The linear wave instability of boundary layer flow induced by a horizontal heated surface in porous media

In this paper we use the parallel-flow approximation to determine the criterion for the onset of instability in the form of travelling waves in a horizontal thermal boundary layer in porous media. We find that waves grow beyond a nondimensional distance of 28.90 from the leading edge, a result which shows, somewhat surprisingly, that waves are to be preferred over vortices, which have been found to grow beyond 33.47 from the leading edge [1]. We discuss very briefly the implications of our analysis for the use of the parallel flow approximation in the determination of stability criteria for thermal boundary layers.     

The effect of local thermal non-equilibrium on forced convection boundary layer flow from a heated surface in porous media

A steady two-dimensional forced convective thermal boundary layer flow in a porous medium is studied. It is assumed that the solid matrix and fluid phase which comprise the porous medium are subject to local thermal non-equilibrium conditions, and therefore two heat transport equations are adopted, one for each phase. When the basic flow velocity is sufficiently high, the thermal fields may be described accurately using the boundary layer approximation, and the resulting parabolic system is analysed both analytically and numerically. Local thermal non-equilibrium effects are found to be at their strongest near the leading edge, but these decrease with distance from the leading edge and local thermal equilibrium is attained at large distances.     

凹凸前缘压气机叶栅旋涡结构探索

为改善压气机叶栅内的分离流动、优化气动性能,以仿生凹凸前缘叶栅为研究对象,基于数值方法分析吸力面特殊流动形成的原因,研究零攻角工况下凹凸前缘叶栅的流动特性,并基于涡系变化和附面层结构的分析,总结了凹凸前缘叶栅的流动控制机理。研究结果表明:由于前缘压力梯度作用使凹凸前缘叶栅形成了特殊的流向涡对,在下游向两侧发展形成特殊的三维分离结构,挤压局部流管收缩,提高了流动附着性并重组附面层结构,降低了角区分离范围且避免了大尺度集中脱落涡的形成,改善了下游流动。探索了凹凸前缘叶栅的典型旋涡模型,并基于对流动控制机理的理解,给出若干优化方案,得到叶栅气动性能提升,其中WFB-2-9叶栅相比原始叶栅总压损失系数降低了10.47%。     

A computational study of unsteady radiative magnetohydrodynamic Blasius and Sakiadis flow with leading‐edge accretion (ablation)

The present study investigates the influence of the magnetic field, thermal radiation, Prandtl number, and leading‐edge accretion/ablation on Blasius and Sakiadis flow. The convective boundary condition is employed to investigate the heat transfer. The nondimensional governing boundary layer equations have been solved by the homotopy analysis method for different values of the pertinent parameters. The effects of these parameters on the dimensionless velocity, temperature, skin friction, and Nusselt number are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity establishing thinner velocity boundary layer for both Blasius and Sakiadis flows while an increase in accretion/ablation effect at leading‐edge manifests in a deceleration in velocity for Blasius case and the opposite trend is observed for Sakiadis flow. Another important outcome is that an increase in radiation and accretion/ablation at leading‐edge upsurges the fluid temperature leading to enhancement in the thermal boundary layer. For both Blasius and Sakiadis flow, the skin friction coefficient and the heat transfer rate decline with the enhancement of the leading‐edge accretion parameter. The results are compared with the existing data and are found in good agreement.     

Mixed convection boundary layer flow adjacent to a vertical surface embedded in a stable stratified medium

The steady mixed convection boundary layer flow through a stable stratified medium adjacent to a vertical surface is investigated. The velocity outside the boundary layer and the surface temperature are assumed to vary linearly from the leading edge of the surface. The transformed ordinary differential equations are solved numerically by the Keller-box method. It is found that dual solutions exist, and the thermal stratification delays the boundary layer separation.     

