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     

Experimental observations of the thermal flow around a square obstruction on a vertical wall in a differentially heated cavity

The transient thermal boundary layer flow around a square obstruction placed at the middle of the hot wall in a differentially heated cavity is visualized using a shadowgraph technique. The results show that the thermal boundary layer flow, which is blocked by the obstruction, firstly forms an intrusion head under the obstruction (the lower intrusion head). Subsequently, the lower intrusion head bypasses the obstruction and reattaches to the down-stream boundary. During the reattachment process, a more complicated flow is induced, and eventually both the lower intrusion head and the thermal boundary layer destabilize. After the lower intrusion head is convected away, the thermal boundary layer flow re-stabilizes. At the quasi-steady state, the thermal boundary layer forms a double-layer structure, which is split into two sections by the obstruction. It is demonstrated that both the transient processes and the quasi-steady state flow structures of the thermal boundary layer are significantly altered by the obstruction in comparison with the case without the obstruction.     

Dynamics of a two-fluid system in a rotating horizontal cylinder under longitudinal vibration

The average dynamics of immiscible fluids with different densities in a horizontal axially vibrating cylinder are studied. The angular velocity is sufficient to sustain the centrifuged state of the fluids. The vibration and rotation frequencies are of the same order. The generation of toroidal vortices periodic along the rotation axis and the formation of quasi-steady interface relief with axially periodic axisymmetric crimps are detected. It is shown that the vortex flow is associated with the generation of an inertial axisymmetric standing wave. The formation of the quasi-steady relief is induced by the development of the Kelvin-Helmholtz instability on the fluid interface under tangential vibration.     

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.     

黄土滑坡流滑机理的试验研究

饱和黄土的稳态强度（残余强度）是黄土边坡是否发生流滑的关键因素,为了评价饱和黄土的残余强度就需要很好的了解饱和黄土的不排水剪切性能。通过对饱和黄土的固结不排水三轴试验研究了饱和黄土的稳态强度理论。试验研究发现饱和黄土有两种典型的不排水剪切特性：稳态特性、准稳态特性。且大多数情况下饱和黄土总表现为稳态特性,只有疏松的黄土表现出准稳态特性;根据试验结果得出了黄土的稳态线与稳态强度线,可以用来分析黄土边坡的流滑机理。探讨了描述黄土稳态性质的参数内摩擦角和粘聚力的物理含义;比较了由地震引发的滑坡与灌溉诱发的滑坡流滑机理的差异,对于地震引起的黄土滑坡土体残余（稳态）强度起决定性作用,而对于灌溉引起的黄土滑坡土体的峰值强度才是关键因素。     

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.     

Flow of a dispersed phase in the Laval nozzle and in the test section of a two-phase hypersonic shock tunnel

An unsteady gas-particle flow in a hypersonic shock tunnel is studied numerically. The study is performed in the period from the instant when the diaphragm between the high-pressure and low-pressure chambers is opened until the end of the transition to a quasi-steady flow in the test section. The dispersed phase concentration is extremely low, and the collisions between the particles and their effect on the carrier gas flow are ignored. The particle size is varied. The time evolution of the particle concentration in the test section is obtained. Patterns of the quasi-steady flow of the dispersed phase in the throat of the Laval nozzle and the flow around a model (sphere) are presented. Particle concentration and particle velocity lag profiles at the test-section entrance are obtained. The particle-phase flow structure and the time needed for it to reach a quasi-steady regime are found to depend substantially on the particle size. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 102–113, September–October, 2008.     

Investigations of gas and particle dynamics in first generation needle-free drug delivery devices

Abstract. Transdermal powdered drug delivery involves the propulsion of solid drug particles into the skin by means of high-speed gas-particle flow. The fluid dynamics of this technology have been investigated in devices consisting of a convergent-divergent nozzle located downstream of a bursting membrane, which serves both to initiate gas flow (functioning as the diaphragm of a shock tube) and to retain the drug particles before actuation. Pressure surveys of flow in devices with contoured nozzles of relatively low exit-to-throat area ratio and a conical nozzle of higher area ratio have indicated a starting process of approximately 200 s typical duration, followed by a quasi-steady supersonic flow. The velocity of drug particles exiting the contoured nozzles was measured at up to 1050 m/s, indicating that particle acceleration took place primarily in the quasi-steady flow. In the conical nozzle, which had larger exit area ratio, the quasi-steady nozzle flow was found to be overexpanded, resulting in a shock system within the nozzle. Particles were typically delivered by these nozzles at 400 m/s, suggesting that the starting process and the quasi-steady shock processed flow are both responsible for acceleration of the particle payload. The larger exit area of the conical nozzle tested enables drug delivery over a larger target disc, which may be advantageous. Received 12 March 2000 / Accepted 8 June 2000     

