scholarly journals fenicsR13

2021 ◽  
Vol 47 (2) ◽  
pp. 1-29
Author(s):  
Lambert Theisen ◽  
Manuel Torrilhon
Keyword(s):  
Gas Flow ◽  
Differential Operators ◽  
Mixed Finite Element ◽  
Test Cases ◽  
Typical Application ◽  
Flow Models ◽  
Computing Platform ◽  
Abstraction Levels ◽  
Variational Formulations ◽  
Rarefaction Effects

We present a mixed finite element solver for the linearized regularized 13-moment equations of non-equilibrium gas dynamics. The Python implementation builds upon the software tools provided by the FEniCS computing platform. We describe a new tensorial approach utilizing the extension capabilities of FEniCS’ Unified Form Language to define required differential operators for tensors above second degree. The presented solver serves as an example for implementing tensorial variational formulations in FEniCS, for which the documentation and literature seem to be very sparse. Using the software abstraction levels provided by the Unified Form Language allows an almost one-to-one correspondence between the underlying mathematics and the resulting source code. Test cases support the correctness of the proposed method using validation with exact solutions. To justify the usage of extended gas flow models, we discuss typical application cases involving rarefaction effects. We provide the documented and validated solver publicly.

A Criterion for the Experimental Validation of the Slip-Flow Models for Incompressible Rarefied Gases Through Microchannels

2004 ◽  
Author(s):  
G. L. Morini ◽  
M. Lorenzini ◽  
M. Spiga
Keyword(s):  
Friction Factor ◽  
Cross Section ◽  
Gas Flow ◽  
Experimental Validation ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Rarefied Gas Flow ◽  
Flow Models ◽  
Flow Through ◽  
Rarefaction Effects

This paper is devoted to analyzing the friction factor of incompressible rarefied gas flow through microchannels. A theoretical investigation is conducted in order to underline the conditions for experimentally evidencing rarefaction effects on the pressure drop. It is demonstrated that for a fixed geometry of the microchannel cross section it is possible to calculate the minimum value of the Knudsen number for which the rarefaction effects can be observed experimentally, taking into account the experimental uncertainties on the evaluation of the friction factor.

Evolutionary heuristic with Gudermannian neural networks for the nonlinear singular models of third kind

2021 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Hafiz Abdul Wahab
Keyword(s):  
Neural Networks ◽  
Differential Operators ◽  
Layer Structure ◽  
Research Work ◽  
Merit Function ◽  
Third Order ◽  
Intelligent Computing ◽  
Computing Platform ◽  
Hybrid Heuristics ◽  
Hidden Layer

Abstract The presented research work articulates a new design of heuristic computing platform with artificial intelligence algorithm by exploitation of modeling with feed-forward Gudermannian neural networks (FFGNN) trained with global search viability of genetic algorithms (GA) hybrid with speedy local convergence ability of sequential quadratic programing (SQP) approach, i.e., FFGNN-GASQP for solving the singular nonlinear third order Emden-Fowler (SNEF) models. The proposed FFGNN-GASQP intelligent computing solver Gudermannian kernel unified in the hidden layer structure of FFGNN systems of differential operators based on the SNEF that are arbitrary connected to represent the error-based merit function. The optimization objective function is performed with hybrid heuristics of GASQP. Three problems of the third order SNEF are used to evaluate the correctness, robustness and effectiveness of the designed FFGNN-GASQP scheme. Statistical assessments of the performance of FFGNN-GASQP are used to validate the consistent accuracy, convergence and stability.

scholarly journals Theoretical stability analysis of mixed finite element model of shale-gas flow with geomechanical effect

2020 ◽  
Vol 75 ◽  
pp. 33
Author(s):  
Mohamed F. El-Amin ◽  
Jisheng Kou ◽  
Shuyu Sun
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Shale Gas ◽  
Gas Flow ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Model ◽  
Mathematical Proofs ◽  
The Stability ◽  
Shale Gas Transport

In this work, we introduce a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects. The differential system was solved numerically by the Mixed Finite Element Method (MFEM). The results include seven lemmas and a theorem with rigorous mathematical proofs. The stability analysis presents the boundedness condition of the MFE solution.

