Equations of Motion of Two-Phase Variable Mass Systems With Solid Base

1994 ◽  
Vol 61 (4) ◽  
pp. 855-860 ◽  
Author(s):  
F. O. Eke ◽  
Song-Min Wang
Keyword(s):  
Solid Phase ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Fluid Phase ◽  
Solid Base ◽  
Phase Variable ◽  
Dynamical Equations ◽  
Two Phase ◽  
Attitude Stability ◽  
Variable Mass Systems

This paper develops dynamical equations for variable mass systems that can be viewed, at any given instant, as comprising a solid phase and a fluid phase. The equations of translational and rotational motion are presented, and several versions of each are given. It is shown that some versions have major advantages over others because they involve parameters that are relatively easy to estimate in practical problems, and make close-form solutions possible without the usual penalty of drastic simplifying assumptions. A simple rocket example is presented, and shows that instability cannot be ruled out for such systems. It is shown that system and combustion chamber geometry play a crucial role in the attitude stability of such systems.

Kinematic and Dynamic Parameters of a Liquid-Solid Pipe Flow Using DPIV∕Accelerometry

2007 ◽  
Vol 129 (11) ◽  
pp. 1415-1421 ◽  
Author(s):  
Joseph Borowsky ◽  
Timothy Wei
Keyword(s):  
Pipe Flow ◽  
Solid Phase ◽  
Fluid Phase ◽  
Central Moment ◽  
Steady Flows ◽  
Dynamic Parameters ◽  
Two Phase ◽  
Turbulence Structures ◽  
Two Phases ◽  
Flat Profile

An experimental investigation of a two-phase pipe flow was undertaken to study kinematic and dynamic parameters of the fluid and solid phases. To accomplish this, a two-color digital particle image velocimetry and accelerometry (DPIV∕DPIA) methodology was used to measure velocity and acceleration fields of the fluid phase and solid phase simultaneously. The simultaneous, two-color DPIV∕DPIA measurements provided information on the changing characteristics of two-phase flow kinematic and dynamic quantities. Analysis of kinematic terms indicated that turbulence was suppressed due to the presence of the solid phase. Dynamic considerations focused on the second and third central moments of temporal acceleration for both phases. For the condition studied, the distribution across the tube of the second central moment of acceleration indicated a higher value for the solid phase than the fluid phase; both phases had increased values near the wall. The third central moment statistic of acceleration showed a variation between the two phases with the fluid phase having an oscillatory-type profile across the tube and the solid phase having a fairly flat profile. The differences in second and third central moment profiles between the two phases are attributed to the inertia of each particle type and its response to turbulence structures. Analysis of acceleration statistics provides another approach to characterize flow fields and gives some insight into the flow structures, even for steady flows.

scholarly journals Determination of Phase-Eigenvalues by Rational Factorization and Enhanced Simulation of Two-Phase Mass Flow

2019 ◽  
Vol 2 (2) ◽  
pp. 61-77
Author(s):  
Puskar R. Pokhrel ◽  
Bhadra Man Tuladhar
Keyword(s):  
Fluid Dynamics ◽  
Debris Flows ◽  
Lateral Pressure ◽  
Solid Phase ◽  
Fluid Phase ◽  
Factorization Method ◽  
Phase Interaction ◽  
Two Phase ◽  
Simulation Results

In this paper, we present simple and exact eigenvalues for both the solid- and fluid-phases of the real two-phase general model developed by Pudasaini (2012); we call these phase-eigenvalues, the solid- phase-eigenvalues and the fluid-phase-eigenvalues. Results are compared by applying the derived phase- eigenvalues that incorporate the phase-interactions in the two-phase debris movements against the simple and classical solid and fluid eigenvalues without any phase interaction. We have constructed several different set of eigenvalues including the coupled phase eigenvalues by using rational factorization method. At first, we consider for general debris height; factorizing the solid and fluid lateral pressure contributions by considering the negligible pressure gradient; negligible solid lateral pressure; negligible fluid lateral pressure; negligible solid and fluid lateral pressure. Secondly, for a thin debris ow height, we also construct the fourth set of eigenvalues in three different cases. These phase-eigenvalues incorporate strong interaction between the solid and fluid dynamics. The simulation results are produced by taking all these different sets of coupled phase-eigenvalues and are compared with the classical uncoupled set of solid and fluid eigenvalues. The results indicate the importance of phase-eigenvalues and supports for a complete description of the phase- eigenvalues for the enhanced description of real two-phase debris flows and landslide motions.