Unsteady flow in a circular sector duct

Analytic solutions for the unsteady flow in a circular sector duct are found using series sums of Bessel integrals. For starting flow due to a step pressure gradient, the velocity profile is initially flat, then approaches the rounded steady state shape in a time scale proportional to the square of opening angle of the sector. For oscillatory flow, the velocity is quasi-steady for low frequencies, but shows “annular effect” at large frequencies. Increased opening angle increases the amplitude and the phase lag. In all cases, the shear stress at the apex is zero for acute sector angles but becomes infinite for obtuse sector angles.     

可变形儒可夫斯基翼型亚音速非定常气动力的研究

对于翼面变形速度远小于来流速度情况下的儒可夫斯翼型亚音速绕流问题,通过仿射变换将可压缩流动转换成不可压缩流动,将解析解和离散涡方法相结合计算变形机翼的不可压缩流动速度场,再利用逆变换得到变形机翼的亚音速流动速度场,进而分析非定常气动力特性,建立变形机翼的准定常升力系数和非定常附加升力系数在可压缩和不可压缩两种状态下的简单近似对应关系。计算结果显示变形机翼的非定常气动升力近似等于准定常计算结果叠加上虚拟质量力导致的非定常附加升力,该非定常附加升力随翼型变形速率呈线性关系,由机翼当前时刻飞行姿态、翼型及其变形速率确定,与具体变形历史过程无关。低来流马赫数时虚拟质量力导致的非定常效应显著,高亚音速流动时准定常升力起主导作用。同时还分析了不同马赫数下机翼往复变形过程中升力的变化特性,指出尽管高亚音速变形机翼的气动升力近似等于准定常气动升力,但不能忽视非定常附加升力的影响,非定常附加升力将导致完成往复变形需要外界输入正比于Ma∞/[(1-Ma2∞)]的功。     

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.     

Fluid–structure interaction analysis of flexible turbomachinery

A method for the performance computation of an expandable-impeller pump is developed and validated. Large deformations of the highly flexible pump impellers result in a strong coupling between the impeller and fluid flow. The computational method therefore requires simultaneous solution of fluid flow and structural response. OpenFOAM provides the flow and mesh motion solvers and is coupled to an author-developed structural solver in a tightly coupled approach using a fixed-point iteration. The structural deformations are time-dependent because the material exhibits stress relaxation. The time-constant of the relaxation, however, is very large, thereby allowing quasi-steady simulations. A water-tunnel test of a viscoelastic hydrofoil is employed to validate the solver. Simulations of the test problem show good agreement with the experimental results and demonstrate the need for several sub-iterations of the solver even for the quasi-steady simulations.     

Transient squeeze flow of viscoplastic materials

The transient, axisymmetric squeezing of viscoplastic materials under creeping flow conditions is examined. The flow of the material even outside the disks is followed. Both cases of the disks moving with constant velocity or under constant force are studied. This time-dependent simulation of squeeze flow is performed for such materials in order to determine very accurately the evolution of the force or the velocity, respectively, and the distinct differences between these two experiments, the highly deforming shape and position of all the interfaces, the effect of possible slip on the disk surface, especially when the slip coefficient is not constant, and the effect of gravity. All these are impossible under the quasi-steady state condition used up to now. The exponential constitutive model, suggested by Papanastasiou, is employed. The governing equations are solved numerically by coupling the mixed finite element method with a quasi-elliptic mesh generation scheme in order to follow the large deformations of the free surface of the fluid. As the Bingham number increases, large departures from the corresponding Newtonian solution are found. When the disks are moving with constant velocity, unyielded material arises only around the two centers of the disks verifying previous works in which quasi-steady state conditions were assumed. The size of the unyielded region increases with the Bingham number, but decreases as time passes and the two disks approach each other. Their size also decreases as the slip velocity or the slip length along the disk wall increase. The force that must be applied on the disks in order to maintain their constant velocity increases significantly with the Bingham number and time and provides a first method to calculate the yield stress. On the other hand, when a constant force is applied on the disks, they slow down until they finally stop, because all the material between them becomes unyielded. The final location of the disk and the time when it stops provide another, probably easier, method to deduce the yield stress of the fluid.     

