scholarly journals Uncertainty of PIV/PTV based pressure, using velocity uncertainty

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Jiacheng Zhang ◽  
Sayantan Bhattacharya ◽  
Pavlos Vlachos
Keyword(s):  
Boundary Condition ◽  
Pressure Gradient ◽  
Velocity Measurement ◽  
Pressure Field ◽  
Uncertainty Estimation ◽  
Linear Transformations ◽  
Reconstruction Process ◽  
Pressure Fields ◽  
Pressure Boundary Condition ◽  
Instantaneous Pressure

Pressure reconstruction from velocity measurements using particle image velocimetry (PIV) and particle tracking velocimetry (PTV) has drawn significant attention as it can provide instantaneous pressure fields without altering the flow. Previous studies have found that the accuracy of the calcualted pressure field depends on several factors including the accuarcy of the velocity measurement, the spatiotemporal resolutions, the method for calculating pressure-gradient, the algorithm for pressure-gradient integration, the pressure boundary condition, etc. Therefore, it is critical and challenging to quantify the uncertainty of the reconstructed pressure field. The recent development of the uncertainty quantification algorithms for PIV and PTV allows for the local and instantaneous uncertainty estimation of velocity measurement, which can be used to infer the pressure uncertainty. In this study, we introduce a framework that propagates the standard velocity uncertainty defined as the standard deviation of the velocity error distribution through the pressure reconstruction process to obtain the uncertainty of the pressure field. The uncertainty propagations through the calculation of the pressure-gradient and the pressure-gradient integration were modeled as linear transformations, which can reproduce the effects of the spatiotemporal resolutions, the numerical schemes, the integration algorithms, and the pressure boundary condition on the accuracy of the resulting pressure fields. The proposed uncertainty estimation approach also considers the effect of the spatiotemporal and componentwise correlation of the velocity errors in common PIV/PTV measurements on the pressure uncertainty.

THE PRESSURE FIELD IN THE RESERVOIR AT A GIVEN WELL FLOW RATE

2020 ◽  
Vol 6 (3) ◽  
pp. 58-78
Author(s):  
Aleksandr I. Filippov ◽  
Oksana V. Akhmetova ◽  
Aleksey A. Kovalskiy ◽  
Marina A. Zelenova
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Finite Difference ◽  
Pressure Field ◽  
Integral Transformation ◽  
Analytical Formula ◽  
Physical Parameters ◽  
Filtration Process ◽  
Integro Differential Equation ◽  
Pressure Fields

Due to the problems of hydrocarbon production, the study of pressure fields in natural reservoirs is the primary task of the filtration theory and special interest to the practitioners. Because of the variety of natural conditions necessary to account for in setting, the number of tasks is steadily increasing. At present, several analytical solutions of problems for homogeneous reservoirs with the simplest boundary conditions have been constructed. Studying the influence of borehole conditions on pressure fields in productive formations presents interest, as in this case, it is expressed as a boundary condition in the form of an integro-differential equation, and the corresponding class of problems is not sufficiently studied in the fundamental sections of the mathematical physics. In contrast to the existing works, this article constructs an analytical solution of the problem about the pressure field in the formation, represented by the classical equation of piezo-pipeline, for the case when the boundary condition in the form of the integro-differential equation describes the process of fluid extraction from the well with the help of a pump of the given productivity. The authors study the oil-saturated porous formation, opened by the producing well for the whole thickness. The pressure field in the reservoir is described by the classical piezoelectricity equation in the cylindrical coordinate system in the assumption of axial symmetry. The function of pressure perturbation distribution across the reservoir is determined considering the influence of the well. The relationship of pressures in the well and formation is established based on the law of mass conservation and Pascal’s law. The dimensionless criteria characterizing the filtration process and allowing to simplify the task definition are defined. It is shown, that all parameters, characterizing influence of well and formation, are grouped in two interrelated criteria, which define filtration process in such conditions. The authors have presented an exact solution of the problem in the space of Laplace — Carson integral transformation with an analytical transition to the original space. In addition, they have created a numerical conversion program, based on Den Iseger’s algorithm, and developed a finite-difference scheme for the task at hand. Having calculated the space-time distributions of pressure fields, the authors have compared the graphical pressure dependencies based on an analytical formula and a numerical program with the results of finite-difference calculations. That increases the reliability of the results obtained, which seems to be of great importance, since the existence and uniqueness theorems are not proved for this class of the problem in question. The analysis of the calculation results allowed determining the contribution of the well and reservoir parameters to the pressure field. The results show that in the relaxation mode, the parameters of the well and pump have a significant influence on the formation of the pressure field. In the stabilization mode, the contribution of its physical parameters is predominant.

