Full Lagrangian methods for calculating particle concentration fields in dilute gas-particle flows

2005 ◽  
Vol 461 (2059) ◽  
pp. 2197-2225 ◽  
Author(s):  
D.P Healy ◽  
J.B Young
Keyword(s):  
Particle Concentration ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Inviscid Flow ◽  
Gradient Field ◽  
Test Case ◽  
Two Phase ◽  
Lagrangian Methods ◽  
Dilute Gas ◽  
Particle Flows

The paper discusses two Full Lagrangian methods for calculating the particle concentration and velocity fields in dilute gas-particle flows. The methods are mathematically similar but crucially different in application. By examining the analytical solution for two-phase stagnation-point flow, it is shown that Osiptsov's method is more general than that of Fernandez de la Mora and Rosner. In Osiptsov's method, the Jacobian of the Eulerian–Lagrangian transformation is computed by integration along particle pathlines. The particle concentration is then obtained algebraically from the Lagrangian form of the particle continuity equation. It is shown that the correct specification of the initial conditions is non-trivial and of vital importance. A technique to alleviate problems of mathematical ‘stiffness’ at small Stokes numbers is also described. Full Lagrangian methods require knowledge of the fluid velocity gradient field and, if the carrier flowfield is calculated numerically, differentiation of a ‘noisy’ field can result in serious errors. The paper describes a method for reducing these errors. The incompressible, inviscid flow over a cylinder provides a useful test case for validation and the Osiptsov method proves its worth by revealing a region, hitherto unknown, of crossing particle pathlines in the mathematical solution. Crossing pathlines and their relationship to Robinson's integral are then discussed, and calculations of particle flow through a turbine cascade at high Mach numbers are presented to illustrate the engineering potential of the method.

A Combined Eulerian and Lagrangian Method for Prediction of Evaporating Sprays

2002 ◽  
Vol 124 (3) ◽  
pp. 481-488 ◽  
Author(s):  
M. Burger ◽  
G. Klose ◽  
G. Rottenkolber ◽  
R. Schmehl ◽  
D. Giebert ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Lagrangian Method ◽  
Phase Flow ◽  
Two Phase Flows ◽  
Two Phase ◽  
Lagrangian Methods ◽  
Eulerian Method ◽  
Lagrangian Modeling

Polydisperse sprays in complex three-dimensional flow systems are important in many technical applications. Numerical descriptions of sprays are used to achieve a fast and accurate prediction of complex two-phase flows. The Eulerian and Lagrangian methods are two essentially different approaches for the modeling of disperse two-phase flows. Both methods have been implemented into the same computational fluid dynamics package which is based on a three-dimensional body-fitted finite volume method. Considering sprays represented by a small number of droplet starting conditions, the Eulerian method is clearly superior in terms of computational efficiency. However, with respect to complex polydisperse sprays, the Lagrangian technique gives a higher accuracy. In addition, Lagrangian modeling of secondary effects such as spray-wall interaction enhances the physical description of the two-phase flow. Therefore, in the present approach the Eulerian and the Lagrangian methods have been combined in a hybrid method. The Eulerian method is used to determine a preliminary solution of the two-phase flow field. Subsequently, the Lagrangian method is employed to improve the accuracy of the first solution using detailed sets of initial conditions. Consequently, this combined approach improves the overall convergence behavior of the simulation. In the final section, the advantages of each method are discussed when predicting an evaporating spray in an intake manifold of an internal combustion engine.

A Combined Eulerian and Lagrangian Method for Prediction of Evaporating Sprays

2001 ◽  
Author(s):  
M. Burger ◽  
G. Klose ◽  
G. Rottenkolber ◽  
R. Schmehl ◽  
D. Giebert ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Initial Conditions ◽  
Lagrangian Method ◽  
Phase Flow ◽  
Two Phase Flows ◽  
Two Phase ◽  
Ic Engine ◽  
Lagrangian Methods ◽  
Eulerian Method ◽  
Lagrangian Modeling

