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Resistance and propulsion 71 limited to the propeller plane. The local velocities were traditionally measured by pitot tubes. Currently, Laser-Doppler velocimetry also allows non-intrusive measurements of the flow field. The results are usually displayed as contour lines of the longitudinal component of the velocity (Fig. 3.6). These data play an important role in the design of a propeller. For optimizing the propeller pitch as a function of the radial distance from the hub, the wake fraction is computed as a function of this radial distance by integrating the wake in the circumferential direction: wr D 1 2 2 0 wr, d 180° 180° 0.4 0.6 0.7 0.8 90° 90° 0° 0° 0.9 1.275 R 1.275 R 0.5 V / V o Figure 3.6 Results of wake measurement The wake field is also used in evaluating propeller-induced vibrations. 3.2.3 Method ITTC 1957 The resistance of the hull is decomposed as: R T D R F C R R R F is the frictional resistance, R R the residual resistance. Usually the resistance forces are expressed as non-dimensional coefficients of the form: c i D R i 1 2 V 2 s S 72 Practical Ship Hydrodynamics S is the wetted surface in calm water, V s the ship speed. The resistance coef- ficient of the ship is then determined as: c Ts D c Fs C c R C c A D c Fs C c Tm c Fm C c A The index s again denotes values for the full-scale ship, the index m values for the model. c R is assumed to be independent of model scale, i.e. c R is the same for model and full scale. The model test serves primarily to determine c R . The procedure is as follows: 1. Determine the total resistance coefficient in the model test: c Tm D R Tm 1 2 m Ð V 2 m Ð S m 2. Determine the residual resistance, same for model and ship: c R D c Tm c Fm 3. Determine the total resistance coefficient for the ship: c Ts D c R C c Fs C c A 4. Determine the total resistance for the ship: R Ts D c Ts Ð 1 2 s V 2 s S s The frictional coefficients c F are determined by the ITTC 1957 formula: c F D 0.075 log 10 R n 2 2 This formula already contains a global form effect increasing the value of c F by 12% compared to the value for flat plates (Hughes formula). Historically c A was a roughness allowance coefficient which considered that the model was smooth while the full-scale ship was rough, especially when ship hulls where still riveted. However, with the advent of welded ships c A sometimes became negative for fast and big ships. Therefore, c A is more appropriately termed the correlation coefficient. c A encompasses collectively all corrections, including roughness allowance, but also particularities of the measuring device of the model basin, errors in the model–ship correlation line and the method. Model basins use c A not as a constant, but as a function of the ship size, based on experience. The correlation coefficient makes predictions from various model basins difficult to compare and may in fact be abused to derive overly optimistic speed prediction to please customers. Formulae for c A differ between various model basins and shipyards. Exam- ples are Table 3.1 and: c A D 0.35 Ð10 3 2 ÐL pp Ð 10 6 c A D 0.11 ÐR n Ð 10 9 2.1 a 2 a C 0.62 with a D max0.6, minC B , 0.8 Resistance and propulsion 73 Table 3.1 Recommended values for C A L pp (m) c A 50–150 0.00035–0.0004 150–210 0.0002 210–260 0.0001 260–300 0 300–350 0.0001 350–4000 0.00025 3.2.4 Method of Hughes–Prohaska This approach decomposes the total resistance (coefficient) as follows: c T D 1 Ck Ð c F0 C c w Both form factor 1 C k and wave resistance coefficient c w are assumed to be the same for model and full scale, i.e. independent of R n . The model test serves primarily to determine the wave resistance coefficient. The procedure is as follows: 1. Determine the total resistance coefficient in the model test as for the ITTC 1957 method: c Tm D R Tm 1 2 m Ð V 2 m Ð S m 2. Determine the wave resistance coefficient, same for model and ship: c w D c Tm c F0m Ð 1 Ck 3. Determine the total resistance coefficient for the ship: c Ts D c w C c F0s Ð 1 Ck C c A 4. Determine the total resistance for the ship: R Ts D c Ts Ð 1 2 s V 2 s S s The frictional coefficients c F0 for flat plates are determined by Hughes’ formula: c F0 D 0.067 log 10 R n 2 2 The correlation coefficient c A differs fundamentally from the correlation coef- ficient for the ITTC 1957 method. Here c A does not have to compensate for scaling errors of the viscous pressure resistance. ITTC recommends universally c A D 0.0004. The Hughes–Prohaska method is a form factor method. The form factor 1 Ck is assumed to be independent of F n and R n and the same for model and ship. The form factor is determined by assuming: c T c F0 D 1 C k C ˛ F 4 n c F0 74 Practical Ship Hydrodynamics 0 0.2 0.4 0.6 0.8 1.0 F n 4 / C Fo 1.0 1.1 1.2 1.3 1.4 C T / C Fo (1+ K ) Figure 3.7 Extrapolation of form factor Model test results for several Froude numbers (e.g. between 0.12 and 0.24) serve to determine ˛ in a regression analysis (Fig. 3.7). 