Trimaran Teknelerde Yan Teknelerin Bilgisayarla Konum Optimizasyonu

Abstract

Son yıllarda, yüksek süratli teknelerin tasarımında farklı fikirler ortaya atılmaktadır. Piyasaların farklı ihtiyaçları, tasarımcıları değişik yöntemlere itmektedir. Bu nedenle yeni yüksek süratli tekne tasarımları üzerinde çalışılmaktadır. Tasarımcılardan talep edilen, geniş güverte alanı, yüksek stabilite ve yüksek sürat gibi özellikleri bir arada sağlamak klasik dizaynlarla hemen hemen imkansızdır. Konvensiyonel deplasman teknelerinde direnci azaltmak için oldukça narin formlar seçilmektedir. Bu formlarda ortaya çıkan stabilite problemi de son yıllarda çok gövdeli dizaynlarla aşılmaya çalışılmaktadır. Bu formlardan biri de trimaranlardır. Bu çalışmada, trimaran teknelerde, yan teknelerin ana tekneye göre konumlarının toplam dalga direnci üzerindeki etkileri araştırılmış, matematiksel programlama yöntemiyle, minimum dalga direnci elde edilecek şekilde yan teknelerin konum optimtzasyonu yapılmaya çalışılmıştır. Dalga direnci, Michell integrali ile hesaplanmış, integralin girişim (interference) terimini içeren ve integrantın hızla salınan kısmı, özel bir algoritma kullanılarak [ SIĞI (1982) ] çözülebilmiş ve hesaplara katılmıştır. Hesaplamalarda kullanılan gemi yüzeyi çadır fonksiyonlarıyla modellenmiştir. Geliştirilen bilgisayar programı farklı formlara uygulanmıştır. Farklı Froude sayılarında yan teknelerin minimum dalga direnci elde edilen konumlan grafikler halinde verilmiştir. Matematiksel uygulamalar göstermiştir ki, ana tekne ve yan teknelerin dalga formlarının girişim (interference) etkisinden dolayı yan teknelerin farklı konumlarında farklı dalga direnci değerleri elde edilmektedir. Böylece tasarımcının diğer dizayn kriterlerini de göz önüne alarak yan tekneleri minimum dalga direnci sağlayacak şekilde yerleştirmesi mümkündür ve bu da daha yüksek hız değerlerinin elde edilmesini sağlayacaktır.

