eulerian-lagrangian method

Turbulent backward step flow, including air and copper nanoparticles, has been simulated using the Computational Fluid Dynamics (CFD) method by the Eulerian-Lagrangian method. The simulation was done using two- and three-dimensional methods with CFX and FLUENT software. The obtained results were compared with each other and with the experimental results. The two-way coupling discrete phase model (DPM) was used for simulation. The Saffman lift force, pressure gradient, and turbulence effects on nanoparticles are considered. Numerical results obtained with Eulerian-Lagrangian models and single-phase models in steady and transient have been compared with experimental data. The effect of the turbulence model on the trajectory of particles and in terms of different diameters of 10, 20, 30, 50, 70, 100, and 200 micrometers have been investigated. The effects of particle diameter on the trajectory and behavior of particles and the effect of Stokes number on the presence of particles in the vortex created behind the step have been investigated. The results have been presented as various contours and graphs for two- and three- dimensional, steady, and transient states. Particle trajectories are shown as contours for different Stokes numbers and particle diameters. The continuous phase velocity variation across the channel for different distances of step are presented as graphs. Standard, RNG, and Realizable k-e and standard and SST k-w models are considered for the modeling of turbulent flow. The results show that SST k-w is more accurate than the experimental data. Furthermore, simulation was done using CFX software. Variations of velocity profile are compared with experimental and Fluent data. The results show that the Stokes number and the turbulence model have a significant effect on the trajectory of particles. Three-dimensional modeling of the flow increases the accuracy of the results. The maximum error in the single-phase method is equal to 25% and for the Eulerian-Lagrangian method is equal to 19%. Particles with a Stokes number smaller than 1.2 (equivalent to a diameter of 35 micrometers in this study) sense the presence of the vortex and enter the vortex. Among the turbulence models, the lowest error for the sst model is equal to 6.25, and the highest error for the standard Kε model is equal to 18.75.

Cavitation is a complex phenomenon in fluid mechanics. The occurrence of this phenomenon depends on the important factors and the different factors. The present study examined the erosion caused by collapse bubbles using the Eulerian - Lagrangian approach in a venturi. Cavitation flow in a venturi can be simulated with ANSYS - FLUENT software and with the development of a numerical code in MATLAB software, Lagrangian bubble behavior is simulated. Using the Keller - Miksis equation to simulate the variation of bubble radius and by considering different forces entering the bubble and using Newton’s second law, the bubble motion equation is extracted. From the Ochiai model to evaluate the compressive strength of bubbles caused by bubble collapse on a venturi can be used and the erosion rate is studied in different conditions. The results show the erosion intensity dependent on the initial radius of bubbles, fluid type and the formation of bubbles in the flow. in this case, by increasing the initial radius of bubbles, we witnessed an increase in wear strength to 100 micron of radius, but when the radius of bubbles exceeds this value, the bubbles will be affected when the radius of bubbles is increased, and the results of the data show that the bubble radius increases in the continuation of the flow path. Although the evidence showed that the number of blows was higher, the power reduction was evident.

In this study, to investigate the intensity of cavitation-induced erosion, the bubble behavior around the NACA0015 2D hydrofoil was simulated from the Eulerian-Lagrangian perspective. Macroscopic examination of the cavitation flow was determined by a homogeneous mixture model (Eulerian method) and the trajectory of bubble motion based on the applied forces using Newton's second law and the development of numerical code (Lagrange method). One way to reduce the computational cost of the Lagrangian perspective is to use the Discrete Phase Model (DPM). In this method, the fluid is considered as a continuous environment, while the discrete phase is solved by tracing a large number of particles in the calculated flow field. The behavior of the bubble arises from the pressure gradient caused by the flow. Bubble oscillations were obtained from the modified Rayleigh-Plesset-Keller-Herring equation. This equation considers the compressible behavior of the bubble as the bubble collapse velocity approaches the speed of sound as well as the slip velocity between the bubble and the moving liquid. To pair the obtained results and solve them, the fourth-order Runge-Kutta method with variable time step was used, which increased the data solution speed up to 10 times. From the Keller& Kolodner relationship, a pressure wave emitted from the collapse of a spherical bubble, and the model of Soyama et al., the total energy of the cavitation-induced shocks, which is the result of the accumulation of all the shocks on each other, is obtained. The actual effects of flow for cavitation inception and erosion were investigated. Different cavitation numbers were used for cavitation inception with different radii. The results showed that the nucleation process occured in the cavitation inception numbers and the cavitation inception for flow with larger nuclei was visible better. As the cavitation number decreases, the bubble growth rate increases and as the bubble radius increases, the erosion intensity increases. At high cavitation numbers, the bubble oscillates around its initial radius; however, at the lowest cavitation number in this article, the number , we see an increase of nearly times the radius compared to the original radius. The erosion power of bubbles with an initial radius of is approximately times that of the erosion power of bubbles with an initial radius of and about times that of the initial bubbles of . The probable site of erosion is at the end of cavity at the hydrofoil level. As the bubbles increase in size, the number of collapses and their strength increase, and the dispersion of the distribution at the hydrofoil surface increases. The results were compared with other published works and had acceptable accuracy.

In this study, effects of the aerocyclone outlet diameter on its performance are studied. The Reynolds Stress Model (RSM) model has been used in order to predict the turbulent flow patterns inside the aerocyclone and its droplet removal efficiency. The EulerianLagrangian method was used for gas droplet flow simulations. Due to the precessing vortex core (PVC), unsteady simulation of the flow is performed for duration of 0.73 s. The results show that for smaller diameter of the outlet pipe, the gas flow pressure loss and tangential velocity are increased. Also, by decreasing the outlet diameters of aerocyclone (e.g. at the velocity of 10m/s) the Euler number increases. Increasing in the velocity can change the Euler number significantly. The wall reflection term effects (in RSM model) on the flow field and droplet trajectories are studied. By implementation of wall reflection effects, the numerical results approach to the experimental data. The simulation results show that the cyclones with the smaller outlet diameter has the higher efficiencies at different velocities than others.