Photoelastic stress analysis of an elliptical hole in a thick plate subjected to uniform in-plane compressive Loading

A three-dimensional photoelastic analysis was conducted to determine the stress distribution and concentration around the periphery of a centrally located elliptical hole in a plate of finite thickness. The edge of the plate was subjected to a uniformly distributed compressive uniaxial in-plane load. The principle of superposition was employed to study the effect of uniform biaxial loading.Elliptical holes with five different major/minor axis ratios () ranging from 1.0 to 2.64 were investigated. Among the results of this study, it was established that the variation of the principal stresses at the edge of the hole is not linear across the plate thickness. It was also found that in loading the plate in a direction parallel to the major axis of the ellipse, the value of the maximum tangential principal stress () occurs in a plane other than the middle plane of the plate. However, in loading the plate in a direction either parallel or perpendicular to the major axis, the maximum transverse stress ( _z ) occurs at the middle plane. In addition, the maximum value of ( _z ) was about 20 percent of the maximum value of the tangential stress for all models tested. Furthermore, the effect of the bixial loading has reduced the value of the maximum tangential stress at the periphery of the hole as compared with uniaxial loading.As a three-dimensional theoretical solution does not exist for this problem, the present findings were correlated with the well established two-dimensional solutions.     

An extension of one of the extremum principles for a Bingham solid

Summary An extension of the extremum principle concerned with velocity fields for boundary value problems of an incompressible rigid visco-plastic (Bingham) solid is derived. This extension can be used to obtain close overestimates for the rate of work of the unknown surface tractions in certain problems of visco-plastic flow.Nomenclature k yield stress in pure shear - coefficient of viscosity - _ij stress tensor referred to rectangular cartesian axes Ox _i - s _ij stress deviator tensor - T _i surface traction - J (1/2s _ijs_ij ^1/2 - F _i body force per unit volume - v _i velocity vector - _ij = rate of deformation tensor - I (2 _ijij ^1/2 - [v] magnitude of a velocity discontinuity in flow of a rigid perfectly plastic solid - S surface - V volume - S _t part of surface upon which T _iis prescribed - S _v part of surface upon which v _iis prescribed - S _d surface of velocity discontinuity in flow of a rigid plastic solid - x, y, z rectangular cartesian coordinates - u, v, w velocity components in the x, y and z directions respectively - rate of twist per unit length - T torque     

A DEVELOPMENT OF BEM TO TWO DIMENSIONAL ELASTICITY

This paper presents a new boundary integral equatiòn for two-dimensional elasticity with the stress component σ_(ij)t_it_j as one of the boundary values,where t_i is the direction cosine of the tangent on the boundary.This form of BEM hasan advantage in that the stress component σ_(ij)t_it_j on the boundary can be calculateddirectly from the numerical solution.The present formulation for plane problems usestwo kernels,the one is logarithmically singular and the other is 1/r singular.Theeffectiveness of the approach is also discussed through test examples.     

Analytical approach to bonded repair of elliptical dent, corrosion grind-out, and cut-out

The problem of an isotropic sheet with an internal elliptical dent, corrosion grind-out, or cut-out repaired with an elliptical bonded patch is analyzed, following the similar two-stage analysis originally proposed by Rose [International Journal of Solid and Structures 17 (1981) 827; in: Bakers, Jones (Eds.), Bonded Repair of Aircraft Structures, Martinus Nijhoff, Dordrecht, 1988, p. 77] for a crack patching problem. For simplicity, the bending effect is ignored in the analysis. In the first stage, an infinite sheet reinforced by an elliptical patch under a prescribed far-field stress is analyzed using the inclusion analogy, without considering the dent, grind-out or cut-out. The constant stresses inside the patched area (σ_0ij) are then calculated and later used as the far-field boundary conditions for the second (stage II) problem. In the second stage, the patch is assumed to be infinite and an integral part of the sheet. Stage II analysis then involves solving a problem of an infinite patched sheet containing a circular dent, grind-out, or cut-out under far-field stresses σ_0ij. The latter problem is also solved using the inclusion analogy. Because the patch in a typical design is much larger than the damage area, the solutions of the first and second problems are approximately the same as the solutions of the original problem inside and outside the patched area, respectively.     

