Advanced Nuclear Energy Systems: Heat Transfer Issues and Trends

Almost 450 nuclear power plants are currently operating throughout the world and supplying about 17% of the world’s electricity. These plants perform safely, reliably, and have no free-release of byproducts to the environment. Given the current rate of growth in electricity demand and the ever growing concerns for the environment, the US consumer will favor energy sources that can satisfy the need for electricity and other energy-intensive products (1) on a sustainable basis with minimal environmental impact, (2) with enhanced reliability and safety and (3) competitive economics. Given that advances are made to fully apply the potential benefits of nuclear energy systems, the next generation of nuclear systems can provide a vital part of a long-term, diversified energy supply. The Department of Energy has begun research on such a new generation of nuclear energy systems that can be made available to the market by 2030 or earlier, and that can offer significant advances toward these challenging goals [1]. These future nuclear power systems will require advances in materials, reactor physics as well as heat transfer to realize their full potential. In this paper, a summary of these advanced nuclear power systems is presented along with a short synopsis of the important heat transfer issues. Given the nature of research and the dynamics of these conceptual designs, key aspects of the physics will be provided, with details left for the presentation.

Nanoscale heat transfer and information technology

The summary from Goodson’s group on their recent work on heat transfer issues in the microelectronics and data storage industries illustrate the critical role of heat transfer for some areas of information technology. In this article, we build on their work and discuss some directions worthy of further research.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.