discussed. The main findings can be drawn that the horizontal vibration characteristics along the composite foundation decrease with increasing the diameter and thickness of friction wheel, and thus the advantages of the monopile-friction wheel composite foundation compared to single pile is proved with great potential of progress.

Wellposedness of a nonlinear parabolic-dispersive coupled system modelling MEMS

In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two parallel plates separated by a gas-filled thin gap. The nonlinear parabolic-dispersive coupled system modelling the device consists of a quasilinear parabolic equation for the gas pressure and a semilinear plate equation for gap width. We show the local-in-time existence of strict solutions for the system, by combining a local-in-time existence result for the dispersive equation, Hölder continuous dependence of its solution on that of the parabolic equation, and then local-in-time existence for a resulting abstract parabolic problem. Semigroup approaches are vital for both main parts of the problem.

Analysis and optimization of injection characteristics and comprehensive performance of low GWP refrigerant HP-1 in high temperature heat pump systems

In the context of low-GWP refrigerants becoming a research hotspot, the environmentally friendly refrigerant HP-1 with independent intellectual property rights in China has demonstrated significant advantages in fields such as data centers and 5G base stations. However, there are few applied studies in the field of high-temperature heat pumps (HTHPs), therefore, in this study, HP-1 was utilized in HTHP system and this process was combined with the injection technology. It has been proven to be an effective approach for performance improvement. The injection characteristics of HP-1-based HTHP were analyzed and optimized with a focus on safety, stability, and efficient operation. The application advantages of HP-1 were compared and analyzed in terms of thermodynamic performance and Total Equivalent Warming Impact. The results indicated that there were three types of characteristic injection pressures based on system performance, corresponding to the maximum coefficient of performance (COP), the lowest electronic expansion valve inlet refrigerant temperature, and the lowest exhaust temperature of the compressor. Further, the corresponding control equations for injection pressure were obtained. Based on the safety injection pressure, the optimal COP under injection pressure could effectively improve the COP of the system by 2.1–5.2 %, and the exhaust temperature also increased by 6.1–10.1 %. When the temperature of the heat source was 50 °C and the target heating temperature was 120 °C, the heating capacity of HP-1 increased by 10.8 % compared with that of R245fa, the COP of the system increased by 2.7 %, and the volume heating capacity increased by 10.3 %. Moreover, the emission reduction effect of HP-1 was significant, and the carbon dioxide emissions were reduced by 15.4–39.1 %. The analysis shows that HP-1 exhibits better performance and environmental characteristics than HFC-245fa. This study is of guiding significance to improve the thermodynamic performance of HTHP, for the safe and efficient operation and energy saving and emission reduction in the industrial field.

The microscopic Ampère formulation for the electromagnetic force density in linear dielectrics

We present a detailed derivation of the electromagnetic force density and pressure in linear dielectric media according to the so-called microscopic Ampère formulation, which considers the classical dipolar sources in matter along with the hidden momentum contribution. It is seen that, among the other formulations existing in the literature, our proposal is the only one universally compatible with the experimental works reported to date. A new radiation pressure equation for non-magnetic dielectrics under oblique illumination from p-polarized beams is also derived.

Study of overflow effects on flow‐induced stress in injection molding

AbstractOverflow is usually used to keep fluid continuously flowing to avoid the fluid from changing flow direction and subsequently inducing large stresses. To explore the mechanism of flow‐induced stress evolution, a flow model was established in terms of compressible, non‐isothermal, and viscoelastic flow. Based on the Leonov model and the mid‐plane approach, a pseudo‐Poisson type equation for pressure was derived to decouple the interdependence between velocity and pressure. To improve computational efficiency, a numerical approach involving double iterations was proposed to solve the flow problem. Two kinds of mold cavities, with and without overflow, were designed and manufactured. Molding experiments were conducted, and corresponding simulations based on the proposed model and algorithm were performed. The results show that the simulated contours of flow‐induced stress are in good agreement with the photoelastic streaks. The use of overflow can significantly reduce flow‐induced stresses. If the slot thickness is set to a proper value, the flow‐induced stress can be reduced by more than 80%. On the other hand, a slot that is too thick does not have significant reducing effects. Therefore, using overflow to reduce flow‐induced stresses during transparent part production is a promising approach if the material cost is worthy of the quality.Highlights A double iteration method is proposed for viscoelastic flow problem. Overflow can reduce the stress as much as 80% if the dimension is properly set. The simulated stress streaks are in good agreement with photoelasticities.

Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state

In this article, the well-known Cargo–Leroux model with isentropic perturbation equation of state is analyzed using the Lie symmetry method. By using invariant conditions of system of partial differential equations, six dimensional Lie algebra is obtained. The optimal system for system of partial differential equations is constructed using adjoint representation and the invariants of associated Lie algebras of the system. Further, with the help of one-dimensional optimal system invariant solutions are constructed. Also, physically significant solutions such as traveling wave solutions, specifically the kink-type solitons and peakon-type solitons are obtained by using traveling wave transformations and all the solutions are graphically demonstrated. Finally, the hyperbolic nature of system of partial differential equations is examined by studying the evolutionary behavior of a discontinuity wave.

The Left Atrial Area Derived Cardiovascular Magnetic Resonance Left Ventricular Filling Pressure Equation Shows Superiority over Integrated Echocardiography.

