Natural Convection And Heat Transfer In A V-shaped Cavity

Buoyancy-induced fluid motions in cavities are very important because of the applications in nature and engineering.A large body of literature exists on the forms of internal and external forcing,various geometry shapes and temporal conditions(steady or unsteady)of the resulting flows.In particular,natural convection in a V-shaped cavity has also received attention owing to its extensive presence in industrial systems and in nature such as in a valley and in a river.Accordingly,in this thesis,natural convection in the V-shaped cavity is investigated using scaling analysis,two and three-dimensional numerical simulation and shadowgraph and thermistor measurement.Firstly,unsteady natural convection flows in a V-shaped cavity with initially stratified water is numerically studied.An extensive range of Rayleigh numbers is considered for different aspect ratios.Numerical results are compared with the previous experimental work.It has been demonstrated that following sudden heating and cooling from the inclined wall,the development of natural convection flows in the cavity from the start-up to the steady state is classified into two stages:an early stage and a transitional stage.Transient natural convection flows in the cavity are described and a spectral analysis is performed for the oscillations in the transitional stage.In addition,a simple scaling analysis is performed for the thermal boundary layer and a time scale of the stratification breakup describing the disappearance of fog in the valley is obtained and validated by numerical results.Further,mass and heat transfer in the cavity is measured and the scaling relation between the Nusselt number and the Rayleigh number for different aspect ratios are presented.Secondly,the transition to chaos of natural convection in the V-shaped cavity is investigated based on two-dimensional numerical results.An extensive range of Rayleigh numbers from 100 to 108 for Pr = 0.71 and Rayleigh numbers from 100 to 106 for Pr = 7.0 are considered.A set of bifurcations in the transition to an unsteady flow are described,which include a Pitchfork bifurcation from symmetric to asymmetric state and a Hopf bifurcation from steady to unsteady state.The critical values for bifurcations are obtained under accuracy guarantee.Further,heat and mass transfer in the cavity is calculated and the corresponding dependence on the Rayleigh number is discussed and quantified.Thirdly,three-dimensional numerical simulation is also performed for natural convection in the V-shaped cavity.A range of Rayleigh numbers from 100 to 106 is considered for Pr = 0.71 and 7.0.Similarly,bifurcations from symmetric to asymmetric state and from steady to unsteady state in the transition to chaos are described.In addition,the power spectral density,the phase space trajectory and the largest Lyapunov exponent of the unsteady flows in the transition to a chaotic state have been described.The dependence of heat and mass transfer on the Rayleigh number is also quantified.Finally,a V-shaped experimental model is designed and constructed.The flow in the fully developed stage is investigated using shadowgraph and thermistor technology.In the experiment,the temperature difference between inclined and top walls ranges from 1K to 40K and the corresponding Rayleigh number varies from 1.29 × 105 to 5.46 × 106.That is,visualization images are obtained using shadowgraph and temperature time series are measured using the thermistor mounted at a fixed point for different ’Rayleigh numbers.Bifurcations and unsteady flows in the cavity are observed and analyzed based on shadowgraph images and thermistor measurements.The experimental results are also compared with the numerical results.By analyzing natural convection flows and heat transfer in the V-shaped cavity,further understanding into the dynamics of the stratification breakup,the transition to an unsteady flow and the corresponding heat transfer is obtained.