Particle methods for pedestrian flow models: From microscopic to nonlocal continuum models

2014 ◽  
Vol 24 (12) ◽  
pp. 2503-2523 ◽  
Author(s):  
R. Etikyala ◽  
S. Göttlich ◽  
A. Klar ◽  
S. Tiwari
Keyword(s):  
Particle System ◽  
Numerical Test ◽  
Particle Methods ◽  
Test Cases ◽  
Pedestrian Flow ◽  
Nonlocal Continuum ◽  
Mean Velocity ◽  
Flow Models ◽  
Interacting Particle ◽  
Microscopic Models

A hierarchy of models for pedestrian flow is numerically investigated using particle methods. It includes microscopic models based on interacting particle system coupled to an eikonal equation, hydrodynamic models using equations for density and mean velocity, nonlocal continuum equations for the density and diffusive Hughes equations. Particle methods are used on all levels of the hierarchy. Numerical test cases are investigated by comparing the above models.

Wet Gas Compressor Model Validation

2019 ◽  
Author(s):  
Martin Bakken ◽  
Tor Bjørge ◽  
Lars E. Bakken
Keyword(s):  
Dynamic Model ◽  
Gas Flow ◽  
Petroleum Industry ◽  
Ambient Air ◽  
Open Loop ◽  
Test Facility ◽  
Centrifugal Impeller ◽  
Test Cases ◽  
Liquid Content ◽  
Wet Gas

Abstract The continuous demand for oil and gas forces the petroleum industry to develop new and cost-efficient technologies to increase recovery from new fields and enhance extraction from existing fields. Subsea wet gas compression stands out as a promising solution to increase field extraction, utilize remote regions and reduce costs. Today, a few subsea compressor systems are already operating while several new installations are expected within the next years. This creates a need for dynamic simulation tools to ensure proper system design and facilitate production. This paper presents the model setup for the wet gas compressor test facility at the Norwegian University of Science and Technology (NTNU). The test facility is an open loop configuration consisting of a single shrouded centrifugal impeller, a vaneless diffuser and a circular volute. The fluid is a mixture of ambient air and water. The analysis presented here validates the dynamic model behavior against transient experimental test cases, which include step changes in liquid content and driver trip in both wet and dry conditions. Further, the discharge valve performance has been analyzed in both dry and wet gas flow. The test reveals that the dynamic model is able to operate in a stable manner while showing a close correspondence to the transient test cases. Care should be taken in utilizing dry gas valve characteristics in multiphase flows as increased liquid content has a distinct impact on the valve performance.

Experimental Study of Entrance Effects on Laminar Gas Flow Through Silicon Orifices

2005 ◽  
Author(s):  
Aaron J. Knobloch ◽  
Joell R. Hibshman ◽  
George Wu ◽  
Rich Saia
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Flow Area ◽  
Fully Developed Flow ◽  
Flow Rates ◽  
Flow Models ◽  
Entry Length ◽  
Orifice Flow ◽  
Measured Flow ◽  
Flow Through

