Lagrangian Method For Simulation Research Articles

Seasonal Dynamics of Flux Footprint for a Measuring Tower in Southern Taiga via Modeling and Experimental Data Analysis

This paper reports on the location of sources contributing to a point flux measurement in the southern taiga, Russia. The measurement tower is surrounded by a coniferous forest with a mean aerodynamically active height of 27 m (h). Aerodynamical parameters of the forest, such as displacement height d and aerodynamic roughness z0, derived from wind speed profile measurements for 2017–2019, were used to estimate the seasonal and daily behavior of the flux footprint. Two analytical footprint models by Schuepp et al. and by Kormann and Meixner driven by d and z0 were used to estimate the footprint for canopy sources. The Lagrangian simulation (LS) approach driven by flow statistics from measurements and modeling was used to estimate the footprint for ground-located sources. The Flux Footprint Prediction (FFP) tool for assessing canopy flux footprint (Kljun et al.) applied as the option in the EddyPro v.7 software was inspected against analytical and LS methods. For model comparisons, two parameters from estimated footprint functions were used: the upwind distance (fetch) of the peak contribution in the measured flux (Xmax) and the fetch that contributed to 80% of the total flux (CF80). The study shows that Xmax varies slightly with season but relies on wind direction and time of day. All methods yield different Xmax values but fall in the same range (60–130 m, around 2–5 h); thus, they can estimate the maximum influence distance with similar confidence. The CF80 values provided by the FFP tool are significantly lower than the CF80 values from other methods. For instance, the FFP tool estimates a CF80 of about 200 m (7 h), whereas other methods estimate a range of 600–1100 m (25–40 h). The study emphasizes that estimating the ground source footprint requires either the LS method or more complex approaches based on Computational Fluid Dynamics (CFD) techniques. These findings have essential implications in interpreting eddy-flux measurements over the quasi-homogeneous forest.

Influences of thermal physical property parameters on operating characteristics of simulated rotating detonation ramjet fueled by C12H23

Two-phase rotating detonation ramjets are considered to be suitable for aerospace applications due to their high thermodynamic cycle efficiency. These engines have an extremely complex internal flow field, in which the liquid fuel undergoes physical and chemical processes such as fragmentation, evaporation, mixing, and combustion; these processes also interact with detonation waves that have significant gradients. This makes it difficult to simulate a three-dimensional (3D) full-process rotating detonation combustion chamber. Here, based on the Euler–Lagrangian simulation method, a 3D numerical combustion chamber was simulated using kinetic theory and the constant thermal physical property parameter (TPPP) calculation method. The accuracy of these methods was then compared with the existing experimental results and theoretical values. Calculating the TPPPs using kinetic theory brought about a relatively high-pressure peak and detonation wave temperature; the detonation wave profile was also finer and more precise. The detonation wave propagation velocity of the two-phase detonation is estimated to be about 60% of the theoretical gas-phase CJ velocity. The calculation method of physical parameters has relatively little influence on the engine’s operating frequency and the detonation wave's propagation velocity but has a more significant influence on the peak pressure. Constant TPPPs can be used when the Kelvin–Helmholtz–Rayleigh–Taylor model with insufficient precision is used to consider the breakup of droplets and leads to the acceleration of the propagation speed of two-phase detonation waves.

An improved multiscale Eulerian–Lagrangian method for simulation of atomization process

The physics of atomization process involve many spatial scales, generating a wide variety of liquid inclusions of different sizes with large density and viscosity ratios between liquid and gas phases. In order to correctly capture the dynamics of these phenomena, each scale needs to be resolved with an appropriate method to ensure the conservation of physical quantities (mass, momentum) as well as the jump conditions across the liquid-gas interface. To address these problems, an original multi-scale methodology has been developed. It consists of a core coupled Level-Set/Volume-of-Fluid method (CLSVOF) for accurate capture of primary atomization, an adaptive mesh refinement technique (oct-tree AMR) to dynamically optimize the structured Cartesian mesh and a particle tracking algorithm to capture droplet dynamics. An improved Eulerian–Lagrangian coupling has been developed to ensure a smooth transition between the Eulerian and the Lagrangian modelling frameworks in the zones where they reach their respective limits of validity. The overall procedure is tested on simplified numerical tests and validated on a realistic planar liquid sheet atomization case. Results highlight the ability of the present method to reproduce the whole atomization process, from large scale instabilities to small droplet dynamics, and allow a preliminary statistical spray analysis.