Residual stresses in thick electrodeposits of a nickel-cobalt alloy

Some electroplated metals contain residual stresses which can cause warpage or premature failure of parts plated or electrofomed with these materials. Noticeably absent from the literature are residual-stress data for finished parts. Typically for plated or electroformed parts, residual stresses are determined independently on thin strips and then piece parts are plated. This research describes a technique which can be used to measure stress on finished parts. The method involves drilling a hole in the part and measuring the resulting change of strain in the vicinity of the hole. Viability of this technique was demonstrated by measuring the stress in a nickel-cobalt deposit plated on an aluminum cylinder. Two separate runs, one 50 deg removed from the other, provided almost identical results; stress was 160 MN/m² (23,200 psi). Two other runs in a region where plating was somewhat thinner provided slightly lower results probably because all boundary-condition requirements were not met. The computed residual-stress values compared quite favorably with independent rigid-strip measurements of 131 MN/m² (19,000 psi) obtained for the solution before and after plating of the cylinder.     

A power-law fluid flow past a porous sphere

Summary A model has been developed for the flow of a non-Newtonian fluid past a porous sphere. The drag force exerted on a porous sphere moving in a power-law fluid is obtained by an approximate solution of equations of motion in the creeping flow regime. It is predicted that the effect of the pseudoplastic anomaly on the drag force is more pronounced at large porosity parameters.

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Zusammenfassung Es wird ein Modell für die Strömung einer nichtnewtonschen Flüssigkeit längs einer porösen Kugel entwickelt. Die auf die in einer Ostwald-DeWaele-Flüssigkeit bewegte Kugel ausgeübte Reibungskraft wird durch eine Näherungslösung der Bewegungsgleichungen für schleichende Strömung gewonnen. Man findet, daß der Einfluß der Abweichung vom newtonschen Verhalten um so ausgeprägter wird, je größer die Porosität ist.

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A, B, C, D a, b, c, d coefficients in eqs. [10] and [18] - F _D drag force - K consistency index in power-law model - k ₁ ,k ₂ coefficients defined by eq. [18] - m porosity parameter - n flow index in power-law model - P pressure - P ^* dimensionless pressure defined by eq. [4] - P pressure difference - R radius of porous sphere - r radial distance from the center of the sphere - U velocity of uniform stream - u _i velocity component - u _i ^* dimensionless velocity component defined by eq. [4] - Y drag force correction factor defined by eq. [27] - _ij rate of deformation tensor - _ij ^* dimensionless rate of deformation tensor defined by eq. [4] - , spherical coordinates - dimensionless radial distance defined by eq. [4] - second invariant of rate of deformation tensor - ^* dimensionless second invariant of rate of deformation tensor defined by eq. [4] - _ij stress tensor - _ij ^* dimensionless stress tensor defined by eq. [4] - stream function - ^* dimensionless stream function defined by eq. [4] - i inside the surface of the sphere - o outside the surface of the sphere With 1 figure and 1 table     

Small deformations superposed on a finite cylindrical deformation of a cord reinforced rubber belt

An equation of admissibility is drived for small deformations superposed upon a cylindrical bending of a block, made of a Mooney-type material. Series solutions are obtained, which can be expressed in generalized hypergeometric functions and functions derivable from them. Boundary conditions which correspond to the deformation of a cord-reinforced rubber belt around a rigid cylindrical pulley are treated in the last section.Nomenclature A _nh , B _nh , C _h arbitrary constants - B reference configuration - B ^ij deformation tensor components - C ₀ constitutive constant defined at equation (18) - f _n , g _n , h _n radial dependent functions in the solution (20–23) - _p F _q generalized hypergeometric functions - g ^ij metric tensor components associated with the undeformed configuration - G ^ij do. for the deformed configuration B. - G _i base vectors - n index defined by (23) - n _i normal vector - p pressure function - Q function defined by equation (14) - R ₀, R ₁, R ₂ inner, cord, resp. outer radii in B - s _h roots of the indicial equation - t _i stress vector - T cord tension per unit width - w _i displacement vector - x ² n ² r ²/16R ₁ ⁴ - _ij ^r Christoffel symbols - axial extension ratio - coefficient of friction between belt and pulley - radius of curvature - ^ij stress tensor components - 2C ₂, a constant of the Mooney strain energy function     

Initiation and growth of wrinkling due to nonuniform tension in sheet metal forming

