MICROFICHE REFERENCE LIBRARY A project of Volunteers Desiun Of . . Su -4 Communitie, by: in Asia Water TUK- for Farms and Small MohammadDt,-ali Published by: Technology Adaptation Program Massachusetts Institute of Technology Cambridge, MA 02139 USA Paper copies are $ 7.00. Available from: Technology Adaptation Program Massachusetts Institute of Technology Cambridge, MA 02139 USA Reproduced by permission of the Technology Adaptation Program, Massachusetts Institute Technology. of Reproduction of this microfiche document in z : form is subject to the same restrictions as ti:;se of the original document. : : t .‘ijI:;j;‘; ,:: I .; A :,:_j::: .: : ‘, /. :;,, ,, ‘. DESIGN OF SMALL WATER TURBINES FOR FARMS AND SMALL COMMUNITIES Mohammad Durali Project David supervisor: Gordon Spring Wilson 1976 TECHNOLOGY ADAPTATION PROGRAM Massachusetts Cambridge, Institute of Technology Massachusetts 02139 L>, ; ‘” . ! , ,, . CONTENTS CONTENTS., *..................... 5 LISTOFFIGURES..................... 7 PREFACE......................... 9 ACXNOWLEDGEMENT. . . . . . . . . . . . . . . . . . . . . 11 ABSTBACT........................13 CHAPTER 1 1.1 1.2 1.3 CHAPTER 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 CHAPTER 3 3.1 3.2 3.3 3.4 3.5 CHAPTER 4 4.1 4.2 INTRODUCTION. . . . . . . . . , . . . . . . . 15 Background, 10 Problem Statement, 10 Principles of Our Approach, DESIGN OF A CROSS-FLOW (BANKI) 11 TURBINE. . . . 19 Description, 19 Advantages of Bank Turbine, 19 Analysis of the Machine, 21 Design of the Rotor, 24 Losses and Efficiencies, 32 Blade Design, 37 Sizing of a Cross Flow Turbine,, 46 Mechanical Design, 51 Evaluation of Efficiencies, 57 Radial-Inflow Partial-Admission Water Turbine, 58 DESIGN OF AXIAL-FLOW TURBINES . . . . . . . . 61 Description, 61 Advantages, 61 Analysis, 63 Design of Blades, 65 Sizing of the Machines, 68 DISCUSSION ON ADVANTAGES OF DIFFERENT TYPES . 89 Improvements on Reaction Off-Design Performance, Machine, 92 91 APPENDIX I TABLE OF PARTS AND WORKING DRAWINGS. . . . . 97 APPENDIX II FRICTION LOSS IN NONCIRCULAR CONDUITS . . ..147 5 APPENDIX III APPENDIX IV EFFICIENCIES. . . . . . . . . . . . . m 149 PERFORMANCE ESTIMATION OF AXIAL-h?LOW TURBINES c . . . . . . . . . . . * .* 153 LIST OF FIGURES PAGE TITLE NUMBER (Banki) Cross-Flow 2-2 Velocity Diagrams of Different Cross-Flow Turbine 2-3 Effect 2-4 Velocity 2-5 Work Coefficient Angle 6, 2-6 Converging Flow Inside 2-7 Cross-Flow Turbine-Blade 2-8 Ratio of Blade Radius of Curvature R and Rotor Length L over Rotor Outer Diameter vs. Rotor Inner-to-Outer Dia. Ratio m. 44 2-9 Ratio of Radius to Hydraulic Diameter R/Dh, and Deflection Angle of the Blade Passage Bc vs. Rotor Inner-to-Outer Dia. Ratio m. 44 2-10 Number of Blades Ratio m. Dia. 45 2-11 Radial-Inflow Turbine 59 3-1 Inlet and &t' -et Velocity Flow Turbine Stage 3-2 Blade 3-3 Impulse 3-4 B?ade Sections Turbine 3-5 Reaction of Blade Water 20 2-l Outlet Diagram Turbine Angle Locations in 26 on Stalling 28 Terminology Iy vsO Relative Z vs. Inlet Flow the Rotor 38 Inner-to-Outer Water Diagrams of Axial- Terminology Velocity 31 35 Terminology Partial-Admission Velocity 22 62 66 Diagram of the Axial-Flow Diagram 7 69 Impulse 75 83 LIST OF FIGURES (Continued) TITLE NUMBER Sections PAGE 3-6 Blade of the Axial-Flow Reaction Turbine 85 4-1 Characteristic Curves Constant Flow Rate of Reaction Machine for 93 4-2 Characteristic Curves Constant Speed of Reaction Machine in 94 1 Loss Factor Nov. 65) (ASCE, J. Hydraulic 2 Friction Factor f vs Re. for Different e/D. (Rohsenow, W.M., and Choi , H.Y., Heat, Ma%, and Momentum Transfer, p. 58) 148 Scheme of Losses 151 APPENDIX II for Bends Div., 148 APPENDIX III 1 in Water Turbo-Generators APPENDIX IV 1 Turbine Blade and Velocity 2 Lift 3 contraction 4 Basic 5 Trailing 6 Profile 7 Secondary Loss-Aspect 8 Secondary Loss-Basic Parameter, 156 156 for Traction Profiles Loss Ratio 157 157 Edge Thickness Loss Notation FL Ratio Profile Triangle Losses Against Ratio Loss 8 Reynolds Factor Factor 157 Number Effect 158 158 158 PREFACE This report is one of a series of publications which describe various studies undertaken under the sponsorship of the Technology Adaptation Program at the Massachusetts Institute of Technology. In 1971, the United States Department of State, through the Agency for International Development, awarded the Massachusetts Institute of Technology a grant. The purpose of this grant was to provide support at M.I.T. for the development, in conjunction with institutions in selected developing countries, of capabilities useful in the adaptation of technologies and problem-solving techniques