Assessment of Different CFD Modeling and Solving Approaches for a Supersonic Steam Ejector Simulation

The effects of different modeling and solving approaches on the simulation of a steam ejector have been investigated with the computational fluid dynamics (CFD) technique. The four most frequently used and recommended turbulence models (standard k-ε, RNG k-ε, realizable k-ε and SST k-ω), two near-wall treatments (standard wall function and enhanced wall treatment), two solvers (pressure- and density-based solvers) and two spatial discretization schemes ( the second-order upwind scheme and the quadratic upstream interpolation for convective kinematics (QUICK) of the convection term have been tested and compared for a supersonic steam ejector under the same conditions as experimental data. In total, more than 185 cases of 17 different modeling and solving approaches have been carried out in this work. The simulation results from the pressure-based solver (PBS) are slightly closer to the experimental data than those from the density-based solver (DBS) and are thus utilized in the subsequent simulations. When a high-density mesh with y+ < 1 is used, the SST k-ω model can obtain the best predictions of the maximum entrainment ratio (ER) and an adequate prediction of the critical back pressure (CBP), while the realizable k-ε model with the enhanced wall treatment can obtain the best prediction of the CBP and an adequate prediction of the ER. When the standard wall function is used with the three k-ε models, the realizable k-ε model can obtain the best predictions of the maximum ER, and the three k-ε models can gain the same CBP value. For a steam ejector with recirculation inside the diffuser, the realizable k-ε model or the enhanced wall treatment is recommended for adoption in the modeling approach. When the spatial discretization scheme of the convection term changes from a second-order upwind scheme to a QUICK scheme, the effect can be ignored for the maximum ER calculation, while only the CBP value from the standard k-ε model with the standard wall function is reduced by 2.13%. The calculation deviation of the ER between the two schemes increases with the back pressure at the unchoked flow region, especially when the standard k-ε model is adopted. The realizable k-ε model with the two wall treatments and the SST k-ω model is recommended, while the standard k-ε is more sensitive to the near-wall treatment and the spatial discretization scheme and is not recommended for an ejector simulation.

A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels

We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These flows are described by a conditionally hyperbolic balance law with non-conservative products. A detailed description of the properties of the model is provided, including entropy inequalities and asymptotic approximations of the eigenvalues of the corresponding coefficient matrix. The scheme extends existing central-upwind semi-discrete numerical methods for hyperbolic conservation and balance laws and it satisfies two properties crucial for the accurate simulation of shallow-water flows: it {\it preserves the positivity} of the water depth for each layer, and it is {\it well balanced}, {\it i.e.}, the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. Along with the description of the scheme and proofs of these two properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.

Formation of Cavitation and Supercavitation in a Rectangular Shape Nozzle

Flow inside a rectangular shape nozzle is simulated in this study. Finite volume scheme is utilized as the main solver for the current study. Second order scheme is utilized to discretize pressure. Second order upwind scheme is utilized for solving momentum equation. Then the momentum equation is coupled with the continuity equation to obtain the pressure and velocity at each cell. Cavitation inception and super cavitation is also found and discussed in this study and the results were also verified with previous Winklhofer et al. experiments.

Numerical dissipation switch for two-dimensional central-upwind schemes

We propose a numerical dissipation switch, which helps to control the amount of numerical dissipation present in central-upwind schemes. Our main goal is to reduce the numerical dissipation without risking oscillations. This goal is achieved with the help of a more accurate estimate of the local propagation speeds in the parts of the computational domain, which are near contact discontinuities and shears. To this end, we introduce a switch parameter, which depends on the distributions of energy in the x- and y-directions. The resulting new central-upwind is tested on a number of numerical examples, which demonstrate the superiority of the proposed method over the original central-upwind scheme.