An experimental investigation was conducted on the initiation and growth of wrinkling due to nonuniform tension using the Yoshida buckling test. The initiation of wrinkling was detected by strain gages mounted on both surfaces of the samples in the loading and transverse directions. The bifurcation of aluminum auto body sheets appeared to be smooth and much less abrupt than that observed in a steel sheet. A special fixture was designed to, perhaps for the first time, continuously measure the in situ growth of the buckle heights so that the rates of buckle growth were monitored as functions of strain and stress in the loading direction. In contrast to what is commonly believed, it was found that the buckle height is not predominantly determined by the material yield strength, and lower averager value does not increase the rate of buckle growth. Crystallographic texture components and pole figures of the test materials were also measured, and the relationship of plastic anisotropy with wrinkling behavior was investigated by experiments with specimens aligned in the rolling direction, the transverse direction and 45-deg to the rolling direction of the sheet materials.     

超临界CO2气爆非均质煤体破裂规律模拟研究

为揭示超临界CO2气爆含割理裂隙非均质煤体的致裂规律,开发了识别实际煤体图像获取其割理裂隙几何信息的M atlab程序,将几何信息与煤体非均质物性参数关联并导入Abaqus中,实现了非均质煤体有限元表征,并采用SPH与FEM联合求解的方法模拟超临界CO2气爆非均质煤体的致裂过程,得到了弱面倾角、弱面到爆孔中心距离及初应力的变化对煤体气爆致裂效果的影响规律.模拟结果表明,初应力对主裂缝的萌生和扩展具有导向作用,气爆裂缝沿最大初应力方向扩展;弱面倾角相同时,弱面离爆孔越近,穿过弱面的裂缝尺度和密度越大,弱面离爆孔较远时,弱面完全阻断了裂缝的扩展;弱面到爆孔中心距离相同时,弱面倾角越大,弱面对裂缝扩展的阻碍作用越大,穿过弱面的裂缝尺度和密度越小,应力波透射率越小.现场气爆增透煤体时,应考虑割理裂隙和地应力特征合理布置气爆孔位置及爆破参数.     

A multilayer-reflection technique for three-dimensional photoelastic studies of perforated plates in bending

A photoelastic investigation was conducted to determine the stress-concentration factors around a large, symmetrically reinforced central hole in a square plate under 1∶1 and 2∶1 biaxial bending. Tapered-edge rings served as the reinforcement, and a major objective was to determine the ring proportions such that the maximum stress at the hole would be equal to the value which would be present in an unperforated plate under the same nominal stress. Because the stress distribution at the periphery of a hole in such a plate structure varies in the radial, tangential and thickness direction, it was necessary to employ a three-dimensional photoelastic technique. There were a number of serious disadvantages in the use of any of the standard procedures and a new three-dimensional technique for room-temperature use was developed which is particularly suitable for the determination of boundary stresses around holes in bending experiments. With the technique in its present state of development, the three-dimensional isochromatic distribution in the plate can be determined from a single model and, from this, the boundary value of stress. The new technique utilized a laminated-plate model. Selective aluminizing of the laminations allowed for the determination of fringe-order distributions in the thickness direction as well as in the radial and circumferential directions at the boundary of the hole in flat models. Uniaxial maximum fringe orders were determined and, from these, the biaxial values were obtained by superposition.     

Anisotropy of the fracture toughness of structurally inhomogeneous ageing alloys

The dependence of the fracture toughness K _1C of rolled ageing alloys with structural and crystallographic textures on the loading direction is established. A formula describing the anisotropy of the K _1C and including structural parameters of structurally textured alloys on planes of growth of mode I cracks is derived and validated for aluminum alloys. The influence of crystallographic planes and crack growth direction on K _1C is analyzed for titanium alloy as a rolled material with crystallographic texture     

Thermoelastic Determination of Individual Stresses in Vicinity of a Near-Edge Hole Beneath a Concentrated Load

Thermoelastic data are combined with an Airy stress function to determine the individual stresses on and near the boundary of a circular hole which is located below a concentrated edge-load in a plate. Coefficients of the stress function are evaluated from the measured temperatures and the local traction-free conditions are satisfied by imposing s_rr = t_rq = 0 {\sigma_{r{\rm{r}}}} = {\tau_{r\theta }} = 0 analytically on the edge of the hole. The latter has the advantage of reducing the number of coefficients in the stress function series. The method simultaneously smoothes the measured input data, satisfies the local boundary conditions and evaluates individual stresses on, and in the neighbourhood of, the edge of the hole. Attention is paid to how many coefficients to retain in the stress function series. Although the presence of high stress concentration factors, together with a hole-diameter-to-plate-thickness ratio of only two, result in some three-dimensional effects, these are relatively small and the agreement between the thermoelastic values, those from recorded strains and FEM-predicted surface stresses is good.     

