Reattachment Process Research Articles

Unsteady flow of shear-thickening fluids around an impulsively moving circular cylinder

Unsteady flow past an impulsively moving circular cylinder in both Newtonian and shear-thickening fluids is investigated numerically. Two impulsive motions are simulated: impulsive start and impulsive stop. The Carreau viscosity model is used for shear-thickening fluids with the range of the power index 1 ≤ n ≤ 2. The Reynolds number is Re=40 base on the cylinder diameter. Simulation results of shear-thickening fluids are compared with the Newtonian case. Significant increase in the viscosity due to the impulsive motion impacts on flow features, including vortical structures, zero shear point on the cylinder surface, pressure profile, and the drag force. Current results indicate that vortical structures generated by the impulsive motion weaken and diffuse faster for a larger power index. The zero shear point on the cylinder surface is associated to the flow separation in impulsively started flow and the re-attachment in the impulsively stopped flow. The shear-thickening effect delays the separation and the re-attachment process, which is intertwined with slow development of adverse pressure gradient in shear-thickening fluids. The total drag increases as the power index increases. Contribution of the friction and the pressure drag to the total is discussed in details. The impact of the Carreau number Cu on the non-Newtonian behavior is numerically investigated as well.

Dynamic Thin-Airfoil Stall and Leading-Edge Stall of Oscillating Wings at Low Reynolds Number

This paper investigates the unsteady aerodynamic characteristics of an oscillating flat plate and the NACA 0012 airfoil around the angle of attack (AoA) close to their static stall angle at a low Reynolds number, 3.2 × 104. The kinematic oscillatory motion is described by a sinusoidal function in which the oscillation frequency and amplitude are variable. Both experimental and numerical methods are applied in the two-dimensional space. The experiment aims at measuring the aerodynamic forces and the moment directly. For numerical simulation, the SST (Shear Stress Transport) gamma theta model is employed to solve the unsteady flow field and to compute the lift coefficients (CLs). Good qualitative agreement between the experimental and numerical results for CL is obtained, which demonstrates the feasibility of the modified RANS model in the flow transition case. In general, NACA 0012 is greatly influenced by the dynamic effect in contrast with the flat plate. For a given reduced frequency, the shape of the hysteresis loop of CL shows some distinguishing features; the process of flow reattachment of NACA 0012 is slower than that of the flat plate in the downstroke phase, so that a smooth transition of CL is observed; there are still vortices shedding from the trailing edge even at small angles of attack, which results in a local instability of CL. By studying the effects of the reduced frequency (K) and the amplitude, it is found that the AoA corresponding to the maximum CL is more sensitive to the former and the reduced pitch rate (a') is the main parameter determining the dynamic stall angle for both flat plate and NACA 0012. In addition, the results for K = 0.07 show that the lift and drag coefficients at a maximum angle of attack are close to their static values for the discussed amplitudes and wing geometries.

Forced Flow Reattachment Process and the Effect of Pressure Gradient

Stereo particle image velocimetry experiments were conducted to explore the flowfield resulting from the interaction of finite-span synthetic jet actuators and a turbulent boundary layer over an S817 airfoil at various angles of attack. Three specific scenarios were investigated: a favorable pressure gradient, an adverse pressure gradient, and a separated flow in which the synthetic jet actuators reattached the flow. Multiple coherent vortical structures were shed during the reattachment process, for which the circulation associated with these structures was composed of the “trapped” vorticity within the separated shear layer. The shedding of this vorticity was shown to be an inherent part of the reattachment mechanism. In a smaller, local measurement domain, volumetric flowfields were reconstructed near the synthetic jet orifice. It was shown that the presence of an adverse pressure gradient resulted in an increase of momentum diffusion through the boundary layer, in addition to the rate at which the jet’s axis switching occurred. At the highest angle of attack tested, where the flow was reattached through actuation, the coherent structures associated with the synthetic jet dissipated significantly quicker spatially, as much of the energy associated with the actuation was used to maintain attached flow.