3.2.5 Method of ITTC 1978 This approach is a modification of the Hughes–Prohaska method. It is gener- ally more accurate and also considers the air resistance. The total resistance (coefficient) is again written in a form factor approach: c Ts D 1 Ckc Fs C c w C c A C c AA c w is the wave resistance coefficient, assumed to be the same for model and ship, i.e. independent of R n . c Fs is the frictional coefficient, following the ITTC 1957 formula. c A is the correlation coefficient which depends on the hull roughness: c A Ð 10 3 D 105 Ð 3 k s L oss 0.64 k s is the roughness of the hull, L oss is the wetted length of the full-scale ship. For new ships, a typical value is k s /L oss D 10 6 ,i.e.c A D 0.00041. c AA considers globally the air resistance as follows: c AA D 0.001 Ð A T S A T is the frontal area of the ship above the waterline, S the wetted surface. The model test serves primarily to determine the wave resistance coeffi- cient. The procedure is similar to the procedure for Hughes–Prohaska, but the frictional coefficient is determined following the ITTC 1957 formula instead of Hughes’ formula. The form factor is also determined slightly differently: c T c F D 1 Ck C ˛ Ð F n n c F Both n and ˛ are determined in a regression analysis. Resistance and propulsion 75 3.2.6 Geosim method of Telfer Telfer proposed in 1927 to perform model tests with families of models which are geometrically similar, but have different model scale. This means that tests are performed at the same Froude number, but different Reynolds numbers. The curve for the total resistance as a function of the Reynolds number is then used to extrapolate to the full-scale Reynolds number. Telfer plotted the total resistance coefficient over log R 1/3 n . For each model, a curve of the resistance is obtained as a function of F n . Points of same Froude number for various model scales are connected by a straight line which is easily extrapolated to full scale. Telfer’s method is regarded as the most accurate of the discussed predic- tion methods and avoids theoretically questionable decomposition of the total resistance. However, it is used only occasionally for research purposes as the costs for the model tests are too high for practical purposes. 3.2.7 Propulsion test Propulsion tests are performed to determine the power requirements, but also to supply wake and thrust deduction, and other input data (such as the wake field in the propeller plane) for the propeller design. The ship model is then equipped with a nearly optimum propeller selected from a large stock of propellers, the so-called stock propeller. The actual optimum propeller can only be designed after the propulsion test. The model is equipped with a propulsive drive, typi- cally a small electro-motor (Fig. 3.8). Acceleration and retardation clutch Mechanical dynamometer F D Trim meter FP Model AP Propeller dynamometer Electr. motor Carriage Figure 3.8 Experimental set-up for propulsion test The tests are again performed for Froude similarity. The total resistance coefficient is then higher than for the full-scale ship, since the frictional resis- tance coefficient decreases with increasing Reynolds number. This effect is compensated by applying a ‘friction deduction’ force. This compensating force is determined as follows (see section 3.2.5): F D D 1 2 Ð V 2 m Ð S m Ð 1 Ckc Fm c Fs c A c AA The propeller then has to produce a thrust that has to compensate the total resis- tance R T minus the compensating force F D . The propulsion test is conducted with constant speed. The rpm of the propeller is adjusted such that the model 76 Practical Ship Hydrodynamics is in self-propelled equilibrium. Usually the speed of the towing tank carriage is kept constant and the rpm of the propeller varied until an equilibrium is reached. A propeller dynamometer then measures