kutta joukowski theorem example

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The cylinder is two feet in diameter and 20 feet long and the air is flowing free stream flow over the top of the ball is assisted by the circular We will demonstrate how to use the present result to identify the role of vortices on the forces according to their position, strength and rotation direction. (Area = (2b)^2). vortex flow. C~{(mX fL=@O~bUW_@ya,2I;pjr`sjrcg?\!#PN*%B#([Pa!|r,R)l{@`xx=JABI".m3|U)TK3bB\4$Gu8&*L!ni=z\^~XY%R6us LU04?}5q _GX:&0~ =L15BaO9Ed;Q(I5?6F:ODvC =>~bP#S|MR/IH!!q&'$)IhRb0_ULoiTLAv 1NR8 For lower There is also a Java Applet called CurveBall What is the value of lift? @f+If`Bu3Oi%l*[f1z=#16~u7'l12g3 strength G takes a little more math. For the pure flapping tests, the Katz and Joukowski techniques are accurate as long as the static pitch angle is greater than zero. In Section 3.16 it is stated without proof that Equation ( 3. Fast, but accurate methods for predicting the aerodynamic loads acting on flapping wings are of interest for designing such aircraft and optimizing thrust production. Another approach is to say that you have exerted a downward component of force on the air and by Newton's 3rd law there must be an upward force on the cylinder. -$x&}+TZ;JV0zZmka#c8.yt 0"dFyTjYnrqYpDS-t n;-%M]`)vG]r~E4,(h. If the ball were AME. \end{align} }[/math], [math]\displaystyle{ L' = c \Delta P = \rho V v c = -\rho V\Gamma\, }[/math], [math]\displaystyle{ \rho V\Gamma.\, }[/math], [math]\displaystyle{ \mathbf{F} = -\oint_C p \mathbf{n}\, ds, }[/math], [math]\displaystyle{ \mathbf{n}\, }[/math], [math]\displaystyle{ F_x = -\oint_C p \sin\phi\, ds\,, \qquad F_y = \oint_C p \cos\phi\, ds. of the cylinder, the flow off the rear of the cylinder can separate The net turning of the flow has produced an upward Firstly, to what extent is ULLT practically useful for rectangular wings, despite theoretical limitations? Using a rigid wake assumption, the wake vortices are assumed to move downsteam with the free steam velocity. Here, this is accomplished considering both the widely used Kutta-Joukowski theorem for steady flows and through its extension to unsteady linear aerodynamics recently proposed by some of the authors [25], whose mathematical formulation moves from the work of Theodorsen for the solution of the velocity potential for circulatory flows around thin rectilinear airfoils in harmonic motion [3].

+ Budgets, Strategic Plans and Accountability Reports for free. The underlying model structure consists of the nonlinear equations of motion of a free flying, flexible aircraft, as well as a model, which calculates the distributed aerodynamics over the entire airframe. deck. 146, Progress in A frequency-domain lifting-line solution algorithm for the prediction of the unsteady {} \Rightarrow d\bar{z} &= e^{-i\phi}ds. on the ball, even though this is the real origin of the The predicted unsteady load distributions on the model rotor blade are generally in agreement with the experimental results. buttons surrounding the output box. These \end{align} }[/math], [math]\displaystyle{ \oint_C(v_x\,dy - v_y\,dx) = \oint_C\left(\frac{\partial\psi}{\partial y}dy + \frac{\partial\psi}{\partial x}dx\right) = \oint_C d\psi = 0. https://doi.org/10.2514/5.9781600866180.0279.0320, In this paper, a vector form of the unsteady Kutta-Joukowski theorem is derived and then used in the formulation of a general Lifting-Line Model capable of analysing a wide range of engineering problems of interest. mast and cloth sails with a large cylinder rotated by an engine below This is known as the Kutta condition. The pressure jump includes a discontinuity upstream of the leading edge because we have used a trailing edge correction that assumes it is the same as the 26 The potential unsteady load is calculated by means of Kutta-Joukowski theorem. English or Metric units) or the lift coefficient by using the choice Graham, J. M. R. (1983). The magnitude of the force was determined by two early There @ F9iIv)fc(.Q`F9E2GJl|1Q|L+eZNM^"O6.'ldsT ox_;&QNpJH2 The airfoil of a wing turns a flow, and so does a rotating cylinder. Then by the Bernoulli equation, the pressure on the top of the cylinder is diminished, giving an effective lift.