to the needs of those countries. the Technology Adaptation Program provides the At M.I.T., means by which the long-term objective for which the A.I.D. grant was made, can be achieved. The purpose of this project was to study alternative water turbines producing 5-kw electric power from an available hydraulic head of 10 m and sufficient amount of flow, and to recommend one for manufacture. The work consisted of the preliminary turbine which could be used for this and designed completely. A complete for the selected type. design of different types of water application. Then one was selected set of working drawings was produced Four different types of water turbine were studies: a cross-flow (Banki); two types of axial-flow turbine; and a radial-flow turbine. Each one has some disadvantages. One of the axial-flow turbine (one with rotor blades having 50% degree of reaction) was chosen for detailed design as presenting the optimum combination of simplicity and efficiency. In the process of making this T.A.P.-supported study, some insight has been gained into how appropriate technologies can be identified and adapted to the needs of developing countries per se, and it is expected that the recommendations developed will serve as a guide to other developing countries for the solution of similar problems which may be encountered there. Fred Moavenzadeh Program Director 9 ACKNOWLEDGMENT This Program tional study which was sponsored is funded Development, and opinions author through United expressed and do not Technology, necessarily This project de Los Andes led in his report, the Agency for of State. The views however, reflect those support of are the during by the Aria those Interna- of the sponsors. the period of Mehr University for by the T.A.P. discussions by Francisco We are grateful from Adaptation the of Iran. was initiated Fred Moavenzadeh, Technology Department financial work has been provided Tehran, a grant States in this Mohammad Durali's research by the M.I.T. this with Rodriguez support program a group and Jorge director, at the Universidad Zapp. and help. David Gordon Wilson, project supervisor department of mechanical 11 engineering DESIGN OF SMALL WATER TURBINES FOR FARMS AND SMALL COMMUNITIES Mohammad Durali ABSTRACT The purpose of this project was to study alternative water turbines producing 5-kw electric power from an available hydraulic head of I.0 m and sufficient amount of flow, and to recommend one for manufacture. The work consisted of the preliminary design of different types of water turbine which could be used for this application. A complete set Then one was selected and designed completely. of working drawings was produced for the selected type. Four different types of water turbine were studied: a crosstwo types of axial-flow turbines; and a radial-flow flow (Banki); Each one has some advantages and some disadvantages. turbine. One of the axial-flow turbines (one with rotor blades having 50% degree of reaction) was chosen for detailed design as presenting the optimum combination of simplicity and efficiency. 13 Chapter 1 INTRODUCTION Not all produced consumers by main power small isolated costs needed Until the early electrical customers if they Sometimes plants. to afford the are to connect 1970's an ideal high wind, energy streams, more economical, small water provided it is power not worthwhile transmission way to produce main power. small available falls a simple for and maintenance amounts or gas-engine-driven naturally prices, to electrical to the nearest power was to use diesel- But with zun, have easy access generators. power and so forth sources can often and cheap device of for as be each case can te made. 1.1 BACKGROUND In the country are situated and there 1.2 plant and also farmers where flow is most needed. is not very main power this on streams is sufficient when power power of Colombia to the because prefer available Although farms their especially the price of transmission may be extremely the demand for to produce most coffee a head of 10 m can easily the cost high, in South America electricity be trapped during of mains the is times electric of power high. farms from Because seasonal, own electricity. PROBLEM STATEMENT The effort here is to design a machine which can produce the of many 16 5 kw electric power machine be used by farmers would technical structures. should than by mains the developed a half-kw model for hight;r total group regularly. been carried because of their one we have is plenty solution 1.3 of water) to energy for of using of engineering on this using this the transmitted units They