Criterial analysis of the effect of vibrations of an airfoil surface element on the transonic flow structure

A criterial analysis of the effect of forced vibrations of airfoil surface elements on the shock wave structure of a transonic flow around the airfoil is performed. The parameter responsible for regimes of interaction of vibrationally moving zones of the airfoil with the closing shock wave is determined. The influence of this parameter on the wave drag of the airfoil is studied.     

NUMERICAL STUDY OF BASE BLEED EFFECTS ON AERODYNAMIC DRAG FOR A TRANSONIC PROJECTILE

ABSTRACT

A numerical study is made to analyze the performance of a secant-ogive-cylinder projectile in the transonic regime in terms of aerodynamic drag. At transonic speeds, the base drag contributes a major portion of the total aerodynamic drag, and hence affects projectile's performances significantly. The base bleed method is applied to reduce the base drag by varying the value of parameters, the bleed quantity (I) and the bleed area ratio (?). The implicit, diagonalized, symmetric Total Variation Diminishing (TVD) scheme, accompanied by a suitable grid, is employed to solve the thin-layer axisymmetric Navier-Stokes equations coupled with the Baldwin-Lomax turbulence model. The computed results show that, in comparison with the case without base bleed, an increase in bleed quantity or a higher injection speed due to a smaller bleed area ratio at fixed bleed quantity can result in a base (and total) drag reduction. At Mach number 0.96, the reductions in base drag and total drag can be as high as 64% and 44%, respectively, for I = 0.1 and ? = 0.3.     

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the prac-ticability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disinte-grates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17%occurs with a triangular shape, while the max-imum increase in aerodynamic efficiency (lift-to-drag ratio) of around 10%happens with a rectangular shape at an angle of attack of 2.26?.     

翼面气动外形对栅格翼减阻的影响

从节约空间的角度考虑,带一定弧度的翼面有利于栅格翼在弹体上的安装.通过风洞实验研究了两种不同安装方式的弧形翼面栅格翼的气动特性,并和翼面无弧度的栅格翼进行比较.结果显示,弧形翼面的栅格翼阻力系数均小于翼面无弧度的栅格翼,升阻比除跨音速阶段外比后者表现更好,同时对一种前缘后掠的栅格翼模型进行了数值计算,比较研究结果显示,对栅格翼的迎风面栅格进行一定角度的后掠能有效减小超音速阶段的波阻,是一种栅格翼减阻设计的新思路.     

Effect of flow regime change from subsonic to transonic on the air loads of an oscillating airfoil

In this research, the effect of flow regime change from subsonic to transonic on the air loads of a pitching NACA0012 airfoil is investigated. To do this, the effect of change in flow regime on the lift and pitching moment coefficients hysteresis cycles is studied. The harmonic balance approach is utilized for numerical calculation due to its low computational time. Verifications are also made with previous works and good agreements are observed. The assessment of flow regime change on the aforementioned hysteresis cycles is accomplished in the Mach number range of M=0.65–0.755. The reduced frequency and pitch amplitude also vary from k=0.03 to 0.1 and α₀=1–2.51°, respectively. Results show that the effect of increase in Mach number is to increase and decrease the lift coefficient during downstroke and upstroke, respectively, whereas at low reduced frequencies, the effect of increase in Mach number may lead to a reverse manner when airfoil moves toward its extremum angle of attack. Results also reveal that as the pitch amplitude varies, the shape of lift coefficient hysteresis cycle depends more on the pitch amplitude than on the appearance of shock. It is shown that as the Mach number increases, the incidence angles correspond to the extremum pitching moment, and depending on the reduced frequency, lie between zero and extremum angle of attack. These incidence angles shift toward the extremum angle of attack as the reduced frequency decreases. Results also show that the increase in pitch amplitude at low Mach number, in such a way that leads to the formation of shock around the extremum angle of attack, causes the extremum pitching moment to appear around these angles and at high Mach number, depending on the reduced frequency, the extremum pitching moment incidence angles would be between zero and extremum incidence angle.     