Heat Transfer in Fixed Bed Elliptic Cylindrical Reactor via Two-Phase Model

2020 ◽  
Vol 400 ◽  
pp. 45-50
Author(s):  
Antonildo Santos Pereira ◽  
Rodrigo Moura da Silva ◽  
Maria Conceição Nóbrega Machado ◽  
Luan Pedro Melo Azerêdo ◽  
Anderson Ferreira Vilela ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Solid Phase ◽  
Homogeneous Model ◽  
Fixed Bed ◽  
Fluid Phase ◽  
Packed Bed ◽  
Two Phase ◽  
Heterogeneous Model ◽  
Fully Implicit ◽  
Cylindrical Reactor

The study of heat transfer in fixed bed tubular reactors of heated or cooled walls has presented great interest by the academy and industry. The adequate and safe design of such equipment requires the use of reliable and realistic mathematical. Unfortunately several studies are restrict to homogeneous model applied to circular and elliptic cylindrical reactors. Then, the objective of this work was to predict heat transfer in packed-bed elliptic cylindrical reactor, by using a proposed heterogeneous model. The mathematical model is composed for one solid phase and another fluid phase, in which the balance equation for each constituent is applied separately. The finite volume method was utilized to solve the partial differential equations using the WUDS scheme for interpolation of the convective and diffusive terms, and the fully implicit formulation. Results of the temperature distribution of the fluid and solid phases along the reactor are presented and analyzed. It was verified that the highest temperature gradients of the phases are located close to the wall and inlet of the reactor.

Extended Kane’s Equations for Nonholonomic Variable Mass System

1982 ◽  
Vol 49 (2) ◽  
pp. 429-431 ◽  
Author(s):  
Z.-M. Ge ◽  
Y.-H. Cheng
Keyword(s):  
Equations Of Motion ◽  
Variable Mass ◽  
Mass System ◽  
Variable Mass System ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Variable Mass Systems

An extension of Kane’s equations of motion for nonholonomic variable mass systems is presented. As an illustrative example, equations of motion are formulated for a rocket car.

scholarly journals A two-phase model for numerical simulation of debris flows

2014 ◽  
Vol 2 (3) ◽  
pp. 2151-2183 ◽  
Author(s):  
S. He ◽  
W. Liu ◽  
C. Ouyang ◽  
X. Li
Keyword(s):  
Debris Flow ◽  
Debris Flows ◽  
Volume Fraction ◽  
Solid Phase ◽  
Fluid Phase ◽  
Viscous Drag ◽  
Finite Volume Scheme ◽  
Viscous Stress ◽  
Two Phase ◽  
One Dimensional

Abstract. Debris flows are multiphase, gravity-driven flows consisting of randomly dispersed interacting phases. The interaction between the solid phase and liquid phase plays a significant role on debris flow motion. This paper presents a new two-phase debris flow model based on the shallow water assumption and depth-average integration. The model employs the Mohr–Coulomb plasticity for the solid stress, and the fluid stress is modeled as a Newtonian viscous stress. The interfacial momentum transfer includes viscous drag, buoyancy and interaction force between solid phase and fluid phase. We solve numerically the one-dimensional model equations by a high-resolution finite volume scheme based on a Roe-type Riemann solver. The model and the numerical method are validated by using one-dimensional dam-break problem. The influences of volume fraction on the motion of debris flow are discussed and comparison between the present model and Pitman's model is presented. Results of numerical experiments demonstrate that viscous stress of fluid phase has significant effect in the process of movement of debris flow and volume fraction of solid phase significantly affects the debris flow dynamics.

