Ming-Jiu Ni

Projection methods for the calculation of incompressible unsteady flows

A general formula for the second-order projection method for solution of unsteady incompressible Navier-Stokes equations is presented. It includes the four- and three-step projection methods. Also, RKCN (Runge-Kutta/Crank-Nicholson) three-step and four-step projection methods are presented, in which the three-stage Runge-Kutta and semi-implicit Crank-Nicholson techniques are employed to update the convective and diffusion terms, respectively. The RKCN projection method is further simplified. The pressure Poisson equation (PPE) is solved only at the final substage for the simplified RKCN projection method, which greatly reduces the computation time. The high-order boundary conditions for the intermediate velocities have also been given for the four-step RKCN projection method and its simplified version. A 2-D vortex flow, a 2-D oscillating cavity flow, and a 3-D lid-driven cavity flow are simulated to validate the analysis. The projection method is also used to do the direct numerical simulation (DNS) of a fully developed channel flow.

Numerical Modeling for Multiphase Incompressible Flow with Phase Change

ABSTRACT A general formula for the second-order projection method combined with the level set method is developed to simulate unsteady, incompressible multifluid flow with phase change. A subcell conception is introduced in a modified mass transfer model to accurately calculate the mass transfer across the interface. The third-order essentially nonoscillatory (ENO) scheme and second-order semi-implicit Crank-Nicholson scheme is employed to update the convective and diffusion terms, respectively. The projection method has second-order temporal accuracy for variable-density unsteady incompressible flows as well. The level set approach is employed to implicitly capture the interface for multiphase flows. A continuum surface force (CSF) tension model is used in the present cases. Phase change and dynamics associated with single bubble and multibubbles in two and three dimensions during nucleate boiling are studied numerically via the present modeling. The numerical results show that this method can handle complex deformation of the interface and account for the effect of liquid–vapor phase change.

A VARIABLE-DENSITY PROJECTION METHOD FOR INTERFACIAL FLOWS

General second-order, variable-density, three-step and four-step projection methods are developed to simulate unsteady incompressible interfacial flows. A high-accuracy, variable-density RKCN projection method is presented, in which the three-stage, low-storage Runge-Kutta technique and second-order semi-implicit Crank-Nicholson technique are employed to temporally update the convective and diffusion terms, respectively. To reduce computation cost, a simplified version of the projection method is also presented, in which the pressure Poisson equation (PPE) is solved only at the last substage. The level set approach is employed to implicitly capture the interface for falling droplet flows. Three-dimensional bubble rising flows and two-dimensional falling droplet flows in a small closed channel are studied numerically via the present method. By the definition of the effective pressure, the flow mechanisms for falling droplet flows with different density ratios, viscosity ratios, Weber numbers, and Reynolds numbers are discussed.

Validation case results for 2D and 3D MHD simulations

Abstract A consistent and conservative scheme designed by Ni et al. for the simulation of MHD flows with low magnetic Reynolds number has been implemented into a 3D parallel code of HIMAG based on solving the electrical potential equation. The scheme and code are developed on an unstructured collocated mesh, on which velocity (u), pressure (p), and electrical potential (φ) are located in the cell center, while current fluxes are located on the cell faces. The calculation of current fluxes is performed using a conservative scheme, which is consistent with the discretization scheme for the solution of electrical potential Poisson equation. The Lorentz force is calculated at cell centers based on a conservative formula or a conservation interpolation of the current density. We validate the numerical methods, and the parallel code by simulating 2D fully developed MHD flows with analytical solutions existed and 3D MHD flows with experimental data available. The validation cases are conducted with Hartmann number from 100 to 104 on rectangular grids and/or unstructured hexahedral and prism grids.

TEMPORAL SECOND-ORDER ACCURACY OF SIMPLE-TYPE METHODS FOR INCOMPRESSIBLE UNSTEADY FLOWS

SIMPLE-type methods are presented in a more concise formulation. This formulation is used to analyze temporal accuracy for unsteady flows. Detailed error formulations are given. Analysis shows that SIMPLE-type methods have second-order temporal accuracy if a second-order temporal updating technique is employed to update both the convective and diffusion terms. Two algorithms for unsteady flows are presented. Algorithm A is an iteration method, which will cost more time than algorithm B, a noniteration algorithm. Also several second-order updating techniques are presented. A classical validation example is employed to validate the temporal accuracy in this article. A new four-step SIMPLE-type method is presented, in which the pressure Poisson equation, not the pressure difference Poisson equation is solved.