A geometrical criterion for absolute instability in separated boundary layers

Laminar separation bubbles on airfoils and low-pressure turbines are generally expected to be dominated by convective inflectional instability. However, absolute instability is possible under certain circumstances, which may lead to important changes in the laminar-turbulent transition, reattachment processes, and their impact on the aerodynamics. This paper revisits the absolute/convective instability properties of different families of boundary-layer velocity profiles with a reversed flow region. A new methodology is employed in the analysis, which incorporates an additional equation to the classic Rayleigh’s equation governing inviscid instability. This allows for the direct recovery of the zero-group-velocity disturbance waves that govern the absolute/convective behavior, at an unprecedented low computational cost that enabled the large parametric study performed here. Present results show that while the peak reversed flow or wall-normal extent of the reversed flow impact the instability character, criteria based on any of them are generally not valid. A new criterion is proposed, based on the relative position of the inflection point: inviscid inflectional instability becomes of an absolute kind when the inflection point is located inside of the recirculation region. Absolutely unstable velocity profiles are identified with peak reversed flow as low as 10% of the free-stream velocity, a value substantially smaller than thresholds previously proposed in the literature.

Numerical investigation of laminar–turbulent transition in laminar separation bubbles: the effect of free-stream turbulence

The role of free-stream turbulence (FST) in the hydrodynamic instability mechanisms and transition to turbulence in laminar separation bubbles (LSBs) was investigated using direct numerical simulations (DNS). Towards this end, a set of highly resolved DNS have been carried out, where isotropic FST fluctuations with intensities from 0.1 % to 3 % are introduced to investigate the relevant physical mechanisms governing the interaction of separation and transition in LSBs. For disturbance-free simulations, i.e. without FST, laminar–turbulent transition involves a Kelvin–Helmholtz (KH) instability of the separated shear layer. For LSBs subjected to FST, vortical FST fluctuations penetrate the approaching attached laminar boundary layer upstream of the separation location and induce slowly growing low-frequency disturbances, so-called Klebanoff (K) modes, which cause a spanwise modulation with a distinct spanwise wavelength. Simultaneously, the FST enhances the initial levels of instability waves with frequencies in the frequency range of the KH instability, but at much smaller amplitude levels compared to the K-modes. Results from the calculations based on the linearized Navier–Stokes equations and comparison with DNS results reveal that the K-mode exhibits exponential growth in the separated shear layer until it reaches a peak amplitude. At the same time, two-dimensional (2D) disturbance waves are also exponentially amplified, in fact at larger growth rate compared to the K-mode, due to the primary (convective) shear-layer instability mechanism until they saturate downstream of the peak amplitude associated with the K-mode. Therefore, based on detailed spectral analysis and modal decompositions for the separation bubbles investigated, the transition process is the result of two different mechanisms: (i) strong amplification of high-frequency (order of the shedding frequency), essentially 2D or weakly oblique fluctuating disturbances and (ii) low-frequency, three-dimensional K-modes caused by FST. Depending on the intensity of the FST, one of these mechanisms would dominate the transition process, or both mechanisms act together and contribute simultaneously. The net effect of these two events is an acceleration of transition for an increased level of FST intensity, which in turn leads to a reduction of the extent of the separation bubble in streamwise and wall-normal directions. The ‘roll-up’ into spanwise large-scale vortical structures resulting from the shear-layer instability, and the eventual breakdown of these structures, strongly contribute to the reattachment process. The spanwise coherence of these ‘rollers’ deteriorates due to the presence of large-amplitude K-modes, thus effectively weakening their strength for high levels of FST intensities ($Tu>1\,\%$).