A Unified Model of Oil/Water Two-Phase Flow in the Horizontal Wellbore

SPE Journal ◽  
2016 ◽  
Vol 22 (01) ◽  
pp. 353-364 ◽  
Author(s):  
Zhiming Wang ◽  
Quan Zhang ◽  
Quanshu Zeng ◽  
Jianguang Wei
Keyword(s):  
Two Phase Flow ◽  
Mechanistic Model ◽  
Variable Mass ◽  
Flow Patterns ◽  
Phase Flow ◽  
Phase Variable ◽  
Two Phase ◽  
Horizontal Wellbore ◽  
Oil Water ◽  
Variable Mass Flow

Summary In this article, a more-general flow-pattern classification of oil/water two-phase flow in the horizontal wellbore is proposed first according to the theoretical analysis and previous research achievements, on the basis of which a simplification is then performed through reasonable incorporation, and the ultimate flow patterns considered for modeling are reduced to two categories containing only six standard patterns. By use of the classical two-fluid and homogeneous modeling methodologies stemming from oil/water two-phase flow in conventional pipes, combined with the simplified classification, a mechanistic model is developed to predict the flow characteristics including the flow patterns and pressure losses for oil/water two-phase variable-mass flow in the horizontal wellbore. Model implementation is performed on the basis of the universal principle that a system will stabilize to the equilibrium state of minimum energy. Overall performance of the mechanistic model is then validated against the new data sets measured upon a large-scale experimental apparatus at the China University of Petroleum (CUP), which is designed and constructed to simulate the gas/oil/water multiphase flow in horizontal wellbores with wall mass transfer. Results show that the model developed in this paper can not only properly predict the flow patterns of oil/water two-phase flow in the horizontal wellbore, but also has high prediction accuracy for the pressure drops. Compared with the new experimental data for oil/water two-phase variable-mass flow that covers a series of input water-volumetric fractions ranging from 10 to 90%, the highest absolute average percentage error of the new unified model is 12% and the whole error is 9.2%, which demonstrates an acceptable performance. Investigations conducted in this study further enrich and develop the theory of hydrodynamic calculation for oil/water flow in the horizontal wellbore with wall influx.

scholarly journals CFD-based numerical simulation of cyclone separator for separating stigmas from petals of saffron

2020 ◽  
Author(s):  
Javad Nemati ◽  
Babak Beheshti ◽  
Ali Mohammad Borghei
Keyword(s):  
Separation Efficiency ◽  
Solid Phase ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Reynolds Stress Model ◽  
Continuous Phase ◽  
Solid Particles ◽  
Inlet Section ◽  
Ansys Fluent ◽  
Discrete Phase

This study numerically modeled the flow of a fluid (air) and solid particles (saffron flower) inside a cyclone using the finite volume method (FVM) in ANSYS Fluent. The continuous phase was simulated under steady state conditions, as the initial condition, using the Reynolds Stress Model (RSM) for turbulence at three constant inlet air velocities of 1.5 m/s, 2.5 m/s, and 3.5 m/s over the inlet section. One-way coupling was assumed to govern all numerical analyses. The fluid phase and particles were treated as the continuous medium (within a Eulerian framework) and discrete phase (within a Lagrangian framework), respectively. The equations governing the gas phase included the compressible Navier–Stokes and the conservation of mass. The discrete phase equations included the equations of motion for three different particles including petals, stigmas, and anthers. According to the numerical results, the cyclone separation efficiency was calculated, and the static pressure and velocity contours were plotted. The results showed the capability of the CFD-based simulation for an accurate demonstration of the behavior of the fluid–solid phase. Accordingly, it can be used to predict the efficiency of stigma separation from petals of saffron using airflow in the cyclone. According to the results, the highest cyclonic separation efficiency of 89% was achieved at an inlet air velocity of 3.5 m/s, which was very close to the experimental data.

