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At least 19 records

Noniterative implicit method for tracking particles in mixed Lagrangian-Eulerian formulations

The existing implicit methods for the current initial value problems (IVPs) concerning particle-laden flows are complicated and iterative in nature. This paper presents a noniterative implicit method which can be used with pressure-based as well as with density-based algorithms. The method is illustrated by analyzing a dilute dispersion of noninteracting solid particles in an isothermal flow in a passage bounded by one straight wall and one wavy wall, in which all particles are spherical and have a finite velociy relative to the continuum phase at the inflow boundary.

Shih, T. I.-P.↗

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Felici, Helene Marie↗

An Eulerian/Lagrangian coupling procedure for three-dimensional vortical flows

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of 3D vortical flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method, added to the Eulerian time-marching procedure, provides a correction of the Eulerian solution. In turn, the Eulerian solution is used to integrate the Lagrangian state-vector along the particles trajectories. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers describe accurately the convection properties and enhance the vorticity and entropy capturing capabilities of the Eulerian solver. The Eulerian/Lagrangian coupling strategies are discussed and the combined scheme is tested on a constant stagnation pressure flow in a 90 deg bend and on a swirling pipe flow. As the numerical diffusion is reduced when using the Lagrangian correction, a vorticity gradient augmentation is identified as a basic problem of this inviscid calculation.

Felici, Helene M.↗

Microscopic Lagrangian description of warm plasmas. III - Nonlinear wave-particle interaction

The averaged-Lagrangian method is applied to nonlinear wave-particle interactions in an infinite, homogeneous, magnetic-field-free plasma. The specific example of Langmuir waves is considered, and the combined effects of four-wave interactions and wave-particle interactions are treated. It is demonstrated how the latter lead to diffusion in velocity space, and the quasilinear diffusion equation is derived. The analysis is generalized to the random phase approximation. The paper concludes with a summary of the method as applied in Parts 1-3 of the paper.

Galloway, J. J.↗

An Automated Refinement Process for Particle Trajectory Methods in GlennICE

Computational methods for ice accretion can simulate the impact of water drops and ice crystals on an aircraft surface in a Lagrangian reference frame or in the Eulerian reference frame. In the Eulerian reference frame, particles are considered a continuous fluid while in the Lagrangian frame individual particle trajectories are calculated. Methods that use the Eulerian reference frame are typically easier to develop as established modules used for continuum mechanics can be leveraged. The Eulerian systems can also be faster since the user does not have to simulate millions of particles in order to achieve good results. It is imperative therefore that a Lagrangian method optimize the release points of trajectories such that accurate solutions can be obtained while minimizing as much as possible the number of trajectories computed. This paper will present a methodology for this refinement process and demonstrate its effectiveness on sample three dimensional test cases.

William B Wright↗

An Automated Refinement Process for Particle Trajectory Methods in GlennICE

Computational methods for ice accretion can simulate the impact of water drops and ice crystals on an aircraft surface in a Lagrangian reference frame or in the Eulerian reference frame. In the Eulerian reference frame, particles are considered a continuous fluid while in the Lagrangian frame individual particle trajectories are calculated. Methods that use the Eulerian reference frame are typically easier to develop as established modules used for continuum mechanics can be leveraged. The Eulerian systems can also be faster since the user does not have to simulate millions of particles in order to achieve good results. It is imperative therefore that a Lagrangian method optimize the release points of trajectories such that accurate solutions can be obtained while minimizing as much as possible the number of trajectories computed. This paper will present a methodology for this refinement process and demonstrate its effectiveness on sample three dimensional test cases.

William Wright↗

Modeling of Cavity Residence Time via Modeled Lagrangian Particle Tracking

One of the critical components in a scramjet is the cavity flame holder. In evaluating the sizing of this component, the residence time of the fuel in the cavity is a common parameter used. However, to obtain the residence time via CFD is an expensive undertaking. One method is to perform an LES simulation of the cavity and use Lagrangian particle tracking to obtain both the mean and probability density function of the time that the particles remain in the cavity. While this method affords a significant amount of information, it is very costly in CPU run time. A simpler method involves performing a time accurate RANS simulation of the cavity, and when converged, overlay a traceable scalar in the cavity region, and then record the decay of this scalar’s flux at a downstream location. The time scale of the decay rate can then be estimated and a residence time inferred. This method is less computationally expensive than the LES approach, but still requires a time-accurate solution while only providing a mean cavity residence time evaluation. In this paper a method of determining the mean cavity residence time as well as the Probability Density Function (PDF) of the residence time is proposed and demonstrated. This method is based on Lagrangian particle tracking modeled by the Generalized Langevin Equation and is implemented as a post-processing step for a steady RANS solution. Computational cost is on the order of minutes and the results are in agreement with values obtained by the LES and scalar decay methods.

