Shadowgraph observations of the transition of the thermal boundary layer in a side-heated cavity

The transition of the thermal boundary layer from start-up to a quasi-steady state in a side-heated cavity is observed using a shadowgraph technique. Three stages of the transition, including an initial growth stage, an entrainment development stage and a quasi-steady stage, are demonstrated. A significant feature of the transition revealed from the present flow visualisation is the formation of a double-layer structure along the sidewall at the entrainment development stage. It is believed that the reverse flow in the double-layer structure is the likely cause responsible for the unstable travelling waves at the quasi-steady state.     

Natural convection in a reservoir sidearm subject to solar radiation: experimental observations

The natural convection in a reservoir sidearm induced by solar radiation is visualised using a shadowgraph technique. The flow visualisation reveals three stages of the flow development, namely an initial growth stage, a transitional stage and a quasi-steady stage. At the initial growth stage, a distinct thermal boundary layer grows rapidly along the sloping bottom. The transitional stage is characterised by the onset of convective instability in a form of rising plumes. At the quasi-steady state, the mean temperature across the enclosure increases steadily in time and the flow is sighted with quasi-regular presence of instabilities with reduced intensities. Received: 3 July 2001/Accepted: 10 December 2001     

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.     

低Pr数流体非稳态自然对流流动的标度分析

施加了恒定热通量的竖直平板置于静止的均匀或线性分层流体中会在板壁上形成自然对流流 动. 它在达到稳态前将先历经起始和过渡两个阶段. 而表征其瞬时流动特征的主要参数是壁温、热边界层厚度、内层和外层速度边界层厚度、边界层内竖直方向的最大速度、以及层流边界层发展达到稳态所需的时间. 利用标度分析得到了均匀和线性分层低普郎特数(Pr<1)流体沿恒定热通量竖直平板的非稳态自然对流流动在各个发展阶段的标度关系.     

The unsteady boundary layer flow in a convergent channel

An incompressible fluid is at rest in a converging channel between intersecting planes when, at some moment of time, the flow towards a sink at the point of intersection is set up impulsively. The motion is taken to be of the boundary layer type, and it is found that the transient part of the flow decays algebraically as the steady state motion becomes dominant. The final decay takes place at the edge of the boundary layer, with the viscous forces affecting the unsteady flow in a region that eventually lies outside the steady state boundary layer.     

Transient natural convection in a cavity with heat input and a constant temperature wall on opposite sides

The transient natural convection of a fluid with Prandtl number of order 200 in a two-dimensional square cavity has been numerically studied. One of the vertical walls of the cavity is kept at a constant (ambient) temperature and a constant heat flux is applied on the opposite wall. The other walls are adiabatic. Initially, a boundary layer is formed near the heated wall; subsequently, a large vortical structure is generated, together with an upper intrusion layer. As time progresses, the average temperature in the cavity increases, and a descending boundary layer is formed near the constant temperature wall. During the transition to the steady-state regime, a thermal stratification pattern is formed. The results are compared with the scale analysis presented by Patterson and Imberger (1980).     

The influence of thermal expansion flow on droplet evaporation

It has been demonstrated recently that it follows from conservation of mass that unsteady temperature fields create flow in an incompressible fluid with a temperature-dependent density even in the absence of gravity. The paper studies the influence of thermal expansion flow on spherically symmetric evaporation of an isolated droplet. A model problem of a droplet evaporating at a constant rate is first considered. In this idealized situation one can use the assumption of a thin thermal boundary layer to solve analytically the unsteady moving-boundary heat conduction problem to find the temperature field inside the droplet both with and without the thermal expansion flow. Next evaporation of a fuel droplet in a diesel engine is studied numerically. The heat diffusion equation is solved in the liquid phase while the standard quasi-steady model is used for the gas phase. The results of the calculation show that for high ambient temperatures the influence of the thermal expansion flow on the droplet lifetime can be considerable.     

