Drag reduction by an elastic rubber band?

The influence on the friction behaviour caused by a rubber band held fixed at one end of a circular tube containing a fully developed turbulent flow was investigated. The drag was slightly higher under these conditions with the drag approaching the Prandtl-Karman law at high Reynolds numbers. The results are in contrast to the behaviour of a polymer thread in heterogeneous drag reduction.     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Drag reduction by polymer solutions in a riblet-lined pipe

The flow of 3 to 100 wppm aqueous solutions of a polyethyleneoxide polymer,M _w=6.2×;10⁶, was studied in a 10.2 mm i.d. pipe lined with 0.15 mm V-groove riblets, at diametral Reynolds numbers from 300 to 150000. Measurements in the riblet pipe were accompanied by simultaneous measurements in a smooth pipe of the same diameter placed in tandem. The chosen conditions provided turbulent drag reductions from zero to the asymptotic maximum possible. The onset of polymer-induced drag reduction in the riblet pipe occurred at the same wall shear stress, * _w =0.65 N/m², as that in the smooth pipe. After onset, the polymer solutions in the riblet pipe initially exhibited linear segments on Prandtl-Karman coordinates, akin to those seen in the smooth pipe, with specific slope increment . The maximum drag reduction observed in the riblet pipe was independent of polymer concentration and well below the asymptotic maximum drag reduction observed in the smooth pipe. Polymer solution flows in the riblet pipe exhibited three regimes: (i) Hydraulically smooth, in which riblets induced no drag reduction, amid varying, and considerable, polymer-induced drag reduction; this regime extended to non-dimensional riblet heightsh ⁺<5 in solvent andh ⁺<10 in polymer solutions. (ii) Riblet drag reduction, in which riblet-induced flow enhancementR>0; this regime extended from 5<h ⁺<22 in solvent and from 10<h ⁺<30 in the 3 wppm polymer solution, with respective maximaR=0.6 ath ⁺=14 andR=1.6 ath ⁺=21. Riblet drag reduction decreased with increasing polymer concentration and increasing polymer-induced flow enhancement S. (iii) Riblet drag enhancement, whereinR<0; this regime extended for 22<h ⁺<110 in solvent, withR;–2 forh ⁺>70, and was observed in all polymer solutions at highh ⁺, the more so as polymer-induced drag reduction increased, withR<0 for allS>8. The greatest drag enhancement in polymer solutions,R=–7±1 ath ⁺=55 whereS=20, considerably exceeded that in solvent. Three-dimensional representations of riblet- and polymer-induced drag reductions versus turbulent flow parameters revealed a hitherto unknown dome region, 8<h ⁺<31, 0<S<10, 0<R<1.5, containing a broad maximum at (h ⁺,S,R) = (18, 5, 1.5). The existence of a dome was physically interpreted to suggest that riblets and polymers reduce drag by separate mechanisms.     

Secondary Instabilities of Wakes of a Circular Cylinder Using a Finite Element Method

This study investigates secondary instabilities of periodic wakes of a circular cylinder with infinitely long span. It has been known that after the wake undergoes a supercritical Hopf bifurcation (the primary instability) that leads to two-dimensional von Kantian vorlex street, the secondary instability occurs sequentially, which results in the onset of three-dimensional flow. Williamson (1996) has reviewed that the periodic wakes over a range of moderate Reynolds number from 140 to 300 are characterized by two critical modes. Mode A and Mode B, which are respectively associated with large-scale and fine-scale structures in span. In order to understand a sequence of bifurcation in transitional wake, in this paper, the stability of periodic Row governed by the linearized Navier-Stokes equations is analyzed by using the Floquet stability theory. By employing the finite elemental discretization with a fine mesh, the numerical results for both simulation and stability analysis have high spatio-resolution. The obtained stability results are in good agreement with experimental data and some relevant numerical results. By means of visualizations of the three-dimensionally critical flow structures. the existence of Mode A and Mode B is verified from the spatial structures in both the two modes.     