A NUMERICAL STUDY OF OPTIMAL DRAG REDUCTION FOR TURBULENT TRANSONIC PROJECTILES USING A PASSIVE CONTROL

Abstract

The purpose of this research is to numerically study a drag reduction method—passive control of shock/boundary layer interaction, which is applied to the boattail portion of a secant-ogive-cylinder-boattail projectile in turbulent transonic flows. The flow pattern and the components of aerodynamic drag computed from numerical data are analyzed. The effectiveness of this method is studied by varying the values of parameters such as porosity distribution, maximum porosity factor and size of porous region. The conditions for optimal drag reduction are investigated and reported. The present results show that the use of this passive control method can not only reduce the boattail drag but also the base drag, and results in an additional 8% total drag reduction compared to that without the passive control technique. This passive control method can be an effective approach for the design of high-performance projectiles in the transonic regime.     

On solitary waves. Part 2 A unified perturbation theory for higher-order waves

A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on (i) the accuracy of the theoretically predicted wave properties and (ii) the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property (e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy), on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ(n) (the relative mean-square difference between successive orders n of wave elevations) reaching a minimum, δ _m , at a specific order, n=n _m , both depending on the base adopted, e.g. n _{m , α} =11-12 based on parameter α (wave amplitude), n _{m , β} =15 on β (amplitude-speed square ratio), and n _{m , ∈} =17 on ∈ ( wave number squared). The asymptotic range is brought to completion by the highest order of n=18 reached in this work.     

Controlling Transonic Flow around Airfoils by Means of Local Pulsed Addition of Energy

The influence of local pulsed-periodic addition of energy into a supersonic region on the flow structure and wave drag of an airfoil in transonic flow regimes is considered by methods of mathematical modeling. The study reveals significant prospects of the considered method of controlling airfoil performance in transonic flow regimes, including wave-drag reduction.     

Performance Improvement of a Supercritical Airfoil by a Multi-point Optimized Shock Control Channel

A shock control channel (SCC) is a flow control method introduced here to control the shock wave/boundarylayer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. An SCC transfers an appropriate amount of mass and momentum from downstream of the shock wave location to its upstream to decrease the pressure gradient across the shock wave and as a result the shock-wave strength is reduced. Here, a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of the SCC. This flow control method is implemented on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow equations are solved using Roe’s averages scheme and a gradient-based adjoint algorithm is used to find the optimum location and shape of the SCC. The solver is validated against experimental works studying effect of cavities in transonic airfoils. It is shown that the application of an SCC improves the average aerodynamic efficiency in a range of off-design conditions by 13.2% in comparison with the original airfoil. The SCC is shown to be an effective tool also for higher angle of attack at transonic flows. We have also studied the SWBLI and how the optimization algorithm makes the flow wave structure and interactions of the shock wave with the boundary layer favorable.     

Nonlinear effects caused by pulsed periodic supply of energy in the vicinity of a symmetric airfoil in a transonic flow

Changes in the structure of a transonic flow around a symmetric airfoil and a decrease in the wave drag of the latter, depending on the energy-supply period and on localization and shape of the energy-supply zone, are considered by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. Energy addition to the gas ahead of the closing shock wave in an immediate vicinity of the contour in zones extended along the contour is found to significantly reduce the wave drag of the airfoil. The nature of this decrease in drag is clarified. The existence of a limiting frequency of energy supply is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 64–71, May–June, 2006.     

Effect of Localization of Pulsed Energy Addition on the Wave Drag of an Airfoil in a Transonic Flow

The possibility of controlling the aerodynamic characteristics of airfoils with the help of local pulsed-periodic energy addition into the flow near the airfoil contour at transonic flight regimes is considered. By means of the numerical solution of two-dimensional unsteady equations of gas dynamics, changes in the flow structure and wave drag of a symmetric airfoil due to changes in localization and shape of energy-addition zones are examined. It is shown that the considered method of controlling airfoil characteristics in transonic flow regimes is rather promising. For a zero angle of attack, the greatest decrease in wave drag is obtained with energy addition at the trailing edge of the airfoil.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 60–67, September–October, 2005.     

Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle

In this paper, we study the transonic shock problem for the full compressible Euler system in a general two-dimensional de Laval nozzle as proposed in Courant and Friedrichs (Supersonic flow and shock waves, Interscience, New York, 1948): given the appropriately large exit pressure p _e(x), if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle, a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes p _e(x). We solve this problem completely for a general class of de Laval nozzles whose divergent parts are small and arbitrary perturbations of divergent angular domains for the full steady compressible Euler system. The problem can be reduced to solve a nonlinear free boundary value problem for a mixed hyperbolic–elliptic system. One of the key ingredients in the analysis is to solve a nonlinear free boundary value problem in a weighted Hölder space with low regularities for a second order quasilinear elliptic equation with a free parameter (the position of the shock curve at one wall of the nozzle) and non-local terms involving the trace on the shock of the first order derivatives of the unknown function.     

Interaction of a shock with a sphere suspended in a vertical shock tube

Shock wave interaction with a sphere is one of the benchmark tests in shock dynamics. However, unlike wind tunnel experiments, unsteady drag force on a sphere installed in a shock tube have not been measured quantitatively. This paper presents an experimental and numerical study of the unsteady drag force acting on a 80 mm diameter sphere which was vertically suspended in a 300 mm x 300 mm vertical shock tube and loaded with a planar shock wave of M _s = 1.22 in air. The drag force history on the sphere was measured by an accelerometer installed in it. Accelerometer output signals were subjected to deconvolution data processing, producing a drag history comparable to that obtained by solving numerically the Navier-Stokes equations. A good agreement was obtained between the measured and computed drag force histories. In order to interpret the interaction of shock wave over the sphere, high speed video recordings and double exposure holographic interferometric observations were also conducted. It was found that the maximum drag force appeared not at the time instant when the shock arrived at the equator of the sphere, but at some earlier time before the transition of the reflected shock wave from regular to Mach reflection took place. A negative value of the drag force was observed, even though for a very short duration of time, when the Mach stem of the transmitted shock wave relfected and focused at the rear stagnation point of the sphere.Received: 31 March 2003, Accepted: 7 July 2003, Published online: 2 September 2003     

Resonant phenomena in a transonic flow around an airfoil with pulsed periodic energy supply

Interaction of a pulsed periodic source of energy with a closing shock wave arising near airfoils in transonic flight is studied. The evolution of the shock-wave structure of the flow around a symmetric airfoil is examined by solving two-dimensional unsteady gas-dynamic equations, and a resonant mechanism of interaction is found, which leads to considerable (by an order of magnitude) reduction of the wave drag of the airfoil.     

Probabilistic design and quality control in probabilistic strength of materials

A numerical simulation method is used here for the design and quality control of a material subject to normal gradual stress σ or a cyclic stress σ, having fixed cumulative probability F and the number of cycles l; capable of achieving a given mechanical property such as yield point, elastic limit stress, fracture strength, etc., as well as the admissible tolerance δF the presence of such property is to be accepted with. With F and δF, the stress of the design σ_C can be determined, as well as the variations δm, δσ₀ and δσ_L of Weibull’s parameters m, σ₀ and σ_L, respectively, that the tolerance δF admits. When cyclic stresses arise, other parameters must be introduced, k₁, k₂ and p, which produce variations δk₁, δk₂, and δp, respectively. The determination of the necessary number of samples to be tested in order to carry out the quality control of the material, with a given probability of effectiveness, is obtained with variations δm, δσ₀, δσ_L, δk₁, δk₂ and δp, with the parameter dispersion estimated by numerical simulation, and with the help of a property deduced from the Fischer’s matrix to obtain the parameter dispersion.     