侧加热腔体内重力波演化过程的数值模拟

利用二维数值模拟的方法研究了侧加热腔体内的自然对流．基于数值模拟结果,描述了水平热入侵流(intrusion)的整个演化过程,并对该过程的物理机制进行了讨论．结果表明：当热入侵流抵达腔体冷壁后,由于冷壁无法卷入所有的热入侵流,热入侵流在冷上角堆积并产生一个反向流动,在冷壁边界层附近形成一个顺时针涡,该涡在浮力效应驱动下可返回热壁,并在腔体的冷热壁之间形成了腔体尺度的流体振荡,即内重力波．     

The final approach to steady state in a nonsteady axisymmetric stagnation point heat transfer

An analysis is presented for the transient thermal response of a laminar boundary layer in the vicinity of an axisymmetric stagnation flow on an infinite circular cylinder. The final approach to steady state temperature field is shown to have exponential decay with time. The characteristic factors appearing in the exponents result in the solution of an eigenvalue problem in ordinary linear differential equations. Numerical results are presented for a range of values of the Reynolds number and Prandtl number.     

LES of transient flows controlled by DBD plasma actuator over a stalled airfoil

Large-eddy simulations (LES) are employed to understand the flow field over a NACA 0015 airfoil controlled by a dielectric barrier discharge (DBD) plasma actuator. The Suzen body force model is utilised to introduce the effect of the DBD plasma actuator. The Reynolds number is fixed at 63,000. Transient processes arising due to non-dimensional excitation frequencies of one and six are discussed. The time required to establish flow authority is between four and six characteristic times, independent of the excitation frequency. If the separation is suppressed, the initial flow conditions do not affect the quasi-steady state, and the lift coefficient of the higher frequency case converges very quickly. The transient states can be categorised into following three stages: (1) the lift and drag decreasing stage, (2) the lift recovery stage, and (3) the lift and drag converging stage. The development of vortices and their influence on control is delineated. The simulations show that in the initial transient state, separation of flow suppression is closely related to the development spanwise vortices while during the later, quasi-steady state, three-dimensional vortices become more important.     

Heat and mass transfer of a fuel droplet evaporating in oscillatory flow

A numerical study of the heat and mass transfer from an evaporating fuel droplet in oscillatory flow was performed. The flow was assumed to be laminar and axisymmetric, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on these assumptions, the conservation equations in a general curvilinear coordinate were solved numerically. The behaviors of droplet evaporation in the oscillatory flow were investigated by analyzing the effects of flow oscillation on the evaporation process of a n-heptane fuel droplet at high pressure.The response of the time history of the square of droplet diameter and space-averaged Nusselt numbers to the main flow oscillation were investigated in frequency band of 1–75 Hz with various oscillation amplitudes. Results showed that, depending on the frequency and amplitude of the oscillation, there are different modes of response of the evaporation process to the flow oscillation. One response mode is synchronous with the main flow oscillation, and thus the quasi-steady condition is attained. Another mode is asynchronous with the flow oscillation and is highly unsteady. As for the evaporation rate, however, in all conditions is more greatly enhanced in oscillatory flow than in quiescent air.To quantify the conditions of the transition from quasi-steady to unsteady, the response of the boundary layer around the droplet surface to the flow oscillation was investigated. The results led to including the oscillation Strouhal number as a criteria for the transition. The numerical results showed that at a low Strouhal number, a quasi-steady boundary layer is formed in response to the flow oscillation, whereas by increasing the oscillation Strouhal number, the phenomena become unsteady.     

Rolling/sliding of a particle on a flat wall in a linear shear flow at finite Re

Recently Lee and Balachandar proposed analytically-based expressions for drag and lift coefficients for a spherical particle moving on a flat wall in a linear shear flow at finite Reynolds number. In order to evaluate the accuracy of these expressions, we have conducted direct numerical simulations of a rolling particle for shear Reynolds number up to 100. We assume that the particle rolls on a horizontal flat wall with a small gap separating the particle from the wall (L = 0.505) and thus avoiding the logarithmic singularity. The influence of the shear Reynolds number and the translational velocity of the particle on the hydrodynamic forces of the particle was investigated under both transient and the final drag-free and torque-free steady state. It is observed that the quasi-steady drag and lift expressions of Lee and Balachandar provide good approximation for the terminal state of the particle motion ranging from perfect sliding to perfect rolling. With regards to transient particle motion in a wall-bounded shear flow it is observed that the above validated quasi-steady drag and lift forces must be supplemented with appropriate wall-corrected added-mass and history forces in order to accurately predict the time-dependent approach to the terminal steady state. Quantitative comparison with the actual particle motion computed in the numerical simulations shows that the theoretical models quite effective in predicting rolling/sliding motion of a particle in a wall-bounded shear flow at moderate Re.     