have to modify our work has not This of sophistication. in a period of a cheap machine that to this previously might For applications needed the design problem. We have reported applications. electricity of the Universidad They plan water-turbine degree limited (i.e. very must not need skilled cost cost turbine. levels. of small to a high to avoid power plants. cross-flow The design As this have little is capital have worked power objects the machine Some members of the faculty de Los Andes in Bogota before. who on average the amortized be less produced mentioned Moreover Finally maintenance. machine the cases one of the major knowledge, complicated power for be like the of year when there may be a good problems. PRINCIPLES OF OUR APPROACH The effort was put into two different approaches to the problem. 3) Designing any simple workshop cut steel parts. a machine having which enough Consequently, can easily facilities the machine be manufactured to weld, can be built drill by and locally in 17 each farming generator tried area. etc., The parts can be shipped to use materials so on which do not more complicated b) shipped layout processes angle were a machine to farming is going like bars, which This to be arranged for like chain, In this sheet approach metal, to be used. round we bars Casting and and other excluded. locations. methods gears, to each area. need much machinery Designing production such as bearings, casting could be manufactured approach a kind manufacturing and of process the machine. and molding, and using The plastic parts seems to be more economical. In both of the next the rapid the capabilities turbine the of the design assumptions. desig? "b" a) and b), contains inflow design the industrial chapter "a" cases design has to be within the country of a cross-flow In the end of Chapter is of 2 modified of the two latter type of approach. discussed very axial-flow types of is turbines the user. turbine 2 design briefly, with based on the the area The based on of a simple Chapter 3 is short blades. assumptions about The made on Chapter 2 DESIGN OF A CROSS-FLOW (BANKI) 2.1 DESCRIPTION This machine Since ago. developed then which was .'irst its is energy The wheel water. curved horizontal plates to which of the nozzle is the tail water the inner 2.2 energy 2-l) is attached. through the inside through fixed impulse wheel of an inward between blades jet of assemblage The jet rotor the another 60 years have been a squirrel-cage-shaped (Fig. shaft of circular end of water coming out inward to twice. to direct the flow cage and then to drain set in another of blades it to the part of circumference. ADVANTAGES OF BANK1 TURBINE The cross-flow a suitable easy turbine solution the lubricated The atmospheric and well-sealed flow, as they and they has significant to our problem. to be manufactured. a complicated with kind from the kinetic space outward of this over good performances. have to be designed open internal Banki radial-flow simply passes by Dr. an atmospheric blades Tine biades the models and have given machine gets designed some low-power in Europe This it TURBINE housing. are out don't advantages Its simple rotor of the housing; need to be sealed. structure avoids The bearings they which make makes it the need for have no contact can simply And finally, when, be 20 TAIL-WATER ----P-P------I_--- -- -----m--e-- --- --- -v----- -- FIG.2-1. -me -- - - CROSS-FLOW (BANKI) - - WATER TURBINE. - 21 for a constant cross section simply 2.3 head and a given is obtained, use a longer higher power fixed levels rotor one can re7 tion in design of a turbomachine is the equation, where U stands component rotor, rotor velocity respectively fluid peripheral Subscripts enthalpy. the for of absolute The rotor of for a simple ANALYSIS OF THE MACHINE Euler the then level rotor. The most useful tion power leaving of the i and (Fig. normally is o fluid CC and stand is h, for the tangential is inlet the stagna- and outlet 2-l). designed the rotor ‘e. speed, is = 0 gc A i-o in so that the absolute the radial direction, velocity so and therefore ‘icei and then be the parameter = "work b coefficient" for the rotor will simply of 22 FIG.2-2. VELOCITY DIAGRAMS OF DIFFERENT LOCATIONS IN CROSS-FLOW TURBINE. 