A combined Lagrangian method for simulation of axisymmetric gas-particle vortex flows

A combined fully Lagrangian approach for meshless modeling of unsteady axisymmetric vortex flows of a gas-particle mixture with an incompressible carrier phase is developed. The approach proposed is based on the combination of a meshless vortex method for calculating axisymmetric flows of the carrier phase described by the Navier–Stokes (or Euler) equations and the full Lagrangian method for calculating the parameters of the dispersed phase. The combination of these methods reduces the problem of modeling the two phase flows to the solution of a high-order system of ordinary differential equations for the coordinates of toroidal vortex elements in the carrier phase and the particle trajectories, the velocity components, and the components of the Jacobian of transformation from the Eulerian to the Lagrangian variables in the dispersed phase. The application of the method is illustrated by modeling the behavior of an admixture of inertial Stokes particles with a small mass concentration in unsteady flows like solitary vortex rings in a viscous carrier phase and groups of vortex rings in an effectively inviscid carrier phase.

Online-simulation of fluidic processes in early design of plant development using SPH

An increasing number of products put focus on the development process. As the early design phase is oftentimes defining for the overall costs, this phase is particularly important. An approach is the use of digital models and simulations. However, due to the high modelling effort in the early design phase and time-consuming simulation runs, the applicability of this approach remains limited. Thus, we describe a method for an online-simulation method, which is capable of both simulating fluids in real-time and enabling instantaneous adaption of the underlying simulation model. This is achieved by the use of Lagrangian simulation methods, efficient exploitation of GPU's potential and a modular simulation model.

Particle-based shallow water simulation for irregular and sparse simulation domains

We propose a shallow water simulation using a Lagrangian technique. Smoothed particle hydrodynamics are used to solve the shallow water equation, so we avoid discretization of the entire simulation domain and easily handle sparse and irregular simulation domains. In the context of shallow water equations, much less attention has been paid to Lagrangian simulation methods than to Eulerian methods. Therefore, many problems remained unsolved, which prevents the practical use of Lagrangian shallow water simulations in computer graphics. We concentrate on several issues associated with the simulation. First, we increase the accuracy of the smoothed particle hydrodynamics approximation by applying a correction to the kernel function that is used in the simulation. Second, we introduce a novel boundary handling algorithm that can handle arbitrary boundary domains; even irregular and complicated boundaries do not pose a problem and introduce only small computational overhead. Third, with the increased accuracy, we use the fluid height to generate a flat fluid surface. All the proposed methods can easily be integrated into the smoothed particle hydrodynamics framework.

Stability of restructured non-fractal aggregates in simple shear flow

The restructuring behavior of non-fractal aggregates in simple shear flow is numerically investigated. The change in internal structure of aggregates having different packing properties is examined by Lagrangian simulation method. The many-body hydrodynamic interaction is rigorously estimated by Stokesian dynamics approach while the adhesion of aggregate is manifested via particle–particle interaction. The simulation results show that the restructuring of aggregate originates from the superimposition of rotational and extensional component of simple shear flow. The aggregate rearranges its particles so that a stable structure corresponding to the applied shear flow is obtained. The stable structure is considered as dynamic equilibrium resulting from the balance of the forming and the disintegrating of the bonds between particles. The stable structure of aggregate is dependent strongly on shear condition but weakly on initial structure of aggregate. Despite of the significant difference in the initial packing properties, the stable structure reveals only slightly different. The dependence of stable structure on high shear tress condition is similar for all aggregates. The difference in stable structure of aggregate at low shear stress arises from the irreversible behavior of particle from quasi-stable structure to static structure.

A cost-effective backward Lagrangian method for simulation of pollutant formation in gas turbine combustors by post-processing of complex 3D calculations

A backward Lagrangian Monte Carlo modelling is proposed to calculate by post-processing the PDF of the thermo-chemical parameters of complex turbulent reactive flows simulated with a simple turbulent combustion model. PDF’s of minor species such as pollutant species (NOx, soot, unburnt hydrocarbons...) can be easily obtained as long as these species have no significant influence on the main features of the flow. A numerical validation and an example of application of the method to a real burner are presented. If the number of points where information is sought is limited the cost of the method in terms of CPU time is very low and the statistical error can be perfectly controlled. With a first application to a semi-technical scale combustor producing soot the method has been proved very promising for the prediction of pollutant in complex turbulent reactive flows of gas turbine combustors.

