Dense Suspension Flows: a Mathematical Model Consistent with Thermodynamics

2021 ◽  
Author(s):  
Vladimir Shelukhin ◽  
Vladimir Neverov
Keyword(s):  
Mass Concentration ◽  
Mass Force ◽  
Continuum Thermodynamics ◽  
Flux Vector ◽  
Virtual Mass ◽  
Suspension Flows ◽  
Dense Suspension ◽  
Dense Suspensions ◽  
Archimedes Force ◽  
Particle Mass Concentration

Abstract We address the flows of dense suspensions of particles within the framework of two-velocity continuum. Thermodynamics of such a continuum is developed by the method suggested in the papers of L. D. Landau and I. M. Khalatnikov. As an application, we consider the convective settling problem. We capture the Boycott effect and prove that the enhanced sedimentation occurs in a 10 tilted vessel due to vortices. We do not call on additional interphase forces like the Stokes drag, the virtual mass force, the Archimedes force, the Basset-Boussinesq force and etc. Instead, we apply a generalized Fick's law for the particle mass concentration flux vector.

Focusing of inertial particles after the shock-wave intersection point

2007 ◽  
Vol 5 ◽  
pp. 145-150
Author(s):  
I.V. Golubkina
Keyword(s):  
Shock Wave ◽  
Mass Concentration ◽  
Gas Flow ◽  
Intersection Point ◽  
Plane Shock ◽  
Inertial Particles ◽  
Dusty Gas ◽  
Focusing Effect ◽  
Aerodynamic Focusing ◽  
Particle Mass Concentration

The effect of the aerodynamic focusing of inertial particles is investigated in both symmetric and non-symmetric cases of interaction of two plane shock waves in the stationary dusty-gas flow. The particle mass concentration is assumed to be small. Particle trajectories and concentration are calculated numerically with the full Lagrangian approach. A parametric study of the flow is performed in order to find the values of the governing parameters corresponding to the maximum focusing effect.

Numerical analysis for interphase forces of gas-liquid flow in a multiphase pump

2018 ◽  
Vol 35 (6) ◽  
pp. 2386-2402 ◽  
Author(s):  
Ming Liu ◽  
Shan Cao ◽  
Shuliang Cao
Keyword(s):  
Drag Force ◽  
Liquid Flow ◽  
Lift Force ◽  
Turbulent Dispersion ◽  
Dispersion Force ◽  
Mass Force ◽  
Virtual Mass ◽  
Content Type ◽  
Multiphase Pump ◽  
Gas Liquid Flow

Purpose The modeling of interphase forces plays a significant role in the numerical simulation of gas–liquid flow in a rotodynamic multiphase pump, which deserves detailed study. Design/methodology/approach Numerical analysis is conducted to estimate the influence of interphase forces, including drag force, lift force, virtual mass force, wall lubrication force and turbulent dispersion force. Findings The results show that the magnitude of the interphase forces can be sorted by: drag force > virtual mass force > lift force > turbulent dispersion force > wall lubrication force. The relations between interphase forces and velocity difference of gas–liquid flow and also the interphase forces and gas volume fraction are revealed. The distribution characteristics of interphase forces in the passages from impeller inlet to diffuser outlet are illustrated and analyzed. According to the results, apart from the drag force, the virtual mass force, lift force and turbulent dispersion force are required, whereas wall lubrication force can be neglected for numerical simulation of gas–liquid flow in a rotodynamic multiphase pump. Compared with the conventional numerical method which considers drag force only, the relative errors of predicted pressure rise and efficiency based on the proposed numerical method in account of four major forces can be reduced by 4.95 per cent and 3.00 per cent, respectively. Originality value The numerical analysis reveals the magnitude and distribution of interphase forces inside multiphase pump, which is meaningful for the simulation and design of multiphase pump.

scholarly journals Simulation of Volcanic Ash Ingestion Into a Large Aero Engine: Particle–Fan Interactions

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Andreas Vogel ◽  
Adam J. Durant ◽  
Massimo Cassiani ◽  
Rory J. Clarkson ◽  
Michal Slaby ◽  
...  
Keyword(s):  
Particle Size ◽  
Stream Flow ◽  
Mass Concentration ◽  
Volcanic Ash ◽  
Particle Mass ◽  
Core Flow ◽  
Turbine Engine ◽  
The Core ◽  
Core Section ◽  
Particle Mass Concentration

