Quadratic Pressure Research Articles

A first order in time wave equation modeling nonlinear acoustics

In this paper we focus on a small amplitude approximation of a Navier-Stokes-Fourier system modeling nonlinear acoustics. Omitting all third and higher order terms with respect to certain small parameters, we obtain a first order in time system containing linear and quadratic pressure and velocity terms. Subsequently, the well-posedness of the derived system is shown using the classical method of Galerkin approximation in combination with a fixed point argument. We first prove the well-posedness of a linearized equation using energy estimates and then the well-posedness of the nonlinear system using a Newton-Kantorovich type argument. Based on this, we also obtain global in time well-posedness for small enough data and exponential decay. This is in line with semigroup results for a linear part of the system that we provide as well.

Comparative study of analytical models with linear and quadratic pressure drop conditions on a perforated plate in water waves

Proper pressure drop conditions are essential in predicting hydrodynamic performance of perforated structures in the framework of a potential flow theory. In this study, we investigate water waves passing through a perforated plate with various pressure drop models to examine how pressure drop conditions affect the hydrodynamic performance of perforated structures. We derive the analytical solutions of waves across the perforated plate by adopting three commonly pressure drop conditions, including one linear pressure drop condition (LPDC), and two quadratic pressure drop conditions (QPDCs). A series of laboratory experiments are conducted to validate the present theoretical results. We compare the hydrodynamic performance between the experimental data and the theoretical solutions with the three different pressure drop models, typically for wave reflection coefficients, dynamic pressures, and velocity fields measured by the technique of particle image velocimetry in the experiments. It is found that the existing pressure drop models can predict well wave reflection coefficients, dynamic pressure, and velocity profiles at certain conditions. However, the linear wave solutions associated with LPDC or QPDCs generally underpredict the amplitude of particle velocity near the free surface on the perforated plate. This underestimation increases largely as the wave steepness increases. The LPDC performance relies much on the selection of empirical coefficients. For the QPDCs, the analytical models show deviated results from the experimental data for wave reflection coefficients when the wave steepness is relatively low.

High-velocity compressible gas flow modelling through porous media considering the quadratic pressure gradient: Part 2. experimental investigations and numerical analysis

This research investigates reliability of existing methods for analysis of transient Pressure Pulse Decay (PPD) test results. Analysis of experimental data reported by previous studies using existing conventional analysis methods revealed significant discrepancies, in some cases with more than 300% error between different experiments on the same sample. New experiments (Knudsen number ranged from 0.22 to 0.34) were designed and conducted in our laboratory, reducing the uncertainty by eliminating slip flow and net stress effects under low and high-pressure conditions. These experimental results aligned much better with the recently proposed analytical solution for improved interpretation of PPD experimental results. The differences are around 25% between different pulses, confirming the reliability of the conducted experiments and newly proposed methodology.Numerical simulations using a commercial software package were conducted to complement experimental and analytical findings. The simulator, which demonstrated good agreement with the proposed analytical solution, facilitated conducting sensitivity analyses on permeability variations and compressive storage capacity effects. These simulations validated the findings of the proposed analytical solution, which accounts for both pressure difference and absolute pressure values, and explains the discrepancies observed in lower pressure scenarios using conventional methods.Overall, this study presents a comprehensive framework integrating experimental, analytical, and numerical approaches to enhance our understanding and better analysis of transient PPD test results for compressible gas flows. The findings also offer a more robust approach for analysing gas flow behaviour in porous media.

Transient Pressure Behavior of CBM Wells during the Injection Fall-Off Test Considering the Quadratic Pressure Gradient.