Projection and simple methods for single-fluid and multiple-fluid incompressible unsteady flows- : General formula

A general second-order fractional-step method is presented for simulation of unsteady single-fluid and multiple-fluid flows. It includes four-step and three-step projection methods. Several existing projection methods can be acquired through this general formula. The SIMPLE method is also a special case of this general fractional-step method. The relationship between the SIMPLE method and the projection method is discussed based on this formula.

A Variable-Density Projection Method for Free Surface Flow with Phase Change

The development of predictive capability for free surface flow with phase change is essential to evaluate transport phenomena in aerospace, geophysical and industrial flows. This paper presents a variable-density projection method, in conjunction with ApproximateFactorization techniques (AF method) for multiphase incompressible Navier-Stokes equations. The level set method was used to capture the interface accurately. The projection method has 2-order temporal accuracy for variable-density unsteady incompressible flows as well. This numerical investigation identifies the physics characterizing transient heat and mass transfer of multiphase free surface flow. The preliminary results show that the numerical methodology is successful in modeling the free surface with heat and mass transfer, though some severe deformation such as breaking and merging occurs.

A Boundary Condition Capturing Method for Multiphase Flow with Phase Change

The development of predictive capability for free surface flow with phase change is essential to evaluate transport phenomena in aerospace, geophysical and industrial flows. This paper presents a boundary condition capturing method, Ghost Fluid Method, to the multiphase flow with phase change problems. The second-order projection method has been used for incompressible Navier-Stokes equations. The 3rd-order ENO scheme and 2nd-order semi-implicit Crank-Nicholson scheme is used to update the convective and diffusion term. This numerical investigation identifies the physics characterizing transient heat and mass transfer of multiphase flow. The preliminary results show that the numerical methodology is successful in modeling the multiphase flow with phase change. The contact discontinuity has been captured very well even when some severe deformation occurs.

Numerical Analysis of Phase Change and Dynamics Associated with Bubbles and Droplets

*† ‡ ** A general formula for the second-order projection method combined with the level set method is developed to simulate unsteady, incompressible multiphase flow with phase change. The ghost fluid method (GFM) idea is used to calculate the interface temperature gradient. . The third-order ENO scheme and second-order semi-implicit Crank-Nicholson scheme is employed to update the convective and diffusion terms respectively. The projection method has second-order temporal accuracy for variable-density unsteady incompressible flows as well. The level set approach is employed to implicitly capture the interface for multiphase flows. Continuum surface force (CSF) tension model is used in the present cases. Phase change and dynamics associated with a single bubble and multi-bubbles in two-and three-dimension during the nucleate boiling are studied numerically via the present modeling. The numerical results show this method can handle complex deformation of the interface and account for the effect of liquid-vapor phase change. Nomenclature l ρ = liquid density g ρ = gas density l µ = liquid viscosity g µ = gas viscosity pl C = liquid specific heat pg C = gas specific heat K = thermal conductivity β = expansion coefficient fg h = heat of vaporization

Exploring liquid metal PFC concepts: Dynamics of fast flowing lithium films under fusion relevant magnetic fields

The use of fast flowing lithium streams for protection of the divertor surface in a magnetic fusion device is a very attractive option for effective particle pumping and surface heat removal. The divertor magnetic field environment tends to create strong flow disrupting magnetohydrodynamic (MHD) forces, which pose a major challenge in establishing a smooth and controllable flow. In this paper the 3D incompressible, multi-material MHD free surface code, HIMAG, developed by HyPerComp Inc. in collaboration with UCLA has been applied to model several problems of interest which are pivotal in understanding the basic MHD behavior of fast flowing lithium streams on rectangular electrically conducting substrates. The parameters used in the numerical studies conform to the outboard divertor region of the NSTX machine at Princeton