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Gemilerde squatın incelenmesi

Gemilerde squatın incelenmesi

##### Dosyalar

##### Tarih

1996

##### Yazarlar

Yılmazer, Soner

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Gemi boyutlarındaki artış dizayn ve operasyon problemlerine sebep olmuştur. Bu problemlerden bir tanesi ' squat * olarak adlandırılan gemilerin sığ sudaki davranışıdır. Squat nedeni ile gemiler karaya oturabilir veya yaralanabilir. Bundan dolayı squat sonuçlarının dizayn aşamasında gemi mühendisleri, operasyonda ise kaptanlar tarafından bilinmesi önemlidir. Squatı açıklamak için birçok teoriler ve ampirik formüller geliştirilmiştir. Bu çalışmada squatı doğru tahmin edebilmek için teori ve ampirik formüller arasında bir uyum sağlanmıştır. Bunun yanında geminin ana parametrelerinin squat üzerindeki etkisini araştırmak için örnek gemiler üzerinde sistematik çalışmada yapılmıştır. Sonuç olarak, squat tahmini için gemi blok katsayısının, tekne draftının ve gemi hızının önemli parametreler olduğu fikrine varılmıştır.

Increase in the size of ships has caused several problems in design and operation. Öne of them is the behaviour of ships in the shallow vvater, called' squat'. it can be determined, below. When a ship proceeds water, she pushes water ahead of her. in order not to leave a ' hole ' in the vvater, this volume of vvater pushed ahead of the ship must retum dovvn the sides and under the keel of the ship. The streamlines of retum flow are speeded up under the ship. This causes a drop in pressure, resulting in the ship dropping vertically in the vvater. As well as dropping vertically, the ship trims for'd ör aft. The overal decrease in the underkeel clearance for'd ör aft is called SHIP SOUAT. Ships may ground ör be damaged due to the squat, so it is important to evaluate results of squat for naval architectures and marine engineers during the design stage and for captains during operation. in order to explain squat, some teories and empirical formulas have been developed över the years. So a compromize betvveen them has been established to predict squat accurately and easily, in this paper. in addition to comparison, empirical formulas have been applied to some sample ships to study its variation on main ship hull parameters systematically. As a result, we have concluded that block coefficient of ship, draft of hull and ship speed are important parameters for prediction of squat Bernoulli Theorem The initial stages of squat can be described using Bemoulli's Theorem. This theorem deals with the conversation of energy in a liquid. Bernoulli's Theorem; Potantiel energy + Pressurre energy + Kinetic energy = Constant m.g.z + (m.P/p) + O.S.m.v2 - Constant 1. x Assuming liqukJ does not change height and therefore the potantiel energy term remains constant (m.P/p) + O.S.m.v2 = Constant 2, thus if the velocity of the liquid is increased then the pressure enrgy term must be reduced. If this happens beneath a ship the redution in pressure must result in sinkage and because the centre of buoyancy will move due to changes in distribution of pressure the ship wiil also change trim. At this point the flow of water past the vessel is becoming more complex, the ship will have slovved down due to the increadsed resistance following the changes in sinkage and trim. The simple Bemoulli theorem will not give a satisfactory assessment of squat. Shallow-Water Flows Past Slender Bodies Suppose a fixed slender obstacle is at ör near the free surface of a stream U of shallow