Conventional coalbed methane (CBM) reservoir models for injection fall-off testing often disregard the quadratic pressure gradient's impact. This omission leads to discrepancies in simulating the transient behavior of formation fluids and extracting critical reservoir properties. Accurate determination of permeability, storability, and other properties is crucial for effective reservoir characterization and production forecasting. Inaccurate estimations can lead to suboptimal well placement, ineffective production strategies, and ultimately, missed economic opportunities. To address this shortcoming, we present a novel analytical model that explicitly incorporates the complexities of the quadratic pressure gradient and dual-permeability flow mechanisms, prevalent in many CBM formations where nanopores are rich, presenting a kind of natural nanomaterial. This model offers significant advantages over traditional approaches. By leveraging variable substitution, it facilitates the derivation of analytical solutions in the Laplace domain, subsequently converted to real-space solutions for practical application. These solutions empower reservoir engineers to generate novel type curves, a valuable tool for analyzing wellbore pressure responses during injection fall-off tests. By identifying distinct flow regimes within the reservoir based on these type curves, engineers gain valuable insights into the dynamic behavior of formation fluids. This model goes beyond traditional approaches by investigating the influence of the quadratic pressure gradient coefficient, inter-porosity flow coefficient, and storability ratio on the pressure response. A quantitative comparison with traditional models further elucidates the key discrepancies caused by neglecting the quadratic pressure gradient. The results demonstrate the proposed model's ability to accurately depict the non-linear flow behavior observed in CBM wells. This translates to more reliable pressure and pressure derivative curves that account for the impact of the quadratic pressure gradient.

Nonlinear identification algorithm for online and offline study of pulmonary mechanical ventilation

This work presents an algorithm for determining the parameters of a nonlinear dynamic model of the respiratory system in patients undergoing assisted ventilation. Using the pressure and flow signals measured at the mouth, the model’s quadratic pressure–volume (P–V) characteristic is fit to these data in each respiratory cycle by appropriate estimates of the model parameters. Parameter changes during ventilation can thus also be detected. The algorithm is first refined and assessed using data derived from simulated patients represented through a sigmoidal P–V characteristic with hysteresis. As satisfactory results are achieved with the simulated data, the algorithm is evaluated with real data obtained from actual patients undergoing assisted ventilation. The proposed nonlinear dynamic model and associated parameter estimation algorithm yield closer fits than the static linear models computed by respiratory machines, with only a minor increase in computation. They also provide more information to the physician, such as the pressure–volume (P–V) curvature and the condition of the lung (whether normal, under-inflated, or over-inflated). This information can be used to provide safer ventilation for patients, for instance by ventilating them in the linear region of the respiratory system.

Modelling the far-field effect of drag-induced dissipation in wave–structure interaction: a numerical and experimental study

In the interaction of water waves with marine structures, the interplay between wave diffraction and drag-induced dissipation is seldom, if ever, considered. In particular, linear hydrodynamic models, and extensions thereof through the addition of a quadratic force term, do not represent the change in amplitude of the waves diffracted and radiated to the far field, which should result from local energy dissipation in the vicinity of the structure. In this work, a series of wave flume experiments is carried out, whereby waves of increasing amplitude impinge upon a vertical barrier, extending partway through the flume width. As the wave amplitude increases, the effect of drag – which is known to increase quadratically with the flow velocity – is enhanced, thus allowing the examination of the far-field effect of drag-induced dissipation, in terms of wave reflection and transmission. A potential flow model is proposed, with a simple quadratic pressure drop condition through a virtual porous surface, located on the sides of the barrier (where dissipation occurs). Experimental results confirm that drag-induced dissipation has a marked effect on the diffracted flow, i.e. on wave reflection and transmission, which is appropriately captured in the proposed model. Conversely, when diffraction becomes dominant as the barrier width becomes comparable to the incoming wavelength, the diffracted flow must be accounted for in predicting drag-induced forces and dissipation.

