A Two-Phase Fluid Model for Simulation of Cavitation Phenomena in Pipe-Line Hydraulic Systems

2003 ◽  
Author(s):  
Claudio Negri
Keyword(s):  
Sound Speed ◽  
Fluid Model ◽  
Test Cases ◽  
Hydraulic Systems ◽  
Homogeneous Fluid ◽  
Two Phase ◽  
Pipe Line ◽  
Line Test ◽  
Phase Fluid ◽  
Energy Conservation Law

This paper presents the details of a new fluid mathematical model developed for the numerical simulation of hydraulic systems that can work in cavitating conditions. The proposed fluid model allows you to obtain physical properties, i.e. density, bulk modulus, enthalpy, entropy, void fraction and sound speed, of a liquid-vapor-gas mixture so that the mixture itself can be treated as a homogeneous fluid (homogeneous two-phase fluid model). The model was applied in the numerical analysis of pipe-line test cases. in particular, both travelling cavitation, followed by a shock-wave, and fixed cavitation due to the superposition of depression waves, are examined and numerically simulated. Besides, relevant results are shown about sound speed variations in the zones of cavitation. The author is then interested in evaluating the approximation affecting the results obtainable by using an isothermal approach, by comparing them to the results obtainable by solving the full set of conservation equations (including the energy conservation law). An analysis on the entropy production due to the propagation of shock waves is proposed, along with an estimation of the inaccuracies occurring if an isentropic or isothermal evolution is assumed.

scholarly journals Estimation of flow velocity for a debris flow via the two-phase fluid model

2015 ◽  
Vol 22 (1) ◽  
pp. 109-116 ◽  
Author(s):  
S. Guo ◽  
P. Xu ◽  
Z. Zheng ◽  
Y. Gao
Keyword(s):  
Debris Flow ◽  
Real World ◽  
Empirical Formula ◽  
Debris Flows ◽  
Fluid Model ◽  
Two Phase ◽  
Liquid Phases ◽  
Two Phases ◽  
Phase Fluid ◽  
Steady Velocity

Abstract. The two-phase fluid model is applied in this study to calculate the steady velocity of a debris flow along a channel bed. By using the momentum equations of the solid and liquid phases in the debris flow together with an empirical formula to describe the interaction between two phases, the steady velocities of the solid and liquid phases are obtained theoretically. The comparison of those velocities obtained by the proposed method with the observed velocities of two real-world debris flows shows that the proposed method can estimate the velocity for a debris flow.

Accuracy of the Operator Splitting Technique for Two-Phase Flow With Stiff Source Terms

2002 ◽  
Author(s):  
Iztok Tiselj ◽  
Andrej Horvat
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Operator Splitting ◽  
Splitting Method ◽  
Water Hammer ◽  
Phase Flow ◽  
Hydraulic Systems ◽  
Source Terms ◽  
Two Phase ◽  
Splitting Technique

Code for analysis of the water hammer in thermal-hydraulic systems is being developed within the WAHALoads project founded by the European Commission [1]. Code will be specialized for the simulations of the two-phase water hammer phenomena with the two-fluid model of two-phase flow. The proposed numerical scheme is a two-step second-order accurate scheme with operator splitting; i.e. convection and sources are treated separately. Operator splitting technique is a very simple and “easy-to-use” tool, however, when the source terms are stiff, operator splitting method becomes a source of a specific non-accuracy, which behaves as a numerical diffusion. This type of error is analyzed in the present paper.

MODE AND PE PREDICTIONS OF PROPAGATION IN RANGE-DEPENDENT ENVIRONMENTS: SWAM'99 WORKSHOP RESULTS

2001 ◽  
Vol 09 (01) ◽  
pp. 205-225
Author(s):  
PETER L. NIELSEN ◽  
FINN B. JENSEN
Keyword(s):  
Normal Mode ◽  
Sound Speed ◽  
Transmission Loss ◽  
Equation Model ◽  
Test Cases ◽  
Homogeneous Fluid ◽  
Flat Bottom ◽  
Propagation Models ◽  
Propagation Analysis ◽  
Model C

Three numerical acoustic models, a coupled normal-mode model (C-SNAP), an adiabatic normal-mode model (PROSIM), and a parabolic equation model (RAM), are applied to test cases defined for the SWAM'99 workshop. The test cases consist of three shallow water (flat bottom) scenarios with range-dependent sound-speed profiles imitating internal wave fields and a shelf-break case, with range-dependent sound-speed profiles and bathymetry. The bottom properties in all the cases are range-independent and modeled as a homogeneous fluid half-space. The results from the modeling are presented as transmission loss for selected acoustic frequencies and source-receiver geometries, and as received time series. The results are compared in order to evaluate the effect of applying different propagation models to the same range-dependent underwater environment. It should be emphasized that the propagation analysis is not an attempt to benchmark the selected propagation models, but to demonstrate the performance of practical, range-dependent models based on different approximations in particular underwater scenarios.

