A Computational Investigation of Dynamic Stabilization of Rayleigh-Bénard Convection Under System Acceleration

2020 ◽  
Author(s):  
Ilker Topcuoglu ◽  
Robert F. Kunz ◽  
Robert W. Smith
Keyword(s):  
Dynamic Stability ◽  
Compressible Flows ◽  
Coupled System ◽  
Boussinesq Approximation ◽  
State Equations ◽  
Bénard Convection ◽  
Flow Stabilization ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract The static and dynamic stability of Rayleigh-Bénard convection in a rectangular flow domain is computationally investigated. Sinusoidal vertical oscillations are applied to the system to provide dynamic flow stabilization. Stability maps are produced for a range of flow and heating conditions, and are compared to experimental measurements and linear stability analysis predictions from existing literature. Density variation is introduced through: 1) the Boussinesq approximation, 2) a linearly varying temperature dependent equation of state (EOS) and 3) the perfect gas EOS. Significant effects of choice of EOS on dynamic stability are observed. These weakly compressible flows are solved efficiently using an implicit numerical method that has been developed to solve the momentum, continuity, enthalpy and state equations simultaneously in fully coupled fashion. This block coupled system of equations is linearized with Newton’s method, and quadratic convergence is achieved. The details of these numerics are presented.

scholarly journals Buoyancy statistics in moist turbulent Rayleigh–Bénard convection

2010 ◽  
Vol 648 ◽  
pp. 509-519 ◽  
Author(s):  
JÖRG SCHUMACHER ◽  
OLIVIER PAULUIS
Keyword(s):  
Piecewise Linear ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Phase Changes ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Layer ◽  
The Impact ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study shallow moist Rayleigh–Bénard convection in the Boussinesq approximation in three-dimensional direct numerical simulations. The thermodynamics of phase changes is approximated by a piecewise linear equation of state close to the phase boundary. The impact of phase changes on the turbulent fluctuations and the transfer of buoyancy through the layer is discussed as a function of the Rayleigh number and the ability to form liquid water. The enhanced buoyancy flux due to phase changes is compared with dry convection reference cases and related to the cloud cover in the convection layer. This study indicates that the moist Rayleigh–Bénard problem offers a practical framework for the development and evaluation of parameterizations for atmospheric convection.

A Model of Rayleigh-Bénard Convection

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Gravity Waves ◽  
Thermal Convection ◽  
Fluid Flows ◽  
Boussinesq Approximation ◽  
Internal Gravity Waves ◽  
Bénard Convection ◽  
Benard Convection ◽  
Key Characteristics ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This chapter presents a model of Rayleigh–Bénard convection. It first describes the fundamental dynamics expected in a fluid that is convectively stable and in one that is convectively unstable, focusing on thermal convection and internal gravity waves. Thermal convection and internal gravity waves are the two basic types of fluid flows within planets and stars that are driven by thermally produced buoyancy forces. The chapter then reviews the equations that govern fluid dynamics based on conservation of mass, momentum, and energy. It also examines the conditions under which the Boussinesq approximation simplifies conservation equations to a form very similar to that of an incompressible fluid. Finally, it discusses the key characteristics of the model of Rayleigh–Bénard convection.

Measuring the departures from the Boussinesq approximation in Rayleigh–Bénard convection experiments

2011 ◽  
Vol 682 ◽  
pp. 543-557 ◽  
Author(s):  
H. KURTULDU ◽  
K. MISCHAIKOW ◽  
M. F. SCHATZ
Keyword(s):  
Algebraic Topology ◽  
Betti Numbers ◽  
Boussinesq Approximation ◽  
Experimental Conditions ◽  
Bénard Convection ◽  
Benard Convection ◽  
The Difference ◽  
Convection Patterns ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Algebraic topology (homology) is used to characterize quantitatively non-Oberbeck–Boussinesq (NOB) effects in chaotic Rayleigh–Bénard convection patterns from laboratory experiments. For fixed parameter values, homology analysis yields a set of Betti numbers that can be assigned to hot upflow and, separately, to cold downflow in a convection pattern. An analysis of data acquired under a range of experimental conditions where NOB effects are systematically varied indicates that the difference between time-averaged Betti numbers for hot and cold flows can be used as an order parameter to measure the strength of NOB-induced pattern asymmetries. This homology-based measure not only reveals NOB effects that Fourier methods and measurements of pattern curvature fail to detect, but also permits distinguishing pattern changes caused by modified lateral boundary conditions from NOB pattern changes. These results suggest a new approach to characterizing data from either experiments or simulations where NOB effects are expected to play an important role.

scholarly journals Natural convection in a model chamber with the Boussinesq approximation utilization

2017 ◽  
Vol 66 (3) ◽  
pp. 75-82
Author(s):  
Weronika Radzikowska-Juś ◽  
Stefan Owczarek
Keyword(s):  
Natural Convection ◽  
Boussinesq Approximation ◽  
The Finite Element Method ◽  
Bénard Convection ◽  
Benard Convection ◽  
Starting Point ◽  
Model Chamber ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Model Room

The paper presents numerical analysis of heat transfer inside a model chamber in time after entering an object of elevated temperature therein. As a result of the temperature difference between the object and the environment in the room, natural convection has occurred. Numerical simulations were performed using ELMER software based on the Finite Element Method. In order to reduce the complexity of the simulation, the Bussinesq approximation was used. The relevant case is similar to Rayleigh-Benard convection, which was starting point to the conducted analysis. Keywords: temperature distribution in the model room, Rayleigh-Benard convection, Bussinesq approximation

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