Polydisperse sprays in complex three dimensional flow systems are important in many technical applications. Numerical descriptions of sprays are used to achieve a fast and accurate prediction of complex two-phase flows. The Eulerian and Lagrangian methods are two essentially different approaches for the modeling of disperse two-phase flows. Both methods have been implemented into the same CFD - package which is based on a 3D body-fitted Finite Volume method. Considering sprays represented by a small number of droplet starting conditions, the Eulerian method is clearly superior in terms of computational efficiency. However, with respect to complex polydisperse sprays, the Lagrangian technique gives a higher accuracy. In addition, Lagrangian modeling of secondary effects such as spray-wall interaction enhances the physical description of the two-phase flow. Therefore, in the present approach the Eulerian and the Lagrangian methods have been combined in a hybrid method. The Eulerian method is used to determine a preliminary solution of the two-phase flow field. Subsequently, the Lagrangian method is employed to improve the accuracy of the first solution using detailed sets of initial conditions. Consequently, this combined approach improves the overall convergence behavior of the simulation. In the final section, the advantages of each method are discussed when predicting an evaporating spray in an intake manifold of an IC-engine.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Finite-dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Irena Lasiecka ◽  
Buddhika Priyasad ◽  
Roberto Triggiani
Keyword(s):  
Besov Space ◽  
Internal Control ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Critical Role ◽  
Boussinesq System ◽  
Heat Equations ◽  
Fluid Equation ◽  
Low Regularity ◽  
Finite Dimensional

Abstract We consider the 𝑑-dimensional Boussinesq system defined on a sufficiently smooth bounded domain and subject to a pair { v , u } \{v,\boldsymbol{u}\} of controls localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . Here, 𝑣 is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrarily small connected portion Γ ~ \widetilde{\Gamma} of the boundary Γ = ∂ ⁡ Ω \Gamma=\partial\Omega . Instead, 𝒖 is a 𝑑-dimensional internal control for the fluid equation acting on an arbitrarily small collar 𝜔 supported by Γ ~ \widetilde{\Gamma} . The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of an explicitly constructed, finite-dimensional feedback control pair { v , u } \{v,\boldsymbol{u}\} localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . In addition, they will be minimal in number and of reduced dimension; more precisely, 𝒖 will be of dimension ( d - 1 ) (d-1) , to include necessarily its 𝑑-th component, and 𝑣 will be of dimension 1. The resulting space of well-posedness and stabilization is a suitable, tight Besov space for the fluid velocity component (close to L 3 ⁢ ( Ω ) \boldsymbol{L}^{3}(\Omega) for d = 3 d=3 ) and a corresponding Besov space for the thermal component, q > d q>d . Unique continuation inverse theorems for suitably over-determined adjoint static problems play a critical role in the constructive solution. Their proof rests on Carleman-type estimates, a topic pioneered by M. V. Klibanov since the early 80s.

scholarly journals CFD Simulation of Solid Suspension for a Liquid–Solid Industrial Stirred Reactor

2021 ◽  
Vol 11 (12) ◽  
pp. 5705
Author(s):  
Adrian Stuparu ◽  
Romeo Susan-Resiga ◽  
Alin Bosioc
Keyword(s):  
Chemical Reaction ◽  
Cfd Simulation ◽  
Simulation Analysis ◽  
Solid Phase ◽  
Initial Conditions ◽  
Chemical Reactor ◽  
Liquid Mixtures ◽  
Multiphase Model ◽  
Chemical Product ◽  
Two Phase

The present study examines the possibility of using an industrial stirred chemical reactor, originally employed for liquid–liquid mixtures, for operating with two-phase liquid–solid suspensions. It is critical when obtaining a high-quality chemical product that the solid phase remains suspended in the liquid phase long enough that the chemical reaction takes place. The impeller was designed for the preparation of a chemical product with a prescribed composition. The present study aims at finding, using a numerical simulation analysis, if the performance of the original impeller is suitable for obtaining a new chemical product with a different composition. The Eulerian multiphase model was employed along with the renormalization (RNG) k-ε turbulence model to simulate liquid–solid flow with a free surface in a stirred tank. A sliding-mesh approach was used to model the impeller rotation with the commercial CFD code, FLUENT. The results obtained underline that 25% to 40% of the solid phase is sedimented on the lower part of the reactor, depending on the initial conditions. It results that the impeller does not perform as needed; hence, the suspension time of the solid phase is not long enough for the chemical reaction to be properly completed.

scholarly journals Automated Search-Based Robustness Testing for Autonomous Vehicle Software

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Kevin M. Betts ◽  
Mikel D. Petty
Keyword(s):  
Monte Carlo ◽  
Performance Metrics ◽  
Initial Conditions ◽  
Autonomous Vehicle ◽  
Vehicle Control ◽  
Test Case ◽  
Test Cases ◽  
Control Software ◽  
Robustness Testing ◽  
Testing Techniques

Autonomous systems must successfully operate in complex time-varying spatial environments even when dealing with system faults that may occur during a mission. Consequently, evaluating the robustness, or ability to operate correctly under unexpected conditions, of autonomous vehicle control software is an increasingly important issue in software testing. New methods to automatically generate test cases for robustness testing of autonomous vehicle control software in closed-loop simulation are needed. Search-based testing techniques were used to automatically generate test cases, consisting of initial conditions and fault sequences, intended to challenge the control software more than test cases generated using current methods. Two different search-based testing methods, genetic algorithms and surrogate-based optimization, were used to generate test cases for a simulated unmanned aerial vehicle attempting to fly through an entryway. The effectiveness of the search-based methods in generating challenging test cases was compared to both a truth reference (full combinatorial testing) and the method most commonly used today (Monte Carlo testing). The search-based testing techniques demonstrated better performance than Monte Carlo testing for both of the test case generation performance metrics: (1) finding the single most challenging test case and (2) finding the set of fifty test cases with the highest mean degree of challenge.

