Tianshi Lu

A magnetohydrodynamic simulation of pellet ablation in the electrostatic approximation

A magnetohydrodynamic numerical model for hydrogenic pellet ablation in the electrostatic approximation has been developed based on the method of front tracking. The main features of the model are the explicit tracking of interfaces that separate the solid pellet from the ablated gas and the cold, dense and weakly ionized ablation cloud from the highly conducting fusion plasma, a surface ablation model, a kinetic model for the electron heat flux and an equation of state accounting for atomic processes in the ablation cloud. The interaction of the pellet ablation flow with the magnetic field including the J ×B Lorentz force is studied here systematically for the first time. The model has also been validated through the comparison with the semi-analytic Transonic Flow model and previous purely hydrodynamic simulations. Contrary to prevailing expectations, the ablation rate is reduced only slightly when the geometry is changed from spherically symmetric to axially symmetric, in the case of purely hydrodynamic models. However, in the magnetohydrodynamic simulations the J ×B force funnels the flow into an extended plasma shield, which intercepts the incident plasma heat flux and reduces the ablation rate, depending on the rise time of heat flux seen by the pellet. Shorter ‘warm-up’ times lead to narrower ablation channels, stronger shielding and reduced ablation rates. This new feature implies that pellets traversing strong plasma gradients, as in the edge pedestal region of the ITER plasma, could have significantly lower ablation rates if injected at higher velocity.

Direct Numerical Simulation of Bubbly Flows and Application to Cavitation Mitigation

The direct numerical simulation (DNS) method has been used to the study of the linear and shock wave propagation in bubbly fluids and the estimation of the efficiency of the cavitation mitigation in the container of the Spallation Neutron Source liquid mercury target. The DNS method for bubbly flows is based on the front tracking technique developed for free surface flows. Our front tracking hydrodynamic simulation code FronTier is capable of tracking and resolving topological changes of a large number of interfaces in two- and three-dimensional spaces. Both the bubbles and the fluid are compressible. In the application to the cavitation mitigation by bubble injection in the SNS, the collapse pressure of cavitation bubbles was calculated by solving the Keller equation with the liquid pressure obtained from the DNS of the bubbly flows. Simulations of the propagation of linear and shock waves in bubbly fluids have been performed, and a good agreement with theoretical predictions and experiments has been achieved. The validated DNS method for bubbly flows has been applied to the cavitation mitigation estimation in the SNS. The pressure wave propagation in the pure and the bubbly mercury has been simulated, and the collapse pressure of cavitation bubbles has been calculated. The efficiency of the cavitation mitigation by bubble injection has been estimated. The DNS method for bubbly flows has been validated through comparison of simulations with theory and experiments. The use of layers of nondissolvable gas bubbles as a pressure mitigation technique to reduce the cavitation erosion has been confirmed. DOI: 10.1115/1.2720477

Rayleigh–Taylor mixing rates for compressible flow

We study Rayleigh–Taylor instability in both the moderately compressible and weakly compressible regimes. For the two-dimensional single mode case, we find that the dimensionless terminal velocities (and associated Froude numbers) are nearly constant over most of this region of parameter space, as the thermodynamic parameters describing the equation of state are varied. The phenomenological drag coefficient which occurs in the single mode buoyancy-drag equation is directly related to the terminal velocities and has a similar behavior. Pressure differences and interface shape, however, display significant dependence on the equation of state parameters even for the weakly compressible flows. For three-dimensional multimode mixing, we expect accordingly that density stratification rather than drag will provide the leading compressibility effect. We develop an analytical model to account for density stratification effects in multimode self-similar mixing. Our theory is consistent with and extends numerically ...

Zeta function on surfaces of revolution

In this paper we applied the contour integral method for the zeta function associated with a differential operator to the Laplacian on a surface of revolution. Using the WKB expansion, we calculated the residues and values of the zeta function at several important points. The results agree with those obtained from the heat kernel expansion. We also obtained a closed form formula for the determinant of the Laplacian on such a surface.

Charging and E×B rotation of ablation clouds surrounding refueling pellets in hot fusion plasmas

The finite resistivity magnetohydrodynamic code FRONTIER-MHD [R. Samulyak et al., Nucl. Fusion 47, 103 (2007)] is used to simulate the ablation rate of refueling pellets, including the novel effect of electrostatically induced E×B rotation of the ablation cloud about its symmetry axis parallel to the magnetic field. The key finding is that the centrifugal force of cloud rotation pushes the cloud density radially outwards, creating a more “transparent” ablation channel. With reduced shielding, the steady state ablation rate of a deuterium pellet significantly increases from ∼35% to 100%, depending on the B-field strength. This new effect brings the ablation rate into better accord with a known theoretical scaling law, which agrees with most current experiments.

Dynamic Phase Boundaries for Compressible Fluids

We present an algorithm for the simulation of a generalized Riemann problem for phase transitions in compressible fluids. We model the transition as a tracked jump discontinuity. The emphasis here is on the coupling of the phase transition process to acoustic waves, which is required for the study of cavitation induced by strong rarefaction waves. The robustness of the proposed algorithm is verified by application to various physical regimes.

Zeta function of self-adjoint operators on surfaces of revolution

In this article we analyze the zeta function for the Laplace operator on a surface of revolution. A variety of boundary conditions, separated and unseparated, are considered. Formulas for several residues and values of the zeta function as well as for the determinant of the Laplacian are obtained. The analysis is based upon contour integration techniques in combination with a WKB analysis of solutions of related initial value problems.

Direct and Homogeneous Numerical Approaches to Multiphase Flows and Applications

We have studied two approaches to the modeling of bubbly and cavitating fluids. The first approach is based on the direct numerical simulation of gas bubbles using the interface tracking technique. The second one uses a homogeneous description of bubbly fluid properties. Two techniques are complementary and can be applied to resolve different spatial scales in simulations. Numerical simulations of the dynamics of linear and shock waves in bubbly fluids have been performed and compared with experiments and theoretical predictions. Two techniques are being applied to study hydrodynamic processes in liquid mercury targets for new generation accelerators.

Nonadiabatic transitions in finite-time adiabatic rapid passage

To apply the adiabatic rapid passage process repetitively [T. Lu, X. Miao, and H. Metcalf, Phys. Rev. A 71, 061405(R) (2005)], the nonadiabatic transition probability of a two-level atom subject to chirped light pulses over a finite period of time needs to be calculated. Using a unitary first-order perturbation method in the rotating adiabatic frame, an approximate formula has been derived for such transition probabilities in the entire parameter space of the pulses.

Observation of Large Optical Forces in Modulated Light

We have observed huge optical forces caused by multiple repetitions of adiabatic rapid passage sweeps with counterpropagating light beams that coherently exchange of momentum between atoms and the light field. It exceeds 10X radiative force.