thrust and torque of the propeller as a function of speed. In addition, dynamical trim and sinkage of the model are recorded. The measured values can be transformed from model scale to full scale by the similarity laws: speed V s D p Ð V m ,rpm n s D n m / p , thrust T s D T m Ð s / m Ð 3 , torque Q s D Q m Ð s / m Ð 4 .A problem is that the propeller inflow is not geometrically similar for model and full scale due to the different Reynolds number. Thus the wake fraction is also different. Also, the propeller rpm should be corrected to be appropriate for the higher Reynolds number of the full-scale ship. The scale effects on the wake fraction are attempted to be compensated by the empirical formula: w s D w m Ð c Fs c Fm C t C 0.04 Ð 1 c Fs c Fm t is the thrust deduction coefficient. t is assumed to be the same for model and full scale. The evaluation of the propulsion test requires the resistance characteris- tics and the open-water characteristics of the stock propeller. There are two approaches: 1. ‘Thrust identity’ approach The propeller produces the same thrust in a wake field of wake fraction w as in open-water with speed V s 1 w for the same rpm, fluid properties etc. 2. ‘Torque identity’ approach The propeller produces the same torque in a wake field of wake fraction w as in open-water with speed V s 1 w for the same rpm, fluid properties etc. ITTC standard is the ‘thrust identity’ approach. It will be covered in more detail in the next chapter on the ITTC 1978 performance prediction method. The results of propulsion tests are usually given in diagrams as shown in Fig. 3.9. Delivered power and propeller rpm are plotted over speed. The results of the propulsion test prediction are validated in the sea trial of the ship introducing necessary corrections for wind, seaway, and shallow water. The diagrams contain not only the full-load design condition at trial speed, but also ballast conditions and service speed conditions. Service conditions feature higher resistance reflecting the reality of the ship after some years of service: increased hull roughness due to fouling and corrosion, added resistance in seaway and wind. 3.2.8 ITTC 1978 performance prediction method The ITTC 1978 performance prediction method (IPPM78) has become a widely accepted procedure to evaluate model tests. It combines various aspects of resistance, propulsion, and open-water tests. These are comprehensively reviewed here. Further details may be found in section 3.2.5, section 3.2.7 and section 2.5, Chapter 2. The IPPM78 assumes that the following tests have Resistance and propulsion 77 40 30 20 P B n 10 Service allowance 0 3 rev / s P B ⋅ 10 3 (kW) 2 1 0 Trial fully loaded Trial fully loaded 6 7 8 9 10 11 V (m/s) Service allowance 80% Ballasted Ballasted 80% 20% 20% Figure 3.9 Result of propulsion test been performed yielding the corresponding results: resistance test R Tm D fV m open-water test T m D fV Am ,n m Q m D fV Am ,n m propulsion test T m D fV m ,n m Q m D fV m ,n m R T is the total resistance, V the ship speed, V A the average inflow speed to the propeller, n the propeller rpm, K T the propeller thrust coefficient, K Q the propeller torque coefficient. Generally, m denotes model, s full scale. The resistance is evaluated using the ITTC 1978 method (for single-screw ships) described in section 3.2.5: 1. Determine the total resistance coefficient in the model test: c Tm D R Tm 1 2 m Ð V 2 m Ð S m 2. Determine the frictional resistance coefficient for the model following ITTC 1957: c Fm D 0.075 log 10 R nm 2 2 The Reynolds number of the model is R nm D V m L osm / m ,whereL os is the wetted length of the model. L os is the length of the overall wetted surface, i.e. usually the length from the tip of the bulbous bow to the trailing edge of the rudder. 78 Practical Ship Hydrodynamics 3. Determine the wave resistance coefficient, same for model and ship: c w D c Tm 1 C kc Fm The determination of the form factor 1 Ck is described below. 4. Determine the total resistance coefficient for the ship: c Ts D c w 1 Ckc Fs C c A C c AA c Fs is the frictional resistance coefficient following ITTC 1957, but for the full-scale ship. c A is a correlation coefficient (roughness allowance). c AA considers the air resistance: c A D 105 3 k s L oss 0.64 Ð 10 3 k s is the roughness D1.5 Ð10 4 m and L oss the wetted length of the ship. c AA D 0.001 A T S s A T is the frontal area of the ship above the water, S s the wetted surface. 