Langevin↗

A combined Eulerian-Lagrangian two-phase flow analysis of SSME HPOTP nozzle plug trajectories. II - Results

An analysis of Space Shuttle Main Engine high-pressure oxygen turbopump nozzle plug trajectories has been performed, using a Lagrangian method to track nozzle plug particles expelled from a turbine through a high Reynolds number flow in a turnaround duct with turning vanes. Axisymmetric and parametric analyses reveal that if nozzle plugs exited the turbine they would probably impact the LOX heat exchanger with impact velocities which are significantly less than the penetration velocity. The finding that only slight to moderate damage will result from nozzle plug failure in flight is supported by the results of a hot-fire engine test with induced nozzle plug failures.

Mcconnaughey, P. K.↗

A combined Eulerian-Lagrangian two-phase analysis of the SSME HPOTP nozzle plug trajectories

As a result of high cycle fatigue, hydrogen embrittlement, and extended engine use, it was observed in testing that the trailing edge on the first stage nozzle plug in the High Pressure Oxygen Turbopump (HPOTP) could detach. The objective was to predict the trajectories followed by particles exiting the turbine. Experiments had shown that the heat exchanger soils, which lie downstream of the turbine, would be ruptured by particles traveling in the order of 360 ft/sec. An axisymmetric solution of the flow was obtained from the work of Lin et. al., who used INS3D to obtain the solution. The particle trajectories were obtained using the method of de Jong et. al., which employs Lagrangian tracking of the particle through the Eulerian flow field. The collision parameters were obtained from experiments conducted by Rocketdyne using problem specific alloys, speeds, and projectile geometries. A complete 3-D analysis using the most likely collision parameters shows maximum particle velocities of 200 ft/sec. in the heat exchanger region. Subsequent to this analysis, an engine level test was conducted in which seven particles passed through the turbine but no damage was observed on the heat exchanger coils.

Garcia, Robert↗

Effect of particle presence on the incompressible inviscid flow through a two dimensional compressor cascade

A computational model for calculating the flow field, in the presence of solid particles, through a two dimensional compressor cascade is presented. The method treats the particle phase in the Lagrangian system and the fluid phase in the Eulerian system. The equations of momentum of the fluid phase are modified to account for the momentum exchange between the two phases. The resulting modified momentum and continuity equations are reduced to the conventional stream function-vorticity formulation. The analysis yields the change in the blade surface pressure distribution, the total pressure and velocity in the flow field. Based on this, it is possible to predict the decrease in compressor performance under the presence of particles.

Balan, C.↗

Coupling of Sph and Finite Element Codes for Multi-Layer Orbital Debris Shield Design

Particle-based hydrodynamics models offer distinct advantages over Eulerian and Lagrangian hydrocodes in particular shock physics applications. Particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of Lagrangian and Eulerian codes respectively. However conventional particle-in-cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points. A new particle-based modeling methodology, termed Hamiltonian particle hydrodynamics, was developed by Fahrenthold and Koo (1997) to provide an alternative, fully Lagrangian, energy-based approach to shock physics simulations. This alternative formulation avoids the tensile and boundary instabilities associated with standard smooth particle hydrodynamics formulations and the diffusive grid- to-particle mapping schemes characteristic of particle-in-cell methods. In the work described herein, the method of Fahrenthold and Koo has been extended, by coupling the aforementioned hydrodynamic particle model to a hexahedral finite element based description of the continuum dynamics. The resulting continuum model retains all of the features (including general contact-impact effects) of Hamiltonian particle hydrodynamics, while in addition accounting for tensile strength, plasticity, and damage effects important in the simulation of hypervelocity impact on orbital debris shielding. A three dimensional, vectorized, and autotasked implementation of the extended particle method described here has been coded for application to orbital debris shielding design. Source code for the pre-processor (PREP), analysis code (EXOS), post-processor (POST), and rezoner (ZONE), have been delivered separately, along with a User's Guide describing installation and application of the software.