Detached-Eddy Simulations Past a Circular Cylinder

The flow is calculated with laminar separation (LS) at Reynolds numbers 50,000 and 140,000, and with turbulent separation (TS) at140,000 and 3 × 10₆. The TS cases are effectively tripped, but compared with untripped experiments at very high Reynolds numbers. The finest grid has about 18,000 points in each of 56 grid planes spanwise; the resolution is far removed from Direct Numerical Simulations, and the turbulence model controls the separation if turbulent. The agreement is quite good for drag, shedding frequency, pressure, and skin friction. However the comparison is obscured by large modulations of the vortex shedding and drag which are very similar to those seen in experiments but also, curiously, durably different between cases especially of the LS type. The longest simulations reach only about 50 shedding cycles. Disagreement with experimental Reynolds stresses reaches about 30%, and the length of the recirculation bubble is about double that measured. The discrepancies are discussed, as are the effects of grid refinement, Reynolds number, and a turbulence-model curvature correction. The finest grid does not give the very best agreement with experiment. The results add to the validation base of the Detached-Eddy Simulation (DES) technique for smooth-surface separation. Unsteady Reynolds-averaged simulations are much less accurate than DES for LS cases, but very close for TS cases. Cases with a more intricate relationship between transition and separation are left for future study. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytic Solution in the Problem of Constructing an Airfoil with Minimum Wave Drag

A solution of the problem of optimization of an airfoil in a supersonic flow is proposed. A symmetric airfoil with minimum wave drag for a given longitudinal cross-sectional area is constructed within the framework of a local analysis of variations of the shape with respect to the exact solution for a wedge and a rhombus. Analytic dependences representing the shape of the airfoil and its drag are found. The solution obtained is tested numerically within the framework of the Euler model.     

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.     

回转体表面条纹沟槽减阻水洞实验研究

本文在条纹沟槽表面减阻理论分析的基础上,对条纹沟槽表面回转体进行了大量的水洞实验研究。实验模型表面条纹沟槽采用直接加工方法,头部线型为双参数平方根圆头曲线,尾部线型为双参数尖尾曲线。实验结果分析表明,与相同形状、尺寸的光滑表面回转体相比,条纹沟槽表面回转体在一定速度范围内存在很好的减阻效果,最大减阻量超过6%,且在小攻角范围内减阻量基本稳定,对回转体升力特性也没有影响。对比不同尺寸条纹沟槽的减阻效果发现,降阻量不但随条纹沟槽宽度S变化,而且随来流速度U∞变化,即与无因次沟槽宽度S (文中近似取S =S.LRe2Ckx,其中k为总阻力Cx的修正因子)存在着一定的关系。对于V型条纹沟槽具有减阻效果的S 的范围在10到60之间。本文研究证明,条纹沟槽表面减阻技术在水下航行器设计领域有着很好的应用前景,同时文中所取得的研究成果对该技术的应用具有一定的促进作用。     

Drag reduction of a nonnewtonian fluid by fluid injection on a moving wall

Summary A boundary layer problem of a nonnewtonian fluid flow with fluid injection on a semi-infinite flat plate whose surface moves with a constant velocity in the opposite direction to that of the uniform mainstream is analyzed. Concluding similarity equations are solved numerically to show the dependence of the problem to the velocity ratio λ of the plate to uniform flow and to the injection velocity parameter C. The critical values of λ and C for each nonnewtonian power-law index n are obtained, and their significance in drag reduction is discussed. Received 26 August 1997; accepted for publication 21 October 1998     

The wake flow structure of an open-slit V gutter

This work experimentally investigates the near-wake flow structure behind an open-slit V gutter at airflow speeds between 1 m/s and 20 m/s. With the aid of Schlieren photography and a Dantec three-beam, two-component laser-Doppler anemometry system, the phenomena of vortex shedding and flow recirculation behind the flameholder are well investigated. The results indicate that the interaction between the flow penetrating through the open slit and the shear layer results in an asymmetric wake flow structure. The lower shear layer develops more stably and smoothly than the upper shear layer. Besides, the vortex formation along the lower wing is delayed and at a location farther downstream. The size of the entire recirculation zone is enlarged, and its center shifts toward one of the two wings. Measurements of wake pressure distribution show that the open-slit V gutter generates higher back pressure and thus induces less drag force than the regular V gutter. Moreover, the maximum values of the pressure fluctuation of the wake flow behind the open-slit V gutter reduce 27% and 9%, for the upper side and the lower side, respectively, much lower than those of the regular V gutter. In general, the application of mass bleed from the open-slit V gutter favors both the flame-holding mechanism and the suppression of the flow-induced oscillation.     

Drag of a sphere in dilute polymer solutions in high Reynolds number range

We have measured by means of four ultrasonic transducers the fall velocity of a sphere at high Reynolds number range in dilute polyacrylamide solutions which have viscoelastic effects. The polymer solutions were 5, 20 and 50ppm in the concentration. Basset-Bousinessq-Oseen equation for the falling sphere was analyzed numerically on Newtonian fluids in order to compare with the fall velocity of a sphere in the polymer solutions, and the experimental data of the fall velocity in tap water is in agreement with the range of no effect of the test tank wall. In polymer solutions, it was shown that the fall velocity is larger than that in Newtonian fluids within the critical Reynolds number range such that the drag reduction occurs and is smaller than that of Newtonian fluids over the range. The experimental data for the drag reduction ratio of polymer solutions is arranged by Weissenberg number calculating the experimental data of the first normal stress differences. It was shown that the maximum drag reduction ratio in the polymer solutions lies in the range of We=3∼10. Received: 15 October 1997 Accepted: 12 May 1998     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

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.     

