Calculation Of Pressure Field Research Articles

Assessment of the pseudo-tracking approach for the calculation of material acceleration and pressure fields from time-resolved PIV: part I. Error propagation

Pseudo-tracking refers to the construction of imaginary particle paths from PIV velocity fields and the subsequent estimation of the particle (material) acceleration. In view of the variety of existing and possible alternative ways to perform the pseudo-tracking method, it is not straightforward to select a suitable combination of numerical procedures for its implementation. To address this situation, this paper extends the theoretical framework for the approach. The developed theory is verified by applying various implementations of pseudo-tracking to a simulated PIV experiment. The findings of the investigations allow us to formulate the following insights and practical recommendations: (1) the velocity errors along the imaginary particle track are primarily a function of velocity measurement errors and spatial velocity gradients; (2) the particle path may best be calculated with second-order accurate numerical procedures while ensuring that the CFL condition is met; (3) least-square fitting of a first-order polynomial is a suitable method to estimate the material acceleration from the track; and (4) a suitable track length may be selected on the basis of the variation in material acceleration with track length.

A direct two-dimensional pressure formulation in molecular dynamics

Two-dimensional (2D) pressure field estimation in molecular dynamics (MD) simulations has been done using three-dimensional (3D) pressure field calculations followed by averaging, which is computationally expensive due to 3D convolutions. In this work, we develop a direct 2D pressure field estimation method which is much faster than 3D methods without losing accuracy. The method is validated with MD simulations on two systems: a liquid film and a cylindrical drop of argon suspended in surrounding vapor.

Error propagation dynamics of PIV-based pressure field calculations: How well does the pressure Poisson solver perform inherently?

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

The Design of Oil Well Production Engineering Analysis System

With the rapid development of oilfield information construction, the requirements for the analysis of oil well production are also getting higher. The traditional method, which is by experience, cannot meet the demand of oilfield information construction for the analysis accuracy. Based on some common problems in the analysis of oil production, this paper designs and implements the oil well production engineering analysis system based on NET. The design of the system mainly includes two parts. One part is the calculation of temperature and pressure field of the wellbore and the other part is the drawing of system efficiency control chart. This system can provide the distribution results of temperature and pressure of the wellbore during the production process, and according to the system efficiency control chart, we can accurately determine the production situation of oil well. This system has the advantages of simple operation, accurate calculation, clear analytical results, and comprehensive analysis.

Thermo acoustic study of carbon nanotubes in near and far field: Theory, simulation, and experiment

Carbon nanotube webs exhibit interesting properties when used as thermo-acoustic projectors. This work studies thermo-acoustic effect of these sound sources both in near and far field regions. Based on two alternative forms of the energy equation, we have developed a straightforward formula for calculation of pressure field, which is consistent with experimental data in far field. Also we have solved full 3-D governing equations using numerical methods. Our three-dimensional simulation and experimental data show pressure waves are highly affected by dimensions of sound sources in near field due to interference effects. However, generation of sound waves in far field is independent of projectors area surface. Energy analysis for free standing Thermo-Acoustic (TA) sound sources show that aerogel TA sound sources like CNT based projectors could act more efficiently compared to the other sources in delivering more than 75% of alternative input energy to the medium gas up to a frequency of 1 MHz.

Nonlinear effects on hydrodynamic pressure field caused by ship moving at supercritical speed in shallow water

Based on the shallow-water wave potential flow theory and the assumption of a slender ship, a mathematical model has been established for the pressure field caused by ship moving at supercritical speed in shallow water, with nonlinear and dispersive effects taken into account. The finite difference method is used for the numerical calculation of the ship hydrodynamic pressure field (SHPF), with the central and upwind difference schemes as a combination for the second derivative of the nonlinear term. And the artificial viscous terms are added in the hull and upstream boundary conditions to ensure the stability of solving the nonlinear equation. The comparison between the calculated results and the experimental results shows that both the mathematical model and the calculation method are effective and feasible. The analysis of the nonlinear effects of different-depth water, different depth Froude number and different-width channel on SHPF indicates that the closer to the critical speed the ship in sailing, the narrower the channel becomes, the greater the nonlinear effects on SHPF are.