Blowoff and Reattachment Dynamics of a Linear Multinozzle Combustor

This paper describes the coupled flow and flame dynamics during blowoff and reattachment events in a combustor consisting of a linear array of five interacting nozzles using 10 kHz repetition-rate OH planar laser-induced fluorescence and stereoscopic particle image velocimetry (S-PIV). Steady operating conditions were studied at which the three central flames randomly blew-off and subsequently reattached to the bluff-bodies. Transition of the flame from one nozzle was rapidly followed by transition of the other nozzles, indicating cross-nozzle coupling. Blow-off transitions were preferentially initiated in one of the off-center nozzles, with the transition of subsequent nozzles occurring in a random order. Similarly, the center nozzle tended to be the last nozzle to reattach. The blow-off process of any individual nozzle was similar to that for a single bluff-body stabilized flame, though with cross-flame interactions providing additional means of restabilizing a partially extinguished flame. Subsequent to blowoff of the first nozzle, the other nozzles underwent similar blow-off processes. Flame reattachment was initiated by entrainment of a burning pocket into a recirculation zone, followed by transport to the bluff-body; the other nozzles subsequently underwent similar reattachment processes. Several forms of cross-nozzle interaction that can promote or prevent transition are identified. Furthermore, the velocity measurements indicated that blowoff or reattachment of the first nozzle during a multinozzle transition causes significant changes to the flow fields of the other nozzles. It is proposed that a single-nozzle transition redistributes the flow to the other nozzles in a manner that promotes their transition.

A direct simulation Monte Carlo study of hypersonic leading-edge separation with rarefaction effects

Hypersonic laminar flow separation preceded by a strong expansion can occur in practical situations such as the base flow of re-entry vehicles and flow over deflected control surfaces. A leading-edge separation configuration provides a case for studying fundamental aspects of such flow separation and reattachment in the absence of a pre-existing boundary layer. In hypersonic low-density flows, the onset of separation is complicated by the presence of rarefaction and thermal non-equilibrium. The reattachment process is also characterized by high compressibility. A computational study of the characteristics of flow separation and reattachment over such a configuration has been carried out using the direct simulation Monte Carlo code SPARTA. The salient features of separation are explained from a fluid dynamic perspective, and distinct characteristics in surface parameters are identified and discussed in detail. The physical mechanisms behind the formation as well as co-existence of primary and secondary vortices are described. The region close to the leading-edge is analyzed in detail, and the prevailing non-equilibrium aspects are presented. Various theoretical concepts, developed based on continuum flow separation, are applied to the present configuration to explore its applicability in the presence of slip, and the resulting relative variations are highlighted. The temporal evolution of flow structures at various wall temperatures is studied, and its strong dependence on the wall-to-stagnation temperature ratio is elucidated.

Comparison of turbulent forced convection between wall jet and channel flow over a heated obstacle

Turbulent forced convection of a wall jet of thickness H impinging on a two-dimensional obstacle is investigated numerically in this study. The influences of two types of turbulent incoming flows (the wall jet and the channel flow) are studied in order to deepen the understanding of the effect of the wall jet outer layer on the reattachment process and heat transfer over an elongated obstacle. The finite volume method is used to solve the governing equations. In the case of the wall-jet incoming flow, the effect of the nozzle thickness ranging from H/4 to 2H is examined as a parameter. The obtained results showed that increasing of the thickness of the nozzle improves the heat transfer and considerably modifies the location of the stagnation point. Both turbulence kinetic energy and temperature contours evidence the effect of the external shear layer of the jet. The average obstacle Nusselt number is observed to increase with the Reynolds number ranging from 10,000 to 50,000 and decrease with the augmentation of the thickness of the incoming flow. A correlation is also proposed for the average Nusselt number of the obstacle as a function of the Reynolds number and the obstacle aspect ratio.