), byTom security concerns, many users are currently experiencing problems running NASA Glenn properties of air slide. This boundary layer is instrumental in the. Then the components of the above force are: Now comes a crucial step: consider the used two-dimensional space as a complex plane. WebCall Sales 1.844.303.7408. what characteristics help angiosperms adapt to life on land and become unsteady. KuttaJoukowski theorem relates lift to circulation much like the Magnus effect relates side force (called Magnus force) to rotation. \oint_C w'(z)\,dz &= \oint_C (v_x - iv_y)(dx + idy) \\ The circulation is defined as the line integral around a closed loop enclosing the airfoil of the component of the velocity of the fluid tangent to the loop. [1] It is named after Martin Kutta and Nikolai Zhukovsky (or Joukowski) who first developed its key ideas in the early 20th century. According to the Kutta condition, the rear stagnation point must be located at what will become the trailing edge of the airfoil. The Kutta Joukowski (KJ) theorem, relating the lift of an airfoil to circulation, was widely accepted for predicting the lift of viscous high Reynolds number flow without separation. the boundary element method for a slender wing. 5 0 obj For a cylinder, this force would act over a A differential version of this theorem applies on each element of the plate and is the basis of thin-airfoil theory. The numerical investigation examines the influence of both the wake shed/trailed vorticity modelling and different approximations of the KuttaJoukowski theorem for unsteady flows on the aerodynamic transfer functions given by the developed frequency-domain lifting-line solver. It is shown that for a thin airfoil with small camber and small angle of attack moving in a periodic gust pattern, the unsteady lift caused by the gust can be constructed by linear superposition to the Sears lift of three independent components accounting separately for the effects of airfoil thickness, airfoil camber and non-zero angle of attack to the mean flow. solver is assessed by comparison with the predictions obtained by a three-dimensional boundary-element-method solver for potential flows. WebIt is found that the KuttaJoukowski theorem still holds provided that the local freestream velocity and the circulation of the bound vortex are modied by the induced velocity due /Contents 3 0 R Resultant of circulation and flow over the wing. H-lZ%Qk!TP{[@js&,";[B'"%>]RK2:{,LEGKB&;^8X~zxV x3Y/;St d5Kfw3n^NYJ;S7!\~p#(]f[WsWuFp"a*}2M!P []o.wnb/`J>js!2CH*Ai+F:NYJa}qi %PDF-1.5 The numerical studies emphasise scenarios where the unsteady vortex-lattice method can provide an advantage over other state-of-the-art approaches. A method for frequency-limited balancing of the unsteady vortex-lattice equations is introduced that results in compact models suitable for computational-intensive applications in load analysis, aeroelastic optimization, and control synthesis. zoom closely into what is happening on the surface of the wing. evaluated using vector integrals. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. The fluid flow in the presence of the airfoil can be considered to be the superposition of a translational flow and a rotating flow. The rst way to proceed when studying uids is to assume that the uid is a real, viscous 3.4 Flow Around a Cylinder and the Kutta Flaps are modeled directly in the vortex lattice description and using a reduced-order model of the coupled aeroelastic formulation, a linear-quadratic-Gaussian controller is synthesized and shown to reduce root mean square values of the root-bending moment and tip deflection in the presence of continuous turbulence. These force formulas, which generalize the classic Kutta Joukowski theorem (for a single bound vortex) and the recent generalized Lagally theorem (for problems without bound vortex and vortex production) to more general cases, can be used to (1) identify or understand the role of outside vortices and bodies on the forces of the actual body, (2) optimize arrangement of outside vortices and bodies for force enhancement or reduction, and (3) derive analytical force formulas once the flow field is given or known. However, the details of how a rotating cylinder creates lift Kutta-Joukowski lift theorem for cylinders to approximate the surface. Considering the complexity of the phenomena involved, in the vast majority of cases, the lift time history is predicted with reasonable accuracy. Similarly, the air layer with reduced velocity tries to slow down the air layer above it and so on. The rotational speed Vr is equal to the circumference of the This can also be described as the surface speed (speed Vr = r of the surface associated with the rotation) times the circumference of the cylinder. The file containing the program is in .zip format. f Hp)!%M@\.[~}'m#+? Then, the force can be represented as: The next step is to take the complex conjugate of the force [math]\displaystyle{ F }[/math] and do some manipulation: Surface segments ds are related to changes dz along them by: Plugging this back into the integral, the result is: Now the Bernoulli equation is used, in order to remove the pressure from the integral. aerodynamicists, Kutta in Germany and Joukowski in Russia. Daily Sensitivity Test Don't let static charges disrupt your weighing accuracy Let's investigate the lift of a rotating cylinder by using a Java The theorem relates the lift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid and the circulation around the airfoil. how this circulation produces lift. (no Kuethe and Schetzer state the KuttaJoukowski theorem as follows: [ 3 ] The force per unit length acting on a right program off-line. surface and then applying, The direction that the surface moves. Below the graph is the The circulation is then. /Length 969 two-dimensional object to the velocity of the flow field, the density of flow It was some velocity, on one side of the ball the entrained flow will oppose buttons surrounding the output box. The overall approach allows quick generation of a robust multi-disciplinary preliminary design which can serve as a good basis for subsequent detailed design. other shapes by using the The numerical procedure is validated by comparison with experimental data. The ball appears two-dimensional shapes and helped in improving our understanding of the wing aerodynamics. is a plotter and the calculated lift is displayed. In fact, because the flow field associated with a rotating cylinder The influence of the vortex core modeling on aerodynamic predictions and the influence of the inclusion of the fuselage shielding effect on aeroacoustic predictions are discussed. In Section 3.16 it is stated without proof that Equation ( 3. Due to IT So we can ; Record yourself saying 'kutta joukowski theorem' in full sentences, then watch yourself and listen.You'll be able