water. The flows f rom left to right in the co-ordinate system of figüre 1, and is of depth h. The fluid is taken to be inviscid and incompressible and flow steady and irrotational, so that there exists a diturbance potantiel 4» satisfying Laplace's equation and tending to zero suitably at infinity, such that the total fluid velocity is UV(x+<(ı). -^rk^_,__4 _-. Figüre 1. Co-ordinate system. The sequel consists of an approximate solution to the boundary-value problem for Laplace'sequation, based on the assumptions that the ship is slender and water shallow. As a result, the theory predicts this behaviour explicity in two special cases. First, if the ship has fore-and-aft symmetry it is possible to prove that CT = CM = O for F,* < 1 3. Cs = CF = O for Fnh > 1 4. So that for such a symmetrical ship we predict a zero subcritical trim and zero supercritical sinkage. Secondly, there exists a non-trival class of ships such that S (x)/B (x) = const. For such ships we can prove rigorously that xi CF > O for Fnh < 1 5. CM>0 for Fnh>1 6. So that simple ships must experience a downward force in the subcritical range and a bow-up moment in the supercritical range. One-Dimensional Theory it is assumed that the origin of the co-ordinate axes is on the centreline of the hull in the water-plane with the x-axis in the longitudinal direction, the z-axis vertically upward and the y-axis to öne side (see Figüre 2.). 3" Figüre 2. Axis system. Suppose we have a canal of rectanguler cross-section area So and ship with a sectional area S(x). Further assume the ship to be fixed while a uniform stream of velocity U flows past. Then the continuity requires, asuming that pertubations in the y and z directions can be neglected, U.So = Ut(x).( So + w.Ç(x) - S(x)) 7. Where U,(x) = U + u(x) Ap2plication of Bemoulli's equation at the free surface yields; 0.5.U2 = 0.5.U,(x)2 + g.Ç(x) 8. After some reduction, equations (7) and (8) yieid the well-known relation (Fnh2/2).( Uı(x) / U )3- (1 - m(x) + ( Fnh2/2 )).( U,(x)/U ) + 1 = O 9. VVhere m(x) is the local blockage ratio S(x) / So. in non-dimensional form equation (8) gives, for the non-dimensional surface elevation Ç*(x). xii C*(X) = Ç(x)/h = - Fj - u*(x).(1 + (u*(x)/2)) 10. VVhere. u*(x) =. u(x) / U. Mean sinkage and trim coefficients are given by Cs = Sw.100 / UP = 100.( h/T).(T/UP)- (Jç"(x).B(x)dx) / (J B(x).dx) 11. CT = T.100 / Lpp = 100.(hn).(T7Lpp).( jÇ*(x).B(x).x.dx)/(J B(x).x2.dx) 12. Where ali moments are taken about the centre of the flotation of the vvater -plane at which the vessel floats at rest and ali x and B(x) have been non-dimensionalised with respect to Lpp. Model Tests Experiments to mesure the squat of ship models have been carried out in the shallovv water section of the NPL No: 2 tank ( width 6.56 m ) and in the Glasgovv Universtty tank ( width 4.92 m ). The experiments used models whose geometrical particulars are given in Table 1. AH models were fitted with bulbous bows and the experiments were carried out for a range of speeds and vvater depths. MODEL A B C D Length(m) 3.048 3.675 3.953 3.898 Beam(m) 0.472 0.576 0.656 0.591 Draught(m) 0.181 0.222 0.223 0.248 CB 0.820 0.830 0.8375 0.895 Table 1. Model details. Investigations were made of the effect on squat of:. Variations in at-rest trim values.. Şelf propulsion.. Propeller loading.. Tovving point height in ali experiments the model was run in calm vvater on the centreline of the tank, free to sink and trim but not to yaw. Modified One-Dimensional Theory Results f rom model tests vvhich were obtained by I.W.Dand shovved that mean sinkage and trim coefficients could be represented by C.n = a(tn).C8l 13. CTn = P(ra).CTi 14. Where a(w) = 1 / (1+ 5.C,), 6.C. = 1.196 - 1.444. ra 15. xiii P(ra) = 1 / ( 1+ 5.CT), 6.CT = 0.056 - 0.714. TO 16. When the assumed effective width is 0.975. Lpp. The subscript n refers to values calculated for the naked towed hull in wide shallow water. Final values of CSp and CTP for a self-propelled model were found to be adequately represented by C» =1.1. C» 17. CTP = y.