Response of a laminar separation bubble to impulsive forcing

The spatial and temporal response characteristics of a laminar separation bubble to impulsive forcing are investigated by means of time-resolved particle image velocimetry and linear stability theory. A two-dimensional impulsive disturbance is introduced with an alternating current dielectric barrier discharge plasma actuator, exciting pertinent instability modes and ensuring flow development under environmental disturbances. Phase-averaged velocity measurements are employed to analyse the effect of imposed disturbances at different amplitudes on the laminar separation bubble. The impulsive disturbance develops into a wave packet that causes rapid shrinkage of the bubble in both upstream and downstream directions. This is followed by bubble bursting, during which the bubble elongates significantly, while vortex shedding in the aft part ceases. Duration of recovery of the bubble to its unforced state is independent of the forcing amplitude. Quasi-steady linear stability analysis is performed at each individual phase, demonstrating reduction of growth rate and frequency of the most unstable modes with increasing forcing amplitude. Throughout the recovery, amplification rates are directly proportional to the shape factor. This indicates that bursting and flapping mechanisms are driven by altered stability characteristics due to variations in incoming disturbances. The emerging wave packet is characterised in terms of frequency, convective speed and growth rate, with remarkable agreement between linear stability theory predictions and measurements. The wave packet assumes a frequency close to the natural shedding frequency, while its convective speed remains invariant for all forcing amplitudes. The stability of the flow changes only when disturbances interact with the shear layer breakdown and reattachment processes, supporting the notion of a closed feedback loop. The results of this study shed light on the response of laminar separation bubbles to impulsive forcing, providing insight into the attendant changes of flow dynamics and the underlying stability mechanisms.

Main Issues for a Fully Predictive Plasma Spray Torch Model and Numerical Considerations

Plasma spray is one of the most versatile and established techniques for the deposition of thick coatings that provide functional surfaces to protect or improve the performance of the substrate material. However, a greater understanding of plasma spray torch operation will result in improved control of process and coating properties and in the development of novel plasma spray processes and applications. The operation of plasma torches is controlled by coupled dynamic, thermal, chemical, electromagnetic, and acoustic phenomena that take place at different time and space scales. Computational modeling makes it possible to gain important insight into torch characteristics that are not practically accessible to experimental observations, such as the dynamics of the arc inside the plasma torch. This article describes the current main issues in carrying out plasma spray torch numerical simulations at a high level of fidelity. These issues encompass the use of non-chemical and non-thermodynamic equilibrium models, incorporation of electrodes with sheath models in the computational domain, and resolution of rapid transient events, including the so-called arc reattachment process. Practical considerations regarding model implementation are also discussed, particularly the need for the model to naturally reproduce the observed torch operation modes in terms of voltage and pressure fluctuations.

Spatial organization of the cytoskeleton enhances cargo delivery to specific target areas on the plasma membrane of spherical cells

Intracellular transport is vital for the proper functioning and survival of a cell. Cargo (proteins, vesicles, organelles, etc) is transferred from its place of creation to its target locations via molecular motor assisted transport along cytoskeletal filaments. The transport efficiency is strongly affected by the spatial organization of the cytoskeleton, which constitutes an inhomogeneous, complex network. In cells with a centrosome microtubules grow radially from the central microtubule organizing center towards the cell periphery whereas actin filaments form a dense meshwork, the actin cortex, underneath the cell membrane with a broad range of orientations. The emerging ballistic motion along filaments is frequently interrupted due to constricting intersection nodes or cycles of detachment and reattachment processes in the crowded cytoplasm. In order to investigate the efficiency of search strategies established by the cell’s specific spatial organization of the cytoskeleton we formulate a random velocity model with intermittent arrest states. With extensive computer simulations we analyze the dependence of the mean first passage times for narrow escape problems on the structural characteristics of the cytoskeleton, the motor properties and the fraction of time spent in each state. We find that an inhomogeneous architecture with a small width of the actin cortex constitutes an efficient intracellular search strategy.