5. Determine the total resistance for the ship: R Ts D c Ts Ð 1 2 s V 2 s S s The form factor is determined in a least square fit of ˛ and n in the function: c Tm c Fm D 1 Ck C˛ Ð F n n c Fm The open-water test gives the thrust coefficient K T and the torque coefficient K Q as functions of the advance number J: K Tm D T m m n 2 m D 4 m K Qm D Q m m n 2 m D 5 m J D V Am n m D m D m is the propeller diameter. The model propeller characteristics are trans- formed to full scale (Reynolds number correction) as follows: K Ts D K Tm C 0.3Z c D s P s D s Ð C D K Qs D K Qm 0.25Z c D s Ð C D Z is the number of propeller blades, P s /D s the pitch-diameter ratio, D s the propeller diameter in full scale, c the chord length at radius 0.7D. C D D C Dm C Ds This is the change in the profile resistance coefficient of the propeller blades. These are computed as: C Dm D 2 1 C 2 t m c m 0.044 R 1/6 nco 5 R 2/3 nco Resistance and propulsion 79 t is the maximum blade thickness, c the maximum chord length. The Reynolds number R nco D V co c m / m at 0.7D m ,i.e.V co D V 2 Am C 0.7n m D m 2 . C Ds D 2 1 C 2 t s c s 1.89 C 1.62 log 10 c s k p 2.5 k p is the propeller blade roughness, taken as 3 Ð 10 5 if not otherwise known. The evaluation of the propulsion test requires the resistance and open-water characteristics. The open-water characteristics are denoted here by the index f v. The results of the propulsion test are denoted by pv: K Tm,pv D T m m Ð D 4 m Ð n 2 m K Qm,pv D Q m m Ð D 5 m Ð n 2 m Thrust identity is assumed, i.e. K Tm,pv D K Tm,fv . Then the open-water diagram can be used to determine the advance number J m . This in turn yields the wake fraction of the model: w m D 1 J m D m n m V m The thrust deduction fraction is: t D 1 C F D R Tm T m F D is the force compensating for the difference in resistance similarity between model and full-scale ship: F D D 1 2 Ð V 2 m Ð S Ð 1 C kc Fm c Fs c A c AA With known J m the torque coefficient K Qm,fv can also be determined. The propeller efficiency behind the ship is then: Á bm D K Tm,pv K Qm,pv Ð J m 2 The open-water efficiency is: Á 0m D K Tm,fv K Qm,fv Ð J m 2 This determines the relative rotative efficiency: Á R D Á bm Á 0m D K Qm,fv K Qm,pv While t and Á R are assumed to be the same for ship and model, the wake fraction w has to be corrected: w s D w m c Fs c Fm C t C 0.04 1 c Fs c Fm 80 Practical Ship Hydrodynamics A curve for the parameter K T /J 2 as function of J is introduced in the open- water diagram for the full-scale ship. The design point is defined by: K T J 2 s D T s s Ð D 2 s Ð V 2 As D S s 2D 2 s Ð c Ts 1 t1 w s 2 The curve for K T /J 2 can then be used to determine the corresponding J s . This in turn determines the torque coefficient of the propeller behind the ship K Qs D fJ s and the open-water propeller efficiency Á 0s D fJ s .The propeller rpm of the full-scale propeller is then: n s D 1 w s Ð V s J s D s The propeller torque in full scale is then: Q s D K Qs Á R s Ð n 2 s Ð D 2 s The propeller thrust of the full-scale ship is: T s D K T J 2 s Ð J 2 s Ð s Ð n 2 s Ð D 4 s The delivered power is then: P Ds D Q s Ð 2 Ðn s The total propulsion efficiency is then: Á Ds D Á 0 Ð Á R Ð Á Hs 3.3 Additional resistance under service conditions The model test conditions differ in certain important points from trial and service conditions for the real ship. These include effects of ž Appendages ž Shallow water ž Wind ž Roughness ž Seaway Empirical corrections (based on physically more or less correct assumptions) are then used to estimate these effects and to correlate measured values from one state (model or trial) to another (service). The individual additional resis- tance components will be briefly discussed in the following. ž Appendages Model tests can be performed with geometrically properly scaled appendages. However, the flow around appendages is predominantly governed by viscous forces and would require Reynolds similarity. Subsequently, the measured forces on the appendages for Froude similarity [...]