Serbest su yüzeyi altında ve sonlu deniz derinliğinde ilerleyen üç boyutlu hidrofoillerin hidrodinamik analizi
Başlık çevirisi mevcut değil.
- Tez No: 55719
- Danışmanlar: PROF.DR. TARIK SABUNCU
- Tez Türü: Doktora
- Konular: Gemi Mühendisliği, Marine Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1996
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 42
Özet
ÖZET Serbest su yüzeyi altında ve sonlu deniz dibi derinliğinde yatay olarak sabit hızla ilerleyen keyfî şekilli, kaldırma kuvveti oluşturabilen cisimlerin hidrodinamik yönden incelenmesi için Green teoremi ve Green fonksiyonu temeline dayanan bir yöntem açıklanmıştır. Bugünkü bilgi ve imkanlar karşısında Navier-Stokes denkleminin uygun sınır koşullan altında tam olarak çözümü mümkün görülmemiştir. Dolayısıyla, bu probleme boyutsuzlaştırılmış momentum denklemi uygulanırsa, Reynolds ve Froude sayılarına bağlı terimler ihmal edilerek (106
Özet (Çeviri)
HYDRODYNAMIC ANALYSIS OF 3-D HYDROFOILS MOVING UNDER FREE SURFACE IN WATER OF FINITE DEPTH SUMMARY Pressure distribution and flow field around 3-D hydrofoils under free surface and with finite depth effects are important for the determination of the hydrodynamic characteristics (lift, drag and wave resistance). At present it is not possible to solve full Navier-Stokes equations with appropriate boundary conditions with the available computational facilities. Using a high Reynolds number approximation, the problem can be reduced to the solution of a thin shear layer problem where the solution obtained from the potential flow theory provide the initial step necessary for the computation of shear layer around hydrofoil. Since the computational techniques for three dimensional shear layers are well documented and understood, in this study the potential flow theory is considered in more detail. In early years, the lifting line and the lifting surface theories were applied to the hydrofoils. However, both methods had some troubles with low aspect ratio of wings and with thick wings, respectively [1-7]. Nowadays, panel methods provide us with a powerful tool in calculation of 2-D or 3-D lifting bodies with free surface effects and with finite depth effects [8-13]. Panel methods have been improved especially in the field of aerodynamics for the design and analysis of 3-D wing and bodies [14-17], The main advantage of the panel methods over the lifting line and lifting surface methods is to allow for more precise representations of complicated wing-body configurations. There exists a wide range of panel methods which uses different types of surface panels, singularity distributions and boundary conditions [18]. The main equation for most of the original panel methods was derived from the requirement that the normal velocity be zero at a selected point on each panel. However, Morino introduced a panel method based on Green's identity in which the primary unknown was the velocity potential [19-23]. In the present study, Morino's panel method is applied to the hydrodynamic analysis of 3-D hydrofoils moving with a constant speed under the free surface with finite depth effects. Now, the formulation of the problem will be briefly discussed below. Consider a hydrofoil moving horizontally with a constant speed U“ under the free surface and over the sea bottom. Let us define a Cartesian coordinate system Oxyz attached to the hydrofoil surface as shown in figure 1. Assume that the fluid viiiis inviscid, incompressible and the flow is irrotati >nal, so that velocity potential ( = 0 (!) 2. Linearized free surface condition: *Jxy,h) * k$z(x,y,h) = 0 (2) where, Au=_iL, U”velocity at infinity. g : gravitational acceleration, h : the depth of the hydrofoil from the free surface. 3. Radiation condition: «»..?**. -te^^jS: 5? ??.2 j.“ 21-1/2 im (Kw) = £}£ Or'*y 4. Bottom condition at z=-d: ) at any field point P(x,y,z) can be written as a distribution of source and doublet over the boundary surface S as follows: 4kE(P)HP) = JjHQ)dG^'P)dS(Q) - jJG(Q;P)^l.dS(Q) (7) where E(P) = 0 // P(xy,z) inside the S, - if P(x,y,z) on the S, 1 if P(x,y,z) outside the S. and G(Q;P) is the Green function of the problem G(Q;P) = -L^ + riiQ-P) (8) where, r(Q;P) is the distance between the field point P(x,y,z) and the boundary point Q(x',y',z ') and 3/3nQ is the normal derivative to the boundary surface S at the point Q and H(Q;P) is a harmonic function in the fluid domain. The Green function which satisfies the boundary conditions (2), (3) and (4) can be given as follows [24-26] (Appendix B) : it/2 - G{Q\P) = - I - + 1 - 1 fsec2G ([k-ktsecietanhk(h+d)]-l{cosh[k(z+d)]. r{Q\P) r'(Q;P) n{ { cos[k(x ' -x)cose].cos[fc(y ' -y)sin0].