This study summarizes a fundamental investigation of flow through an array of silicon micromachined rectangular slots. The purpose of the study is to evaluate the effect of entrance pressure, flow area, orifice thickness, slot length, and slot width of the orifice on flow rate. These orifices were fabricated using a simple frontside through wafer DRIE process on a 385 μm thick wafer and wafer bonding to create thicker orifices. The dies were then packaged as part of a TO8 can and flow tested. To complement the results of this experimental work, two simple flow models were developed to predict the effect of geometrical and entrance conditions on the flow rate. These models were based on macroscale assumptions that were not necessarily true in the case of thin orifices. One relationship was based on Pouiselle flow which assumes fully developed flow conditions. Calculation of the entry length required for fully developed flow indicate that in the low Reynolds Number regime (32-550) evaluated, the entry flow development requires 2-8 times the thickness of the thickest orifices used for this study. Therefore, calculations of orifice flow based on a Pouiselle model are an overestimate of the actual measured flow rates. Another model examined typical orifice relationships using head loss at the entrance and exit of the slots did not accurately capture the particular flow rates since it overestimated the expansion or constriction losses. A series of experiments where the pressure was varied between 75 and 1000 Pa were performed. A comparison of the Pouiselle flow solution with experimental results was made which showed that the Pouiselle flow model overpredicts the flow rates and more specifically, the effect of width on the flow rates. The results of these tests were used to develop a transfer function which describes the dependence of flow rate on orifice width, thickness, length, and inlet pressure.

Comparison of isothermal and non-isothermal pipeline gas flow models

2001 ◽  
Vol 81 (1-3) ◽  
pp. 41-51 ◽  
Author(s):  
Andrzej J. Osiadacz ◽  
Maciej Chaczykowski
Keyword(s):  
Gas Flow ◽  
Flow Models

Viscous Dissipation and Rarefaction Effects on Laminar Forced Convection in Microchannels

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Arman Sadeghi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Knudsen Number ◽  
Parallel Plate ◽  
Gas Flow ◽  
Dimensionless Temperature ◽  
Viscous Heating ◽  
Laminar Forced Convection ◽  
Rarefaction Effects

Fluid flow in microchannels has some characteristics, which one of them is rarefaction effect related with gas flow. In the present work, hydrodynamically and thermally fully developed laminar forced convection heat transfer of a rarefied gas flow in two microgeometries is studied, namely, microannulus and parallel plate microchannel. The rarefaction effects are taken into consideration using first-order slip velocity and temperature jump boundary conditions. Viscous heating is also included for either the wall heating or the wall cooling case. Closed form expressions are obtained for dimensionless temperature distribution and Nusselt number. The results demonstrate that for both geometries, as Brinkman number increases, the Nusselt number decreases. However, the effect of viscous heating on the Nusselt number at greater values of Knudsen number becomes insignificant. In the absence of viscous heating, increasing values of Knudsen number lead to smaller values of Nusselt number. Furthermore, it is observed that viscous heating causes singularities in Nusselt number values. Also, asymmetry causes singularities in Nusselt numbers of both microannulus walls and the parallel plate wall having lower heat flux, even in the absence of viscous heating. For parallel plate microchannel, in the absence of viscous heating, Nusselt number of the wall having larger heat flux is an increasing function of the wall heat fluxes ratio.

Comparative assesment of steady-state pipeline gas flow models / Analiza porównawcza modeli przepływu gazu w rurociągu w stanach ustalonych

2012 ◽  
Vol 57 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Maciej Chaczykowski ◽  
Andrzej J. Osiadacz
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Gas Flow ◽  
Energy Equation ◽  
Momentum Equation ◽  
Analytical Models ◽  
Energy Term ◽  
Convective Term ◽  
Flow Models ◽  
Kinetic Energy Term

One-dimensional, non-isothermal flow of gas in a straight pipe has been considered to predict pressure and temperature profiles along the horizontal pipeline under steady-state conditions. Selected analytical models for the simplified calculation of these profiles are evaluated on the basis of the numerical solution of the accurate model, which incorporates the convective term in the momentum equation and the kinetic energy term in the energy equation, while treating the enthalpy as a function of pressure and temperature. For closure of the system of the conservation equations, the GERG 2004 equation of state was chosen. In order to present the discrepancies introduced by the models, the results of the numerical and analytical solutions are compared with the field data. The results show that in the case of the high pressure gas transmission system, the effects of the convective term in the momentum equation and the kinetic energy term in the energy equation are negligible for pipeline pressure and temperature calculation accuracies. It also indicates that real gas effects play an important role in the temperature distribution along the pipeline and cannot be neglected from the calculation when approximate analytical equations are used.

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