Preliminary experiments on the control of natural convection in differentially-heated cavities

Aiming at the control of natural convection flows and heat transfer in air-filled differentially-heated cavities, experimental attempts were carried out in order to achieve the stability of such flows to various excitations. The mechanism of control chosen in these experiments introduces thermal disturbances via a thin pipe located inside the boundary layer at the bottom of the hot wall. Its temperature varies periodically due to alternating electrical heating and continuous water cooling. The effects of this disturbance in temperature are investigated for a Rayleigh number value chosen just greater than the first bifurcation value from a steady state flow to a monoperiodic state. The results show the distribution of the overall and local Nusselt numbers. The introduction of this obstacle induces a 10% decrease in heat transfer. Temperature oscillations of the actuator provoke modifications of the flow field. In particular, an amplification of unsteadiness in the outer borders of boundary layers is observed and a displacement of secondary vortices is encountered. Explanations are given by a detailed examination of flow structures, such as the spatial distribution of velocities and their fluctuations.     

Enhancement of convective cooling using oscillating fins

Tailoring the local flow field around a fin can substantially enhance the forced convection heat transfer from a conventional heat sink. A fin is set into oscillation leading to rupture of the thermal boundary layer developed on either side of the fin. This enhancement in heat transfer is demonstrated through an increase in the time-averaged Nusselt Number (Nu) on the fin surfaces. Nu has been found to be strongly dependent on the flow Reynolds Number (Re), the frequency and amplitude of the fin oscillations. A threshold amplitude and frequency is identified beyond which Nu improvements are observed for fixed Re.     

The effect of longitudinal surface waves on free convection from vertical surfaces in porous media

In this paper we consider the effect of longitudinal surface waves on the thermal boundary layer flow induced by a vertically aligned heated surface embedded in a porous medium. The full governing equations are considered and the boundary layer equations are derived in a systematic way. It is found that, for a wide range of values of x, the distance from the leading edge, the boundary layer equations for the three—dimensional flowfield are satisfied by a two-dimensional similarity solution.     

Local thermal non-equilibrium effects in the Darcy–Bénard instability with isoflux boundary conditions

The Darcy–Bénard problem with constant heat flux boundary conditions is studied in a regime where the fluid and solid phases are in local thermal non-equilibrium. The onset conditions for convective instability in the plane porous layer are investigated using a linear stability analysis. Constant heat flux boundary conditions are formulated according to the Amiri–Vafai–Kuzay Model A, where the boundary walls are assumed as impermeable and with a high thermal conductance. The normal mode analysis of the perturbations imposed on the basic state leads to a one-dimensional eigenvalue problem, solved numerically to determine the neutral stability condition. Analytical solutions are found for the limit of small wave numbers, and in the regime where the conductivity of the solid phase is much larger than the conductivity of the fluid phase. A comparison with the corresponding results under conditions of local thermal equilibrium is carried out. The critical conditions for the onset of convection correspond to a zero wave number only when the inter-phase heat transfer coefficient is sufficiently large. Otherwise, the critical conditions correspond to a nonzero wave number.     

The influence of higher order effects on the linear wave instability of vertical free convective boundary layer flow

We examine the stability of free convective boundary layer flow over a vertical heated flat plate with respect to two-dimensional wave disturbances. In particular we determine the effect of the overall external geometry on the stability criterion. The fluid domain is taken to be bounded by two semi-infinite flat plates forming a wedge of angle α. The vertical plate is held at a uniform hot temperature while the other is either insulated or is held at the ambient temperature of the fluid. The basic flow used in the analysis is a two-term boundary-layer approximation using the method of matched asymptotic expansions. A modified version of the Keller-box method is used to solve the linearised wave-disturbance equations numerically. The neutral curves have been delineated for different values of wedge angle, α, where the working fluids are water and air. We find that the critical distance from the leading edge beyond which disturbances grow is strongly dependent on α, and this suggests that the external geometry of the fluid domain exerts a considerable influence on stability criteria.     