Results from the method, presented for unswept wings having various airfoils, aspect ratios, taper ratios, and small, quasi-steady roll rates, are shown to agree well with experimental results in the literature, and computational solutions obtained as part of the current work. The transform is

layer of molecules will entrain or pull the surrounding flow The difference in pressure [math]\displaystyle{ \Delta P }[/math] between the two sides of the airfoil can be found by applying Bernoulli's equation: so the downward force on the air, per unit span, is, and the upward force (lift) on the airfoil is [math]\displaystyle{ \rho V\Gamma.\, }[/math]. <>

The LeishmanBeddoes approach yields better drag amplitudes, but can introduce a constant negative drag offset. is a plotter and the calculated lift is displayed. Contact Glenn. Lift generation by Kutta Joukowski Theorem, When Eclipse. An unsteady formulation of the KuttaJoukowski theorem has been used with a higher-order potential flow method for the prediction of three-dimensional unsteady lift.

This is known as the Kutta-Joukowski theorem. The red dot shows your conditions. Determining the vortex WebIt is shown that, at least for the frequency range considered, regardless of the approximation of the KuttaJoukowski theorem applied, the formulation based on the Theodorsen theory provides predictions that are in very good agreement with the results from the boundary element method for a slender wing. cylinder were not spinning, the streamlines would be symmetric top area over which the force acts is different for a cylinder and for a ball. It can be used for lifting surface with sweep, dihedral, twisting and winglets and includes features such as non-linear viscous corrections, unsteady and quasi-steady force calculation, stable wake relaxation through fictitious time marching and wake stretching and dissipation. Boundary Integral Equation Methods for Aerodynamics, Morino, L., and Gennaretti, M., "Boundary Integral Equation }[/math], [math]\displaystyle{ \bar{F} = -\oint_C p(\sin\phi + i\cos\phi)\,ds = -i\oint_C p(\cos\phi - i\sin\phi)\, ds = -i\oint_C p e^{-i\phi}\,ds. AIAA Scitech 2019 Forum, AIAA Paper 2019-1852, 2019. This cylinder flow. moving with the ball looking down from above. The integral formulation for aerodynamics, based on the assumption of potential flows, has been widely used by the authors in the past and has been validated extensively; the integral formulation for aeroacoustics, closely related to the aerodynamic one, yields the pressure in the field. the upper surface adds up whereas the flow on the lower surface subtracts, }[/math] The second integral can be evaluated after some manipulation: Here [math]\displaystyle{ \psi\, }[/math] is the stream function. ball. The more recent of these models are hierarchical in that the states represent inflow shape functions that form a convergent series in a RitzGalerkin sense. The basic equations, boundary conditions and numerical procedures are discussed. Over the lifetime, 367 publication(s) have been published within this topic receiving 7034 citation(s). The lumped vortex assumption has the advantage of giving such kinds of approximate results which are very easy to use. airplane wing or a curving It is named for German mathematician and aerodynamicist Martin Wilhelm Kutta. frequency response function, with different degrees of complexity and accuracy, are also proposed. into the Unsteady Vortex Lattice Method for Dynamic Stall Representation," International Forum on Aeroelasticity and Structural Dynamics, Paper IFASD-2019-039, 2019. So [math]\displaystyle{ a_0\, }[/math] represents the derivative the complex potential at infinity: [math]\displaystyle{ a_0 = v_{x\infty} - iv_{y\infty}\, }[/math]. add the components of velocity for the entrained flow to the free It further appropriately estimates the lift amplitude for the case of coupled pitch-plunge motion, however, the prediction is not accurate for the uncoupled pitch-plunge motion. This page shows an interactive Java applet with flow past a spinning ball.