Particle image velocimetry measurements of induced separation at the leading edge of a plate

The free shear layer that separates from the leading edge of a round-nosed plate has been studied under conditions of low (background) and elevated (grid-generated) free stream turbulence (FST) using high-fidelity particle image velocimetry. Transition occurs after separation in each case, followed by reattachment to the flat surface of the plate downstream. A bubble of reverse flow is thereby formed. First, we find that, under elevated (7 %) FST, the time-mean bubble is almost threefold shorter due to an accelerated transition of the shear layer. Quadrant analysis of the Reynolds stresses reveals the presence of slender, highly coherent fluctuations amid the laminar part of the shear layer that are reminiscent of the boundary-layer streaks seen in bypass transition. Instability and the roll-up of vortices then follow near the crest of the shear layer. These vortices are also present under low FST and in both cases are found to make significant contributions to the production of Reynolds stress over the rear of the bubble. But their role in reattachment, whilst important, is not yet fully clear. Instantaneous flow fields from the low-FST case reveal that the bubble of reverse flow often breaks up into two or more parts, thereby complicating the overall reattachment process. We therefore suggest that the downstream end of the ‘separation isoline’ (the locus of zero absolute streamwise velocity that extends unbroken from the leading edge) be used to define the instantaneous reattachment point. A histogram of this point is found to be bimodal: the upstream peak coincides with the location of roll-up, whereas the downstream mode may suggest a ‘flapping’ motion.

Sliding of microtubules by a team of dynein motors: Understanding the effect of spatial distribution of motor tails and mutual exclusion of motor heads on microtubules

Molecular motors are natural nanomachines that use the free energy released from ATP hydrolysis to generate mechanical forces. Cytoplasmic dynein motors often work collectively as a team to drive important processes such as axonal growth, proplatelet formation and mitosis, as forces generated by single motors are insufficient. A large team of dynein motors is used to slide cytoskeletal microtubules with respect to one another during the process of proplatelet formation and axonal growth. These motors attach to a cargo microtubule via their tail domains, undergo the process of detachment and reattachment of their head domains on another track microtubule, while sliding the cargo microtubule along the track. Traditional continuum/mean-field approaches used in the past are not ideal for studying the sliding mechanism of microtubules, as they ignore spatial and temporal fluctuations due to different possible distributions of motor tails on cargo filament, as well as binding/unbinding of motors from their track. Therefore, these models cannot be used to address important questions such as how the distribution of motor tails on microtubules, or how the mutual exclusion of motor heads on microtubule tracks affects the sliding velocity of cargo microtubule. To answer these, here we use a computational stochastic model where we model each dynein motor explicitly. In our model, we use both random as well as uniform distributions of dynein motors on cargo microtubule, as well as mutual exclusion of motors on microtubule tracks. We find that sliding velocities are least affected by the distribution of motor tails on microtubules, whereas they are greatly affected by mutual exclusion of motor heads on microtubule tracks. We also find that sliding velocity depends on the length of cargo microtubule if mutual exclusion among motor heads is considered.

Arc reattachment driven by a turbulent boundary layer: implications for the sweeping of lightning arcs along aircraft

A lightning channel attached to an aircraft in flight will be swept along the aircraft’s surface in response to the relative velocity between the arc’s root (attached to a moving electrode) and the bulk of the arc, which is stationary with respect to the air. During this process, the reattachment of the arc to new locations often occurs. The detailed description of this swept stroke is still at an early stage of research, and it entails the interaction between an electrical arc and the flow boundary layer. In this paper we examine the implications of the structure of the boundary layer for the arc sweeping and reattachment process by considering different velocity profiles, both for laminar and turbulent flow, as well as a high fidelity description, using large eddy simulation, of transitional flow over an airfoil. It is found that the local velocity fluctuations in a turbulent flow may be important contributors to the reattachment of the arc, through a combination of an increased potential drop along the arc and local approaches of the arc to the surface. Specific flow features, such as the presence of a laminar recirculation bubble, can also contribute to the possibility of reattachment.