On impulsively started convection: The case of stagnation point flow

Transient convection in incompressible planar and axisymmetric point flow is analyzed numerically in this work, and the thermal boundary layer response to surface sudden heating and cooling in the two settings is presented and compared over a range of Prandtl number between 0.5 and 100. A comparison between surface sudden cooling and heating is performed and different criteria are established as to when surface sudden heating and cooling are equivalent in terms of the transition time. With no initial thermal boundary layer (surface and fluid are at the same temperature), the transition time from the initial steady state to the final steady state upon surface sudden cooling or heating is found to be a constant regardless of the surface heating or cooling extent above or below the initial surface temperature, and is dependent only on the Prandtl number. With the existence of an initial thermal boundary layer, the transition time is dependent upon the heating or cooling extent, the initial surface temperature, the Prandtl number and whether heating/cooling is towards building-up or demolishing the thermal boundary later. It takes longer time when surface sudden heating or cooling is towards demolishing the thermal boundary layer than building it up. With symmetric surface sudden cooling or heating above or below the far-field fluid temperature, the transition time is independent on the surface cooling or heating extent and is a function of only the Prandtl number. A considerable difference in the thermal boundary layer response in the two settings is found. The transition time from the initial to the final steady state in axisymmetric stagnation point flow is less than that in plane stagnation flow under the same conditions.     

The influence of higher order effects on the vortex instability of thermal boundary layer flow in a wedge-shaped domain

We reconsider the onset of streamwise vortices in the thermal boundary layer flow induced by an inclined upward-facing heated semi-infinite surface placed within a Newtonian fluid. Particular emphasis is laid upon how the induced flow in the isothermal region outside the boundary layer affects the boundary layer itself at higher order, and how this, in turn, affects the stability criterion for the onset of vortices. We find that the stability criterion for thermal boundary layers in air is less susceptible to changes in external geometry than for boundary layers in water. In general, we conclude that the variation of the stability criterion with wedge angle (between the heated and the outer boundary surface) is too great for the theory to predict reliably where disturbances first begin to grow.     

柴油机近气缸盖壁面气流速度和热边界层的研究

研究了倒拖工况下直喷式柴油机气缸盖近壁气流速度场的分布规律，并利用一维传热模型计算了气缸盖近壁的热边界居，得出了气缸盖近壁不同位置的气流速度和热边界层是不同的，速度边界层基本上在压缩中期形成并达到一定厚度，以及热边界层和速度边界层数量级相同等结论。     

NUMERICAL INVESTIGATION OF AN INTERNAL LAYER IN TURBULENT FLOW OVER A CURVED HILL

The development of an internal layer in a turbulent boundary layer flow over a curved hill is investigated numerically. The turbulent flow equations are solved by a control volume based, finite-difference method. The turbulence is described by a multiple-time-scale turbulence model. Computational results show that the internal layer is a strong turbulence field that develops beneath the external boundary layer and is located very close to the wall. The turbulence field of the boundary layer flow over the curved kill is compared with that of a turbulent flow over a symmetric airfoil (which has the same geometry as the curved hill except that the leading and trailing edge plates were removed) to study the influence of a strongly curved surface on the turbulence field. The turbulence structure in the near-wall region of the curved hill is almost the same as that of the airfoil in most of the curved region even though the approaching external flows are quite different. Results show that the development of the wall shearing stress and separation of the boundary layer at the rear of the curved hill depend mostly on the streamline curvature and are only slightly influenced by the external boundary layer flow.     

Convective instability of a vertical thermal boundary layer in a differentially heated cavity

The convective instability of a vertical thermal boundary layer adjacent to the sidewall of a water-filled differentially heated cavity over a range of Rayleigh numbers (5 × 10⁷–3.44 × 10⁹) is investigated using direct stability analysis. The results show that the dominant frequency of the convective instability changes as perturbations travel downstream due to the presence of the horizontal boundaries, which is different from that of the vertical thermal boundary layer adjacent to an infinite or semi-infinite thermal wall. The features of the convective instability of the vertical thermal boundary layer adjacent to the sidewall are described, and the dependence of the dominant frequency on the Rayleigh number is obtained. Furthermore, the dependence of the flow rate and heat transfer through the cavity on the Rayleigh number is quantified by numerical results.     