... allows one to estimate the speed loss for weak shallow-water influence The figure √Am /H 0.9 0.8 % 10 9 0.7 8 7 6 5 0.6 4 3 0 .5 2 0.4 1% 0.3 0.1 % 0.2 0.1 0 Figure 3.10 0.1 0.2 0.3 0.4 0 .5 0.6 0.7 0.8 V 2/ (g.H) Percentage loss of speed in shallow water (Lackenby (1963)) 82 Practical Ship Hydrodynamics follows Schlichting’s hypothesis that the wave resistance is the same if the wave lengths of the transversal... created by the ship do not propagate ahead (This condition is not valid for shallow water cases when the flow becomes unsteady and soliton waves are pulsed ahead For subcritical speeds with depth Froude number Fnh < 1, this poses no problem.) ž Decay condition: the flow is undisturbed far away from the ship 86 Practical Ship Hydrodynamics ž Open-boundary condition: waves generated by the ship pass unreflected... the conversion from parent ship to design ship Such a more or less sophisticated plus/minus conversion from a parent ship is currently the preferred choice for a quick estimate All of the systematical series and most of the regression analysis approaches are outdated They often underestimate the actual resistance of modern ship hulls It may come as a surprise that older ships were apparently better... cross-section S¨ ding o (19 95) gives a Fortran routine to compute Michell’s integral The classical methods (thin ship theories, slender-body theories) introduce simplifications which imply limitations regarding the ship s geometry Real ship geometries are generally not thin or slender enough The differences between computational and experimental results are consequently unacceptable Practical applications... approaches are: ž estimate from parent ship, e.g by admiralty or similar formulae ž systematical series, e.g Taylor–Gertler, Series-60, SSPA ž regression analysis of many ships, e.g Lap–Keller, Holtrop–Mennen, Hollenbach The estimate from a parent ship may give good estimates if the parent ship is close enough (in geometrical properties and speed parameters) to the design ship The admiralty formula is very... unconventional ships with many and complex appendages, the difficulties in estimating the resistance of the appendages properly leads to a larger margin of uncertainty for the global full-scale prediction Schneekluth and Bertram (1998) compile some data from shipbuilding experience: properly arranged bilge keels contribute only 1–2% to the total resistance of ships However, trim and ship motions in... limited to global predictions, as they represent the hull shape by few global parameters 3 .5 CFD approaches for steady flow 3 .5. 1 Wave resistance computations The wave resistance problem considers the steady motion of a ship in initially smooth water assuming an ideal fluid, i.e especially neglecting all viscous effects The ship will create waves at the freely deformable water surface The computations involve... expression ‘wave resistance problem’ is easier than ‘steady, inviscid straight-ahead course problem’, and thus more popular 84 Practical Ship Hydrodynamics The work of the Australian mathematician J H Michell in 1898 is seen often as the birth of modern theoretical methods for ship wave resistance predictions While Michell’s theory cannot be classified as computational fluid dynamics in the modern sense,... Michell expressed the wave resistance of a thin wall-sided ship as: Rw D 4 2 1 V2 2 2 1 jA j2 d 1 with: A D e i 2 zCi x f x, z dz dx S V is the ship speed, water density, D g/V2 , g gravity acceleration, f x, z halfwidth of ship, x longitudinal coordinate (positive forward), z vertical coordinate (from calm waterline, positive upwards), S ship surface below the calm waterline The expression gives realistic... added resistance of a ship in a seaway is generally determined by computational methods and will be discussed in more detail in the chapters treating ship seakeeping Such predictions for a certain region or route depend on the accuracy of seastate statistics which usually introduce a larger error than the actual computational simulation Ship size is generally more important than ship shape Schneekluth . 73 Table 3.1 Recommended values for C A L pp (m) c A 50 – 150 0.000 35 0.0004 150 –210 0.0002 210–260 0.0001 260–300 0 300– 350 0.0001 350 –4000 0.000 25 3.2.4 Method of Hughes–Prohaska This approach decomposes. from the ship. 86 Practical Ship Hydrodynamics ž Open-boundary condition: waves generated by the ship pass unreflected any artificial boundary of the computational domain. ž Equilibrium: the ship is. 0 .5 0.6 0.7 0.8 V 2 /( g . H ) 0.1 0.2 0.3 0.4 0 .5 0.6 0.7 0.8 0.9 √ A m / H 10% 9 8 7 6 5 4 3 2 1% 0.1% Figure 3.10 Percentage loss of speed in shallow water (Lackenby (1963)) 82 Practical Ship
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