(e ”^^cosh^Cz ' +cO]()tcos2e+Â:0)+/tcos2esinh[it(z ' +h+2d)] Jt/2 -£0cosh[Â:(z ' +h+2d)]))dk-4 f(l -k0d.scc2Q.sech 2.c0d)-llsec2Q.sech(c0d).cosh[cl}(z+d)] e“.sin[c0(jc ' -jr)cos6].cos[c0Cy ' -;y)sin8].{\ and r'(Q;P) = \l(x' -x)2+(y' -y)2+(z+2d+z')2It is shown in Appendix C that the integrals on the right-hand side of equation (7) over the cylindrical surface, bottom surface and the free surface (when the hydrofoil is not piercing the free surface) are zero. It is also shown in Appendix D that by combining the zero normal force condition on the wake surface and the Kutta condition the equation (7) can be written as follows: 2ti) = ffr(Q)aG(Q;P)P)dS(Q') JfUjixG(Q;P)dS(Q) (10) + where SB is the hydrofoil surface, Sw is the wake surface of the hydrofoil. Q ' is any point on the wake surface and a«j>T£ = r ~ ”(Q). and nxU0o are assumed to be constant over each panel. Then, the collocation method is used, that is, equation (10) is satisfied at the centroid of each panel. This yields the following linear algebraic equation system, [8.-C-W.. ]{) = ~[B.]n (12) 1/ IJ IJJ ~J L IJJ X where 8^ is the Kronecker delta, C. = _L f (^IdS. (13a) ; 27C-V 3«- B» - -i/M (l3b) w* '- *//?*'' (13c> For the panels not in contact with the trailing edge, W^O. Sj- is the strip of the wake (bounded by two streamlines) emanating from the trailing edge. The upper (lower) sign must be used for the upper (lower) side of the wake. The influence coefficients Cy, B(j and Wjj can be evaluated more precisely in xithe near field [15,27] (Appendix E). On the other hand, they can be evaluated as a point source and doublet distribution in the far-field in order to save the computation time. In addition, the partial fraction expansion method can be used for the wave terms in the Green function [24,26,28]. The integrals over the wake strips can also be evaluated by dividing the strip into hyperbo.'oidal quadrilateral panels. An iteration scheme used for obtaining the rolled-up wake geometry is based on the condition that there is zero net normal force on the wake surface. First, equation (12) is solved numerically to yield the values of unknown velocity potential, then the velocities in the x,y,z directions are calculated on the wake by taking the gradient of the velocity potential as follows: V(P) = VJ(P) = A-CfomV, dG^P) )dS(Q) 4n ^ anQ +_L [ \um nx(Q)[ V,,G(Q;P)]dS(Q) +-L (faTE(Q ')[VpdG^P)}dS{Q ') (14) 4% J J 47C*'"' dnn, Then, the panels of the wake streamlines are alinged with the velocity vector. To recalculate the wake velocities and geometry, the velocity potential distribution must be evaluated again. The process is repeated until the difference between successive velocity potential distributions becomes sufficiently small. The velocity and pressure distribution on the hydrofoil surface can be evaluated in a manner similar to the one used for the wake velocities. However, this takes too much computation time because the influence coefficients for the induced velocities must be recalculated. In this study, the velocities and pressures on the hydrofoil surface are obtained by differentiating the velocity potential over the surface using the technique suggested by Hoshino [19]. For the numerical calculations, first a rectangular hydrofoil with AR=4 has been chosen. The hydrofoil has NACA632A015 profiles which are constant along the spanwise direction. The effects of the submergence depth of the hydrofoil from the free surface, from the horizontal finite bottom and of Froude numbers on lift and drag coefficients have been obtained and discussed. Second, a rectangular flat hydrofoil with AR=6 has been chosen. The effects of the submergence depth of the hydrofoil from free surface and from finite bottom on circulation distribution have been discussed. The results for the above examples are compared with the ones given in the literature [7,13]. Third, a circular hydrofoil having NACA0009 profiles along the spanwise direction has been chosen. The pressure coefficient values for different h/c and d/c ratios have also been given. From all the examples given above, it has been found that the free surface effect causes a decrease in the lift coefficient of the hydrofoil for Froude numbers xiihigher than nearly 0.4, while an increase in the wave resistance for increasing Froude numbers. The finite bottom causes an increased wave resistance of the hydrofoil for increasing Froude numbers and decreasing d/c ratios. XUl
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