Challenge Problem 1: Benchmark Specifications for the Direct Numerical Simulation of Canonical Flows

Abstract

60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. DOCUMENT AVAILABILITYOnline Access: U.S. Department of Energy (DOE) reports produced after 1991 and a growing number of pre-1991 documents are available free at OSTI.GOV (http://www.osti.gov/), a service of the US Dept. of Energy's Office of Scientific and Technical Information.

Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches

“…These include acceleration at the cold wall and heat transfer suppression at certain buoyancy conditions driven by laminarization. Future work will include simulations at higher Reynolds number [17] to study the high Peclet regime where turbulent heat transfer is more significant in both the low and high Prandtl fluids.…”

“…where 𝒖 * = 𝒖/𝑢 𝑟𝑒𝑓 , 𝑝 * = 𝑝/𝜌𝑢 𝑟𝑒𝑓 2 , 𝑇 * = (𝑇 − 𝑇 𝑟𝑒𝑓 )/Δ𝑇 𝑟𝑒𝑓 , and 𝑡 * = 𝑡𝑢 𝑟𝑒𝑓 /𝐿 𝑟𝑒𝑓 are nondimensional velocity, pressure, temperature, and time; 𝝉 is RS tensor, 𝒖 * ′ 𝑇 * ′ is THF vector; Re, Ri 𝑞 , and Pr are Reynolds, modified Richardson, and Prandtl numbers; 𝒆 𝑧 is unit vector in the direction of vertical 𝑧 axis. The reference scales are briefly discussed in Sub-section 4.2; see also more details in [17,23,24].…”

“…Equations ( 11) -( 12) require appropriate closures for RS tensor 𝜏 * 𝑖𝑗 = 𝑢 * ′ 𝑖 𝑢 * ′ 𝑗 and THF vector 𝒖 * ′ 𝑇 * ′ . Traditional turbulence closures such as two equation (e.g., k-ε [25], k-τ [26]) or 4 equation (e.g., k-ε-kT-εT [27]) and others models have limited predictive capability for complex flows where anisotropy presents, including buoyancy affected thermally stratified flows [28,17]. Such buoyant flows are of nuclear industry interest as they potentially exist in operating reactors and advanced rector designs [17].…”

“…Traditional turbulence closures such as two equation (e.g., k-ε [25], k-τ [26]) or 4 equation (e.g., k-ε-kT-εT [27]) and others models have limited predictive capability for complex flows where anisotropy presents, including buoyancy affected thermally stratified flows [28,17]. Such buoyant flows are of nuclear industry interest as they potentially exist in operating reactors and advanced rector designs [17]. The task is to improve predictive capability of RANS modeling by developing DD turbulence closures for such scenarios.…”

“…More complex cases of Ri 𝑞 ≠ 0 ("mixed convection") will be addressed in the future work. A channel with symmetrically heated / cooled walls is considered (referred to as "Case 1" in [17]). In a such situation, to solve Equations ( 14) -( 16) one needs to specify the following nondimensional quantities: For more information on the DNS methodology and results, please refer to [17,23,24].…”