Study On Instability Of Natural Convection Boundary Layer Of Pr=0.7 Adjacent To A Vertical Surface

With the increasing energy consumption and heat flux density of equipment,it is difficult to break through the limitation of conventional heat dissipation,so it becomes more and more urgent to find a new heat dissipation method.The buoyancy-driven natural convection is a common flow phenomenon that arises from thermal surfaces,and its application prospects in the field of heat and mass transfer have been widely concerned by the academic community.The thorough studies of the flow mechanism and essential properties of natural convection may open up the development of new fields combining fluid mechanics and heat transfer,which opens up a new heuristic ideas for the enhanced heat transfer model in the future,and also provide theoretical support for its application in practical engineering.Therefore,the direct stability analysis is used to explore the basic properties of natural convection in semi-infinite space and its influence on natural convection heat transfer.The heat transfer characteristics and flow characteristics in natural convection boundary layer under different conditions are discussed by numerical simulation.The numerical model of natural convection boundary layer adjacent to an isothermal vertical wall is established by CFD software.And the convective instability of the natural convection boundary layers of air(Pr=0.7)in the laminar-to-turbulent transition regime(Ra=8.7×107～1.1×109)is investigated by stability analysis in the framework of direct numerical simulations(DNS).To understand the spatial and temporal evolution of the convective instability of the thermal boundary layers,small-amplitude random-mode numerical perturbations are first introduced into the boundary condition of the boundary layer flow.By performing the Fourier transform on the temperature time series of the distribution of the flow direction in the boundary layer,the flow evolution of the power spectrum in the boundary layer is obtained.The results show that the prescribed full spectral perturbations(i.e.white noise)are mostly damped out immediately by a limited upstream boundary layer.A low-frequency band is initially distinct in the upstream near the leading edge,but decays spatially as the instability propagates downstream.In contrast,in the process of developing the boundary layer downstream,a high-frequency band is gradually highlighted and replaces the low frequency band as the dominant frequency band in the thermal boundary layer transition regime.In order to obtain further insights into the nature of the high-frequency band preserved during the development of the boundary layer,single-mode perturbations of various frequencies are then artificially introduced into the boundary layer near the leading edge of the isothermal vertical wall.It is found that the introduction of single-mode perturbation at the peak frequency within the high-frequency band excites the maximum response of the thermal boundary layer,which indicates that the peak frequency obtained by the random-mode numerical perturbation studies is in fact the characteristic frequency or resonance frequency of the thermal boundary layer.Through the studies on a series of Rayleigh numbers in the laminar-turbulent transition region,The dimensionless form of the dependence of the characteristic frequency on Ra is then found to be fc=0.07Ra2/3.The single-mode perturbation numerical experiments also revealed the propagation speed of convective unstable waves.The results of data show that it is surprisingly greater than the convection speed of the thermal boundary layer,and it is proved that the smaller the Ra,the larger the difference between the two propagation speeds.A semi-analytical scaling of the wave propagation speed in the form csc～Ra1/2y1/2Pr was derived(y denoting the streamwise location of the boundary layer),providing a predictive correlation that can be used for thermal boundary layer control.This study aims to solve the control equation containing the disturbance source term by direct stability analysis,so that not only the unstable characteristics of the boundary layer can be obtained,but also the heat transfer characteristics of the boundary layer under the disturbed state can be obtained,and the full disclosure is fully revealed.The theoretical mechanism of heat transfer enhancement in natural convective boundary layers.