Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session M34: Convection & Buoyancy Driven Flows: Numerical Simulations 
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Chair: Yogesh Jaluria, Rutgers University Room: Georgia World Congress Center B406 
Tuesday, November 20, 2018 8:00AM  8:13AM 
M34.00001: Transient Flow in a Wall Plume and its Application to Solve an Inverse Problem Yogesh Jaluria, Ardeshir Bangian Tabrizi The transient buoyancyinduced flow generated by a line heat source on a vertical surface is investigated. The transient characteristics of this wall plume are of particular interest in wall fires and electronic systems. The nature of the flow as the leading edge effects move downstream and the flow gradually approaches steady flow is studied in detail. These results are then applied to solve an inverse problem, where the temperature variation downstream is known but the boundary conditions, in terms of heat input and source location, are not. The method presented here is a search and optimization algorithm developed to approach the inverse twodimensional wall plume flow using only transient data. The data are taken at particular locations on the wall rather than at arbitrary locations. In the forward problem, downstream locations experience a peak in the temperature before attaining the steady state temperature. Here, the time when the peak temperature is achieved is determined at selected points. Then, an interpolation function is presented to relate these peak times with source strength and location. A system of equations is solved to find these. Particle swarm optimization is then applied to solve for the unknown source strength and location with minimum uncertainty. 
Tuesday, November 20, 2018 8:13AM  8:26AM 
M34.00002: Solving coupled Stefanflow problems using Immersed Boundary Smooth Extension Jinzi Mac Huang, David Stein, Michael John Shelley Natural convection accompanies many Stefan problems such as the dissolution and melting of solid objects in fluid. Gravity driven flows are responsible for many landforming processes, for example the formation of Karst landscapes and the "stone forests" of China and Madagascar. Smaller structures, like iceberg "scallops", are also a consequence of natural convection. Recent experimental results show that even much simpler cases of dissolution or melting of initially spherical solids can lead to very nontrivial pattern formation. In this talk, we will present a numerical study of fluidcoupled Stefan problems, based on a highorder Immersed Boundary Smooth Extension method for evolving the boundaries of soluble solids immersed in a fluid. The method yields solutions with high regularity across boundaries, which allows us to evolve the geometry with high order of accuracy. An efficient spectral method reduces the computational cost and allows for high resolution. We demonstrate the efficacy of our approach with examples of melting and dissolution that produce high Grashof number flows. 
Tuesday, November 20, 2018 8:26AM  8:39AM 
M34.00003: Large eddy simulations of turbulent thermal convection using renormalized viscosity and thermal diffusivity Sumit Vashishtha, Mahendra K Verma We use renormalized viscosity and thermal diffusivity to construct a subgridscale model for large eddy simulations (LES) of turbulent thermal convection. This model is based on the observations [1, 2] that the behavior of turbulent thermal convection is similar to that of hydrodynamic turbulence. Therefore, for LES, we add renormalization viscosity, ν_{ren }∼ Π^{1/3}(π/Δ)^{4/3}, which is similar to that obtained for hydrodynamic turbulence, to the kinematic viscosity; here Π is the kinetic energy flux in the inertial range of wavenumbers and Δ is the grid spacing. The subgrid thermal diffusivity is assumed to be equal to subgrid viscosity; i.e. turbulent Prandtl number is assumed to be unity. We present a comparison between results  fluxes and spectra of temperature and velocity fields, time series of different quantities, temperature isosurfaces, scaling of Nusselt number with Rayleigh number  obtained using LES on a 128^{3} grid and DNS on a 512^{3} grid. A good agreement between LES and DNS results is obtained. [1] M.K. Verma, A. Kumar, and A. Pandey, New J. Physics 19, 025012 (2017). [2] A. Kumar, A.G. Chatterjee, and M.K. Verma, Phys. Rev. E 90, 023016 (2014)

Tuesday, November 20, 2018 8:39AM  8:52AM 
M34.00004: Simulating LowMach Compressible Flow at Large Prandtl Numbers with a HighOrder FullyImplicit AllSpeed Flow Solver Brian Weston, Amanda Braun, Robert Nourgaliev, JeanPierre Delplanque We present a highorder, fullyimplicit fluid dynamics solver for simulating very lowMach compressible flow. The work is motivated by the development of largescale simulations of highexplosive cookoff, which requires modeling multispecies/multiphase reactive flow at high Peclet numbers. The governing equations are discretized in space up to 5^{th}order with a reconstructed Discontinuous Galerkin method and integrated in time with Lstable fully implicit time discretization schemes. The resulting set of nonlinear equations is converged using a robust physicsblock based preconditioned NewtonKrylov solver, with the Jacobianfree version of the GMRES solver. We implement the lowMach version of the AUSM+up Riemann solver, which correctly mimics the pressure fluctuations of an incompressible flow solver in the asymptotic limit of small Mach number. We demonstrate that our fullyimplicit flow solver is able to robustly converge compressible flow calculations with Mach numbers less than 1.e5. Furthermore, thin thermal boundary layers at high Prandtl numbers are easily resolved with a highorder discretization scheme. 