A Poroelastic-Viscoelastic Limit for Modeling Brain Biomechanics

2015 ◽  
Vol 1753 ◽  
Author(s):  
Md. Mehedi Hasan ◽  
Corina S. Drapaca
Keyword(s):  
Brain Tissue ◽  
Solid Phase ◽  
Soil Mechanics ◽  
Equations Of Motion ◽  
Elastic Solid ◽  
Two Phase ◽  
Fluid Mixture ◽  
Brain Responses ◽  
Brain Biomechanics ◽  
The Central Nervous System

ABSTRACTThe brain, a mixture of neural and glia cells, vasculature, and cerebrospinal fluid (CSF), is one of the most complex organs in the human body. To understand brain responses to traumatic injuries and diseases of the central nervous system it is necessary to develop accurate mathematical models and corresponding computer simulations which can predict brain biomechanics and help design better diagnostic and therapeutic protocols. So far brain tissue has been modeled as either a poroelastic mixture saturated by CSF or as a (visco)-elastic solid. However, it is not obvious which model is more appropriate when investigating brain mechanics under certain physiological and pathological conditions. In this paper we study brain’s mechanics by using a Kelvin-Voight (KV) model for a one-phase viscoelastic solid and a Kelvin-Voight-Maxwell-Biot (KVMB) model for a two-phase (solid and fluid) mixture, and explore the limit between these two models. To account for brain’s evolving microstructure, we replace in the equations of motion the classic integer order time derivatives by Caputo fractional order derivatives and thus introduce corresponding fractional KV and KVMB models. As in soil mechanics we use the displacements of the solid phase in the classic (fractional) KVMB model and respectively of the classic (fractional) KV model to define a poroelastic-viscoelastic limit. Our results show that when the CSF and brain tissue in the classic (fractional) KVMB model have similar speeds, then the model is indistinguishable from its equivalent classic (fractional) KV model.

Modeling Welding by Surface Heating

1992 ◽  
Vol 114 (4) ◽  
pp. 439-449 ◽  
Author(s):  
I. C. Sheng ◽  
Y. Chen
Keyword(s):  
Energy Equation ◽  
Solid Phase ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Equation Of Motion ◽  
Avrami Equation ◽  
Moving Heat Source ◽  
Stress Evolution ◽  
Fluid Mixture ◽  
Traction Boundary Conditions

A mathematical model has been developed in describing the temperature distribution, the flow of the molten fluid and the stress field in the solid during welding. In modeling the properties of the material during welding, the solid phase is assumed to behave as a thermoviscoplastic solid obeying Bodner-Partom/Walker type constitutive equation, whereas the fluid phase as a thermoviscous incompressible fluid. Three regions exist: pure solid, pure fluid, and the transition (solid-fluid mixture). In the formulation of the boundary value problem, the energy equation is coupled to the equation of motion through the terms of mechanical work and the latent heat of the phases, whereas the equations of motion of the solid and the fluid are decoupled. Appropriate thermal and traction boundary conditions are detailed in the text. Phase transformation activities during cooling are monitored by CCT diagram and Avrami equation. An arbitrary Lagrangian and Eulerian method is used to accommodate the kinematic description of both the solid and the fluid phases. A representative plane perpendicular to the moving heat source is analyzed. Results of sample calculations are presented to show the temperature and the stress evolution in time. Residual stress and microstructure patterns are presented.

Virtual mass and drag in two-phase flow

1991 ◽  
Vol 225 ◽  
pp. 177-196 ◽  
Author(s):  
B. U. Felderhof
Keyword(s):  
Equilibrium Distribution ◽  
Hard Spheres ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Spherical Particles ◽  
Inviscid Fluid ◽  
Virtual Mass ◽  
Ensemble Averaging ◽  
Two Phase ◽  
Numerical Predictions

We study virtual mass and drag effects in a fluid suspension consisting of spherical particles immersed in an incompressible, nearly inviscid fluid. We derive average equations of motion for the fluid phase and the particle phase by the method of ensemble averaging. We show that the virtual mass and drag coefficients may be expressed exactly in terms of the dielectric constant of a corresponding dielectric suspension with the same distribution of particles. We make numerical predictions for the case of an equilibrium distribution of hard spheres.

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