Characterizing texture in polycrystalline materials by ultrasonic waves

A method for characterizing texture from measurements of ultrasonic wave velocities is proposed. In polycrystalline aggregates, ultrasonic wave velocities are strongly affected by orientation distribution coefficients (ODCs), which are usually used to describe the degree of preferred grain orientation in textured materials. In this work, velocities of longitudinal and transverse waves propagating into aluminum alloy 6061 were measured under pure shear, simple shear and uniaxial tension. From the measured ultrasonic wave velocities, the ODCs W₄₀₀ and W₄₂₀ were calculated to infer the deformation-induced texture. The predicted pole figures, obtained using ultrasonic velocities, were in good qualitative agreement with the finite element polycrystal model analyzed pole figures.     

Reinforcement of perforated metal sheets by thermal shock with laser beams

A quantitative study was conducted on the improvement of load-bearing capacity and fatigue life of a thin aluminum sheet containing a small hole by means of thermal shock generated by a pulsed laser. A finite-element computer code based on the thermoelastic-plasticity theory was used to assess the distributions of temperature and residual stresses in the affected region. Analytical results were verified by the measured values from various techniques including the X-ray diffraction method for the residual-stress measurements. The improvement of fatigue life of the sheet metals resulting from this thermal shock process has been demonstrated by tests and correlates well with a postulated empirical model with the calculated induced residual stress.     

The application of the extremum principles for a Bingham solid

Summary An extension of the extremum principle concerned with statically admissible stress fields for boundary value problems of an incompressible rigid visco-plastic (Bingham) solid is derived. This extension is an inequality that gives a lower bound for the rate of work of the unknown surface tractions in certain visco-plastic boundary value problems. Lower bounds are obtained for the torque required to twist a prismatic visco-plastic bar of square crossection and these lower bounds are presented along with upper bounds obtained from an inequality that was derived in a previous paper¹).Nomenclature k yield stress in pure shear - coefficient of viscosity - _ij stress tensor referred to rectangular cartesian axes Ox _i - s _ij stress deviator tensor - T _i surface traction - J (1/2s _ij s _ij )^1/2 - v _i velocity vector - _ij = rate of deformation tensor - n _i outward unit normal to surface - I (2 _{ij ij} )^1/2 - [v] magnitude of a velocity discontinuity in flow of a rigid perfectly plastic solid - S surface - V volume - S _t part of surface upon which T _i is prescribed - S _v part of surface upon which v _i is prescribed - S _d surface of velocity discontinuity in flow of a rigid plastic solid - x, y, z rectangular cartesian coordinates - u, v, w velocity components in the x, y and z directions respectively - rate of twist per unit length - T torque     

On the higher order asymptotic analysis of a non-uniformly propagating dynamic crack along an arbitrary path

Transient mixed-mode elastodynamic crack growth along arbitrary smoothly varying paths is considered. Asymptotically, the crack tip stress field is square root singular with the angular variation of the singular term depending weakly on the instantaneous values of the crack tip speed and on the mode-I and mode-II stress intensity factors. However, for a material particle at a small distance away from the moving crack tip, the local stress field will depend not only on the instantaneous values of the crack tip speed and stress intensity factors, but also on the past history of these time dependent quantities. In addition, for cracks propagating along curved paths the stress field is also expected to depend on the nature of the curved crack path. Here, a representation of the crack tip fields in the form of an expansion about the crack tip is obtained in powers of radial distance from the tip. The higher order coefficients of this expansion are found to depend on the time derivative of crack tip speed, the time derivatives of the two stress intensity factors as well as on the instantaneous value of the local curvature of the crack path. It is also demonstrated that even if cracks follow a curved path dictated by the criterion K ₁₁ ^d =0, the stress field may still retain higher order asymmetric components related to non-zero local curvature of the crack path.     