Experimental study of extreme thrust on a tidal stream rotor due to turbulent flow and with opposing waves

Time-varying thrust has been measured on a rotor in shallow turbulent flow at laboratory scale. The onset flow has a turbulence intensity of 12% at mid depth and a longitudinal turbulence length scale of half the depth, about 5 times the vertical scale, typical of shallow flows. The rotor is designed to have thrust and power coefficient variations with tip speed ratio close to that of a full-scale turbine. Three extreme probability distributions give similar thrust exceedance values with the Type 1 Pareto in mid range which gives 1:100, 1:1000 and 1:10 000 exceedance thrust forces of 1.38, 1.5 and 1.59 times the mean value. With opposing waves superimposed the extreme thrust distribution has a very similar distribution to the turbulent flow only. Exceedance forces are predicted by superposition of a drag force with drag coefficient of 2.0 based on the wave particle velocity only and with an unchanged mean thrust coefficient of 0.89. These values are relevant for the design of support structures for marine turbines.     

基于PCE方法的翼型不确定性分析及稳健设计

由于能够获得一个既经济又对参数变化不敏感的设计结果,稳健型设计在工程设计中备受关注. 不确定性分析是稳健型设计的关键. 因此研究了基于混沌多项式的不确定性分析方法,并将其与CFD 方法结合,对计算空气动力学设计中的不确定性影响进行了量化分析. 首先以RAE2822 翼型为算例,对其跨音速马赫数不确定影响进行了分析,研究了多项式阶次对计算的影响,分析了平均流场和方差. 接着结合超临界翼型的马赫数稳健型设计验证了混沌多项式方法在稳健型设计中的有效性. 优化结果表明,稳健型优化后的翼型阻力系数明显降低,同时对于马赫数的敏感性显著减小. 通过分析表明混沌多项式方法能够大幅提高稳健型优化设计效率,能很好地应用于气动稳定性设计.      

Experimental study of single bubble motion in a liquid metal column exposed to a DC magnetic field

The motion of single Argon bubbles rising in the eutectic alloy GaInSn under the influence of a DC longitudinal magnetic field (parallel to the direction of bubble motion) was examined. The magnetic field strength was varied up to 0.3 T corresponding to a magnetic interaction parameter N (which measures the ratio of electromagnetic forces to inertial forces) slightly greater than 1. The liquid metal was at rest in a cylindrical container. Bubble and liquid velocities were measured using ultrasound Doppler velocimetry (UDV). The measured bubble terminal velocity showed oscillations indicating a zigzag movement of ellipsoidal bubbles. For small bubbles (d_e ⩽ 4.6 mm) an increase of the drag coefficient with increasing magnetic interaction parameter N was observed, whereas for larger bubbles (d_e ⩾ 5.4 mm) the application of the magnetic field reduces the drag coefficient. The measurements revealed a distinct electromagnetic damping of the bubble induced liquid velocity leading to more rectilinear bubble trajectories when the magnetic field is applied. Moreover, significant modifications of the bubble wake structure were observed. Raising of the magnetic field strength caused an enlargement of the eddies in the wake. The Strouhal number decreases with increasing magnetic interaction parameter N.     

Evaluation of some high‐order shock capturing schemes for direct numerical simulation of unsteady two‐dimensional free flows

The present study addresses the capability of a large set of shock‐capturing schemes to recover the basic interactions between acoustic, vorticity and entropy in a direct numerical simulation (DNS) framework. The basic dispersive and dissipative errors are first evaluated by considering the advection of a Taylor vortex in a uniform flow. Two transonic cases are also considered. The first one consists of the interaction between a temperature spot and a weak shock. This test emphasizes the capability of the schemes to recover the production of vorticity through the baroclinic process. The second one consists of the interaction of a Taylor vortex with a weak shock, corresponding to the framework of the linear theory of Ribner. The main process in play here is the production of an acoustic wave. The results obtained by using essentially non‐oscillatory (ENO), total variation diminishing (TVD), compact‐TVD and MUSCL schemes are compared with those obtained by means of a sixth‐order accurate Hermitian scheme, considered as reference. The results are as follows; the ENO schemes agree pretty well with the reference scheme. The second‐order accurate Upwind‐TVD scheme exhibits a strong numerical diffusion, while the MUSCL scheme behavior is very sensitive to the value on the parameter β in the limiter function minmod. The compact‐TVD schemes do not yield improvement over the standard TVD schemes. Copyright © 2000 John Wiley & Sons, Ltd.