Computation of Pressure Fields around a Two-Dimensional Circular Cylinder Using the Vortex-In-Cell and Penalization Methods

The vorticity-velocity formulation of the Navier-Stokes equations allows purely kinematical problems to be decoupled from the pressure term, since the pressure is eliminated by applying the curl operator. The Vortex-In-Cell (VIC) method, which is based on the vorticity-velocity formulation, offers particle-mesh algorithms to numerically simulate flows past a solid body. The penalization method is used to enforce boundary conditions at a body surface with a decoupling between body boundaries and computational grids. Its main advantage is a highly efficient implementation for solid boundaries of arbitrary complexity on Cartesian grids. We present an efficient algorithm to numerically implement the vorticity-velocity-pressure formulation including a penalty term to simulate the pressure fields around a solid body. In vorticity-based methods, pressure field can be independently computed from the solution procedure for vorticity. This clearly simplifies the implementation and reduces the computational cost. Obtaining the pressure field at any fixed time represents the most challenging goal of this study. We validate the implementation by numerical simulations of an incompressible viscous flow around an impulsively started circular cylinder in a wide range of Reynolds numbers: Re=40, 550, 3000, and 9500.

Speckle tracking in multiple-scattered pressure field

Speckle tracking using ultrasound B-scan image sequences to quantify myocardial strain has the potential to become a standard method in echocardiography. A pressure field for a modulated Gaussian pulse traveling in inhomogeneous media is constructed. This model is based on computation of pressure field using Kirchoff integral formulation in frequency domain. Each pressure term of Neumann Series is converted into time domain and used in computation of Pade approximants. Pressure field in time and space is constructed utilizing Pade approximants and includes multiple-scattering effects. The scatterers of interest are large enough in size and contrast to contribute to strong and multiple-scattering. The signals at transducer point for each time frame are analyzed and speckles are tracked utilizing an optical flow algorithm. A velocity field which can be utilized to quantify strain is computed and visualized. The efficiency of this method will be discussed.

Acoustic cloak/anti-cloak device with realizable passive/active metamaterials

Utilizing the coordinate transformation method, together with exchange of variables between Maxwell's equations and the acoustic equations with axial-invariance in cylindrical coordinates, the acoustic parameters (anisotropic density and scalar bulk modulus) for an ideal cloak and an ideal anti-cloak are obtained. An anti-cloak allows the inside object to ‘see’ outside, but to be invisible from outside; whereas a cloak is invisible from outside, but ‘blind’ from inside. Utilizing a scattering algorithm developed in this paper, the pressure field calculation of the cloak/anti-cloak is performed and the concepts and characteristics of the acoustic cloak/anti-cloak are revisited. To be more easily achievable experimentally, a multilayered cloak/anti-cloak model with homogeneous isotropic materials is introduced, and its corresponding pressure distributions are calculated. Also, the total scattering cross-section curves for the multilayered cloak and anti-cloak over a certain frequency range are presented and compared. Finally, an active acoustic metamaterial made up of piezo-diaphragm cavity arrays is designed for the cloak/anti-cloak. Taking into account the coupling between adjacent cavity cells, a multi-control strategy for piezo-diaphragm cavity arrays is exploited, rendering possible wide ranges of effective densities and effective bulk moduli (or acoustic speeds), or even double-negative transformation medium (i.e. both density and bulk modulus parameters are negative). With such sets of active acoustic metamaterials, the cloak and anti-cloak may become both theoretically and experimentally realizable.

Assessment of pressure field calculations from particle image velocimetry measurements

This paper explores the challenges associated with the determination of in-field pressure from DPIV (digital particle image velocimetry)-measured planar velocity fields for time-dependent incompressible flows. Several methods that have been previously explored in the literature are compared, including direct integration of the pressure gradients and solution of different forms of the pressure Poisson equations. Their dependence on grid resolution, sampling rate, velocity measurement error levels and off-axis recording was quantified using artificial data of two ideal sample flow fields—a decaying vortex flow and pulsatile flow between two parallel plates, and real DPIV and pressure data from oscillating flow through a diffuser. The need for special attention to mitigate the velocity error propagation in the pressure estimation is also addressed using a physics-preserving approach based on proper orthogonal decomposition (POD). The results demonstrate that there is no unique or optimum method for estimating the pressure field and the resulting error will depend highly on the type of the flow. However, the virtual boundary, omni-directional pressure integration scheme first proposed by Liu and Katz (2006 Exp. Fluids 41 227–40) performed consistently well in both synthetic and experimental flows. Estimated errors can vary from less than 1% to over 100% with respect to the expected value, though in contrast to more traditional smoothing algorithms, the newly proposed POD-based filtering approach can reduce errors for a given set of conditions by an order of magnitude or more. This analysis offers valuable insight that allows optimizing the choice of methods and parameters based on the flow under consideration.