scholarly journals Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a $$\upmu$$PIV measurement

2021 ◽  
Vol 62 (4) ◽  
Author(s):  
Ulrich Mießner ◽  
Thorben Helmers ◽  
Ralph Lindken ◽  
Jerry Westerweel
Keyword(s):  
Energy Dissipation ◽  
Pressure Gradient ◽  
Pressure Field ◽  
Estimation Method ◽  
Dissipated Energy ◽  
Spatial Integration ◽  
Mean Flow ◽  
Bypass Flow ◽  
Taylor Flow ◽  
Piv Measurement

Abstract In this study, we reconstruct the 3D pressure field and derive the 3D contributions of the energy dissipation from a 3D3C velocity field measurement of Taylor droplets moving in a horizontal microchannel ($$\rm Ca_c=0.0050$$ Ca c = 0.0050 , $$\rm Re_c=0.0519$$ Re c = 0.0519 , $$\rm Bo=0.0043$$ Bo = 0.0043 , $$\lambda =\tfrac{\eta _{d}}{\eta _{c}}=2.625$$ λ = η d η c = 2.625 ). We divide the pressure field in a wall-proximate part and a core-flow to describe the phenomenology. At the wall, the pressure decreases expectedly in downstream direction. In contrast, we find a reversed pressure gradient in the core of the flow that drives the bypass flow of continuous phase through the corners (gutters) and causes the Taylor droplet’s relative velocity between the faster droplet flow and the slower mean flow. Based on the pressure field, we quantify the driving pressure gradient of the bypass flow and verify a simple estimation method: the geometry of the gutter entrances delivers a Laplace pressure difference. As a direct measure for the viscous dissipation, we calculate the 3D distribution of work done on the flow elements, that is necessary to maintain the stationarity of the Taylor flow. The spatial integration of this distribution provides the overall dissipated energy and allows to identify and quantify different contributions from the individual fluid phases, from the wall-proximate layer and from the flow redirection due to presence of the droplet interface. For the first time, we provide deep insight into the 3D pressure field and the distribution of the energy dissipation in the Taylor flow based on experimentally acquired 3D3C velocity data. We provide the 3D pressure field of and the 3D distribution of work as supplementary material to enable a benchmark for CFD and numerical simulations. Graphical abstract

scholarly journals A Solution to Pressure Equation with Its Boundary Condition of Combining Tangential and Normal Pressure Relations

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1507
Author(s):  
Hui Xiao ◽  
Wei Liu
Keyword(s):  
Boundary Condition ◽  
Numerical Algorithm ◽  
Iteration Process ◽  
Normal Pressure ◽  
Constitutive Law ◽  
Navier Stokes ◽  
Numerical Verification ◽  
Pressure Equation ◽  
Navier Stokes Equation ◽  
Pressure Boundary Condition

Pressure is a physical quantity that is indispensable in the study of transport phenomena. Previous studies put forward a pressure constitutive law and constructed a partial differential equation on pressure to study the convection with or without heat and mass transfer. In this paper, a numerical algorithm was proposed to solve this pressure equation by coupling with the Navier-Stokes equation. To match the pressure equation, a method of dealing with pressure boundary condition was presented by combining the tangential and normal direction pressure relations, which should be updated dynamically in the iteration process. Then, a solution to this pressure equation was obtained to bridge the gap between the mathematical model and a practical numerical algorithm. Through numerical verification in a circular tube, it is found that the proposed boundary conditions are applicable. The results demonstrate that the present pressure equation well describes the transport characteristics of the fluid.