Dissipative potential flow models and energy evolution characteristics for curtain-wall caisson breakwaters under wave action

Curtain-wall caisson breakwaters are a kind of coastal protection structure, which is composed of semi-submersible vertical thin curtain walls, a rear vertical caisson, and wave chambers formed by the curtain walls and rear caisson. When water waves interact with the curtain-wall caisson breakwater, the wave energy may be partially dissipated owing to the flow separation and vortex formation near the edges of curtain walls. The conventional potential flow solution without considering wave energy dissipation gives unreasonable results of full wave reflection by the curtain-wall caisson breakwater. To address this issue, this study develops a dissipative potential flow model for predicting the hydrodynamic performance of the curtain-wall caisson breakwaters. The wave energy dissipation near the breakwater is considered by introducing a quadratic pressure loss condition at the entrances of wave chambers. By adopting appropriate dimensionless dissipation coefficients, the analytical predictions of the reflection coefficient and the wave amplitude inside chambers are in good agreement with published experimental results. The differences in the hydrodynamic quantities predicted by the dissipative and conventional potential flow solutions are examined, and further discussion based on the dissipative analytical solution is performed. Moreover, viscous numerical simulations based on a meshless particle method are carried out to clarify the characteristics of wave energy evolution, wave energy dissipation, and local fluid motion near the curtain-wall caisson breakwaters. The results show that the front curtain wall plays the leading role in the wave energy dissipation process of the whole double-chamber curtain-wall breakwater.

The collision-induced absorption of H2 near 1.20 µm: Subatmospheric measurements and validation tests of calculations

The weak binary collision-induced absorption (CIA) of molecular hydrogen is measured at room temperature in the first overtone region near 1.20 µm. Binary absorption coefficients are derived by cavity ring down spectroscopy (CRDS) at 28 selected spectral points sampling the (2–0) band between 7974 and 8650 cm−1. While all previous studies used high density samples, the sensitivity of the CRDS method allowed deriving accurate CIA by using pressure ramps of pure H2 limited to a maximum pressure of 1 atm. After subtraction of the Rayleigh contribution, a purely quadratic pressure dependence is obtained for the absorption coefficient at each measurement point and the CIA binary coefficients are derived with a 1.5 % accuracy. The comparison to theoretical values widely used for astronomical applications shows deviations values between 5 and 25 %.

The water vapor self-continuum absorption at 8.45 µm by optical feedback cavity ring down spectroscopy

The accurate knowledge of the water vapor absorption in the 10 µm atmospheric window is of strong importance because this spectral range coincides with the maximum black body emission of Earth. Presently, the water vapor self-continuum is measured at the 1185 cm−1 (8.45 µm) spectral point, located in the most transparent interval of the 10 µm window. Measurements are performed at four temperatures ranging from 296 to 308 K using a newly developed Optical Feedback Cavity Ring Down Spectrometer (OF-CRDS). Self-continuum cross-sections, CS, are derived from the pressure dependence of the absorption during pressure ramps of pure water vapor up to 18 mbar. From the quadratic pressure dependence observed for the absorption coefficient at each temperature, we derived the value of the cross-section (CS=0.996(12)×10−22cm2 molecule−1atm−1 at 296 K) and its temperature dependence. These results are discussed in relation with previous literature measurements available in the 10 µm window. Our cross-section is found about 20% smaller than the MT_CKD_4.1 value and the available experimental works seem to indicate that the MT_CKD_4.1 temperature dependence is overestimated.

Multipole solution with nonlinear pressure loss for oblique waves action on a submerged partially perforated semi-circular breakwater

This study is an extension of the research on semi-circular breakwater based on Lyu et al. (2020). This time, we focus on the changes in the flow field when waves obliquely interact with the axis of the partially perforated semi-circular breakwater, as well as the nonlinear effects resulting from variations in wave height to some extent. The analytical solution of the flow field is still obtained using the multipole expansion method based on potential flow theory and the method of separation of variables. The analytical solution for oblique incidence is primarily achieved through the cylindrical form of the Bessel equation. Separately considering viscous effects and potential flow, we estimate the impact of wave height variation on the perforated boundary through the quadratic pressure loss term. By employing an iterative solving approach, we comprehensively discuss the influence of wave height, water depth, perforation form, and oblique incidence angle on the flow field and the forces acting on the breakwater.