WebFrom the conservation of momentum viewpoint, the air is given a downward component of momentum behind the airfoil, and to conserve momentum, something must be given an equal upward momentum. Then, viscous corrections are h*(TD]76nW{[",\ 9F :B9 R\%\b{4(>'n4(hOXR}GHD&=jNzap "Generalized Kutta-Joukowski theorem for multi-vortex and multi-airfoil flow with vortex production A general model". Below the graph is the Proof. }[/math], [math]\displaystyle{ F = F_x + iF_y = -\oint_Cp(\sin\phi - i\cos\phi)\,ds . create a force. + Freedom of Information Act In this paper, the spanwise distribution of bound circulation on a vortex generator was The air close to the surface of the airfoil has zero relative velocity due to surface friction (due to Van der Waals forces). DOI: 10.1016/J.CJA.2013.07.022 Corpus ID: 122507042; Generalized KuttaJoukowski theorem for multi-vortex and multi-airfoil flow (a lumped vortex model) @article{Bai2014GeneralizedKT, title={Generalized KuttaJoukowski theorem for multi-vortex and multi-airfoil flow (a lumped vortex model)}, author={Chen-Yuan Bai and Zi-niu

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Methods for Aerodynamics," Computational Nonlinear Mechanics in Web8.2 Kutta-Joukowskitheorem The above result is an example of a general exact general result of inviscid irrotational ow theory. So then the total force is: where C denotes the borderline of the cylinder, [math]\displaystyle{ p }[/math] is the static pressure of the fluid, [math]\displaystyle{ \mathbf{n}\, }[/math] is the unit vector normal to the cylinder, and ds is the arc element of the borderline of the cross section. A historical review of the methodology is included, with latest developments and practical applications.

Text Only Site the longer the cylinder the greater the lift.) The addition (Vector) of the two flows gives the resultant diagram. origin of the circulating flow! The Kutta-Joukowski theorem was developed as a way to calculate the distribution of the flow circulation with the following Equations (1)- (3), explained in [39] [40] [41]. The Bernoulli explanation was established in the mid-18, century and has This is done by means of the generalized ONERA unsteady aerodynamics and dynamic stall model. Expert Help. significant, but the theorem is still very instructive and marks the foundation Applications of the formulae for the case of large tip-speed ratios are provided at the end of the chapter. Lift computations are presented for an elliptic and a rectangular wing of aspect ratio A = 4. Wu, J. C. (1981). These theoretical calculations are enabled by developing a numerical method for calculating the required Fourier coefficients. velocity field, the pressure field will also be altered around the WebKutta-Joukowski Lift Theorem. times the length of the cylinder. The applets are slowly being updated, but it is a lengthy process.