(Fnh, h/T)sn. CTP 18. Experimental Method The experimental tests were made in the No.2 Tank of British Maritime Technology Ltd. The tank is 195 m long and 6.1 wide with more than half of the length being of normal depth ( 2.7 m ). The remainder of the tank is shallovv with the bottom flat and level to a close tolerance of +" 3 mm altough not ali of the 76 m length was available during these tests. The depth of water in the shallow section can be set vvithin the range O to 0.6 m. The hulls used in the experiments were chosen from a number that were readily available in order to give a reasonable variety and representation of ali types of ship. Details of the majör parameters of the hulls are given in Table 2. Identifier Type Appan. Lpp Lpp/T Lpp/B CB A Light disp. round bilge None 3.167 20.70 6.463 0.444 hull B Light disp. Stub round bilge bosssing 3.715 24.28 7.887 0.502 hull and A brackets C Container Bulb 3.810 20.93 7.003 0.595 ship D LNGcarrier Bulb 3.115 23.25 6.242 0.735 E Tanker None 3.344 18.27 7.831 0.763 F Tanker Bulb 3.387 18.02 6.464 0.820 G Tanker Bulb 3.536 14.92 6.128 0.828 Table 2. Model details For each model measurements were made of resistance, trim, and squat for speeds corresponding to the Froude number range Fnh, based on hull length, from approximately 0.1 to 0.2 for four shallovv water depths. The hull length / depth ratios (Lpp/h) chosen were 6, 8,10,12. xiv Effects of Ship Velocity and Shallow Water depth on Squat Results obtained by model tests were plotted in Figure 3. At subcritical speeds (Fnh < 1) with the squat curve falling to a minimum at a Froude number of approximately 0.9 and then rising abrubtly close to the critical Froude number (Fnh = 1) At supercritical speeds ( Fnh > 1 ) the squat may become negative. Sl*nd«r Light Duptocemtnt Hull Squat 0 IV. L") V s Ship Speed h » Wat«r D»pth if, « Ungth of Hull BİT Ftrry ot «Knots Figure 3. Variation of squat with speed for several hulls. The squat results from the various ship models, which ranged from fast patrol boats to tankers, seemed to follow a similar shape of curve even though the actual magnitude of the squat was different. An empirical approach was therefore adopted to see whether a common family of curves could be devised to fit the data and therefore be used to give initial design guidance on the magnitude of squat in shallow water for a range of ships. Various simple curve shapes were considered from which the most suitable seemed to be : % _ (s/L)b" = a.Fnh" + b.Fnh + c 19. The final form of the equation was found to be : (s / L)b% = (56.248.CB.(T/L)+0.1574)F6nh2 + (-8.34.CB.(T/L)+0.0396).Fnh 20. Conclusions Ships may ground or be damaged due to the squat, so it is important to evaluate results of squat. As a result, we have concluded that block coefficient of ship, draft of hull, ship speed and form factor are important parameters for prediction of xv squat. In addition to them, the formulas have been shown to be able to give better predictions in the real case than most existing simple formulas.