Application of quadratic pressure drop condition in hydroelastic analysis of floating structures protected by perforated barrier

This paper presents the application of the quadratic pressure drop condition in hydroelastic analysis of large floating structures protected by perforated barrier. An iterative procedure is proposed to incorporate the quadratic pressure drop condition into the recently developed finite element – dual boundary element method. Numerical examples are carried out to compare the proposed quadratic model with the existing model involving the conventional linear pressure drop condition. It is found that the proposed quadratic model agrees rather well with the linear model for small wave amplitudes. However, for strong waves, there are significant differences between the quadratic model and linear model in terms of the resulting excitation force on the barrier and hydroelastic responses of floating structures. The excitation force from the quadratic model may be up to 100% higher than that from the linear model.

Characterization of the productivity of basement aquifers at Bagoué region (North of Côte d’Ivoire)

This study aims to characterize the productivity of basement aquifers based on a database built by pumping test and drilling report from eighteen boreholes exploited in Bagoue region of Cote d’Ivoire. By using last version of a tool to assist in pumping test interpretation suggested by the French Mining and Geological Survey, Transmissivity parameter values of confined aquifers were determined through the well-known Theis method. In the same approach, critical yield value of borehole was determined at the equivalence point of linear and quadratic pressure drop from short-term pumping test data. Geostatistical analysis and kriging of transmissivity of aquifers were realized. Then, it was elaborated few predictive equations between hydrodynamic and hydraulic parameters based on their relationship level. Comparison of aquifers productivity and boreholes hydraulic capacity ended the methodology. Transmissivity ranged from 9.10-7 to 4.10-5 m2.h-1 while specific yield of boreholes reached between 0.34 and 23.07 m3.h-1. Yields from exploited boreholes varied between 0.5 m3.h-1 and 12 m3.h-1 with an average reaching 3.44 m3.h-1. Critical yield varied between 2.11 and 18.8 m3.h-1 with an average of 6.95 m3.h-1. According to geostatistical analysis of Transmissivity, its spatial spreading adjusted spherical model with a range reaching 0.13 meters. Findings highlighted 44 % of aquifer areas characterized by low value of transmissivity with great value of exploited outflow. That suggests a short-term availability of drinking water for living communities. In the same way, 11.11 % of boreholes were established into aquifer areas characterized by great transmissivity and low outflow values that suggests a better supply environment with long-term groundwater availability.

Mathematical modelling of nonlinear pressure drops in arbitrarily shaped port utilizing dual boundary element method

A mathematical model is developed to analyze the wave-trapping characteristics of different types of porous and non-porous barriers in arbitrarily shaped domains utilizing the iterative Dual Boundary Element Method (DBEM) under the resonance conditions. In this analysis, Vertical, Wavy, Inverted V-shaped, and Inverted L-shaped barriers are utilized to investigate the effect of incident waves over the boundary of the harbor. The harbor is divided into an interconnected domain with variable bathymetry, and the Helmholtz equation is solved in each subdomain utilizing the prescribed boundary conditions. Further, the semi-empirical discharge equation with quadratic pressure drop is considered on the porous barrier to incorporate the effect of incident wave amplitude on the energy loss. The present numerical scheme is validated with existing studies and verified with convergence analysis. Further, the mathematical model is implemented on the Visakhapatnam port at four key locations with improved performance of different types of barriers. Moreover, the influence of the partial reflection coefficient is also investigated by considering the various combination of partially reflecting boundaries of the port. The wave trapping or absorbing characteristics of porous barriers proves an efficient tool to reduce the wave resonance inside the port.

Analytical study on an oscillating buoy integrated with a perforated structure with a quadratic pressure drop condition: A case study on a WEC-perforated breakwater integration system

A general analytical method for solving the linear wave interactions with the integration systems comprising an oscillating buoy and perforated structure is presented, with a quadratic pressure drop condition on the perforated surface. Using the method of variable separation and eigenfunction expansion, the motion response of the buoy and total velocity potential can be solved using a two-loop iterative method. The method is validated against the published results. The integration system with a heaving WEC arranged inside a perforated breakwater was investigated particularly. Under the quadratic pressure drop condition, the symmetry of the hydrodynamic coefficients and Haskind relation, are found no longer satisfied, and the dissipation through the perforated wall also contribute to the damping coefficient. Effects of the damping of the power take-off system, front wall porosity, wave amplitude, and position of the WEC are investigated in particular. It was found that the horizontal and vertical wave forces on the WEC increase significantly as wave amplitude increases; however, the hydrodynamic efficiency decreases. When the WEC is near the solid rear wall, the horizontal wave forces on the WEC and solid rear wall increase significantly at the frequencies of piston mode gap resonance and heave motion resonance.