Natural Convection Induced by a Heated Vertical Plate Embedded in a Porous Medium with Transpiration: Local Thermal Non-equilibrium Similarity Solutions

This paper is concerned with the thermal non-equilibrium free convection boundary layer, which is induced by a vertical heated plate embedded in a saturated porous medium. The effect of suction or injection on the free convection boundary layer is also studied. The plate is assumed to have a linear temperature distribution, which yields a boundary layer of constant thickness. On assuming Darcy flow, similarity solutions are obtained for governing the steady laminar boundary layer equations. The reduced Nusselt numbers for both the solid and fluid phases are calculated for a wide range of parameters, and compared with asymptotic analyses.     

A numerical study of transient natural convection under time-dependent gravitational acceleration field

A transient natural convection caused by abruptly heating of a vertical wall in a square enclosure which is under time-dependent gravitational acceleration field is studied numerically. During the computing process, a penalty finite element method is adopted to solve the governing equations. The factor of the time-dependent gravitational acceleration is included in Rayleigh number, therefore two variation of Rayleigh number are considered, one is from 10⁵ via 10⁶ to ? 10⁵ and the other is from 10⁴ via 10⁵ to ? 10⁴. Since the variations of flow field and temperature distribution of the fluid in the square enclosure are complicated and unpredictable, the isotherms, streamlines and time dependent heat transfer rate are examined for investigating the heat transfer mechanism during the transient process. The results show that the agreement of the heat transfer rate of this study with that of quasi-steady state is mainly dependent on the response of the variation rate of boundary layer along the vertical walls to that of time-dependent gravitational acceleration.     

Convection mixte en régime transitoire de couche limite laminaire sur une plaque verticale

This work deals with transient laminar boundary layer along a vertical surface and system of equations is solved using finite difference implicite scheme. We show that the nature of the plate influence thermal and dynamical boundary layer thicknesses as well as the flow velocity. Moreover, we observe that a small perturbation of the velocity implies to flow laminar instabilities.     

Heat and mass transfer on a MHD third grade fluid with partial slip flow past an infinite vertical insulated porous plate in a porous medium

The influence of third grade, partial slip and other thermophysical parameters on the steady flow, heat and mass transfer of viscoelastic third grade fluid past an infinite vertical insulated plate subject to suction across the boundary layer has been investigated. The space occupying the fluid is porous. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. An efficient numerical scheme of midpoint technique with Richardson’s extrapolation is employed to solve the governing system of coupled nonlinear equations of momentum, energy and concentration. Numerical calculations were carried out for different values of various interesting non-dimensional quantities in the slip flow regime with heat and mass transfer and were shown with the aid of figures. The values of the wall shear stress, the local rate of heat and mass transfers were obtained and tabulated. The analysis shows that as the fluid becomes more shear thickening, the momentum boundary layer decreases but the thermal boundary layer increases; the magnetic field strength is found to decrease with an increasing temperature distribution when the porous plate is insulated. The consequences of increasing the permeability parameter and Schmidt number decrease both the momentum and concentration boundary layer thicknesses respectively whereas an increase in the thermal Grashof number gives rise to the thermal boundary layer thickness.     

Unsteady boundary layer and its separation over a heated circular cylinder

A numerical method is developed to solve the coupled unsteady laminar momentum and thermal boundary layers over a circular cylinder impulsively started from rest. The present non-iterative finite difference method, which requires relatively fewer grid points in the reversed flow region than any other method, can easily handle the separating boundary layer flows. The results indicate that the present method has accuracy comparable with the earlier methods, while consuming computer time approximately one order of magnitude less. The present numerical method allowed investigation of the effect of buoyancy parameter on the starting boundary layer. The time-dependent behaviour of the boundary layer is studied in terms of the appearance of the singularity, the distribution of skin friction and wall heat flux, and the wall position of the inflection point of the velocity profile. The transient as well as buoyancy-dependent patterns of the streamlines and isotherms are also studied.