Increase in the size of ships has caused several problems in design and operation. Öne of them is the behaviour of ships in the shallow vvater, called' squat'. it can be determined, below. When a ship proceeds water, she pushes water ahead of her. in order not to leave a ' hole ' in the vvater, this volume of vvater pushed ahead of the ship must retum dovvn the sides and under the keel of the ship. The streamlines of retum flow are speeded up under the ship. This causes a drop in pressure, resulting in the ship dropping vertically in the vvater. As well as dropping vertically, the ship trims for'd ör aft. The overal decrease in the underkeel clearance for'd ör aft is called SHIP SOUAT. Ships may ground ör be damaged due to the squat, so it is important to evaluate results of squat for naval architectures and marine engineers during the design stage and for captains during operation. in order to explain squat, some teories and empirical formulas have been developed över the years. So a compromize betvveen them has been established to predict squat accurately and easily, in this paper. in addition to comparison, empirical formulas have been applied to some sample ships to study its variation on main ship hull parameters systematically. As a result, we have concluded that block coefficient of ship, draft of hull and ship speed are important parameters for prediction of squat Bernoulli Theorem The initial stages of squat can be described using Bemoulli's Theorem. This theorem deals with the conversation of energy in a liquid. Bernoulli's Theorem; Potantiel energy + Pressurre energy + Kinetic energy = Constant m.g.z + (m.P/p) + O.S.m.v2 - Constant 1. x Assuming liqukJ does not change height and therefore the potantiel energy term remains constant (m.P/p) + O.S.m.v2 = Constant 2, thus if the velocity of the liquid is increased then the pressure enrgy term must be reduced. If this happens beneath a ship the redution in pressure must result in sinkage and because the centre of buoyancy will move due to changes in distribution of pressure the ship wiil also change trim. At this point the flow of water past the vessel is becoming more complex, the ship will have slovved down due to the increadsed resistance following the changes in sinkage and trim. The simple Bemoulli theorem will not give a satisfactory assessment of squat. Shallow-Water Flows Past Slender Bodies Suppose a fixed slender obstacle is at ör near the free surface of a stream U of shallow water. The flows f rom left to right in the co-ordinate system of figüre 1, and is of depth h. The fluid is taken to be inviscid and incompressible and flow steady and irrotational, so that there exists a diturbance potantiel 4» satisfying Laplace's equation and tending to zero suitably at infinity, such that the total fluid velocity is UV(x+<(ı). -^rk^_,__4 _-. Figüre 1. Co-ordinate system. The sequel consists of an approximate solution to the boundary-value problem for Laplace'sequation, based on the assumptions that the ship is slender and water shallow. As a result, the theory predicts this behaviour explicity in two special cases. First, if the ship has fore-and-aft symmetry it is possible to prove that CT = CM = O for F,* < 1 3. Cs = CF = O for Fnh > 1 4. So that for such a symmetrical ship we predict a zero subcritical trim and zero supercritical sinkage. Secondly, there exists a non-trival class of ships such that S (x)/B (x) = const. For such ships we can prove rigorously that xi CF > O for Fnh < 1 5. CM>0 for Fnh>1 6. So that simple ships must experience a downward force in the subcritical range and a bow-up moment in the supercritical range. One-Dimensional Theory it is assumed that the origin of the co-ordinate axes is on the centreline of the hull in the water-plane with the x-axis in the longitudinal direction, the z-axis vertically upward and the y-axis to öne side (see Figüre 2.). 3" Figüre 2. Axis system. Suppose we have a canal of rectanguler cross-section area So and ship with a sectional area S(x). Further assume the ship to be fixed while a uniform stream of velocity U flows past. Then the continuity requires, asuming that pertubations in the y and z directions can be neglected, U.So = Ut(x).( So + w.Ç(x) - S(x)) 7. Where U,(x) = U + u(x) Ap2plication of Bemoulli's equation at the free surface yields; 0.5.U2 = 0.5.U,(x)2 + g.Ç(x) 8. After some reduction, equations (7) and (8) yieid the well-known relation (Fnh2/2).( Uı(x) / U )3- (1 - m(x) + ( Fnh2/2 )).( U,(x)/U ) + 1 = O 9. VVhere m(x) is the local blockage ratio S(x) / So. in non-dimensional form equation (8) gives, for the non-dimensional surface elevation Ç*(x). xii C*(X) = Ç(x)/h = - Fj - u*(x).(1 + (u*(x)/2)) 10. VVhere. u*(x) =. u(x) / U. Mean sinkage and trim coefficients are given by Cs = Sw.100 / UP = 100.( h/T).(T/UP)- (Jç"(x).B(x)dx) / (J B(x).dx) 11. CT = T.100 / Lpp = 100.