Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV

This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Kármán wake of a cylindrical rod. The 3D velocity field measured at 5 kHz is used to evaluate the instantaneous planar pressure field by integration of the pressure gradient field. The experimental data are treated with a discretized model based on multiple velocity measurements. The time separation used to evaluate the Lagrangian derivative along a fluid parcel trajectory has to be taken into account to reduce precision error. By comparing Lagrangian and Eulerian approaches, the latter is restricted to shorter time separations and is found not applicable to evaluate pressure gradient field if a relative precision error lower than 10% is required. Finally, the pressure evaluated from tomographic velocity measurements is compared to that obtained from simulated planar ones to discuss the effect of 3D flow phenomena on the accuracy of the proposed technique.     

Leading edge design process using a commercial flow solver

A design process of an asymmetric leading edge, for laminar stability measurements in a flat plate boundary layer, is reported. The purpose is to minimize the leading edge pressure gradient region, which affects the stability characteristics of the flow. Finally, the design success is verified by wind tunnel testing.     

Numerical simulation of flapping‐wing insect hovering flight at unsteady flow

A computational fluid dynamics (CFD) analysis was conducted to study the unsteady aerodynamics of a virtual flying bumblebee during hovering flight. The integrated geometry of bumblebee was established to define the shape of a three‐dimensional virtual bumblebee model with beating its wings, accurately mimicking the three‐dimensional movements of wings during hovering flight. The kinematics data of wings documented from the measurement to the bumblebee in normal hovering flight aided by the high‐speed video. The Navier–Stokes equations are solved numerically. The solution provides the flow and pressure fields, from which the aerodynamic forces and vorticity wake structure are obtained. Insights into the unsteady aerodynamic force generation process are gained from the force and flow‐structure information. The CFD analysis has established an overall understanding of the viscous and unsteady flow around the virtual flying bumblebee and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. A coherent leading‐edge vortex with axial flow and the attached wingtip vortex and trailing edge vortex were detected. The leading edge vortex, wing tip vortex and trailing edge vortex, which caused by the pressure difference between the upper and the lower surface of wings. The axial flow, which include the spanwise flow and chordwise flow, is derived from the spanwise pressure gradient and chordwise pressure gradient, will stabilize the vortex and gives it a characteristic spiral conical shape. Copyright © 2006 John Wiley & Sons, Ltd.     

Super ellipse as tyre-ground contact area

In tyre-ground interaction studies there is a need to describe the contact area between a tyre and the ground. Tyre load and contact area give the ground pressure, which is important in evaluating environmental impact. The super ellipse provides an excellent means for describing, in a simple mathematical way, the shape and size of widely varying contact areas ranging from circles over ellipses to squares or rectangles. In the most complicated case, eight parameters are used, but usually only five are needed. The suggested mathematical expression gives greater flexibility in designing contact areas. It provides explicit border values for integration of ground pressure over the contact area. Thus a more accurate location of ground pressure centre is expected.     

Effects of longitudinal grooves on the Couette–Poiseuille flow

The effects of longitudinal grooves on the flow resistance in a channel where the flow is driven by movement of one of the walls and modified by a streamwise pressure gradient have been studied. The reducedorder geometrymodel has been used to extract geometric features that are hydraulically relevant. Three distinct zones leading to the reduced resistance have been identified, depending on the flow pressure gradient and the groove wave number. Two of these zones correspond to grooves with long wavelengths and one to grooves with short wavelengths. Optimization has been used to determine shapes that provide the largest flow rate. In the case of the long-wavelength grooves, the optimal shapes depend on the constraints. These shapes are well approximated by a certain universal trapezoid for grooves that have the same height and depth. There exists an optimum depth which, combined with the corresponding shape, defines the optimal geometry in the case of the unequal-depth grooves; this shape is well approximated by a Gaussian function. No optimal shape exists for the short-wavelength grooves if the groove amplitude is sufficiently small; the shortest admissible wavelength dominates system performance under such conditions. The most effective groove wave number does exist for higher grooves, but the optimal shape cannot be determined due to numerical limitations.     