Diffusion flame calculations for composite propellants predicting particle-size effects

The complexities of the flame structure above a composite propellant containing 86% ammonium perchlorate (AP) and 14% hydroxy-terminated-polybutadiene (HTPB) have been elucidated using a two-dimensional, detailed gas-phase kinetic mechanism diffusion flame model. The model utilizes a vorticity formulation of the transport equations, which essentially eliminates the pressure field calculation and speeds convergence. Mass and energy coupling between the condensed and gas phases are achieved through iteration with one-dimensional, premixed combustion models to dynamically update the inlet boundary conditions. The model uses a detailed gas-phase kinetic mechanism consisting of 37 species and 127 reactions. Numerical studies have been performed to examine the influence of particle size on the flame structure above the AP/HTPB propellant. Three different combustion zones, based on AP particle size, were predicted: the AP monopropellant limit, the diffusion flame region, and the premixed limit. The modeled flame structure changed dramatically with particle size and was found to be qualitatively similar to the Beckstead–Derr–Price Model. Mechanistic insights are presented to explain AP’s unique ability to modify a propellant burning rate based on particle size alone. The premixed limit at which decreasing the size of the AP particles no longer influences the burning rate was also predicted. Results show promise in predicting formulistic effects using fundamental calculations.

Uma implementação do método da refletividade para modelagem eficiente de dados sísmicos marítimos e de OBC

Neste trabalho é demonstrado como o método da refletividade pode ser eficientemente implementado para simular aquisições sísmicas marítimas. Isto inclui o registro de pressão no caso da fonte e dos receptores (hidrofones) estarem localizados na camada de água, o deslocamento (ou velocidade de vibração) vertical e horizontal no caso dos receptores estarem plantados no leito do oceano, simulando aquisições multicomponentes tipo OBC (Ocean Bottom Cable) ou OBS (Ocean Bottom Sensor). Uma das vantagens do presente método é a facilidade de seleção dos eventos que farão parte da resposta, tais como múltiplas internas, múltiplas associadas à superfície livre e ondas convertidas no caso P-Sv. Os fenômenos da atenuação e da dispersão podem ser levados em conta facilmente considerando as velocidades complexas, já que o método é desenvolvido no domínio ω-p. O algoritmo proposto possui custo computacional bem menor quando comparado com métodos puramente numéricos como diferenças finitas ou elementos finitos. Sendo assim, no caso onde um modelo de camadas planas horizontais seja suficiente para descrever a subsuperfície, este torna-se uma ferramenta prática para tarefas como prever com bastante precisão e rigor a sensibilidade sísmica de um determinado reservatório com relação à substituição de fluidos ou prever como uma determinada mudança de propriedade petrofísica pode influenciar a resposta de AVO multicomponente.

Principles and application of velocimetry-based planar pressure imaging in compressible flows with shocks

The paper addresses the computation of pressure fields from velocimetry data, such as provided by Particle Image Velocimetry (PIV), with specific attention to its application in compressible flows with shocks. An essential extension with respect to incompressible flow is that in view of the variable density occurring in compressible flow, the velocimetry data has to be supplemented with additional relations, derived from the flow governing equations. Secondly, compressible flows display specific flow features, notably shocks but also thin shear layers, that pose particular difficulties for the flow velocity measurement itself, as well as for the subsequent determination of the pressure field. The present communication addresses the basic principles of the pressure-field extraction method, as well as its feasibility of application under realistic experimental conditions.

Ertel—Grubin methods in elastohydrodynamic lubrication – a review

With the arrival of powerful computers and sophisticated numerical methods the calculation of film thickness and pressure fields in elastohydrodynamically lubricated (EHL) contacts is now a common task. Complete moving-roughness solutions are easily found in literature including thermal effects, non-Newtonian rheology, and mixed-lubrication. Therefore, the pioneering days of analytical and semi-analytical EHL solutions lead by Ertel, Grubin, Crook, and others might be perceived as unfit for modern problems. However, it is important to recognise that despite their apparent simplicity these solutions have provided engineers with substantial insight of the lubrication problem. The present paper reviews Ertel—Grubin methods and shows the potential they still have in providing engineers with physical understanding and practical solutions in modern lubrication problems, including friction, transient effects, roughness, minimum film thickness, and shear thinning. The review is, however, not exhaustive.

Numerical study on the underground coal gasification for inclined seams

AbstractAccording to the characteristics for combustion and gasification reactions occurring in the gasification gallery, the mathematical functional relationship between the chemical reaction rate and every influencing factor is studied. The dynamic nonlinear coupling mathematical models on underground coal gasification of inclined seams are established. The determination methods of major model parameters are introduced. Additionally, the control volume method is adopted to find the numerical solution to the mathematical models. The patterns of development and variation for temperature field, concentration field and pressure field in gasification panel are studied. On the basis of the model test, calculation results are analyzed. From the distribution of temperature field, its calculation value is a little higher than the experimental one, with the relative error of every measuring point virtually within 17%. Research shows that, the experiment value of gas heat value and calculated value take on a good conformity; due to the influence of temperature, in the high temperature zone, the change gradient of the experiment value for concentration field of gas compositions is greater than that of the calculation value. The simulated results indicate that the relative error of the pressure field calculation is 4.13%–12.69% and 8.25%–17.47%, respectively, 7 h and 45 h after the ignition. The drop rate for the fluid pressure is 6.01% and 10.91%, respectively. Research shows that the simulated values conform with experimental values comparatively well, which demonstrates that the numerical simulation on the “three fields” in underground coal gasification is correct. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Rapid calculations of time-harmonic nearfield pressures produced by rectangular pistons

