Second-Order Spatial Accuracy in Lagrangian–Eulerian Spray Calculations

Are, Sasanka; Hou, Shuhai; Schmidt, David P.

doi:10.1080/10407790590936019

Cited by 23 publications

(20 citation statements)

References 11 publications

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“…The current paper goes up to sixth order and explains how to go further, and to generalize the results to two and three dimensions. The beginning of the present derivation repeats Are et al [1], who stopped at second order.…”

Section: Spatial Error In Particle-to-gas Couplingsupporting

confidence: 63%

“…This gives secondorder global accuracy (see Reference [1] for a demonstration of this assertion with a spray calculation) The use of a second-order polynomial of the form…”

Section: Spatial Error In Particle-to-gas Couplingmentioning

confidence: 98%

“…For example, Miller and Bellan [3] uses a variant of Aggarwal et al's cloud-in-cell weighting [2]. Are et al [1] analysed particleto-gas coupling with the goal of achieving second-order accuracy. Their results provided a method of deriving the accuracy of weighting schemes and were contrary to some of Aggarwal et al's observations.…”

Section: Introductionmentioning

confidence: 98%

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Theoretical analysis for achieving high‐order spatial accuracy in Lagrangian/Eulerian source terms

Schmidt

2006

Numerical Methods in Fluids

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SUMMARYIn a fully coupled Lagrangian=Eulerian two-phase calculation, the source terms from computational particles must be agglomerated to nearby gas-phase nodes. Existing methods are capable of accomplishing this particle-to-gas coupling with second-order accuracy. However, higher-order methods would be useful for applications such as two-phase direct numerical simulation and large eddy simulation. A theoretical basis is provided for producing high spatial accuracy in particle-to-gas source terms with low computational cost. The present work derives fourth-and sixth-order accurate methods, and the procedure for even higher accuracy is discussed. The theory is also expanded to include two-and three-dimensional calculations. One-and two-dimensional tests are used to demonstrate the convergence of this method and to highlight problems with statistical noise. Finally, the potential for application in computational uid dynamics codes is discussed. It is concluded that high-order kernels have practical beneÿts only under limited ranges of statistical and spatial resolution. Additionally, convergence demonstrations with full CFD codes will be extremely di cult due to the worsening of statistical errors with increasing mesh resolution.

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Section: Spatial Error In Particle-to-gas Couplingsupporting

confidence: 63%

“…This gives secondorder global accuracy (see Reference [1] for a demonstration of this assertion with a spray calculation) The use of a second-order polynomial of the form…”

Section: Spatial Error In Particle-to-gas Couplingmentioning

confidence: 98%

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Theoretical analysis for achieving high‐order spatial accuracy in Lagrangian/Eulerian source terms

Schmidt

2006

Numerical Methods in Fluids

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“…Schmidt and Senecal (2002) and Hou and Schmidt (2006) developed a new collision algorithm with a secondary collision mesh. Schmidt and Rutland (2004) and Are et al (2005) developed a collision sub model, a collision mesh approach, and secondorder gas-to-liquid coupling to better predict the dense spray on a typical mesh size using the RANS approach within the Lagrangian-Eulerian framework. By using fine meshes for gas-droplet two-way coupling and large number of parcels for Lagrangian particle description, Senecal et al (2014Senecal et al ( , 2013b; Xue et al (2013b) showed that grid convergency was achieved with 0.125 mm resolution with RANS and 0.0625 mm resolution with LES in terms of spray liquid and vapor penetrations.…”

mentioning

confidence: 99%

An Eulerian CFD model and X-ray radiography for coupled nozzle flow and spray in internal combustion engines

Xue

Battistoni

Powell

et al. 2015

International Journal of Multiphase Flow

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This paper implements a coupled approach to integrate the internal nozzle flow and the ensuing fuel spray using a Volume-of-Fluid (VOF) method in the finite-volume framework. A VOF method is used to model the internal nozzle two-phase flow with a cavitation description closed by the homogeneous relaxation model of Bilicki and Kestin (1990). An Eulerian single velocity field approach by Vallet et al. (2001) is implemented for near-nozzle spray modeling. This Eulerian approach considers the liquid and gas phases as a complex mixture with a highly variable density to describe near nozzle dense sprays. The liquid mass fraction is transported with a model for the turbulent liquid diffusion flux into the gas. Fully-coupled nozzle flow and spray simulations are performed in three dimensions and validated against the x-ray radiography measurements of Kastengren et al. (2014) for a diesel fuel surrogate. A standard k − ǫ Reynolds Averaged Navier Stokes based turbulence model is used in this study and the influence of model constants is evaluated. First, the grid convergence study is performed. The effect of grid size is also evaluated by comparing the fuel distribution against experimental data. Finally, the fuel distribution predicted by the coupled Eulerian approach is compared against that by Lagrangian-Eulerian spray model along with experimental data. The coupled Eulerian approach provides a unique way of coupling the nozzle flow and sprays so that the effects of in-nozzle flow can be directly realized on the fuel spray. Both experiment and numerical simulations show noncavitation occurring for this injector with convergent nozzle geometry. The study shows that the Eulerian approach has advantages over near-field dense spray distributions.

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“…For a detailed discussion of the numerical accuracy of this scheme, the reader is referred to Are et al (2005). The gas phase Navier-Stokes solver uses a finite difference method with a uniform, regular block-structured, co-located mesh.…”

Section: Satellite Droplet Modelmentioning

confidence: 99%