大跨度脊谷式膜屋盖风载分布的实验研究

基于台州某风雨操场脊谷式张拉膜屋盖缩尺模型风洞试验的数据结果,选取典型测点,研究了屋面迎风前缘、过渡区及中轴区的平均风压和脉动风压系数的分布特性。同时,鉴于屋盖的不规则曲面造型,表面风压梯度变化较大,采用单一体型系数反映屋面风载已不能满足要求。文中在结合屋盖自身复杂体型和风压分布特征基础上,按各榀各边片将屋面划分为不同区域,对5个不利风向角下的区域体型系数进行统计分析,并给出各区域体型系数建议取值。最后,针对这类体型屋盖特点和风压分布特性,得出一些结论和建议,为进一步研究该类屋盖的风荷载特性和结构抗风设计提供了依据。     

Hydrodynamic pressure during reflection of a bore from a vertical wall

This paper presents the results of experiments in which a nonlinear wave was reflected from a vertical wall. It is shown that the hydrodynamic pressure of the wave depends significantly on the shape of its leading edge. It is found that the highest pressure is reached during reflection of a wave with a cumulative jet at the leading edge.     

Features of the turbulent flow around symmetric elongated bluff bodies

The flow fields around three elongated bluff bodies with the same chord-to-thickness ratios but distinct leading and trailing edge details were measured at a Reynolds number of 3×10⁴. These models each represent a case where: leading edge shedding dominates, trailing edge shedding dominates and a case where there is a balance between the two. The results show that the vortex street parameters vary between the models, and in particular, the shedding frequencies are significantly altered by the geometry. However, contrary to the current understanding for shorter bluff bodies, the scale of the recirculation region is found to be similar for each model, even though the shedding frequency changes within the range from 0.15 to 0.24. Also, the base pressure does not follow trends with shedding frequency expected from shorter bluff bodies. A force balance of the recirculation region shows that the near wake of each body is significantly affected by the Reynolds shear stress distribution and the resultant force due to the pressure field in the mean recirculation region. These differences infer that the distinct vortex formation characteristics depend on the state of the trailing edge shear layers. The boundary layers at the trailing edge have been quantified, as have the leading edge separation bubbles, and the marked differences in the wake details are shown to depend on the leading edge separation.     

Motion of a piston under the influence of gas pressure in the presence of an initial temperature gradient

A study is made of the motion of a piston without initial velocity under the influence of gas pressure. Under the assumption that the temperature gradient is constant and fairly small, expressions are obtained for the distributions of the gas-dynamic parameters in the disturbed region between the piston and the leading edge of the sound wave propagating through the gas at rest.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–180, March–April, 1984.     

基于实验设计方法的高超声速飞机前缘型线优化分析

为探索前缘线变化对吸气式高超声速飞机气动性能的影响,基于一种旁侧进气布局翼身融合体构型,在飞行马赫数6,攻角4°和高度26 km的巡航飞行条件下,结合运用增量修正参数化设计方法、均匀实验设计方法和计算流体力学模拟,分析了飞行器前缘型线与其升阻力系数及纵向压心等性能参数间的关系.计算结果表明,前缘线形状对飞行器升阻力系数明显高于其对纵向压心影响,设计空间范围内升力系数变化约21.3%,阻力系数变化约31.8%,升阻比变化范围约10.63%,但相对压心变化范围仅为3.87%.在此基础上,通过对典型构型物面压力分布进行分析,发现前缘线形状适当弯曲可利用飞行器下表面侧壁压缩产生的高压气流,利用二者的耦合效应使飞行器获得额外的升力增量.      

Variable viscosity squeeze films and bubble removal in the manufacture of panel material

A mathematical model is developed for the two-dimensional flow of an incompressible Newtonian fluid which is being squeezed between two rigid, impermeable plates. The fluid viscosity varies linearly with temperature. The model is intended to elucidate a problem of air bubble entrapment which arises in the manufacture of panel material, particularly in the manufacture of ‘corner’ profiles. The results show that when the two plates have the same shape, the pressure gradient is such that bubbles are likely to be expelled throughout the contact, except in the central region. When a corner profile is manufactured it is likely that bubbles will be retained, thereby leading to flaws in the final product.     

