scholarly journals A fifth order WENO scheme for numerical simulation of shallow granular two-phase flow model

2021 ◽  
Vol 13 (9) ◽  
pp. 168781402110452
Author(s):  
Omar Rabbani ◽  
Saqib Zia ◽  
Asad Rehman
Keyword(s):  
Numerical Technique ◽  
Momentum Equation ◽  
Weno Scheme ◽  
Two Phase ◽  
Contact Discontinuities ◽  
Two Phases ◽  
Solid Liquid ◽  
Fifth Order ◽  
The Mathematical Model ◽  
Derivatives Of

In this article, a weighted essentially non-oscillatory (WENO) scheme is implemented to simulate two-phase shallow granular flow (TPSF) model. The flow is assumed to be incompressible and it is regarded as shallow layer of granular and liquid material. The mathematical model consists of two phases, that is, solid and liquid. Each phase has its continuity and momentum equation. The presence of the equations are coupled together involving the derivatives of unknowns which make it more challenging to solve. An efficient numerical technique is needed to tackle the numerical complexities. Our main intrigue is the numerical approximation of the above-mentioned solid-liquid model. The weighted essentially non-oscillatory (WENO) scheme of order 5 is utilized to handle the shock waves and contact discontinuities appear in the solution. The results are compared with the results already available in the literature by conservation element and solution element (CESE) scheme. It is observed the WENO scheme produces less errors as compared to CESE scheme and also effectively handle the shocks.

Reactor Safety Analysis Based on a Developed Two-Phase Compressible Flow Simulation

Volume 1 ◽  
2004 ◽  
Author(s):  
A. F. Nowakowski ◽  
B. V. Librovich ◽  
L. Lue
Keyword(s):  
Multiphase Flow ◽  
Compressible Flow ◽  
Fluid Model ◽  
Numerical Technique ◽  
Computational Simulation ◽  
Safety Analysis ◽  
State Equations ◽  
Pressure Relief ◽  
Two Phase ◽  
Two Phases

The direct numerical simulation of multiphase flow is a challenging research topic with various key applications. In the present work, a computational simulation of multi-phase compressible flow has been proposed for safety analysis of chemical reactors. The main objective of a pressure relief system is to prevent accidents occurring from over pressurisation of the reactor. We are particularly interested in understanding the phenomena associated with emergency pressure relief systems for batch-type reactors and storage vessels. Existence of multiphase flow is significantly influenced by the interface between the phases and the associated discontinuities across the phase. The approach, which builds on the method first introduced by Saurel and Abgrall [1], was developed for solving two-phase compressible flow problems. Each phase is separately described by conservation equations. The interactions between two phases appear in the basic equations as transfer terms across the interface. The equations are complemented by state equations for the two phases and by additional correlations for the right-hand side coupling terms. The method is able to deal with multiphase mixtures and interface problems between compressible fluids. The key difference compared to classical two-fluid model is the presence of separate pressures fields associated with phases and introduction of pressure and velocity relaxation procedures. The relaxation operators tackle the boundary conditions at the interface and consequently the model is valid for fluid mixtures, as well as for pure fluids. The numerical technique requires the system to be decomposed and involves a non-conservative hyperbolic solver, an instantaneous pressure relaxation procedure and source term operators. The solution is obtained by succession of integrators using a second-order accurate scheme. The ultimate goal of this research is to use the method for studying the venting problem in reactor systems after verifying its performance on a series of standardised test cases documented in the literature.

scholarly journals NUMERICAL SIMULATIONS FOR NON CONSERVATIVE HYPERBOLIC SYSTEM. APPLICATION TO TRANSIENT TWO-PHASE FLOW WITH CAVITATION PHENOMENON

2019 ◽  
Vol 24 (2) ◽  
pp. 218-235
Author(s):  
Abdelmjid Qadi El Idrissi ◽  
Boujemâa Achchab ◽  
Abdellatif Agouzal
Keyword(s):  
Numerical Technique ◽  
Liquid Mixtures ◽  
Dissolved Gas ◽  
Two Phase ◽  
Gas Concentration ◽  
Transient Flows ◽  
Cavitation Phenomenon ◽  
The Mathematical Model ◽  
Theoretical Results ◽  
Good Agreement

A numerical method for simulating transient flows of gas-liquid mixtures is proposed. The mathematical model, established for a suspension of gas bubbles in liquid, includes an equation taking into account the relative velocity between the gas and liquid. A numerical technique based on the Mac Cormack scheme combined with the method of characteristics is presented. Theoretical results for transients initiated by a rapid closing valves are compared with measurements. A good agreement is found particularly for large values of initial dissolved gas concentration.

scholarly journals Mechanism Research and Discussion of the Quality of Precision Machining of a Fifth-order Variable-diameter Pipe Using Abrasive Flow

2020 ◽  
Vol 66 (6) ◽  
pp. 358-374
Author(s):  
Junye Li ◽  
Lixiong Wang ◽  
Hengfu Zhang ◽  
Jinglei Hu ◽  
Xinming Zhang ◽  
...  
Keyword(s):  
Surface Quality ◽  
Incident Angle ◽  
Precision Machining ◽  
Two Phase ◽  
Variable Diameter ◽  
Diameter Pipe ◽  
Order Variable ◽  
Solid Liquid ◽  
Fifth Order