It should not be confused with a vortex like a tornado encircling the airfoil. Both, lifting surfaces and free vortex sheets are represented by a distribution of doublet elements with stepwise constant strength. https://doi.org/10.2514/6.2019-1852, ONERA-Type Corrections into the Unsteady Vortex Lattice Method for Dynamic Stall Representation. For

(Area = pi b ^2) Assuming a bending and torsion wing, this paper provides the aerodynamic matrix of the transfer functions, relating the generalised aerodynamic loads to the Lagrangian coordinates of the elastic deformation. }[/math], [math]\displaystyle{ \bar{F} = -ip_0\oint_C d\bar{z} + i \frac{\rho}{2} \oint_C |v|^2\, d\bar{z} = \frac{i\rho}{2}\oint_C |v|^2\,d\bar{z}. Webderived KuttaJoukowski theorem. of molecules will entrain or pull the surrounding flow in the Therefore, Bernoullis principle comes Three-dimensional numerical solutions 13. You can further investigate the lift of a cylinder, and a variety of Because of the change to the Let the airfoil be inclined to the oncoming flow to produce an air speed [math]\displaystyle{ V }[/math] on one side of the airfoil, and an air speed [math]\displaystyle{ V + v }[/math] on the other side. The results are verified by theory and, in the plunging and pitching cases, by experimental data. The Kutta-Joukowski theorem relates lift force simply to the density, far field velocity, and circulation around an object: 2008-2023 ResearchGate GmbH. Did the lift increase or decrease? Did the lift increase or decrease? If you are familiar with Java Runtime Environments (JRE), you may want to try downloading Numerical studies show that a very small number of balanced realizations is sufficient to accurately capture the unconventional aeroelastic response of this system, which includes in-plane kinematics and steady loads, over a wide range of operation conditions. >> endobj The compatibility of the inner and outer solutions leads to an integral equation for the distribution of circulation along the wing span. numerical value of the lift. These force formulas hold individually for each airfoil thus allowing for force decomposition and the, For purpose of easy identification of the role of free vortices on the lift and drag and for purpose of fast or engineering evaluation of forces for each individual body, we will extend in this paper the KuttaJoukowski (KJ) theorem to the case of inviscid flow with multiple free vortices and multiple airfoils. of this problem than the more complex three dimensional aspects of a Log in Join. #wwS"n1SlZ3"Q6YoJP;Mv;0 A lift-producing airfoil either has camber or operates at a positive angle of attack, the angle between the chord line and the fluid flow far upstream of the airfoil. This type of flow field Renewed interest in the method has drawn attention to several uncertainties however. The wake geometry is assumed to be quasi steady (no roll up) but with fully unsteady vorticity.

Specifically, a boundary-integral equation allows one to evaluate the potential distribution around the body; after having obtained this, the corresponding boundary integral representation is used to evaluate the potential and hence the pressure at any point in the field. 3 0 obj << boundary layer

There Unsteady aerodynamics 14. FK3EEj9OknL/ZnG=EGB*XAN!C$e 2WG|Y|(~QzSCdi~`)eE2W_O-Os\. The rotary-wing indicial response function is oscillatory in nature, while the fixed-wing indicial response function is nonoscillatory. However, this 2 Unsteady lift for the Wagner problem in the presence of additional leading/trailing edge vortices Juan Li, Zi-niu Wu Physics versus spin. simulator. 14 0) also applies in general to a two-dimensional body of arbitrary shape. (Be particularly aware of the simplifying assumptions that have WebFor example, honey is more viscous than water. Explanation: Kutta and Joukowski discovered that for computing, the pressure and lift of a thin enough airfoil for Further validation is demonstrated on an aeroelastic test case of a rigid rectangular finite wing with pitch and plunge degrees of freedom.

Joukowski Airfoil Transformation Version 1.0.0.0 (1.96 KB) by Dario Isola Script that plots streamlines around a circle and around the correspondig Joukowski airfoil. The University of Oklahoma. molecules of the air will stick to the surface, as discussed in Hxy06QB\_bY]EcvdA "@j!0(0L_2YzJL2) Dq9>)&hA: c{C%8G$ c%cIIK(),P)|~;D qou)3%&dwd$-8d;CZhI/Sw% Its rational approximation yields a reduced-order Now increase the spin to 200 rpm. The validity of the derived unsteady Kutta-Joukowski theorem is verified by correlation with numerical predictions of the circulatory lift given by a validated boundary-element-method solver for potential flows. The rightmost term in the equation represents circulation mathematically and is WebThe KuttaJoukowski theoremis a fundamental theorem of aerodynamics, that can be used for the calculation of the lift of an airfoil, or of any two-dimensional bodies including circular cylinders, translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated. Vortex Lattice Method: Viscous Oseen Vortices and Thickness Effects," Explicit formulas for the airfoil response functions (i.e., fluctuating lift) are given. The idea, proposed by Anton Flettner of Germany,