Response of a skewed turbulent boundary layer to favourable pressure gradient

Experimental results are reported for the response to a favourable pressure gradient of an initially turbulent boundary layer (Re _θ?≈?1600) developing on a flat plate with its leading edge skewed at 60° to the approach flow. The pressure gradient orthogonal to the leading edge is nominally the same as that which was shown by Escudier et?al. [(1998) Exp Fluids 25: 491–502] to cause extreme thinning of a two-dimensional (2D) (i.e. unskewed) turbulent boundary layer and the intermittency in the immediate vicinity of the surface to fall to zero, i.e. an apparent laminarisation of the boundary layer. In the case of the skewed boundary layer, the responses of the turbulence and mean-flow structures are qualitatively similar to those for the 2D situation. However, the streamwise pressure gradient is much weaker than for the 2D experiment and the extent of the changes it produces is much reduced. Even so, the changes are considerably greater than would be expected from the magnitude of the streamwise pressure gradient.     

Onset of Mobilization and the Fraction of Trapped Foam in Porous Media

Usually, foam in a porous medium flows through a small and spatially varying fraction of available pores, while the bulk of it remains trapped. The trapped foam is under a pressure gradient corresponding to the pressure gradient imposed by the flowing foam and continuous wetting liquid. The imposed pressure gradient and coalescence of the stationary foam lamellae periodically open flow channels in the trapped foam region. Foam lamellae in each of these channels flow briefly, but channels are eventually plugged by smaller bubbles entering into the trapped region. The result is a cycling of flow channels that open and close throughout the trapped foam, leading to intermittent pulsing of foam flow in that region.The dynamic behavior of foam trapped in porous media is modeled here with a pore network simulator. We predict the magnitude of the pressure drop leading to the onset of flow of foam lamellae in the region containing trapped foam. This mobilization pressure drop depends only on the number of lamellae in the flow path and on the geometry of the pores that make up this path.The principles learned in this study allow us to predict the fraction of foam that is trapped in a porous medium under given flow conditions. We present here the first analytic expression for the trapped foam fraction as a function of the pressure gradient, and of the mean and standard deviation of the pore size distribution. This expression provides a missing piece for the continuum foam flow models based on the moments of the volume-averaged population balance of foam bubbles.     

Prediction of Unsteady Aerodynamic Forces on Maneuvering Delta Wings

A semi-empirical model was developed to study the breakdown effects on maneuvering delta wings performing very high angle of attack excursions. The basic vortical flow model used was the Brown & Michael model and an unsteady source distribution was found to simulate the breakdown of the leading edge vortices. The source distribution is based on experimental observations of the vortex breakdown chordwise propagation during pitch-down and pitch-up motion. In spite of the simplicity of the vortical model used, the new model simulates the present complicated flow field. This model succeeds in predicting the leading edge core position hysteresis, the hysteresis in the unsteady pressure distribution and the corresponding airloads at extreme angles of attack. The normal force and pitching moment results are in good agreement with experimental measurements.     

Multiple laminar-turbulent transition cycles around a swept leading edge

Certain interesting flow features involving multiple transition/relaminarization cycles on the leading edge of a swept wing at low speeds are reported here. The wing geometry tested had a circular nose and a leading edge sweep of 60°. Tests were made at a chord Reynolds number of 1.3 × 10⁶ with model incidence α varied in the range of 3°?18° in discrete steps. Measurements made included wing chord-wise surface pressure distributions and wall shear stress fluctuations (using hot-film gages) within about 10 % of the chord in the leading edge zone. Results at α = 16° and 18° showed that several (often incomplete) transition cycles between laminar-like and turbulent-like flows occurred. These rather surprising results are attributable chiefly to the fact that the Launder acceleration parameter K (appropriately modified for swept wings) can exceed a critical range more than once along the contour of the airfoil in the leading edge region. Each such crossing results in a relaminarization followed by direct retransition to turbulence as K drops to sufficiently low values. It is further shown that the extent of each observed transition zone (of either type) is consistent with earlier data acquired in more detailed studies of direct transition and relaminarization. Swept leading edge boundary layers therefore pose strong challenges to numerical modelling.     

Specific Features of the Flow in the Supercritical Boundary Layer Near a Break Point on a Cold Surface

The interaction between a boundary layer and a supersonic flow past a plate with a flap deflected at a small angle in the presence of strong cooling of the body surface is considered. For supercritical regimes, the entire interaction region is located behind the leading edge of the flap and the pressure distribution has a discontinuity of the derivative near the corner point. The flow in a break-point neighborhood with a characteristic length x of the order of the boundary layer thickness is studied. It is shown that in this region a substantial pressure difference arises. The pressure distribution along the surface is found. The viscous sublayer in this region develops under the action of the given pressure gradient.     

