Eulerian Model

[Dorthea Seate]

CanI understand the mixture model to be a cheaper and simpler substitute for the Eulerian model which we should use unless parameters require for greater accuracy, in which case we would use the Eulerian model?

The GEKO (GEneralized K-Omega) turbulence model offers a flexible, robust, general-purpose approach to RANS turbulence modeling. Introducing 2 videos: Part 1 provides background information on the model and a...

Due to the accuracy of numerical calculation of fluid flow inside a hydro cyclone can be obtained using Computational Fluid Dynamics (CFD), highly modified super computers are used to simulate the fluid flow and track particle motion inside a hydro cyclone. This paper deals with the numerical study using three multiphase models viz. Volume of fluid, Mixture and Eulerian model. The dimensions of the hydrocyclone taken into consideration for numerical analysis are same as considered by Rajamani. Validation of axial and tangential velocities at different strategically decided axial stations, RMS axial and tangential velocity profiles of the hydro cyclone is done using Reynolds Stress Model (RSM). The hydro cyclone model has been designed in Creo 3.0 using the same dimensions which later was imported to CFD for meshing. Fine hexagonal mesh numbering up to 5 lacs were constructed to obtain optimum results. Fluid flow was allowed to be developed in ANSYS FLUENT 16.2. Entire simulation took 96 hours to generate results and track particle movements inside the hydro cyclone. The particle tracking has been done using three multiphase model. The first being the volume of fluid was used for validation purposes and the comparison of the Mixture and Eulerian model are the basic focus of this research work. Conclusive results indicate that usage of different multiphase model does not result in variation in particle motion. The slight variation in grade efficiency values is hardly noticeable. The Mixture model and Eulerian model predict lower separation efficiency as compared with Volume of fluid multiphase model.

Vertical cross sections of (a) supersaturation (S), (b) droplet activation rate (Act), and (c) condensation/evaporation rate (Cond) for different times in the 3D simulation. The condensation/evaporation rate expresses the rate of change of the mean droplet size due to condensation or evaporation. Each row represents a different simulation time, labeled to the right of the plots.

The entrainment of dry air and aerosols has also been considered as a source of DSD broadening in clouds. Inhomogeneous mixing of entrained air, where the microphysical response is fast compared to the mixing time scale (in contrast to homogeneous mixing, where the opposite occurs), decreases the droplet concentration (Latham and Reed 1977; Baker and Latham 1979; Baker et al. 1980; Pinsky et al. 2016), favoring the diffusional growth of the remaining droplets when the diluted air ascends. The activation of new droplets from entrained aerosols also broadens the DSD toward the smaller sizes, which can even result in bimodality (Baker et al. 1980; Blyth 1993; Brenguier and Grabowski 1993; Lasher-Trapp et al. 2005; Cooper et al. 2013; Hoffmann et al. 2015). However, there is no consensus regarding the role of these processes in the development of observed DSDs (see discussion in Khain et al. 2000). For instance, Khain et al. (2013) suggest that adiabatic processes play a dominant role in DSD evolution and the formation of precipitation from warm processes in deep convective clouds, given observational and modeling evidence showing that the formation of the first raindrops occurs in undilute or mostly undilute cloud cores.

In both 2D and 3D simulations, we use a 20-km horizontal domain with open lateral boundary conditions. The top of the model vertical grid is located at 10 km height, with a 3-km damping layer, where the vertical grid spacing is coarser than at lower levels for a more efficient use of computational resources. We analyze the simulations before the cloud reaches the bottom of the damping layer.

where Δt is the model time step, and Na represents the number mixing ratio of aerosols with radii larger than a critical radius (rc), for a given temperature (T) and supersaturation (S). According to Khler theory,

