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Mathematics & Computation
Division members promote the advancement of mathematical and computational methods for solving problems arising in all disciplines encompassed by the Society. They place particular emphasis on numerical techniques for efficient computer applications to aid in the dissemination, integration, and proper use of computer codes, including preparation of computational benchmark and development of standards for computing practices, and to encourage the development on new computer codes and broaden their use.
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Utility Working Conference and Vendor Technology Expo (UWC 2024)
August 4–7, 2024
Marco Island, FL|JW Marriott Marco Island
Standards Program
The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
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Latest News
ARPA-E announces $40 million to develop transmutation technologies for UNF
The Department of Energy’s Advanced Research Projects Agency–Energy (ARPA-E) announced $40 million in funding to develop cutting-edge technologies to enable the transmutation of used nuclear fuel into less-radioactive substances. According to ARPA-E, the new initiative addresses one of the agency’s core goals as outlined by Congress: to provide transformative solutions to improve the management, cleanup, and disposal of radioactive waste and spent nuclear fuel.
Avinash Vaidheeswaran, William D. Fullmer, Martin Lopez de Bertodano
Nuclear Science and Engineering | Volume 184 | Number 3 | November 2016 | Pages 353-362
Technical Paper | doi.org/10.13182/NSE16-23
Articles are hosted by Taylor and Francis Online.
It is well-known that an incomplete two-fluid model (TFM) leads to imaginary roots of the characteristic polynomial, thus rendering the model ill-posed. A common approach to fix this problem has been to introduce sufficient numerical/artificial diffusion or nonphysical hyperbolizing terms to stabilize the model. The disadvantage of this approach is that the physical instabilities that can be accurately predicted by the TFM either get severely dampened or disappear entirely. The preferred alternative is to introduce appropriate physics that may stabilize the TFM at short wavelengths while preserving the physical long-wavelength instabilities. For instance, in near-horizontal stratified flows, the appropriate physical mechanism is surface tension. However, it is not apparent what such a mechanism should be in dispersed bubbly flows.
Researchers in the past have demonstrated that the inclusion of the momentum transfer due to interfacial pressure along with virtual mass force makes the model conditionally well-posed up to a gas volume fraction of 26%. However, in practice, one may observe bubbly flows having gas concentrations beyond this theoretical limit. Hence, it is important to make the behavior of the TFM well-posed for the entire range of gas volume fractions that is physically permissible. In this paper, the often-neglected phenomenon of bubble collisions is considered. The colliding bubbles generate a dispersed-phase pressure that is resistive to increased compaction. The inclusion of bubble pressure in the TFM renders the model well-posed up to the maximum packing limit. Furthermore, it is also shown that the collision force is necessary to predict the wave propagation velocities for bubbly flows over the entire range of void fractions observed in reality. Comparisons are made with the data, and a reasonable agreement is seen. Finally, it is demonstrated with computational fluid dynamics calculations that the addition of appropriate physical mechanisms (i.e., interfacial pressure and collision) makes the multidimensional TFM well-posed.