A fast Lagrangian simulation method for flow analysis and runner design in Pelton turbines

In the present work, an alternative numerical methodology is developed for a fast and effective simulation and analysis of the complex flow and energy conversion in Pelton impulse hydro turbines. The algorithm is based on the Lagrangian approach and the unsteady free-surface flow during the jet-bucket interaction is simulated by tracking the trajectories of representative fluid particles at very low computer cost. Modern regression tools are implemented in a new parameterization technique of the inner bucket surface. Key-feature of the model is the introduction of additional terms into the particle motion equations to account for various hydraulic losses and the flow spreading, which are regulated and evaluated with the aid of experimental data in a Laboratory Pelton turbine. The model is applied to study the jet-runner interaction in various operation conditions and then to perform numerical design optimization of the bucket shape, using a stochastic optimizer based on evolutionary algorithms. The obtained optimum runner attains remarkably higher hydraulic efficiency in the entire load range. Finally, a new small Pelton turbine (150 kW) is designed, manufactured and tested in the Laboratory, and its performance and efficiency verify the model predictions.

Post-Dryout Heat Transfer Analysis Model with Droplet Lagrangian Simulation

Post-dryout heat transfer analysis was carried out considering droplet behavior by using the Lagrangian simulation method. Post-dryout heat transfer is an important heat transfer mechanism in many industrial appliances. Especially in recent Japanese BWR licensing, the standard for assessing the integrity of fuel that has experienced boiling transition is being examined. Although post-dryout heat transfer analysis is important when predicting wall temperature, it is difficult to accurately predict the heat transfer coefficient in the post-dryout regime because of the many heat transfer paths and non-equilibrium status between droplet and vapor. Recently, an analysis model that deals with many heat transfer paths including droplet direct contact heat transfer was developed and its results showed good agreement with experimental results. The model also showed that heat transfer by droplet could not be neglected in the low mass flux condition. However, the model deals with droplet deposition behavior by experimental droplet deposition correlation, so it cannot estimate the effect of droplet flow on turbulent flow field and heat transfer. Therefore, in this study we deal with many droplets separately by using the Lagrangian simulation method and hence estimate the effect of droplet flow on the turbulent flow field. We analyzed post-dryout experimental results and found that they correlated well with the analysis results.

Thermodynamic approach to rheological modeling and simulations at the configuration space level of description

The so-called matrix model is a general thermodynamic framework for microrheological modeling. This model has already been proven to be applicable for a wide class of systems, in particular to models formulated at the configuration tensor level of description. For models formulated at the configuration space level of description a matrix formulation is readily obtained, but for the subsequent analysis one still needs an explicit solution of the configuration space distribution functions. In the present paper we describe an approach in which this problem is solved by combining the matrix model with a Lagrangian simulation method in configuration space developed recently by Szeri and Leal. The result is a consistent and unified formulation of stress tensor expressions, including the stress averaging, and the evolution equations. This formulation is also suited for numerical simulations. In this way, the range of applicability of the matrix model is extended substantially. In order to clarify the principles of the method and some aspects of its implementation, a simple example is discussed in some detail.

Monte-Carlo Simulation of Turbulent Deposition of Charged Particles in a Plate-Plate Electrostatic Precipitator

ABSTRACT The characteristics of turbulent deposition of charged particles in a plate-plate electrostatic precipitator (ESP) are analyzed by the Lagrangian simulation method which uses the concept of time series analysis for the particle motion in a turbulent flow field. With the advantage of the Lagrangian method, several important parameters are taken into account such as the effect of nonuniform diffusivity on the particle motion and the effects of particle inertia including the crossing trajectory effect, boundary layer trapping and the lift force near the wall. Collection efficiencies are obtained without any simplified treatment for a wide range of Peclet number (Pe*) of interest, where it is found that the collection efficiency is mainly the function of Pe* and Deutsch number, and the dependency on particle relaxation time is negligible in the range about Pe* > 0.1. Moreover, the characteristics of deposition at the intermediate Pe* is analyzed clearly, where both the diffusion and migration by exte...