(hn).(T7Lpp).( jÇ*(x).B(x).x.dx)/(J B(x).x2.dx) 12. Where ali moments are taken about the centre of the flotation of the vvater -plane at which the vessel floats at rest and ali x and B(x) have been non-dimensionalised with respect to Lpp. Model Tests Experiments to mesure the squat of ship models have been carried out in the shallovv water section of the NPL No: 2 tank ( width 6.56 m ) and in the Glasgovv Universtty tank ( width 4.92 m ). The experiments used models whose geometrical particulars are given in Table 1. AH models were fitted with bulbous bows and the experiments were carried out for a range of speeds and vvater depths. MODEL A B C D Length(m) 3.048 3.675 3.953 3.898 Beam(m) 0.472 0.576 0.656 0.591 Draught(m) 0.181 0.222 0.223 0.248 CB 0.820 0.830 0.8375 0.895 Table 1. Model details. Investigations were made of the effect on squat of:. Variations in at-rest trim values.. Şelf propulsion.. Propeller loading.. Tovving point height in ali experiments the model was run in calm vvater on the centreline of the tank, free to sink and trim but not to yaw. Modified One-Dimensional Theory Results f rom model tests vvhich were obtained by I.W.Dand shovved that mean sinkage and trim coefficients could be represented by C.n = a(tn).C8l 13. CTn = P(ra).CTi 14. Where a(w) = 1 / (1+ 5.C,), 6.C. = 1.196 - 1.444. ra 15. xiii P(ra) = 1 / ( 1+ 5.CT), 6.CT = 0.056 - 0.714. TO 16. When the assumed effective width is 0.975. Lpp. The subscript n refers to values calculated for the naked towed hull in wide shallow water. Final values of CSp and CTP for a self-propelled model were found to be adequately represented by C» =1.1. C» 17. CTP = y.(Fnh, h/T)sn. CTP 18. Experimental Method The experimental tests were made in the No.2 Tank of British Maritime Technology Ltd. The tank is 195 m long and 6.1 wide with more than half of the length being of normal depth ( 2.7 m ). The remainder of the tank is shallovv with the bottom flat and level to a close tolerance of +" 3 mm altough not ali of the 76 m length was available during these tests. The depth of water in the shallow section can be set vvithin the range O to 0.6 m. The hulls used in the experiments were chosen from a number that were readily available in order to give a reasonable variety and representation of ali types of ship. Details of the majör parameters of the hulls are given in Table 2. Identifier Type Appan. Lpp Lpp/T Lpp/B CB A Light disp. round bilge None 3.167 20.70 6.463 0.444 hull B Light disp. Stub round bilge bosssing 3.715 24.28 7.887 0.502 hull and A brackets C Container Bulb 3.810 20.93 7.003 0.595 ship D LNGcarrier Bulb 3.115 23.25 6.242 0.735 E Tanker None 3.344 18.27 7.831 0.763 F Tanker Bulb 3.387 18.02 6.464 0.820 G Tanker Bulb 3.536 14.92 6.128 0.828 Table 2. Model details For each model measurements were made of resistance, trim, and squat for speeds corresponding to the Froude number range Fnh, based on hull length, from approximately 0.1 to 0.2 for four shallovv water depths. The hull length / depth ratios (Lpp/h) chosen were 6, 8,10,12. xiv Effects of Ship Velocity and Shallow Water depth on Squat Results obtained by model tests were plotted in Figure 3. At subcritical speeds (Fnh < 1) with the squat curve falling to a minimum at a Froude number of approximately 0.9 and then rising abrubtly close to the critical Froude number (Fnh = 1) At supercritical speeds ( Fnh > 1 ) the squat may become negative. Sl*nd«r Light Duptocemtnt Hull Squat 0 IV. L") V s Ship Speed h » Wat«r D»pth if, « Ungth of Hull BİT Ftrry ot «Knots Figure 3. Variation of squat with speed for several hulls. The squat results from the various ship models, which ranged from fast patrol boats to tankers, seemed to follow a similar shape of curve even though the actual magnitude of the squat was different. An empirical approach was therefore adopted to see whether a common family of curves could be devised to fit the data and therefore be used to give initial design guidance on the magnitude of squat in shallow water for a range of ships. Various simple curve shapes were considered from which the most suitable seemed to be : % _ (s/L)b" = a.Fnh" + b.Fnh + c 19. The final form of the equation was found to be : (s / L)b% = (56.248.CB.(T/L)+0.1574)F6nh2 + (-8.34.CB.(T/L)+0.0396).Fnh 20. Conclusions Ships may ground or be damaged due to the squat, so it is important to evaluate results of squat. As a result, we have concluded that block coefficient of ship, draft of hull, ship speed and form factor are important parameters for prediction of xv squat. In addition to them, the formulas have been shown to be able to give better predictions in the real case than most existing simple formulas.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996

##### Anahtar kelimeler

Gemi Mühendisliği,
Gemiler,
Squat,
Marine Engineering,
Ships,
Squat