Changes induced in the model dynamics by reducing the number of spatial dimensions from three to two lead to some differences between the simulations. First, as a consequence of its weaker updraft, the cloud develops later in 2D than in 3D. This is consistent with previous studies that compared the updraft strength in 2D and 3D simulations, for the same environmental and initial conditions (e.g., Wilhelmson 1974; Tao et al. 1987; Phillips and Donner 2006; Zeng et al. 2008). The studies of Morrison (2016a,b) showed that differences in vertical velocity between 3D and 2D arise directly from the differences in the continuity equation for each geometry. Figure 4 also shows that, from the initial time of the cloud development, the toroidal circulation of the thermal is stronger in the 2D simulation and, consequently, the cloud appears to entrain more than in 3D, as indicated by the shape of the cloud area encompassed by the θe = 350-K isoline. A stronger toroidal circulation in 2D than 3D is consistent with greater vertical pressure gradient forcing (Morrison 2016a,b) and regions of divergence near cloud top and convergence near cloud base in 2D.

Given the qualitative consistency between the results obtained with the 3D and 2D configurations of the model, specifically those regarding the microphysical characteristics of the cloud, we employ the latter to explore mechanisms of DSD broadening in the WRF-TAU framework. Being computationally cheaper and easier to analyze and interpret results, the 2D configuration is used to perform numerous sensitivity tests varying the resolution and turning off the representation of various physical processes that affect the DSDs. Having fewer degrees of freedom, 2D simulations can respond differently to a given change in the model configuration or forcing than 3D simulations. For instance, Wang and Sobel (2011) found that precipitation increases more rapidly in 2D than in 3D as sea surface temperature is increased. However, we expect the sensitivities to have the correct sign, although their magnitude might be somewhat different in 2D than 3D.

Figure 8 shows the microphysical properties of the cloud at t = 16 min for the 100 100 and 30 30 simulations, where all the processes mentioned in Table 1 are considered (CTRL simulations). This configuration is similar to those discussed in the previous section except that the weight of the droplets is neglected in the buoyancy calculation here. This has the effect of increasing the vertical velocity and increasing the physical size of the cloud.

Also note that droplet activation along the cloud top may be augmented by the generation of high supersaturation due to the separated advection of temperature and water vapor (Stevens et al. 1996b; Grabowski and Morrison 2008), with contributions from evaporation as the cloud edge advects into noncloudy grid cells depending on the ratio of the phase relaxation and advective time scales (Hoffmann 2016). However, sharp peaks in supersaturation right at cloud top are not evident in the supersaturation field (similar to results from the 3D simulation seen in Fig. 3a), outside of a few isolated grid points; thus, this mechanism appears to be relatively unimportant here.

The results for the lateral cloud edges described above contrast with the situation along cloud top; in ACT, there are sharp maxima in σ and ΔD99 along the cloud top for all model resolutions tested (Figs. 12c,d). Whereas in CBACT, there are either weak local maxima in σ and ΔD99 at cloud top in the lower-resolution simulations (first, third, and fourth rows in Fig. 13) or no apparent maxima at all at cloud top in the 30 30 simulation (second row from the top in Fig. 13). This result again indicates the important role of droplet activation along the cloud top in broadening the modeled DSDs.

The diagnosed CCrate is generally smaller in CBACT than ACT (Figs. 12e, 13e), consistent with smaller Nd, σ, and ΔD99 in the cloud core without any in-cloud activation. Nonetheless, there are some small, isolated regions of higher CCrate near the cloud edges in CBACT compared to ACT, reflecting the relatively broad DSDs there compared to those in ACT.

The results discussed above are further supported by comparing DSDs from selected locations inside the cloud at t = 16 min from ACT (Fig. 14) and CBACT (Fig. 15). It is seen that the DSDs are narrower in the cloud interior (left panels in the figures) for CBACT than ACT because of the absence of a tail to small sizes in the absence of in-cloud droplet activation. In contrast, DSDs are fairly wide in CBACT near the cloud edge (right panels in the figures) with a shoulder of the DSDs extending to large sizes; significant concentrations of droplets exceed a diameter of 100 μm. This DSD shoulder extending to large droplet sizes is absent in ACT. These DSD results are consistent with stronger condensational growth of droplets associated with much higher supersaturations along the lateral cloud edges in CBACT (not shown).

3a8082e126