Fahrenthold, Eric P.↗

Simulation of Hypervelocity Impact on Aluminum-Nextel-Kevlar Orbital Debris Shields

An improved hybrid particle-finite element method has been developed for hypervelocity impact simulation. The method combines the general contact-impact capabilities of particle codes with the true Lagrangian kinematics of large strain finite element formulations. Unlike some alternative schemes which couple Lagrangian finite element models with smooth particle hydrodynamics, the present formulation makes no use of slidelines or penalty forces. The method has been implemented in a parallel, three dimensional computer code. Simulations of three dimensional orbital debris impact problems using this parallel hybrid particle-finite element code, show good agreement with experiment and good speedup in parallel computation. The simulations included single and multi-plate shields as well as aluminum and composite shielding materials. at an impact velocity of eleven kilometers per second.

Fahrenthold, Eric P.↗

Full field flow visualization and computer-aided velocity measurements in a bank of cylinders in a wind tunnel

The full field flow tracking (FFFT) method that is presented in this paper uses a laser-generated, mechanically strobed planar sheet of light, a low luminosity TV camera coupled with a long distance microscope, and a computer-controlled video recorder to study nonintrusively and qualitatively the flow structures in a bank of cylinders that are placed in a wind tunnel. This setup simulates an upscale version of the geometry of internal cooling passageways characteristic of small air-cooled radial turbines. The qualitative images supplied by the FFFT system are processed by means of a computer-integrated image quantification (CIIQ) method into quantitative information, trajectories and velocities, that describe the flow upstream of and within the bank of cylinders. The tracking method is Lagrangian in concept, and permits identification and tracking of the same particle, thus facilitating construction of time dependent trajectories and the calculation of true velocities and accelerations. The error analysis evaluates the accuracy with which the seed particles follow the flow and the errors incurred during the quantitative processing of the raw data derived from the FFFT/CIIQ method.

Braun, M. J.↗

Lagrangian methods in plasma dynamics. II - Construction of Lagrangians for plasmas

Consideration of the construction of suitable Lagrangian functions for the dynamics of a cold plasma in such a way as to retain the relativistically covariant formalism. In one method, this is achieved by the introduction of a set of three variables which label the world lines of the particles. A second method results in a Clebsch-type representation. Sturrock's relativistic Lagrangian and Low's hot plasma Lagrangian are also briefly discussed in the context of the present work. The behavior of the canonical stress tensor is considered. The applicability of many of the general results in part I (Dougherty, 1970) is ensured by establishing the existence of the Lagrangian function.

Dougherty, J. P.↗

An efficient pressure-velocity procedure for gas-droplet two-phase flow calculations

This paper presents a noniterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully interacting combination of Eulerian fluid and Lagrangian particle calculations. The interaction calculations between the two phases are formulated on a pressure-velocity-coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data as well as efficiency assessments are given for some sprays typical of spray combustion applications.

Chen, C. P.↗

A novel gas-droplet numerical method for spray combustion

This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.

Chen, C. P.↗

A laser based computer aided non-intrusive technique for full field flow characterization in macroscopic curved channels

This paper presents the application of a laser based, computer aided image processing technique for the nonintrusive evaluation of field velocities and accelerations in a 180 deg curved channel geometry, characteristic of inlet passages of the cowls of airbreathing aircraft engines. The method based on the illumination of the test section with a laser generated planar sheet of light, allows microscopic or macroscopic surveillance of fluid flow across or along large cross sections for relatively long (greater than 1 sec) periods of time. The method is Lagrangian in concept and permits identification and tracking of the same particle, thus facilitating construction of more comprehensive trajectories and the calculation of velocities and accelerations.

Braun, M. J.↗

A Lagrangian method for a two layer shallow water model

One of the biggest drawbacks of Eulerian methods is the presence of the nonlinear convective terms which leads to inaccurate representations of advection and fronts. An alternative and conceptually simpler approach is the Lagrangian approach in which the fluid particles themselves are tracked and equations are derived based on local spatial interaction. In this formulation the nonlinear convective terms do not appear. The main drawback with the Lagrangian formulation, however, is that the local spatial interactions are time dependent. That is, at each time level, one must know the current neighbors of a given particle to accurately compute the forces acting on the particle. The Voroni Mesh which is continuously deforming and always linking nearest neighbors is needed. The effectiveness of a simple Lagrangian method for simulating the onset of a Kelvin-Helmholtz instability in a 2 layer fluid is demonstrated.

Augenbaum, J. M.↗