Background and objectives: Evaluating left ventricular filling pressure (LVFP) plays a crucial role in diagnosing and managing heart failure (HF). While traditional assessment methods involve multi-parametric transthoracic echocardiography (TTE) or right heart catheterisation (RHC), cardiovascular magnetic resonance (CMR) has emerged as a valuable diagnostic tool in HF. This study aimed to assess a simple CMR-derived model to estimate pulmonary capillary wedge pressure (PCWP) in a cohort of patients with suspected or proven heart failure and to investigate its performance in risk-stratifying patients. Materials and methods: A total of 835 patients with breathlessness were evaluated using RHC and CMR and split into derivation (85%) and validation cohorts (15%). Uni-variate and multi-variate linear regression analyses were used to derive a model for PCWP estimation using CMR. The model's performance was evaluated by comparing CMR-derived PCWP with PCWP obtained from RHC. Results: A CMR-derived PCWP incorporating left ventricular mass and the left atrial area (LAA) demonstrated good diagnostic accuracy. The model correctly reclassified 66% of participants whose TTE was 'indeterminate' or 'incorrect' in identifying raised filling pressures. On survival analysis, the CMR-derived PCWP model was predictive for mortality (HR 1.15, 95% CI 1.04-1.28, p = 0.005), which was not the case for PCWP obtained using RHC or TTE. Conclusions: The simplified CMR-derived PCWP model provides an accurate and practical tool for estimating PCWP in patients with suspected or proven heart failure. Its predictive value for mortality suggests the ability to play a valuable adjunctive role in echocardiography, especially in cases with unclear echocardiographic assessment.

Three-dimensionality effects on the flow past a horizontal heated cylinder under mixed convection heat transfer

The three-dimensionality has a significant effect on the flow-field and heat transfer, especially when the geometry is affected by thermal buoyancy. In the present research, the interaction of three-dimensionality, thermal buoyancy, and vortex shedding on the flow around an isothermal horizontal cylinder and its mixed convection heat transfer were numerically investigated. Both the secondary flow due to the thermal buoyancy and the free stream had an upward direction. The problem was simulated in a constant Prandtl number of 0.7, a range of Reynolds numbers (based on the cylinder's diameter) between 100 and 300, and Richardson numbers ranging between 0 and 0.5. The aspect ratio of the cylinder was 6. The numerical simulation of the problem was based on the discretization of the Navier–Stokes, energy, and k–ω SST turbulence equations. A finite-volume and pressure-based method with second-order spatial and temporal accuracy was utilized. The momentum, energy, and turbulence equations were explicitly solved, while the pressure equation was solved, implicitly. Comparison of the two-dimensional and three-dimensional simulations showed that the thermal buoyancy had a significant impact on the flow three-dimensionality, so that the flow could become three-dimensional even at low Reynolds numbers such as Re = 130. In addition, the results demonstrated that for each Reynolds number, there was a critical Richardson number where the mean drag coefficient and Nusselt number reached their minimum value. Moreover, for Richardson numbers higher than the critical value, the flow entered a new low amplitude vortex shedding mode.

REGULARIZED EQUATIONS FOR DYNAMICS OF THE HETEROGENEOUS BINARY MIXTURES OF THE NOBLE-ABEL STIFFENED-GASES AND THEIR APPLICATION

We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form arising after excluding the volume concentrations from the sought functions and based on a quadratic equation for the common pressure of the components. We present new properties of this equation and a simple formula for the squared speed of sound, suggest an alternative derivation for a formula relating it to the squared Wood speed of sound and state the pressure balance equation. For the first time, we give quasi-gasdynamic-type regularization of the heterogeneous model (in the quasi-homogeneous form), construct explicit two-level in time and symmetric three point in space finite-difference scheme without limiters to implement it in the 1D case and present numerical results.

On a doubly reduced model for dynamics of heterogeneous mixtures of stiffened gases, its regularizations and their implementations.

We deal with the reduced four-equation model for the dynamics of heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations, and with a quadratic equation for the common pressure of the components; this form can be called a quasi-homogeneous form. We prove new properties of the equation, derive simple formulas for the squared speed of sound, and present an alternative proof for a formula that relates it to the squared Wood speed of sound; also, a short derivation of the pressure balance equation is given. For the first time, we introduce regularizations of the heterogeneous model (in the quasi-homogeneous form). Previously, regularizations of such types were developed only for the homogeneous mixtures of perfect polytropic gases, and it was unclear how to cover the case considered here. In the 1D case, based on these regularizations, we construct new explicit two-level in time and symmetric three-point in space finite-difference schemes without limiters and provide numerical results for various flows with shock waves.

Atmospheric Meridional Circulation Between South Asia and Tibetan Plateau Caused by the Change of Planetary Boundary Layer Depth

AbstractPlanetary boundary layer (PBL) influences the vertical exchanges of momentum, heat, water vapor, atmospheric pollutants, and the efficacy of climate forcing between land surface and atmosphere. Over the western Tibetan Plateau (TP), PBL can stretch into the middle‐upper troposphere. In this study, we investigate an effect of the PBL depth change on atmospheric circulations between South Asia and the TP through the formula derivation, the observation, and the model data set. The derivation first gives the PBL depth‐generalized pressure equation. It reveals an effect of PBL depth on the pressure change with time. The data analysis further shows that an increase of PBL depth in the western TP can cause the subsequent development of the PBL low (high) pressure anomalies in the northwestern TP (northern South Asia) and the upper‐tropospheric high (low) pressure anomalies over the TP (South Asia), with an anticlockwise meridional‐vertical circulation (MVC) anomaly from South Asia to the TP. In this process, the peak of PBL depth may be ahead of that of the low‐pressure occurrence, which may cause the MVC development to lag behind surface heating. The anticlockwise MVC anomaly strengthens the transport of water vapor from the lower troposphere over South Asia to the TP PBL, producing convective precipitation in the TP.