The solid-liquid two-phase abrasive flow precision machining technology is widely used in aerospace, precision machinery, the automotive industry and other fields, and is an advanced manufacturing technology that effectively improves the inner surface quality of workpieces. In this paper, the fifth-order variable-diameter pipe parts are researched. By discussing the collision between the abrasive particles and the wall surface, it is revealed that the material removal of the workpiece is caused by plastic deformation, and the mechanism of precision machining of the abrasive flow is clarified. Through numerical analysis and experimental research, it is found that the incident angle can affect the precision machining quality of the abrasive flow. When the inlet velocity of the abrasive flow is 45 m/s and the incident angle is 15°, the fifth-order variable-diameter pipe can obtain the best surface quality. Abrasive flow machining improves the surface quality of small holes better than that of large holes. To obtain uniform surface quality, it is necessary to use two-way machining to perform abrasive flow machining. The surface texture of the fifth-order variable-diameter pipe workpiece after precision machining by abrasive flow becomes clear and smooth, and the surface quality is significantly improved. The research results can provide theoretical guidance and technical support for the popularization and application of solid-liquid two-phase abrasive flow precision machining technology, with significant academic value and application value.

On the Riemann Problem Simulation for the Drift-Flux Equations of Two-Phase Flows

2016 ◽  
Vol 13 (01) ◽  
pp. 1650009 ◽  
Author(s):  
S. Kuila ◽  
T. Raja Sekhar ◽  
D. Zeidan
Keyword(s):  
Riemann Problem ◽  
Analytical Techniques ◽  
Momentum Equation ◽  
Two Phase ◽  
Computational Framework ◽  
Drift Flux ◽  
Numerical Predictions ◽  
Godunov Methods ◽  
Model Equations ◽  
Two Phases

This work presents computational simulations and analytical techniques for solving the drift-flux two-phase flow model. The model equations are formulated to describe the exact solution of the Riemann problem. The solution is constructed by solving the conservation of mass for each phase and the mixture conservation momentum equation of the two phases under isothermal conditions. Particular attention is given to address the expressions for jump relationships and the Riemann invariants. The performance of the developed Riemann solver is assessed with respect to different test cases selected from the literature. Comparisons with Godunov methods of centred-type are provided to demonstrate the use of the proposed exact and computational framework. Excellent agreement is observed between analytical results and numerical predictions.

Numerical modeling of the influence of bubbles on flow and heat transfer in the descending gas-liquid flow in a pipe

2012 ◽  
Vol 9 (1) ◽  
pp. 131-135
Author(s):  
M.A. Pakhomov
Keyword(s):  
Heat Transfer ◽  
Gas Phase ◽  
Liquid Flow ◽  
Bubble Diameter ◽  
Gas Content ◽  
Two Phase ◽  
Eulerian Description ◽  
Flow And Heat Transfer ◽  
Gas Liquid Flow ◽  
The Mathematical Model

The paper presents the results of modeling the dynamics of flow, friction and heat transfer in a descending gas-liquid flow in the pipe. The mathematical model is based on the use of the Eulerian description for both phases. The effect of a change in the degree of dispersion of the gas phase at the input, flow rate, initial liquid temperature and its friction and heat transfer rate in a two-phase flow. Addition of the gas phase causes an increase in heat transfer and friction on the wall, and these effects become more noticeable with increasing gas content and bubble diameter.

Some 1-substitution derivatives of 4-aryl-2,3-dihalogeno-1-naphthols

1984 ◽  
Vol 49 (1) ◽  
pp. 110-121 ◽  
Author(s):  
Jiří Křepelka ◽  
Drahuše Vlčková ◽  
Milan Mělka
Keyword(s):  
Thionyl Chloride ◽  
Oxirane Ring ◽  
Secondary Amines ◽  
Two Phase ◽  
Lytic Effect ◽  
Primary And Secondary Amines ◽  
Phase Medium ◽  
Chloro Derivatives ◽  
Derivatives Of

Alkylation of derivatives of 4-aryl-1-naphthols (I-V) by 2,3-epoxypropyl chloride in methanolic sodium hydroxide gave epoxy derivatives VI, VIII, IX, XI and XII, apart from products of cleavage of the oxirane ring, VII and X. Analogous alkylation of compounds I, IV and V by 2-(N,N-diethylamino)ethyl chloride hydrochloride in a two-phase medium afforded basic ethers XIII to XV. The cleavage of the oxirane ring in compound VI by the action of primary and secondary amines, piperidine and substituted piperazines led to compounds XVI-XXIV. Reaction of thionyl chloride with compounds XXI, XXII and XXIV gave chloro derivatives XXV-XXVII.Exposure of compound XXII to 4-methylbenzenesulfonyl chloride produced compound XXVIII, retaining the secondary alcoholic group. In an antineoplastic screening in vivo none of the compounds prepared had an appreciable activity. Compound XVII, being an analogue of propranolol, was used in the test of isoproterenolic tachycardia, and showed a beta-lytic effect comparable with that of propranol.

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