Research on nonlinear spherical seepage model solution of fractal composite reservoir considering quadratic pressure gradient under elastic outer boundary

In order to break the limitation that only three ideal outer boundaries (infinity, constant pressure and closed) are considered in the traditional reservoir model, the paper introduces elasticity into the outer boundary condition, and establishes a nonlinear spherical seepage model for fractal composite reservoir that considers the quadratic pressure gradient, wellbore storage, skin factor and effective radius under the elastic outer boundary condition. The dimensionless bottom-hole pressure in real space is obtained by the process of variable substitution, similar construction method and numerical inversion, while the characteristic curves are plotted to analyze the influence laws of main parameters and elasticity. The results show that the ideal outer boundary conditions previously studied are only special cases of the elastic outer boundary conditions. Furthermore, the elastic outer boundary expands the scope of data interpretation, and makes the model more general. Meanwhile, it can be seen that the similar construction method is simpler and more effective than the traditional methods for solving nonlinear models. In addition, it is further demonstrated that neglecting the quadratic pressure gradient can cause large errors. This study not only provides a new idea for well testing analysis of reservoirs but also for solving more complex seepage models.

A semi-analytical solution for water wave scattering by partially immersed perforated and solid barriers with a quadratic pressure discharge condition

Partially immersed perforated and/or solid barriers in the ocean are often considered as important components of many marine applications, and they have received significant attentions by ocean engineering research community with potential flow methods. In this study, water wave interaction with a system that consists of a vertical perforated front barrier and a vertical impermeable rear barrier, as a representative unit, is investigated based on the linear potential flow theory. A semi-analytical solution for this problem is derived using an eigenfunction expansion method and an iterative resolution method. To model the flow passing through the perforated barrier, a quadratic pressure discharge condition of practical validity is applied. The reflection coefficient predicted by the present analytical model agrees well with the published theoretical result. The validated model is used to perform a parametric study to examine the effects of the width, submergence depth, porosity, incident wave steepness and wave frequency on the hydrodynamic characteristics of the perforated system. It is found that larger incident wave steepness can result in smaller transmission coefficient and dimensionless horizontal wave force acting on the impermeable rear barrier and larger dimensionless horizontal wave force acting on the perforated front barrier due to the nonlinear nature of the quadratic pressure discharge condition. By examination over a broad range of circumstances, we find that the partially immersed perforated system is more effective when the ratio of the width to the incident wavelength B/L is located between 0.2+0.5n and 0.35+0.5n (n=1,2,…). The present study can be utilized for a range of marine applications in wave preventing and wave energy absorption or conversion.

Accurate absolute frequency measurement of the S(2) transition in the fundamental band of H2 near 2.03 μm.

A series of spectra of the quadrupolar electric S(2) transition of H2 in the 1-0 band near 4917 cm-1 has been recorded at seven pressure values between 2 and 100 Torr. The comb-referenced cavity ring down spectroscopy (CR-CRDS) technique was used for the recording of this very weak transition. The accuracy of the spectrum frequency axis is achieved by linking the CRDS setup to an optical frequency comb referenced to a GPS-referenced 10 MHz rubidium clock. Applying a multi-spectrum fit procedure to the seven averaged spectra with a quadratic speed dependence Nelkin-Ghatak profile, the transition frequency is determined (ν0 = 147 408 142 357 kHz) with an uncertainty of 150 kHz (∼1 × 10-9 in relative). This represents the smallest uncertainty achieved so far for a transition in the fundamental band of H2. The experimental frequency reported in this work is 1.53 MHz higher than the best-to-date theoretical value. This difference represents 1.5 times the 1σ-uncertainty (about 1 MHz) of the calculated frequency. The measurements also allow for the determination of the absolute intensity value of the S(2) line which shows an agreement with the ab initio value at the per mil level. In addition, the cross section of the collision induced absorption (CIA) underlying the S(2) line is accurately retrieved from the quadratic pressure dependence of the baseline level of the recorded spectra.

