2. PROPELLER GEOMETRY

Transcription

1 a) Fames of Refeence 2. PROPELLER GEOMETRY 10 th Intenational Towing Tank Committee (ITTC) initiated the pepaation of a dictionay and nomenclatue of ship hydodynamic tems and this wok was completed in shaft axis X (fowad) O Y (stabod) Z (downwad) The global efeence fame poposed by the ITTC is a ight-handed ectangula Catesian system. Fo popelle geomety it is convenient to define a local efeence fame having a common axis such that OX and Ox ae coincident but Oy and Oz otate elative to the OY and OZ fixed global fame. z x X Global fame Local fame φ O Y y Z 1

2 b) Popelle Refeence Lines The line nomal to the shaft axis is called eithe popelle efeence line o diectix. In the case of contollable pitch popelle the spindle axis is used as synonymous with the efeence line. Geneato line: The line fomed by intesection of the pitch helices and the plane containing the shaft axis and popelle efeence line. The aeofoil sections which togethe compise the blade of a popelle ae defined on the sufaces of cylindes whose axes ae concentic with the shaft axis. 2

3 Face: The side of a popelle blade which faces downsteam duing ahead motion is called face o pessue side (when viewed fom aft of a ship to the bow the seen side of a popelle blade is called face o pessue side). Back: The side of a popelle blade which faces geneally diection of ahead motion is called back o suction side (when viewed fom aft of a ship to the bow the unseen side of a popelle blade is called back o suction side). Leading Edge: When the popelle otating the edge piecing wate is called leading edge. Tailing Edge: When the popelle otating the edge tailing the leading edge is called tailing edge. c) Pitch Conside a point P lying on the suface of a cylinde of adius which is at some initial point P 0 and moves as to fom a helix ove the suface of a cylinde. The popelle moves fowad as to otate and this movement ceates a helix. When the point P has completed one evolution of helix that means the angle of otation: 3

4 φ = 360 o o 2π the cylinde intesects the X-Z plane and moves fowad at a distance of P. If the cylinde is opened out the locus of the point P lies on a staight line. In the pojection one evolution of the helix aound the cylinde measued nomal to the OX axis is equal to 2π. The distance moved fowad by the helical line duing this evolution is p and the helix angle is given by: p θ = tan 1 2π The angle θ is temed the pitch angle and the distance p is the pitch. Thee ae seveal pitch definitions. α whee θ 0 is the effective pitch angle of the popelle θ nt o θ is the geometic pitch angle of the popelle β i is the hydodynamic pitch angle α is the angle of attack of section 1- Nose-tail pitch: The staight line connecting the extemities of the mean line o nose and tail of a popelle blade is called nose-tail pitch line The section angles of attack ae defined to the nose-tail line. 2- Face pitch: The face pitch line is basically a tangent to section s pessue side suface and you can daw so many lines to the pessue side. Theefoe its 4

5 definition is not clea. It is aely used but it can be seen in olde dawings like Wageningen B seies. 3- Effective o no-lift pitch: It is the pitch line of the section coesponding to aeodynamic no-lift line which esults zeo lift. 4- Hydodynamic pitch: The hydodynamic pitch angle (β i ) is the pitch angle at which the incident flow encountes the blade section. Effective pitch angle (θ 0 ) = Noise-tail pitch angle (θ, θ nt ) + 3-D zeo-lift angle whee 3-D zeo lift angle is the diffeence between θ 0 and θ. θ 0 = Hydodynamic pitch angle (β i ) + Angle of attack of section (α) + 3-D zeo lift angle Pitch values at diffeent adii ae called adial pitch distibution. Slip Ratio If the popelle woks in a solid medium (has no slip), i.e. if the wate which the popelle scews itself though does not yield (i.e. if the wate did not acceleate aft), the popelle will move fowad at a speed of V = p n, whee n is the popelle s ate of evolution, as seen in the below figue. The simila situation is shown fo a cokscew, and because the cok is a solid mateial, the slip is zeo and, theefoe, the cok scew always moves fowad at a speed of V = p n. Howeve, as the wate is a fluid and does yield (i.e. acceleate aft), the popelle s appaent speed fowad deceases with its slip and becomes equal to the ship s speed V, and its appaent slip can thus be expessed as p n V. 5

6 The appaent slip atio S A, which is non-dimensional, is defined as: S A pn V = = 1 pn V pn The eal slip atio S R, which gives a tue function of the popelle function, is: S R pn VA VA = = 1 pn pn 6

7 d) Skew It is the angle between the mid-chod position of a section and the diectix (θ s ). The popelle skew angle (θ sp ) is defined as the geatest angle measued at the shaft cente line which can be dawn between lines passing fom the shaft centeline though the mid chod position of any two sections. The skew can be classified into two types: i- Balanced skew: Diectix intesects with the mid-chod line at least twice. ii- Biased skew: Mid-chod locus cosses the diectix not moe than once nomally in the inne sections. 7

8 8 e) Rake The displacement fom the popelle plane to the geneato line in the diection of the shaft axis is called ake. The popelle ake is divided into two components: geneato line ake (i G ) and skew induced ake (i s ) which ae defined as: ) tan( ) ( ) ( ) ( ) ( nt s s s G T i i i i θ θ = + =

9 f) Popelle Outlines and Aeas Thee ae five diffeent outlines and associated aeas of popelle in use. These ae: 1. Disc outline (aea) (A 0 ) 2. Pojected outline (A p ) 3. Developed outline (A D ) 4. Expanded outline (A E ) 5. Swept outline (A S ) 1. Disc aea: The aea of the cicle swept out by the tips of the blades of a 2 πd popelle diamete ( A0 = ) Pojected outline: It is the view of the popelle blade that is actually seen when the popelle is viewed along the shaft centeline nomal to y-z plane (when viewed fowad). R A = Z ( θ θ ) d whee Z is the numbe of blades. h is the hub adius of the popelle. R is the tip adius of the popelle. p h TE 3. Developed outline: It is a helically based view, but the pitch of each section has been educed to zeo. The intesection of the blade with the axial cylinde is otated along the blade efeence line into a plane paallel to the popelle. The amount of otation is equal to the pitch angle at evey adius. 4. Expanded blade outline: It is eally not an outline in any tue geometic sense at all. It is a plotting of the chod lengths at thei coect adial stations about the diectix. Such that the outline is constucted by laying off at each LE 9

10 adius, the chod length along a staight line. The outline is fomed by the locus of the end points of the chod lines laid out in the above manne. 5. Swept Outline: This outline is swept by the leading and tailing edges when the popelle is otating. In geneal, the developed aea is geate than the pojected aea and slightly less than the expanded aea. g) Blade Sections-NACA Definitions Mean line o cambe line: is the location of mid-points between uppe and lowe sufaces when measued pependicula to the cambe line. Chod length (c): The distance between the leading edge and tailing edges when measued along the chod line is temed as chod length of the section Cambe: is the maximum distance between the cambe line and chod line. Thickness: of a section is the distance between uppe and lowe sufaces of the section also measued pependicula to the chod line. Leading edges ae usually cicula having a leading edge adius defined about a point on the cambe line. Typical section used fo ship popelle is NACA66 seies with the mean line a=0.8 The uppe and lowe coodinates of the pofile ae given as: x U = x C x L =x C y U =y C +y t y L =y C -y t whee y C is the cambe odinate obtained fom the table, y t is the odinate of the chosen symmetical thickness distibution. 10