Entrainment of Air at the Transoms of Full-Scale Surface Ships

2015 ◽  
Vol 59 (01) ◽  
pp. 49-65
Author(s):  
Eric J. Terrill ◽  
Genevieve R.L. Taylor
Keyword(s):  
Initial Conditions ◽  
Air Entrainment ◽  
Full Scale ◽  
Far Field ◽  
Two Phase ◽  
Cfd Models ◽  
Surface Ship ◽  
Full Speed ◽  
Bubbly Wake ◽  
Scale Surface

We report on the results from a series of full-scale trials designed to quantify the air entrainment at the stern of an underway vessel. While an extremely complex region to model air entrainment due to the confluence of the breaking transom wave, bubbles from the bow, turbulence from the hull boundary layer, and bubbles and turbulence from propellers, the region is a desirable area to characterize and understand because it serves as the initial conditions of a ship's far-field bubbly wake. Experiments were conducted in 2003 from R/V Revelle and 2004 from R/VAthena II using a custombuilt conductivity probe vertical array that could be deployed at the blunt transom of a full-scale surface ship to measure the void fraction field. The system was designed to be rugged enough to withstand the full speed range of the vessels. From the raw timeseries data, the entrainment of air at speeds ranging from 2.1 to 7.2 m/s is computed at various depths and beam locations. The data represent the first such in-situ measurements from a full-scale vessel and can be used to validate two-phase ship hydrodynamic CFD codes and initialize far-field, bubbly wake CFD models.

scholarly journals Simulation of the Effect of Oil Volume Fractions in an Oil-Water Flows Along a Circular Pipe: A Finite Element Approach

2018 ◽  
Vol 10 (5) ◽  
pp. 19
Author(s):  
Ferdusee Akter ◽  
Md. Bhuyan ◽  
Ujjwal Deb
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Galerkin Approximation ◽  
Computational Domain ◽  
Two Phase Flows ◽  
Two Phase ◽  
Volume Fractions ◽  
Oil In Water ◽  
Element Approach

Two phase flows in pipelines are very common in industries for the oil transportations. The aim of our work is to observe the effect of oil volume fraction in the oil in water two phase flows. The study has been accomplished using a computational model which is based on a Finite Element Method (FEM) named Galerkin approximation. The velocity profiles and volume fractions are performed by numerical simulations and we have considered the COMSOL Multiphysics Software version 4.2a for our simulation. The computational domain is 8m in length and 0.05m in radius. The results show that the velocity of the mixture decreases as the oil volume fraction increases. It should be noted that if we gradually increase the volume fractions of oil, the fluid velocity also changes and the saturated level of the volume fraction is 22.3%.

scholarly journals Flow topologies in bubble-induced turbulence: a direct numerical simulation analysis

2018 ◽  
Vol 857 ◽  
pp. 270-290 ◽  
Author(s):  
Josef Hasslberger ◽  
Markus Klein ◽  
Nilanjan Chakraborty
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Small Scale ◽  
Flow Topology ◽  
Two Phase ◽  
Local Flow ◽  
Interface Curvature

This paper presents a detailed investigation of flow topologies in bubble-induced two-phase turbulence. Two freely moving and deforming air bubbles that have been suspended in liquid water under counterflow conditions have been considered for this analysis. The direct numerical simulation data considered here are based on the one-fluid formulation of the two-phase flow governing equations. To study the development of coherent structures, a local flow topology analysis is performed. Using the invariants of the velocity gradient tensor, all possible small-scale flow structures can be categorized into two nodal and two focal topologies for incompressible turbulent flows. The volume fraction of focal topologies in the gaseous phase is consistently higher than in the surrounding liquid phase. This observation has been argued to be linked to a strong vorticity production at the regions of simultaneous high fluid velocity and high interface curvature. Depending on the regime (steady/laminar or unsteady/turbulent), additional effects related to the density and viscosity jump at the interface influence the behaviour. The analysis also points to a specific term of the vorticity transport equation as being responsible for the induction of vortical motion at the interface. Besides the known mechanisms, this term, related to surface tension and gradients of interface curvature, represents another potential source of turbulence production that lends itself to further investigation.

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