叶片根部倒角对离心叶轮气动性能影响

叶轮是决定离心压气机气动性能的关键因素之一,在保持叶轮设计参数不变的条件下,调整叶根倒角的分布,对比分析叶根倒角对压气机性能的影响.利用Numeca软件对跨声速离心压气机进行全三维稳态流动数值模拟方案分为等半径倒角与变半径倒角两种.结果表明:主叶片后半弦长的倒角是决定压气机气动性能的关键性因素,尾缘倒角比前缘更敏感;根...     

Heat Transfer from Pulsating Laminar Impingement Slot Jet on a Flat Surface with Inlet Velocity: Sinusoidal and Square Wave

Heat transfer from a pulsating laminar impingement slot jet on a flat surface was investigated numerically and experimentally. Inlet velocity was considered sinusoidal velocity and square wave velocity. Experimental studies were done only for the sinusoidal velocity state. An inverse heat conduction method, conjugated gradient method with adjoint equation, was used for the experimental estimation of the local heat transfer coefficient along the target surface. Effect of the square wave velocity of the laminar impingement slot jet was studied numerically. The results show pulsations in flow change flow patterns and the thermal boundary layer thickness because of the newly forming thermal boundary layer is extremely small each time the flow is resumed. Heat transfer rate in this state enhances due to pulsating inlet velocity in comparison with steady state. Heat transfer increases with increasing pulsation amplitude. Enhancement in mean heat transfer on the target plate for sinusoidal velocity is rather than square wave velocity.     

Effects of buoyancy assisting and opposing flows on mixed convection boundary layer flow over a permeable vertical surface

The present study deals with new similarity solution of steady mixed convection boundary layer flow over a permeable surface for convective boundary condition. It has been shown that a self similar solution is possible when the mass transfer velocity at the surface of the plate varies like x^−1/2, where x is the distance from the leading edge of the solid surface. Two point boundary value problem governed by non-linear coupled ordinary differential equations have been solved numerically using implicit finite difference scheme in combination with the quasi-linearization technique. It is interesting to note that dual solutions exist for buoyancy assisting flow, besides that usually reported in literature for buoyancy opposing flow. Further, the buoyancy assisting force causes considerable overshoot in the velocity profile and the Prandtl number strongly affects the thermal boundary layer thickness including the surface heat transfer rate.     

A study of the unsteady tip flow field of a transonic compressor

An experimental investigation on the unsteady tip flow field of a transonic compressor rotor has been performed.The casing-mounted high frequency response pressure transducers were arranged along both the blade chord and the blade pitch.The chord-wise ones were used to indicate both the ensemble averaged and time varying flow structure of the tip region of the rotor at different operating points under 95% design speed and 60% design speed.The pitch-wise circumferential transducers were mainly used to analyze the unsteadiness frequency of the tip leakage flow in the rotor frame at the near stall condition.The contours of casing wall pressure show that there were two clear low pressure regions in blade passages,one along the chord direction,caused by the leakage flow and the other along the tangential direction,maybe caused by the forward swept leading edge.Both low pressure regions were originated from the leading edge and formed a scissor-like flow pattern.At 95% design speed condition,the shock wave interacted with the low pressure region and made the flow field unsteady.With the mass flow reduced,the two low pressure regions gradually contracted to the leading edge and then a spike disturbance emerged.     

Natural convection from isothermal flat surfaces

Local heat-transfer coefficients along a flat plate in natural convection in air were measured using Boelter-Schmidt type heat flux meters. Experiments were carried out for different temperature differences in heating and cooling, and with inclinations varying from the horizontal “facing upwards” position, through the vertical position, to the horizontal “facing downwards” position.

The results are presented in terms of local Nusselt number as a function of the local Grashof number “tangential component”. All runs were in the range accepted as that of laminar boundary layer flow. However, under certain conditions when the normal velocity component of the air is directed away from the surface, separated flow is indicated along the trailing part of the surface, well before turbulence sets in in the boundary layer. Separation starts at a certain point along the surface. This point is nearer to the leading edge the higher the temperature difference, and the larger the inclination of the surface to the vertical.

In a separation region, the flux density is uniform. In all other regions the results agreed closely with established theories of laminar boundary layer flow.

A leading adiabatic section, used in some of the experiments, did not affect the results. An appendix gives relations recommended for engineering calculations.