Horizontal capillary flow of a Newtonian liquid in a narrow gap between a plane wall and a sinusoidal wall

An experimental and theoretical study of the capillary flow of a Newtonian liquid (mineral oil) in a Hele-Shaw cell in which the gap varies sinusoidally in one coordinate direction, and flow takes place in the direction of constant channel cross-sectional area is reported. The geometric non-uniformity of the gap is observed to produce interface fingering. Finger length is observed to increase with decreasing spacing between plates of fixed shape, and with increasing gross penetration distance. In the regime of interest, finger length is observed to increase slowly with increasing interface advancement, motivating a quasi-steady model in which gross interface advancement is predicted by a Lucas–Washburn model and interface fingering is predicted by a Hele-Shaw model of steady flow. The steady interface velocity in the Hele-Shaw model is set equal to the instantaneous interface velocity predicted by the Lucas–Washburn model. Fingering predicted by the quasi-steady model matches the experimentally observed trends with regards to plate spacing and gross penetration distance.     

Investigation of the annular nozzle start in actual and virtual intermittent aerodynamic setups

The results of a numerical and experimental investigation of the starting of jet-engine annular nozzle blown with the air at room temperature and high-temperature combustion products of a stoichiometric acetylene-air mixture in an intermittent aerodynamic setup are presented. The regimes and the times of the attainment of quasi-steady stAte of the flow are studied in the virtual full-scale counterpart of the experimental setup. The special features of the starting stage and the quasi-steady flow are studied for entry channels of different shapes. The values of starting times, the pressures at different points of the flow duct, and the thrusts produced by the annular nozzle measured in the physical experiment and obtained in the virtual experimental setup are compared.     

Laminar/turbulent oscillating flow in circular pipes

A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re_max = 1,920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are here compared with experimental results of previous investigators. Predictions of the flow regime on present oscillating flow conditions are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k-ε turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k-ε model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.     

ROUTE TO SURGE FOR A THROTTLED COMPRESSOR — A NUMERICAL STUDY

Aerodynamic instabilities of axial compressors are investigated numerically and compared with experimental results. The compressor flow in the interblade-row spaces is simulated by means of 2-D Euler equations while the blade rows are modelled as quasi-steady actuator disks. The coupling of different unbladed regions of the compressor by actuator disks, which is characterized by the influence of stator and rotor, is captured in terms of conservation laws and source terms by means of compressor characteristics. At inflow and outflow nonreflecting boundary conditions are used in order to avoid any nonphysical reflections at the boundary. Numerically simulating this model for selected initial and boundary conditions, we observe that for increasing values of the imposed exit pressure the compressor flow undergoes several qualitative changes. At some critical value of exit pressure a primary stable steady state losses stability to several coexisting time-periodic states with a number of rotating stall cells. While for these time-periodic states the mass flow does not depend on time, all solution branches lead finally to surge, i.e., to states with an oscillation of mass flow in time if the exit pressure is sufficiently large. In addition, the numerical results are compared with experimental measurements.     

Micromechanical modelling of shear banding in single crystals

Plastic deformation of a single crystal in double-conjugate single slip was considered. A micromechanical model based on dislocation density evolution was used. The mobile dislocation densities were assumed to relax rapidly to quasi-steady state values dictated by the current values of the slowly varying immobile dislocation densities (“adiabatic” approximation). In this approximation, a uniform time (or strain) dependent solution of the set of the governing equations was obtained. Linear analysis of stability of the uniform plastic flow with respect to band-shaped perturbations was carried out. The correspondence of the instability condition obtained with the results of previous, more macroscopic analyses was examined. Numerical examples illustrating the onset of instability were considered.