横流冲击射流尾迹涡结构的实验研究

本文采用LIF（激光诱导荧光）流动显示和PIV（粒子图像速度场仪）测量对横流冲击射流的尾迹涡结构进行了实验研究。水槽实验是在三种流速比和两种冲击高度实验工况下进行的。由实验结果可得到两种明显的尾迹涡结构、，即射流尾迹涡和横流尾迹涡。横流冲击射流中形成的主要尾迹涡结构主要依赖于流速比。本文还对横流冲击射流近区范围内射流尾迹涡和横流尾迹涡的形成机理和演化特征进行了分析。     

Hilbert-Huang变换方法在Duffing方程和圆柱尾迹流分析中的应用

本文采用N．E Huang最近提出的Hilbert-Huang变换方法分析了使用三阶Runge-Kutta方法数值求解的Duffing方程的性质和圆柱绕流尾流特性,分解得到了有限阶经验模态（Empirical Modes）,给出了相应的Hilbert谱。结果表明,Hilbert-Huang变换得到的主要含能模态物理意义清晰,相应的瞬时频率存在着明显的波内频率调制,很好地刻画了信号的时空局部特性。     

Study of the Effect of the Depth of the Cavity of a Braking Device on the Aerodynamic Drag of a Model in Transonic and Supersonic Flow

The flowfield and the aerodynamic drag of a model consisting of a pair of bodies (leading body a cylinder and trailing body a hollow cylinder) connected by a cylindrical bar along the axis of symmetry is experimentally investigated at Mach numbers ranging from 0.6 to 1.7. In the course of the experiments, the trailing body cavity depth and the connecting bar length were varied.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 186–192.Original Russian Text Copyright © 2005 by Pilyugin and Khlebnikov.     

Minimization of the Wing Airfoil Drag Coefficient Using the Optimal Control Method

The problem of designing a wing airfoil starting from the surface velocity (or pressure) distribution, given in multi-parameter form, is considered. In the diffuser region, the velocity decrease law is determined from the conditions of minimum drag and separationless flow for a given Reynolds number. The case of boundary layer suction for the purpose of improving the aerodynamic characteristics of the airfoil is studied. A solution is obtained using optimal control theory.     

超声速钝体逆向喷流减阻的数值模拟研究

为研究逆向喷流技术对超声速钝体减阻的影响,采用标准k-ε湍流模型,通过求解二维Navier-Stokes方程对超声速球头体逆向冷喷流流场进行了数值模拟,并着重分析了喷口总压、喷口尺寸对流场模态和减阻效果的影响。计算结果显示:随着喷流总压的变化,流场可出现两种流动模态,即长射流穿透模态和短射流穿透模态;喷流能使球头体受到的阻力明显减小;存在最大减阻临界喷流总压值(在所研究参数范围内最大减阻可达51.1%);在其它喷流物理参数不变时,随着喷口尺寸的增大,同一流动模态下的减阻效果下降。本文的研究对超声速钝体减阻技术在工程上的应用具有一定的参考价值。     

To formulating a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil

A general formulation of a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil by an ideal incompressible fluid is considered. The problem is formulated for a complex velocity. Conditions of shedding of vortex wakes from the airfoil are analyzed in detail. The proposed system of functional relations allows constructing algorithms for solving a wide class of problems of the wing theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 48–56, March–April, 2007.     

Effusing core at the center of A potential vortex

Experiments were carried out to measure the base pressure distribution of a flow field induced by a potential vortex with its axis normal to a stationary disk. The center base pressure coefficient of the vortex, C₀(0), was found to be proportional to Reynolds number from Re = 2.0 × 10³ to Re > 2.5 × 10⁴, where Re is based on the disk radius and azimuthal velocity at the disk edge. This behavior of C₀(0) is at variance with the experimental results of Phillips (Phys. Fluids, 27, 2215, 1984) and Khoo (M. Eng. Thesis, Natl. Univ. Singapore, 1984), which showed vastly different trends depending on Re. Plausible reasons are suggested for the apparent discrepancies observed. Finally, the extent of the effusing core at the center, r₁ (taken to be the radial position where departure from the outer potential flow took place), was found to be proportional to Re^−1/2 for all Re values considered.