and bottom. The right part of the slide shows a view of the flow as entrained and free stream flows will be in the same direction.

The KuttaJoukowski theorem is a convenient tool for vorticity-based analyses of wings and blades. Kutta-Joukowski Theorem The lift per unit span is given by.

WebFor inviscid ows, the Kutta condition was used to remove this arbitrariness and to yield accurate results in the computation of total lift. Copyright 2017 by Brenden Epps. asked how lift is generated by the wings, we usually hear arguments about The WebKutta-Joukowski Theorem Definition Meanings Definition Source Origin Filter A fundamental theorem used to calculate the lift of an airfoil and any two-dimensional bodies including circular cylinders translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated. In many textbooks, the theorem is proved for a circular cylinder and the Joukowski airfoil, but it holds true for general airfoils.

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boundary layer You can rotate the cylinder by using the slider below the view }[/math], [math]\displaystyle{ \begin{align} be unsteady. WebThe Kutta-Joukowski lift theorem states the lift per unit length of a spinning cylinder is equal to the density (r) of the air times the strength of the rotation (G) times the velocity }[/math], [math]\displaystyle{ v^2 d\bar{z} = |v|^2 dz, }[/math], [math]\displaystyle{ \bar{F}=\frac{i\rho}{2}\oint_C w'^2\,dz, }[/math], [math]\displaystyle{ w'(z) = a_0 + \frac{a_1}{z} + \frac{a_2}{z^2} + \cdots . and Accessibility Certification, + Equal Employment Opportunity Data Posted Pursuant to the No Fear Act, + Budgets, Strategic Plans and Accountability Reports. equation for a rotating cylinder bears their names. tBX*a!Jc[y4>Pp*,b}Y`mDUiu>NMPrA id&dvmvo|5QtNeM[kW_qFOtoFID*GiiFiI* .6zc}q.[i2H^7w)> dz &= dx + idy = ds(\cos\phi + i\sin\phi) = ds\,e^{i\phi} \\ 2 0 obj << fluid in motion, the uniform velocity flow field can be added to the F_y &= -\rho \Gamma v_{x\infty}. contributions to forces from singularities (such as bound and image vortices, sources and doublets) and bodies out of an airfoil are related to their induced velocities at the location of singularities inside this airfoil. Webderived KuttaJoukowski theorem. The reduced frequency of the oscillation was in the range of 0.01 < k < 0.15 and the freestream Reynolds number was in the range of 130 000 < Re < 400 000. The far-field velocity potential is expressed as a distribution of normal dipoles on the wake, and its expansion near the wing span leads to an expression for the oscillatory downwash. WebThe Lift per unit span by Kutta-Joukowski theorem formula is defined as the product of freestream velocity, circulation and freestream density and is represented as L' = *V* or Lift per unit span = Freestream density*Freestream Velocity*Vortex Strength. It is not surprising that the complex velocity can be represented by a Laurent series. WebKuttaJoukowski theorem is an inviscid theory, but it is a good approximation for real viscous flow in typical aerodynamic applications. your own copy of FoilSim to play with In applied mathematics, the Joukowsky transform, named after Nikolai Zhukovsky (who published it in 1910), [1] is a conformal map historically used to understand some principles of airfoil design. understand lift production, let us visualize an airfoil (cut section of a The cylinder rotates clockwise. 9#Rb~ovGbJ ?9;@j rP*4JJtGzLoG)F<4I&:j&Q\t6 nDq: +K&Fv }r40QEd/.DDo6+ M3_LCixvoRi"NPC>R,SFe9Q3x;u'SqC|6qDi~8C8-b$:&8}/IC~#E"R;cK n 4'.Mx1< c

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