Verification of a Free-Surface Pressure Term Extension to Represent Ships in a Nonhydrostatic Shallow-Water-Equations Solver

Abstract In recent years, increasing ship sizes and associated increasing wave loads have led to a demand for prediction tools quantifying the ship-induced loads on waterways. Depth-averaged numerical models, using a free-surface pressure term, are a prominent method to obtain the relevant design parameters. These models incorporate the wave deformation processes due to attributes of complex bathymetries, while allowing for an efficient simulation of large computational domains. The nonhydrostatic shallow-water-equations (SWE) model REEF3D::SFLOW uses a quadratic pressure approximation and high-order discretization schemes. This paper presents the implementation of a pressure term to account for the displacement of the free surface by solid moving objects. Two test cases verifying the implementation are shown based upon the analytical one-dimensional solution of the wave propagation due to surface pressure and the estimation of Havelock angles. These verification tests are the first step toward a holistic model, combining a large scale model with computational fluid dynamics (CFD) simulations near waterway banks.

Search for sub-eV axion-like particles in a stimulated resonant photon-photon collider with two laser beams based on a novel method to discriminate pressure-independent components

Sub-eV axion-like particles (ALPs) have been searched for by focusing two-color near-infrared pulse lasers into a vacuum along a common optical axis. Within the focused quasi-parallel collision system created by combining a creation field (2.5 mJ/47 fs Ti:Sapphire laser) and a background inducing field (1.5 mJ/9 ns Nd:YAG laser), the detection of signal photons via stimulated resonant photon-photon scattering by exchanging ALPs was attempted in a vacuum chamber. The signal wavelength can be determined via energy-momentum conservation in the vacuum, and it coincides with that determined from the atomic four-wave-mixing (aFWM) process. In this work, the pulse energies were one order of magnitude higher than those in the previous search, allowing aFWM from optical elements to be observed as a pressure-independent background for the first time, in addition to the residual-gas-originating aFWM following a quadratic pressure dependence. In principle the four-wave-mixing process in vacuum via ALP exchanges (vFWM) must also be pressure-independent, so the development of a new method for discriminating the optical-element aFWM is indispensable for increasing the pulse energies to the values needed for future upgraded searches. In this paper, we will present the established method for quantifying the yield from the optical-element aFWM process based on the beam cross- section dependence. With the new method, the number of signal photons was found to be consistent with zero. We then successfully obtained a new exclusion region in the relation between ALP-photon coupling, g/M, and the ALP mass m, reaching the most sensitive point g/M = 1.14 × 10−5 GeV−1 at m = 0.18 eV.

Static and Dynamic Performance of the RBRargo3 CTD

Abstract The static and dynamic performances of the RBRargo3 are investigated using a combination of laboratory-based and in situ datasets from floats deployed as part of an Argo pilot program. Temperature and pressure measurements compare well to co-located reference data acquired from shipboard CTDs. Static accuracy of salinity measurements is significantly improved using 1) a time lag for temperature, 2) a quadratic pressure dependence, and 3) a unit-based calibration for each RBRargo3 over its full pressure range. Long-term deployments show no significant drift in the RBRargo3 accuracy. The dynamic response of the RBRargo3 demonstrates the presence of two different adjustment time scales: a long-term adjustment O(120) s, driven by the temperature difference between the interior of the conductivity cell and the water, and a short-term adjustment O(5–10) s, associated to the initial exchange of heat between the water and the inner ceramic. Corrections for these effects, including dependence on profiling speed, are developed.