In recent years, because of different demands of boat market, designers have been directed to different concepts of high speed vessels. Many ideas are proposed in order to pursue the design of high speed vessels. Most of them are based on unconventional concepts. The demand as large deck area, strong transverse stability and high speed is nearly impossible to carry out To overcome these problems, new concepts of high speed vessels based on the displacement type are also proposed and studied, and very slender hull forms are generally employed. For the hull of such type, stability problems are recognized and the choise is multi - hull forms. Catamaran and trimaran forms belong a group of this type of ships. Recently, designers has been interested in catamaran forms and now trimaran forms begin to be favourite. The important problem on trimaran forms is their higher resistance. Because, the total resistance of trimaran is higher than that of monohull with the same length, draft and displacement One of the important factor of resistance is the wave making interference. So, the wave making interference between the main hull and outriggers is expected to be minimized. In mis study, position of outriggers are optimized in order to minimize the wave resistance. It was in 1898 that J.H. Michell gave the first approximate hydrodynamical solution to the problem of wave making resistance of a thin ship moving on the surface of an inviscid fluid of infinite extent. The Michell integral use linear wave resistance theory based on the thin-ship assumption. The well-known Michell integral for monohulls is; IX Rw = 4(pg2/(jrc2))/((u2+1)2/(Vu2 + 2))(P2(u) + Q2(u))du D (1a) P Q LT A COS JJ HÇ(Ç,Ç) {ko£o(u2+1) + kDT]Ou(u2+1)Vu2 + 2} (1b) oo sin taKı^+lffÇo-T) e dŞodÇo @.y) -J (i-WJ.) -İ - j-1.-1 (A.P) i+1 i (-1 (F.P) Fig 1 Fig 2 Following the same formulation given by Hsiung ( 1981 ), the coordinate system is chosen as in fig 1 and ship hull function is defined as ti-F(W) (2) The variables £,t|,Ç are non dimensionalized ; x = £/L y=T!/(B/2) z = Ç/T (3) Non dimensionalized hull form expressed as f(x,z) = (2/B)F(Ç,Ç) (4) The wave resistance function (1a-1b) can be nondimensionaiized by the factor [ 8pgB2 T2 ]. Then Michell integral turns out to be QO (U2+1)2 Cw =(yo/2) J (F + Q2) du 0 Vu2+2 (5a) 2to(T/L)(u2+1)2(z-1) "{270x(u2+1)}e dxdz (5b) To calculate wave resistance as given above ship surface has to be defined. Therefore, tent functions are used to define ship surface and the ship center-plane is meshed as shown fig 2. The first station is the fore-perpendicular of the ship, the first waterline is the base line. The last station is the aft-perpendicular of the ship, the waterline is loaded waterline. Then the unit tent function at the grid point ( xi,zj ) is given as (i,j) I'-X V - X*-1 Zj-Z Zj - Zj-1 r * -x 1- h (x.z) I L X' - xn Xi-X 1- r zj - z ""i 1- Zj-Zj+1 X' " X'-1 Xi-X Zj-z 1- L zj-zj-1 1- X' - X»+1 Zj-Z 1- Zj-Zj+1 ; 3CH < X ^ Xi. Zi-1 ^ z ^ Zj XM < x < X>. Zj < z < Zj+1 ; Xi < X ^ Xi+1. zj-1 < z < zj (6) ;xf^X^X'+1,zj<z<="" (18)="" (0).="" original="" lower="" bound="" for="" unkown="" offset="" (0)="" style="margin: 0px; padding: 0px; outline: 0px; color: rgb(34, 34, 34); font-family: Verdana, Arial, sans-serif; font-size: 10px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-style: initial; text-decoration-color: initial;"> yij (19) The waterplane area coefficient is kept constant ; (0) CWL = CWL (20) Waterline slope is less than or equal to tan6 y i+1, j - y i,j < ( x i+1 - x i ) (2L/B) tanG (21) The wave resistance of trimaran forms can be expressed as follows n/2 Cw=8ityo2J ({P(9)}2 + {QiS)3}) secede yo = ge/u2= 1 /(2Fn2) (22a) o In case of the linear theory, amplitude functions P(6) and Q(6) can be represented by the linear superposition such as P(9) Q(e) J y = < Pm(9) I Qm(6) J > +< Po(e) I Qo(6) J (22b) XIV The first term of the right hand side of equation (22b) represents the wave making effect of the main hull, its second term represents total wave making effect of outriggers at port and starboard sides. Amplitude functions can be integrated by Michell's theory based on the thin ship assumption as follows Pm(0) "I +1 cos o 70 z sec^G V => (-1/2*) / {cf{x)ld x) (70 x secB ) dx J g(z) e dz (23a) Qm(0)J -1 sin -t Po(e) j xo+to f => (-1/2*) J (a/o(x-xo)/öx) 00(9) J xo-Ao cos {70 sec5^ ( x cosG + yo sine )} (23b) sin cos + {70 sec^G ( x cosG - yo sinG )} sin 0 70 z sec^G dx J go(z) e dz or Po(e) "] xo+Xo COS V => (-1/31) cos ( 70 yo sec9 tane ) / (d/(x-xo)/d x) (70 x secG ) dx Qo(0) J xo-Xo sin 0 Tozsec^e J go(z) e dz -to (23c) Po(e) Qq(G) Poo(e)- Qoo(e), fPoo(ef 2cos (70 yo secG tane K > [Ooo^ (24) xo+to cos 0 Tozsec^ (-1/2*) J (ö/(x-xo)/5x) (70 x sece ) dx / go(z) e dz (25) xo-to sin -t XV We can separate trimaran wave making resistance in three parts Cw = Cw1 + Cw2 + Cw3 (26) jc/2 Cw1 = frito2 J { Pm«(e) + 0.^(0) } sec^e d9 (27) 0 Cw2 = 2>2x%& J { Pm(e)Qoo(9) + Poo^Qm^G) } cos(yoyosec9 tan9) sec^G d9 (28) o Cw3 = 32îtXo2 1 { Pcx)2(e) + Qoo^e) } cos(yoyosec9 tan9) sec^ d9 (29) o Cw1 is the wave making resistance of main hull, Cw2 is the interference effects between main hull and outriggers and Cw3 is the wave making resistance of outriggers. The computer program is developed to calculate the wave-making resistance of trimaran forms. Simpson's integration method is used by employing Michel) integral for the resistance of monohull and outriggers. A special integration technique SIDI (1982) is used in the evaluation of Michel) integral because of the highly oscillatory integrant due to the interference effects. Two different trimaran forms are used as computational examples. One of them is the mathematical hull form whose wateriines and frame lines are cosine curve and parabolic curve, the other one is a yacht form. Two methods are used for the optimization; 1. Variations in outriggers separation from the main hull. 2. Variations in the longitudinal position of the outriggers relative to the main hull. XVI Using the method explained above, position of outriggers have been optimized to minimize the wave resistance by means of the wave making interference between the main hull and outriggers.The main conclusions obtained as follows; 1. Optimum position of outriggers can be determined by minimization of wave making resistance based on the linear superposition of amplitude functions for the main hull and outriggers. 2. Wave resistance of a trimaran hull becomes higher than that of the monohull. However, the wave resistance of a trimaran with the optimized positions of outriggers are smaller than that of the trimaran form which is not optimized 3. At different Froude numbers, the optimum position curves of outriggers have different characteristics. 4. When outriggers are far away from the main hull, the wave resistance due to interference effects is reduced. So, main hull and outriggers behave as separated monohulls. 5. At high Froude numbers, the differences of wave making resistance is reduced for different position of outriggers and total wave making resistance goes to one point.