Tuesday, November 20, 2018 8:52AM  9:05AM 
M34.00005: A Numerical Study of Turbulent Thermal Convection in a Cavity with Evaporation at the Free Surface William Hay, Miltiadis V. Papalexandris 
Tuesday, November 20, 2018 9:05AM  9:18AM 
M34.00006: Abstract Withdrawn The physical phenomena of heat transfer due to mixed convection in porous media are encountered in various industrial and engineering applications such as cooling of electronic devices, metal casting etc. The relative direction of forced convection w.r.t natural convection in a mixed convective flow may increase or decrease the heat transfer rate. Most of the current studies in this area are based on Darcy’s model for porous media i.e. an approach in which the geometrical effect of porous media is not taken into consideration. The size effects of porous media and conjugate heat transfer between the fluid and porous media may considerably affect the heat transfer process, when the porous length scales are comparable to the flow and thermal length scales. We numerically investigate the porescale flow and thermal characteristics in a coarsegrained porous media (spherical hydrogel beads arranged in structured packing) with conjugate heat transfer in opposing mixed convection. The simulations are carried out at different Richardson number, Ri in a cavity filled with water (Pr_{f}=5.4) at Rayleigh number, Ra=10^{7} and at different opposing forced convective flow. The studies indicate the influence of local flow and temperature distribution in the overall heat transfer mechanism. 
Tuesday, November 20, 2018 9:18AM  9:31AM 
M34.00007: Laminar Natural Convection from Two Vertically Attached Horizontal Cylinders Immersed in Unconfined PowerLaw Fluids Subhasisa Rath, Sukanta K. Dash Natural convection have emerging potential applications in nonNewtonian fluids. The apparent viscosity of a Powerlaw fluid exhibits a measurable variation with shear rates. Thus, the coupled velocity and thermal fields are further accentuated in Powerlaw fluids. Owing to the pragmatic significance, free convection from two vertically attached cylinders has been investigated numerically to elucidate the shearthinning and shearthickening behavior of a Powerlaw fluid using a modified Powerlaw model. Average Nusselt number shows a positive dependence on both Grashof and Prandtl numbers, whereas it shows an adverse dependence on Powerlaw index. Overall, shearthinning behavior enhances the convection whereas shearthickening behavior impedes it with reference to the generalized Newtonian fluids. Two competing mechanisms determine the resulting heat transfer: decreasing driving force due to preheating of the fluid by the lower cylinder and the mixed convection contribution due to the flow induced by the lower cylinder. As a result, the heat transfer from the upper cylinder has been strongly influenced by the plumes from the lower cylinder. Owing to the interaction of plumes, the heat transfer was found to decrease for both the cylinders compared to that of a single cylinder. 
Tuesday, November 20, 2018 9:31AM  9:44AM 
M34.00008: Heat Transfer in Wallbounded Flows at Transcritical Conditions Jack Guo, Xiang Yang, Werner M. Ihme Despite the prevalence of fluids at transcritical conditions in engineering applications, the structure of the thermoviscous boundary layer and heat transfer in wallbounded flows are only incompletely understood. To address this, DNS of a channel flow at transcritical conditions is performed, in which a temperature differential at the bottom and top walls is prescribed so that the thermodynamic state of the fluid crosses the Widom line and the density varies by a factor of 18. The DNS is analyzed with the specific focus on examining the thermoviscous boundary layer structure and testing the scaling relations. It is found that the canonical van Driest transformation performs well in describing the logarithmic wall layer region, and the observed scaling behavior of the streamwise energy spectrum provides support of the attachededdy model at transcritical conditions. 
Tuesday, November 20, 2018 9:44AM  9:57AM 
M34.00009: New model for turbulent heat transfer accounting for radiation convective coupling in RANS framework Simone Silvestri, Dirk Roekaerts, Rene Pecnik In high temperature participating flows, radiation tends to be the most relevant heat transfer mechanism. Radiative heat transfer differs from conduction due to its peculiarity of being nonlocal. This non locality causes counter intuitive interactions with turbulent temperature field and conductive heat transfer. While some theoretical knowledge has been gathered regarding the mechanism underlying these interactions, standard models have not yet been adapted to these recent findings. In particular, solving the RANS equations relies on the modeling of unclosed terms, one of which is the turbulent heat transfer. This quantity is severely modified by the presence of radiative heat transfer, leading to erroneous temperature predictions if standard models are employed. Therefore, this work provides the inclusion of radiative convective coupling in the modeling of the turbulent heat transfer. The proposed model consists in a first order approximation of the fluctuating radiative field which is expressed as a linear function of temperature fluctuations. This concept is applied to modify the existing standard two equation model and tested against various DNS cases. The results show very good agreement both in terms of average temperature and turbulent heat transfer. 
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