A two-phase fluid model of crystal settling under variable gravity

1999 ◽  
Author(s):  
A. Alexandrou ◽  
H. Shi ◽  
N. Gatsonis ◽  
A. Sacco, Jr.
Keyword(s):  
Fluid Model ◽  
Two Phase ◽  
Crystal Settling ◽  
Variable Gravity ◽  
Phase Fluid

A FRACTAL TWO-PHASE FLOW MODEL FOR THE FIBER MOTION IN A POLYMER FILLING PROCESS

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050093 ◽  
Author(s):  
XUEJUAN LI ◽  
ZHI LIU ◽  
JI-HUAN HE
Keyword(s):  
Fiber Orientation ◽  
Fluid Model ◽  
Polymer Melt ◽  
Element Model ◽  
Filling Process ◽  
Governing Equations ◽  
Two Phase ◽  
Fiber Motion ◽  
Fractal Space ◽  
Phase Fluid

This paper suggests a fractal two-phase fluid model for the polymer melt filling process to deal effectively with the unsmooth front interface. An infinitesimal fluid element model in a fractal space is proposed to establish the governing equations according to the conservation laws in fluid mechanics, the fractal divergence and fractal Laplace operator are defined. The unsmooth interface is solved numerically, and fibers’ motion properties on the interface are also elucidated. Moreover, the distribution of fibers on the interface at different stages shows the fractal property of the fibers’ motion. However, the motion of fibers is affected by the flow of macroscopic polymer melt, and the fiber orientation in the interface shows a certain statistical regularity. Based on the characters of fiber orientation, the fractal interface can be used for the optimal design of the polymer melt filling process.

Numerical Simulation of Bubble Migration in Liquid Titanium Melts under Hypergravity Field

2013 ◽  
Vol 762 ◽  
pp. 387-391
Author(s):  
Qin Xu ◽  
Shi Ping Wu ◽  
Xiang Xue
Keyword(s):  
Reference Frames ◽  
Fluid Model ◽  
Water Model ◽  
Rotating Shaft ◽  
Two Phase ◽  
Liquid Titanium ◽  
Multiple Reference Frames ◽  
Phase Fluid ◽  
Multiple Reference ◽  
Titanium Melt

Bubble migrations in liquid titanium melt under hypergravity field is modeled using commercial computational fluid dynamics software FLUENT 6.3 (Fluent inc., USA). The two-phase fluid model, incorporated with the Multiple Reference Frames (MRF) method is used to predict the movement of the bubble in the melt. Simulated results are compared with experimental data from the water model measurement and reasonable agreements are obtained. Furthermore, the computed results show that the bubble migration under hypergravity field includes the movement forward to the casting rotating shaft and the movement opposite to the direction of the rotating mould. In addition, the initial bubble size and the surface tension between the melt and the gas bubble have an important effect on the distortion of the bubble.

The Effect of Shape Factor on the Magnetic Targeting in the Permeable Microvessel With Two-Phase Casson Fluid Model

2011 ◽  
Vol 2 (4) ◽  
Author(s):  
Sachin Shaw ◽  
P. V. S. N. Murthy
Keyword(s):  
Magnetic Field ◽  
Volume Fraction ◽  
Fluid Model ◽  
Casson Fluid ◽  
Magnetic Drug Targeting ◽  
Magnetic Targeting ◽  
Two Phase ◽  
Coupled Equations ◽  
Casson Fluid Model ◽  
Phase Fluid

The present investigation deals with magnetic drug targeting in a microvessel of radius 5 μm using two-phase fluid model. The microvessel is divided into the endothelial glycocalyx layer wherein the blood obeys Newtonian character and a core region wherein the blood obeys the non-Newtonian Casson fluid character. The carrier particles, bound with nanoparticles and drug molecules, are injected into the vascular system upstream from the malignant tissue and are captured at the tumor site using a local applied magnetic field near the tumor position. Brinkman model is used to characterize the permeable nature of the inner wall of the microvessel. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size and shape of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel, are considered in the present problem. The system of coupled equations is solved to obtain the trajectories of the carrier particle in the noninvasive case.

A Numerical Modelling of Two-Phase Flow System

2008 ◽  
Author(s):  
Moon-Sun Chung ◽  
Jong-Won Kim
Keyword(s):  
Sound Speed ◽  
Two Phase Flow ◽  
Flow System ◽  
Fluid Model ◽  
Equation System ◽  
Pressure Jump ◽  
Phase Flow ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Phase

A two-dimensional two-fluid model for two-phase flow system is proposed. This two-dimensional model is based on the hyperbolic one-dimensional model which is improved in its mathematical property by adopting the interfacial pressure jump terms in the momentum equations. Owing to this surface-tension effect incorporated in the momentum equations, eigenvalues of the equation system can be obtained analytically and they are proved to be all real. The eigenvectors can also be obtained analytically with linearly independent form. Further, they consist of phasic convective velocities, the sound speed of gas phase, and the sound speed of liquid phase. Consequently, the governing equation system is mathematically hyperbolic with reasonable characteristic speeds by which the upwind numerical method avails. Advantages and possibility of the present model are discussed in some detail.

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