Discontinuous solutions of an interacting three-dimensional hypersonic boundary layer

The paper is a mathematical study of the three-dimensional flow of viscous gas in a hypersonic boundary layer that develops along a flat wing whose leading edge has a step shape. The flow interacts with a flap on the wing set at a small angle. A linear solution to the problem is constructed under the assumption that the deflection angle of the flap is small and the difference between the length of the plates is of order unity. It is shown that an important part in the formation of the flow near and behind the flap may be played by the change in the pressure along the span of the wing due to the step shape of the leading edge. It is significant that although the pressure and displacement thickness are continuous functions of the transverse coordinate, the longitudinal and transverse components of the friction force have discontinuities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 19–26, March–April, 1991.I thank V. V. Sychev and A. I. Ruban for suggesting the problem, for valuable advice, and assistance.     

Stability of preseparation boundary layer on the leading edge of a thin airfoil

Numerous experiments on subsonic flow of gas past thin wing profiles (see the reviews [1, 2]) have shown that the flow near the leading edge of an airfoil is separationless only at angles of attack less than a certain critical value, which depends on the shape of the airfoil. If the angle of attack reaches the critical value, a closed region of recirculation flow of small extension is formed on the upper surface of the airfoil. Under ordinary flow conditions, the boundary layer on the leading edge of the airfoil remains laminar in the entire preseparation range of angles of attack. However, the appearance of the closed separation region is, as a rule, accompanied by transition from a laminar to a turbulent flow regime. Moreover, generation of turbulence is observed precisely in the flow separation region. The present paper is devoted to a study of the stability of the boundary layer on the leading edge of a thin airfoil in a flow of incompressible fluid. The case when the angle of attack of the airfoil relative to the oncoming flow differs little from the critical value is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 55–63, November–December, 1982.     

Effect of incidence angle with wake passing on a film cooled leading edge: A numerical study

This work presents the numerical study of a film‐cooled blade under the influence of wake passing at different incidence angles. The film cooling technology has been proven to be effective to increase the blade life of first turbine stages. However, the leading edge is affected by an high heat transfer rate and cooling this region is difficult. Moreover, separated regions downstream the coolant injection increases the local heat transfer coefficient and can have a detrimental effect in terms of airfoil life. This work analyses how the flow field is affected by the wake passing at different incidence angles (?5, 0, 5) and the impact on heat transfer coefficient. The test case is a linear cascade with two rows of cylindrical holes at the leading edge. Two different holes arrangements are compared in terms of film cooling structures, namely AGTB‐B1 and AGTB‐B2 with 0 and 45^° spanwise inclination. The numerical results show a good agreement with the experiments. A deeper investigation is carried out on AGTB‐B1. The results obtained show that the wake passing and the incidence angle have a strong effect on coolant jets. In particular, there is a significative impact on coolant redistribution near the leading edge. The wake passing has a stronger effect on pressure side, mainly at negative incidence. The predictive approach is based on an U‐RANS in‐house CFD solver using a conventional two‐equations closure. In order to avoid extra turbulence production, critical in the leading edge region, the turbulence model incorporates an extra algebraic equation that enforces a realizability constraint. The unsteady formulation is based on a dual time stepping approach with a sliding plane between the moving bars and the cascade. Copyright © 2009 John Wiley & Sons, Ltd.     

Mechanics of thermophoretic and thermally induced edge forces in carbon nanotube nanodevices

A double walled carbon nanotube thermal actuator consisting of a short outer tube sliding along a long inner tube under a temperature gradient is used as a model system to investigate the mechanics of thermophoretic and thermally induced edge forces in nanoscale contact based on the theory of lattice dynamics. It is shown that the total thermophoretic force has two components: a gradient force due to the change in van der Waals energy in the direction of temperature gradient and an unbalanced edge force due to the temperature difference between the two tube ends. Closed-form analytical expressions are derived for the gradient and unbalanced edge forces, with results in excellent agreement with molecular dynamics simulations. This study represents a first analytical study of thermophoretic and thermally induced edge forces between two solid bodies, and may have far reaching implications on thermomechanical nanodevices and nanoscale contact.