A METHOD FOR THE TREATMENT OF A SLOPING SEA BOTTOM IN THE PARABOLIC APPROXIMATION

1996 ◽  
Vol 04 (01) ◽  
pp. 89-100 ◽  
Author(s):  
J. S. PAPADAKIS ◽  
B. PELLONI
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Pressure Field ◽  
Impedance Boundary Condition ◽  
Parabolic Approximation ◽  
Impedance Boundary ◽  
Local Boundary ◽  
Sea Bottom ◽  
Local Boundary Condition ◽  
Non Local

The impedance boundary condition for the parabolic approximation is derived in the case of a sea bottom profile sloping at a constant angle, as a non-local boundary condition imposed exactly at the interface. This condition is integrated into the IFD code for the numerical computation of the pressure field and implemented to test its accuracy in some benchmark cases, for which the backscattered field is negligible. It is shown that by avoiding the sloping interface, the results obtained are closer to the benchmark results given by normal mode codes solving the full Helmholtz equation, such as the 2-way COUPLE code, than those of the standard IFD or other 1-way codes, at least for problems that do not have significant backscattering effects.

scholarly journals Designing a top cooling system for an electromagnetic calorimeter

2021 ◽  
Vol 345 ◽  
pp. 00015
Author(s):  
Matěj Jeřábek ◽  
Michal Volf ◽  
Daniel Duda
Keyword(s):  
Numerical Simulation ◽  
Pressure Field ◽  
Cooling System ◽  
Flow Simulation ◽  
Electromagnetic Calorimeter ◽  
3D Flow ◽  
Commercial Software ◽  
Pressure Fields ◽  
Detailed Evaluation ◽  
Temperature And Pressure

The article describes a numerical simulation of flow in the cooling system of an electromagnetic calorimeter by analysing the temperature and pressure fields. Two fundamentally different approaches were used to analyse the pressure field - analytical 1D calculation and numerical 3D flow simulation. The article contains a detailed evaluation and description of individual analyses using the commercial software ANSYS 2020 R1.

Vortex street impinging upon an elliptical leading edge

1990 ◽  
Vol 211 ◽  
pp. 211-242 ◽  
Author(s):  
Ismet Gursul ◽  
Donald Rockwell
Keyword(s):  
Velocity Field ◽  
Flow Visualization ◽  
Pressure Field ◽  
Leading Edge ◽  
Vortex Street ◽  
Transverse Displacement ◽  
Vorticity Field ◽  
Measured Velocity ◽  
Vortical Structures ◽  
Pressure Fields

The interaction of a Kármán vortex street with an elliptical edge is investigated experimentally. Basic types of interaction, as a function of scale and transverse displacement of the incident vortex street, are revealed using flow visualization. Unsteady pressure fields induced by these interactions are measured by a phase-averaging technique and correlated with the visualized flow patterns for basic classes of interactions.For a generic vortex–edge interaction, measurements of the phase-averaged velocity field allow construction of streamlines and vorticity contours showing the details of the interaction, including distortion of the vortical structures near the edge. The pressure field is calculated from the measured velocity field and interpreted in relation to the vortical structures.Simulation of flow visualization using the measured velocity field demonstrates possible misinterpretations related to the underlying vorticity field.

scholarly journals A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180642 ◽  
Author(s):  
H. Alemi Ardakani ◽  
T. J. Bridges ◽  
F. Gay-Balmaz ◽  
Y. H. Huang ◽  
C. Tronci
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Variational Principle ◽  
Stream Function ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Fluid Sloshing ◽  
Pressure Boundary Condition ◽  
Vessel Motion

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seung-Jae Lee ◽  
Jun-Hyeok Lee ◽  
Jung-Chun Suh
Keyword(s):  
Circular Cylinder ◽  
Solid Body ◽  
Pressure Field ◽  
Stokes Equations ◽  
Computational Cost ◽  
Fixed Time ◽  
Computational Grids ◽  
Penalty Term ◽  
Pressure Fields ◽  
Wide Range

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.

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