Unsteady aerodynamic characteristics investigation of rotor airfoil under variational freestream velocity

Numerical investigations based on CFD method have been accomplished to illustrate the unsteady aerodynamic characteristics of the SC1095 airfoil under conditions of coupled freestream velocity/pitching oscillation. In order to simulate the variational freestream velocity of airfoil, the moving-embedded grid method is employed to calculate the fluctuating velocity. The unsteady RANS equations coupling with the dual time-stepping approach are chosen as the governing equations to predict flowfield of airfoil under variational freestream velocity condition. The implicit Lower–Upper Symmetric Gauss–Seidel scheme and Spalart–Allmaras turbulence model are employed to improve the calculation efficiency and accuracy, respectively. Based on the present CFD method, the unsteady aerodynamic characteristics of the airfoil with variational freestream velocity are simulated under conditions of fixed angle and variational angle. The simulated results indicate that the peaks of lift coefficient, drag coefficient and pitching moment coefficient of airfoil are enlarged with the increasing of fluctuating velocity, and the start of airflow reattachment process on airfoil is delayed with the increasing of fluctuating velocities and reduced frequencies due to the effects of the airflow hysteresis and compressibility. Additionally, it is illustrated in the case of different phase angles that these peaks would be reduced by increasing phase angle.

Numerical investigations of the vortex interactions for a flow over a pitching foil at different stages

The fluid–structure interaction is investigated numerically for a two-dimensional flow (Re=2.5·106) over a sinusoid-pitching foil by the SST (Shear Stress Transport) k–ω model. Although discrepancies in the downstroke phase, which are also documented in other numerical studies, are observed by comparing with experimental results, our current numerical results are sufficient to predict the mean features and qualitative tendencies of the dynamic stall phenomenon. These discrepancies are evaluated carefully from the numerical and experimental viewpoints.In this study, we have utilized Λ, which is the normalized second invariant of the velocity gradient tensor, to present the evolution of the Leading Edge Vortex (LEV) and Trailing Edge Vortex (TEV). The convective, pressure, and diffusion terms during the dynamic stall process are discussed based on the transport equation of Λ. It is found that the pressure term dominates the rate of the change of the rotation strength inside the LEV. This trend can hardly be observed directly by using the vorticity transport equation due to the zero baroclinic term for the incompressible flow.The mechanisms to delay the stall are categorized based on the formation of the LEV. At the first stage before the formation of the LEV in the upper surface, the pitching foil provides extra momentum into the fluid flows to resist the flow separation, and hence the stall is delayed. At the second stage, a low-pressure area travels with the evolution of the LEV such that the lift still can be maintained. Three short periods at the second stage corresponds to different flow patterns during the dynamic stall, and these short periods can be distinguished according to the trend of the pressure variation inside the LEV. The lift stall occurs when a reverse flow from the lower surface is triggered during the shedding of the LEV. For a reduced frequency kf=0.15, the formation of the TEV happens right after the lift stall, and the lift can drop dramatically. With a faster reduced frequency kf=0.25, the shedding of the LEV is postponed into the downstroke, and the interaction between the LEV and TEV becomes weaker correspondingly. Thus, the lift drops more gently after the stall. In order to acquire more reliable numerical results within the downstroke phase, the Large Eddy Simulation (LES), which is capable of better predictions for the laminar-to-turbulent transition and flow reattachment process, will be considered as the future work.

On Conductivity of Cold Gas Layer Separating Arc Column and Nozzle in Nontransferred Plasma Arc (Anode Reattachment Process in Plasma Spray Systems)

The nozzle serves as an anode in systems for plasma arc spraying. In these systems, the anode attachment moves downstream along the nozzle under the influence of the gas flow. The arc length increases and the arc voltage rises. At a specific arc voltage, the anode attachment jumps upstream and the arc voltage drops: reattachment occurs. The frequency of reattachment and the location of the new anode spot are determined by the conductivity of the cold gas layer that separates the extended arc column and the metallic anode. The conductivity of this layer in calculated in this paper. Two important effects are taken into account: 1) the difference between the electron and the heavy particle temperatures and 2) deviation from ionization equilibrium. Disregarding these effects leads to, practically, a completely insulating characterization of the cold gas layer. Calculations for an argon plasma showed that as opposed to the frequently accepted opinion, the electrical conductivity of the layer in the arc trail remains at a very substantial level. They also showed, in accordance with experiments, that admixing even small amounts of helium to argon decreases the layer conductivity that leads to reattachment delay and high voltage fluctuations. Analysis of the spatial distribution of the layer conductivity allows one to predict the new location of the anode spot after reattachment.