A rapid method for calculating the nearfield pressure distribution generated by a rectangular piston is derived for time-harmonic excitations. This rapid approach improves the numerical performance relative to the impulse response with an equivalent integral expression that removes the numerical singularities caused by inverse trigonometric functions. The resulting errors are demonstrated in pressure field calculations using the time-harmonic impulse response solution for a rectangular source 5 wavelengths wide by 7.5 wavelengths high. Simulations using this source geometry show that the rapid method eliminates the singularities introduced by the impulse response. The results of pressure field computations are then evaluated in terms of relative errors and computational speeds. The results show that, when the same number of Gauss abscissas are applied to both approaches for time-harmonic pressure field calculations, the rapid method is consistently faster than the impulse response, and the rapid method consistently produces smaller maximum errors than the impulse response. For specified maximum error values of 10% and 1%, the rapid method is 2.6 times faster than the impulse response for pressure field calculations performed on a 61 by 101 point grid. The rapid approach achieves even greater reductions in the computation time for smaller errors and larger grids.

Mixed Vortex-Finite Volume Method for the Computation of Pressure Fields in Fluid Flows

Mixed Vortex-Finite Volume Method for the Computation of Pressure Fields in Fluid Flows

Rapid continuous-wave pressure field calculations for spherically focused radiators

A new accelerated expression for the continuous-wave pressure field generated by a spherically focused radiator is obtained when the impulse response formulation is transformed and optimized for numerical evaluations. The resulting integral expression converges much more quickly than the impulse response approach, resulting in far fewer function evaluations for the same numerical error. The optimized integral expression is between two and seven times as fast as the impulse response approach, where the increase in speed depends on the peak value of the specified error. In addition, this new result completely eliminates the cone-shaped regions required for impulse response calculations, so the resulting computer code for the accelerated expression is less complicated than the corresponding code for the impulse response. Results also show that the new expression eliminates the numerical artifact that is encountered near the boundary between regions defined for impulse response calculations. All of these features are useful in thermal therapy computer simulations that employ spherically focused transducer geometries.

Calculation of three-dimensional flow and pressure fields in cracking furnaces

The simulation of correct flow and pressure fields in the radiation section of industrial thermal cracking furnaces is of practical interest since the amount of combustion air taken in by the burners in general is partly determined by the pressure field. For such engineering purposes often a (practical) simplified numerical treatment of the viscous terms in the flow equations is used to reduce the computational cost. It is shown that the interaction between such a simplified numerical treatment of the viscous terms and the alignment of the cell interfaces with the coordinate system can result in an erroneous (non-physical) calculation of the pressure field. This alignment problem is predominantly present when using a semi non-structured prismatic grid to solve the flow equations. Using a fully non-structured tetrahedral grid avoids this problem because of the random orientation of the cell interfaces for this type of grid. This is confirmed by assuring that the calculation results are independent with respect to grid refinement. At the same time the influence of the presence of the reactor tubes on the velocity field inside the furnace is examined.

Simultaneous Calculation of Roll Deformation and Polymer Flow in the Calendering Process

Abstract Calender units with rotating rolls are used to produce foils or sheets from polymer material with viscous or elastomeric flow properties. Up to now, the design process of calender units, the calculation of flow and pressure fields in the calender gap and the calculation of resulting deformations of the rotating rolls are implemented with different computer programs. In this work a design concept that integrates design and calculation programs is being developed in order to achieve integrated design and calculation. With this concept, it is possible to design calenders and calculate flow fields and deformations. After designing the rolls with the Computer Aided Design program Pro/Engineer, the flow field in the calender gap is calculated with the Finite Volume Method program CFX4, and the deformation of the rolls is calculated with the Finite Element Method program ANSYS. The iterative process of design, calculation and modification of shape is continued until sheets or foils of constant thickness leave the calender gap. The design concept has an object-oriented operational structure. The data transfer between the programs takes place via a central data base in STEP format. As examples, calenders with combinations of solid rolls are designed. The flow field in the calender gap is calculated for Newtonian and for viscoelastic fluids with use of an integral rheological equation of state. The flow field is compared to a measured flow field. The resulting deformations of the rolls are calculated and represented graphically. Furthermore, a design process for elastomer-coated rolls is implemented and their deformations as well as the interior stress fields are calculated.