Volcanic ash (VA) clouds in flight corridors present a significant threat to aircraft operations as VA particles can cause damage to gas turbine engine components that lead to a reduction of engine performance and compromise flight safety. In the last decade, research has mainly focused on processes such as erosion of compressor blades and static components caused by impinging ash particles as well as clogging and/or corrosion effects of soft or molten ash particles on hot section turbine airfoils and components. However, there is a lack of information on how the fan separates ingested VA particles from the core stream flow into the bypass flow and therefore influences the mass concentration inside the engine core section, which is most vulnerable and critical for safety. In this numerical simulation study, we investigated the VA particle–fan interactions and resulting reductions in particle mass concentrations entering the engine core section as a function of particle size, fan rotation rate, and for two different flight altitudes. For this, we used a high-bypass gas-turbine engine design, with representative intake, fan, spinner, and splitter geometries for numerical computational fluid dynamics (CFD) simulations including a Lagrangian particle-tracking algorithm. Our results reveal that particle–fan interactions redirect particles from the core stream flow into the bypass stream tube, which leads to a significant particle mass concentration reduction inside the engine core section. The results also show that the particle–fan interactions increase with increasing fan rotation rates and VA particle size. Depending on ingested VA size distributions, the particle mass inside the engine core flow can be up to 30% reduced compared to the incoming particle mass flow. The presented results enable future calculations of effective core flow exposure or dosages based on simulated or observed atmospheric VA particle size distribution, which is required to quantify engine failure mechanisms after exposure to VA. As an example, we applied our methodology to a recent aircraft encounter during the Mt. Kelud 2014 eruption. Based on ambient VA concentrations simulated with an atmospheric particle dispersion model (FLEXPART), we calculated the effective particle mass concentration inside the core stream flow along the actual flight track and compared it with the whole engine exposure.

scholarly journals Calculation Analysis of Pressure Wave Velocity in Gas and Drilling Mud Two-Phase Fluid in Annulus during Drilling Operations

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Yuanhua Lin ◽  
Xiangwei Kong ◽  
Yijie Qiu ◽  
Qiji Yuan
Keyword(s):  
Wave Velocity ◽  
Void Fraction ◽  
Pressure Wave ◽  
Angular Frequency ◽  
Mass Force ◽  
Virtual Mass ◽  
Drilling Mud ◽  
Influx Rate ◽  
Drilling Operations ◽  
Well Depth

Investigation of propagation characteristics of a pressure wave is of great significance to the solution of the transient pressure problem caused by unsteady operations during management pressure drilling operations. With consideration of the important factors such as virtual mass force, drag force, angular frequency, gas influx rate, pressure, temperature, and well depth, a united wave velocity model has been proposed based on pressure gradient equations in drilling operations, gas-liquid two-fluid model, the gas-drilling mud equations of state, and small perturbation theory. Solved by adopting the Runge-Kutta method, calculation results indicate that the wave velocity and void fraction have different values with respect to well depth. In the annulus, the drop of pressure causes an increase in void fraction along the flow direction. The void fraction increases first slightly and then sharply; correspondingly the wave velocity first gradually decreases and then slightly increases. In general, the wave velocity tends to increase with the increase in back pressure and the decrease of gas influx rate and angular frequency, significantly in low range. Taking the virtual mass force into account, the dispersion characteristic of the pressure wave weakens obviously, especially at the position close to the wellhead.

scholarly journals Effect of virtual mass force on prediction of pressure changes in condensing tubes

2012 ◽  
Vol 16 (2) ◽  
pp. 613-622 ◽  
Author(s):  
Hamid Saffari ◽  
Nemat Daur
Keyword(s):  
Experimental Data ◽  
Annular Flow ◽  
Fluid Model ◽  
Mass Force ◽  
Virtual Mass ◽  
Vertical Pipe ◽  
Pressure Drops ◽  
Factors Affecting ◽  
Pressure Changes ◽  
Significant Factors

Three-fluid model is used to calculate the pressure drops in a vertical pipe with the annular flow pattern for condensing steam. The three-fluid models are based on the mass, momentum, and energy balance equations for each of the fluid streams in the annular flow. There are discrepancies between predictions of three-fluid model for pressure drops and the experimental data for pressure drops when using the avail?able correlations for steam-film interfacial friction. The correlation by Stevanovic et at provides good match with experimental data, but it does not take into account some important factors affecting the pressure drops in its three-fluid model. One of these significant factors which is considered in the three fluid model used in the present paper is virtual mass (added mass) force term. Inclusion of the virtual mass force improves the pressure drop predictions such that they agree much better with the experiments.

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