A burst wave-induced plasma actuator for controlling separated flow over a backward-facing step at low Reynolds numbers

Recently, dielectric barrier discharge plasma actuators have been extensively studied as flow control devices for controlling separated flow. It is known that a periodic disturbance is an effective way to excite a separated shear layer and control the separation in the low Reynolds number region around Re=500. In this study, the fundamental transient behavior of a burst wave-induced plasma actuator (BWPA) was investigated to control separated flow over a backward-facing step at low Reynolds numbers. The time-resolved induced velocity in quiescent air was measured using particle image velocimetry, and we found that the induced velocity exponentially grew and decayed independently of the burst frequency and duty ratio. For the flow over a backward-facing step, the reattachment process was drastically improved by BWPA operation when the oscillation frequency of the induced flow matched the acceptance frequency of the separated shear layer. We show the relations among BWPA operating parameters and the reattaching behavior of the separated flow.

Numerical Study of Heat Transfer and Separated Flow over Rectangular Obstacle in Jet

This paper is about a separated reattaching flow over a hot rectangular obstacle. Two types of incoming flow are examined in order to show the influence of the external zone of the flow on the reattachment process. It comes about due to a wall jet and a boundary layer. The inner region of these two flows is similar, but their external regions are extremely different. The separating and reattaching flow phenomena are of particular interest in engineering fields such as for an aeronautical application. Wall jet flow over an obstacle occurs in many engineering applications such as environmental discharges, heat exchangers, fluid injection systems, cooling of combustion chamber wall in a gas turbine, automobile design, and others. In electronics cooling, the prediction of the Nusselt number distribution along the obstacles is necessary before the design of the apparatus. For a heated obstacle at a constant temperature, T = 350 K and an aspect ratio of 10 (L = 10 H), the problem parameters are: (a) jet exit Reynolds number (Re) ranged from 1000 to 50000, (b) incoming flow configuration (boundary layer and wall jet). The ratio between the thickness of the nozzle (b) to the obstacle height (H) are examined simultaneously. The formulation is based on the SST k–ω turbulence model. The results show that the increasing of nozzle thickness; enhances the heat transfer and considerably modifies the stagnation point location. The highest incoming flow momentum provides the greatest values of average Nusselt number. Such as the boundary layer case in comparison with the wall jet cases. The average Nusselt number is correlated according to problem parameters .

A study of long separation bubble on thick airfoils and its consequent effects

A parametric study has been performed to analyse the flow around the thick-symmetric NACA 0021 airfoil in order to better understand the characteristics and effects of long separation bubbles (LoSBs) that exist on such airfoils at low Reynolds numbers and turbulence intensities. In the article, the prediction capabilities of two recently-developed transition models, the correlation-based γ–Reθ model and the laminar-kinetic-energy-based κ–κL–ω model are assessed. Two-dimensional steady-state simulations indicated that the κ–κL–ω model predicted the separation and reattachment process accurately when compared with published experimental work. The model was then used to study the attributes and the effects of LoSBs as a function of the angle of attack, freestream turbulence intensity and Reynolds number. It was observed that LoSBs considerably degrade the aerodynamic performance of airfoils and lead to abrupt stall behaviour. It is, furthermore, illustrated that the presence of the LoSB leads to an induced camber effect on the airfoil that increases as the airfoil angle of attack increases due to the upstream migration of the bubble. An increase in the Reynolds number or turbulence levels leads to a reduction in the bubble extent, considerably improving the airfoil performance and leading to a progressive trailing-edge stall.