The dynamic stability of Rayleigh-Bénard convection subject to sinusoidal system acceleration is computationally investigated using CFD methods. Sinusoidal vertical oscillations are used for dynamic flow stabilization, an approach analogous to Kapitza’s pendulum, whose dynamic behavior serves as a reduced order model for any “top-heavy” dynamic system under gravity. Rayleigh-Bénard stabilization has been previously studied (Carbo) using linear and Floquet stability analyses, and through laboratory experiments (Swaminathan). Specifically, measurements carried out for bottom heated (statically unstable) rectangular box configurations, subject to varying amplitude and frequency vertical system acceleration, are studied using an efficient buoyancy driven, enclosed domain, low Mach-number CFD method. Stability maps are computationally created for a range of flow conditions, and the static/dynamic stability behavior is compared to experimental data and stability analysis. Density variation is introduced by three different methods including: Boussinesq approximation, perfect gas and linearly varying temperature dependent density. The effects of choice of state function on dynamic stability are also demonstrated in the results given in this paper. Flow solutions are compared to analytical stability theory to confirm their validity.

 

For this work, a fully implicit and fully coupled finite volume solver was developed. Traditional segregated methods perform very poorly for solving weakly compressible flows in closed domains due to weak coupling of velocity, pressure and energy variables. Non-linear error is not propagated out of a flow domain without conventional inlet/outlet boundaries in the case of completely confined flows, which leads to numerical schemes having to purely rely on internal error damping capability to reduce error. The Finite Volume algorithm described in this paper solves momentum, continuity and enthalpy equations simultaneously with full Newton linearization to create a scheme that has superb error damping capability for confined, weakly compressible flows which are of relevance to thermo-acoustic refrigeration and cryo-cooler devices. A modified Rhie-Chow interpolation scheme is used for constructing face mass fluxes that accounts for buoyancy and vertical acceleration terms. This approach also eliminates the need for using low-Mach preconditioning since the diagonal term of the continuity equation never approaches zero as it does with non-preconditioned density based schemes due to pressure diffusion terms that are introduced via artificial dissipation. An agglomerated block Algebraic Multigrid method is used for solving the linear system of equations that is constructed at each non-linear iteration. Grid coarsening is performed using an anisotropic/strong coefficient agglomeration approach, which reduces equation anisotropy, while also increasing low wavenumber error damping capability. A Block Incomplete LU (BILU0) smoother is used for solving the 4x4 block coupled linear system at each non-linear iteration and at each grid level. Details of this solution algorithm are given in numerical methods paper by the authors (Topcuoglu et al.).

 

 

Carbo, R. M. (2012). Dynamic Stabilization of the Rayleigh-Bénard Instability in Rectangular Enclosures: A Computational Approach. The Pennsylvania State University.

 

Swaminathan, A. (2017). Experimental Investigation of Dynamic Stabilization of the Rayleigh-Bénard Instability by Acceleration Modulation. The Pennsylvania State University.

 

Topcuoglu, I., Kunz, R.F., 2020. “A Fully Implicit Low Mach Number Algorithm for Flows with Heat Transfer”. *In preparation for Numerical Heat Transfer, Part B: Fundamentals*.


A Computational Investigation of Dynamic Stabilization of Rayleigh-B\xe9nard Convection Under System Acceleration

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

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