Oblique stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation

An analysis is made of steady two-dimensional oblique stagnation-point flow and radiative heat transfer of an incompressible viscous fluid towards a shrinking sheet which is shrunk in its own plane with a velocity proportional to the distance from a fixed point. Here the axis of the stagnation flow and that of the shrinking sheet are not aligned. A similarity transformation reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations and are solved numerically using a shooting technique. The analysis of the results obtained shows that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity. The effect of non-alignment for the wall shear stress and the horizontal velocity components are discussed. Streamline patterns are also shown for shrinking at the sheet with aligned and non-aligned cases. It is found that the temperature at a point in the fluid decreases with increase in effective Prandtl number (Pr _eff ). The results pertaining to the present study indicate that as Pr _eff increases, the rate of heat transfer also increases. The reported results are in good agreement with the available published work in the literature.     

Tensorial strength analysis of paperboard

Tensorial-type failure criteria with linear and quadratic terms are used to calculate the strength of paperboard under plane stress. Theoretical predictions and experimental data are correlated in all four quadrants of biaxial normal stress with various levels of shear. Several methods are examined for determining the interaction coefficientF ₁₂. Comparisons are made with optimum values obtained from least-squares analyses. The best analytical-experimental agreement at all levels of shear is obtained approximately by using coefficientF ₁₂ equal to zero. The sensitivity ofF ₁₂ to errors in experimental input data is also studied. Reliable correlation with experiment, as well as operational simplicity, make these criteria attractive for predicting the strength of paperboard.     

A numerical study of turbulent flow over a two‐dimensional hill

Calculations of mean velocities and Reynolds stresses are reported for the recirculating flow established in the wake of two‐dimensional polynomial‐shaped obstacles that are symmetrical about a vertical axis and mounted in the water channel downstream of a fully developed channel flow for Re=6×10⁴. The study involves calculations of mean and fluctuating flow properties in the streamwise and spanwise directions and include comparisons with experimental data [Almeida GP, Durão DFG, Heitor MV. Wake flows behind two‐dimensional model hills. Experimental Thermal and Fluid Science 1993; 7: 87–101] for flow around a single obstacle with data resulting from the interaction of consecutive obstacles, using two versions of the low‐Reynolds number differential second‐moment (DSM) closure model. The results include analysis of the turbulent stresses in local flow co‐ordinates and reveal flow structure qualitatively similar to that found in other turbulent flows with a reattachment zone. It is found that the standard isotropization of production model (IPM), based on that proposed by Gibson and Launder [Ground effects on pressure fluctuations in the atmospheric boundary layer. Journal of Fluid Mechanics 1978; 86(3): 191–511], with the incorporation of the wall reflection model of Craft and Launder [New wall‐reflection model applied to the turbulent impinging jet. AIAA Journal 1992; 32(12): 2970–2972] predicts the mean velocities quite well, but underestimates the size of the recirculation region and turbulent quantities in the shear layer. These inadequacies are circumvented by adopting a new cubic Reynolds stress closure scheme based on that more recently developed by Craft and Launder [A Reynolds stress closure designed for complex geometries. International Journal of Heat and Fluid Flow 1996; 17: 245–254] which satisfies the two component limit (TCL) of turbulence. In this model the geometry‐specific quantities, such as the wall‐normal vector or wall distance, are replaced by invariant dimensionless gradient indicators. Also, the model captures the diverse behaviour of the different components of the stress dissipation, ε_ij, near the wall and uses a novel decomposition for the fluctuating pressure terms. Copyright © 2001 John Wiley & Sons, Ltd.     

Direct drag measurements in a turbulent flat-plate boundary layer with turbulence manipulators

The effect of turbulence manipulators on the turbulent boundary layer above a flat plate has been investigated. These turbulence manipulators are often referred to as Large Eddy Break Up (LEBU) devices. The basic idea is that thin blades or airfoils are inserted into the turbulent flow in order to reduce the fluctuating vertical velocity component v above the flat plate. In this way, the turbulent momentum transfer and with it the wall shear stress downstream of the manipulator should be decreased. In our experiments, for comparison, a merely drag-producing wire also was inserted into the boundary layer.In particular, the trade-off between the drag of the turbulence manipulator and the drag reduction due to the shear-stress reduction on the flat plate downstream of the manipulator has been considered. The measurements were carried out with very accurate force balances for both the manipulator drag and the shear stress on the flat plate. As it turns out, no net drag reduction is found for a fairly large set of configurations. A single thin blade as a manipulator performed best, i.e., it was closest to break-even. However, a further improvement is unlikely, because the device drag of the thin blade elements used here has already been reduced to only that due to laminar skin friction, and is thus the minimum possible drag. Airfoils performed slightly worse, because their device drag was higher. A purely drag-producing wire device performed disastrously. The wire device, which consisted of a wire with another thin wire wound around it to suppress coherent vortex shedding and vibration, was designed to have (and did have) the same drag as the airfoil manipulator with which it was compared. The comparison showed that airfoil and blade manipulators recovered 75–90% of their device drag through a shear-stress reduction downstream, whereas the wire device recovered only about 25–30% of its device drag.Conventional LEBU manipulators with airfoils or thin blades produce between 0.25% and 1% net drag increase, whereas the wire device (with equal device drag) produces as much as 4% net drag increase. These data are valid for the specific plate length of our experiments, which was long enough in downstream extent to realize the full effect of the LEBU manipulators. Turbulence manipulators do indeed decrease the turbulent momentum exchange in the boundary layer by rectifying the turbulent fluctuations. This generates a significant shear-stress reduction downstream, which is much more than just the effect of the wake of the manipulator. However, the device drag of the manipulator cannot be reduced without simultaneously reducing the skin friction reduction. Thus, the manipulator's device drag exceeds, or at best cancels, the drag reduction achieved by the shear-stress reduction downstream. A critical survey of previous investigations shows that the suggestion that turbulence manipulators may produce net drag reduction is also not supported by the available previous drag force measurements. The issue had been stirred up by less conclusive measurements based on local velocity data, i.e., data collected using the so-called momentum balance technique.List of symbols b lateral breadth of test plate - c chord length of turbulence manipulator - d diameter of wire manipulator - e distance of the elastic center from the leading edge of the manipulator airfoil - h height of manipulator above test plate - q dynamic pressure of the potential flow above the test plate - s spacing of turbulence manipulator elements - t thickness of turbulence manipulator elements - u,v,w fluctuating velocities in downstream, platenormal, and lateral directions - x distance from the leading edge of the test plate in the downstream direction - x ₀ location of the trailing edge of the first manipulator - z distance from test plate center in the lateral direction - C _D drag coefficient - C _L lift coefficient - D _m drag of manipulated plate including device drag and shear stress, calculated from manipulator location to downstream location - D ₀ drag of unmanipulated plate boundary layer, consisting of the shear stress calculated from manipulator location to downstream location - F drag force - F ₀ total skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream of manipulator, measured without turbulence manipulator - F _LEBU device drag force of the LEBU, i.e., the turbulence manipulator - F _m total drag force of manipulated plate, consisting of - F _LEBU and skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream - F _cf skin friction force as measured by the floating element balance, manipulated case - F _cfo skin friction force, as measured by the floating element balance, unmanipulated case - F _cf skin friction saving, defined as F _cf = F _cf – F _cfo - F _cf cumulative skin friction savings, i.e., the sum of the skin friction savings F _cf , added up from the location of the manipulator to the downstream location , as shown in Fig. 11. In Fig. 13 the cumulative skin friction savings are summarized up to their asymptotic value, reached at 200 - Re _c Reynolds number of the manipulator elements, calculated with the chord length c and the local velocity in the boundary layer - Re ₀ Reynolds number at the location x ₀ of the manipulator, calculated with the momentum thickness of the boundary layer and the mean flow velocity U - U mean flow velocity in the potential regime of the wind tunnel test section - angle of attack of the manipulator airfoils - ₀ boundary layer thickness at the location x ₀ of the manipulator - dimensionless distance from the manipulator in the downstream direction, defined as - density of the air - ₀ local skin friction shear stress, unmanipulated case - _{0 Average} skin friction shear stress, average value over the lateral span (b = 2 m) of the test plate, unmanipulated case - _m local skin friction shear stress, manipulated case - momentum thickness of the undisturbed turbulent boundary layer at the location x ₀ The authors would like to thank Prof. H. H. Fernholz for his scientific and administrative support. The hardware for the experiments was designed and built by C. Daase, W. Hage and R. Makris. Funding for the project was provided by the Deutsche Forschungsgemeinschaft and is gratefully acknowledged.