23 From the first law of thermodynamics, = = A i-o lil but for water static are turbines enthaipy to study the rate are very the drop h, small = A i-0 (h +" of heat and for in height from + zg) transfer small inlet units to outlet , and change like in the one we is negligible, so that, l3 T m using = the equations Ah, = we had before, uicei = Yu2 = i 3 (Cf - Ci) , $ cc; - 2) or finally u: = k (CI- cf, For an impulse equal AHo to 2.0. and cf kinetic written nN If the be taken energy machine total the value hydraulic as nozzle through of head before efficiency the nozzle) 'Y is then taken the nozzle is (which covers the equation (a) can be as follows, u2= & (2g AHorlN - cz,, i normally loss 24 or C2 = f (AH, ‘I~ - $ 1 ui From Eq. choice and hence that diagrams rotor for a given enables hydraulic head, us to determine the rotor dimensions. DESIGR OF THE ROTOR The choice important jet part of water through of of the blade the design. transfers to the circles deviation work this to the rotor is the so that in both angles are measured positive in direction point the at design angle geometry is is we have for true for one may question to 90" and the choice angles analysis very small we assume the derivation equal and outlet They have to be chosen useful and are we assume that This inlet the passes the blades. Throughout if we find of the velocity speed 2.4 (2.1) (LJ) inlet is all all angle as follows. of so that angle the design to be zero. shaft the incidence of rotation. is will zero Also and the not be affected From Fig. (2-2) inlet velocities. by simple cases why the (i.e. the from tangents speeds inter outlet and flow stage angle the second angle of of the first stage). the blades "stage" The reasoning But is taken or pass, behind this 25 in the Assume zero deviation angle for first therefore, the flow be equal pass; to the blade the blade at the outlet As you see there This time will situation is 8, < 90" take shown with the 9o". Now assume 6 (Fig. 2-3d). the If second slightly be near blade at the In this outlet the will angle 90' of (Fig. second 2-3a). pass. case positive in Fig. (2-3~) angle has a value angle at outlet of the is kept equal as deviation angle "i" (equal the values Therefore between 91" to 94O. not so that if the to 90 + 6/2) around first to 90" then i = 6 (in the blade's pressure there of a blade the of deviation optimum Obviously cause much effect Because water optimum 90' to 8O. not than angle there the inlet outlet angle the incidence then pass of is will to zero. Normally would that 2-3b). Consequently more than Now suppose Now as a comparison of incidence pass). velocity is bigger the blades B = 90". the blade be an angle relative incidence (Fig. place. leaving pass be negative Therefore will angle. of first will assume incidence outlet the flow the is cross-flow and flow Therefore or diffuse. passes through for taking are the tlade the blade of the order of Z" outlet is angle angle equal to 90 on the performance. turbine no static-pressure passage. accelerate value angle the In fact, rotor works difference flow through blade the blade totally from passage inlet a blade passages at atmospheric to outlet passage do not as a jet fill deflecting does with 26 \ 2 0 \ \ \ (4 (b) I FIG-z-3, \ EFFECT OF BLADE OUTLET ANGLE ON STALLING. along the pressure ,have a constant of friction) area (2-4a) velocity C, Let is at angle = U2 Consequently through will direction the the passage be determined the inner diameter are then as follows (first pass) and the absolute 2 is in radial rotor (Notice which specifications relative Fig. velocity and the maximum flow of the passage outlet of the blade. relative The rotor the side (Fig. 2-4b) (in side will the by the absence smaller of the (Fig. B, = 90" velocity flow rotor. 2-4): so from of water leaving 01~ = 90". us define that in this particular case x is equal to the work coefficient.) and r2 m3- rl r2 and r are 1 inner and outer radii of the blading respectively, therefore m= u2 u3 'il The above definitions = will UC help l us to write simpler geometric relations. From Fig. x (Z-4a) f -51 ul we have = Cl cos a1 ul = cos a - cl 1 -cl cos a1 + w1 cos (3, (2.2) 28 (4 FIG.2-4. VELOCITY DIAGRAM TERMINOLOGY. 29 Also, C rl from (2.2) = Cl sin(IT - al> = Wl sin(?I - 8,) (2,3) and (2.3) tan B, x = B, = B, - tan al) (tan Therefore From the outlet tan-'(( velocity 2 1 tan al) triangle (Fig. (2.4) 2-4a) c2=J wf+u; If we assume no loss then along the relative the blade c2 of kinetic velocity passage, energy of the water so using Eqs. through the blade has to remain (2.2) and (2.3) = ulpyi$7 . passage, unchanged we have 0.5) But c2 Combining (2.6) -5z u2 cos a and (2.5) = 2 m 3 cos c% (2.6) 2 we have, u2 =cos-lJ$$-j- (2.7) 30 From Fig. (2-4b) we have; cos(lT-f3) but 4 as illustrated and deviation (2.8) before angles = u2 Therefore "stage" we found geometry second-stage -1 (2.8) at any condition ~1~ = a2 are assumed to be zero then and if B, = B, incidence so from ' (- 1 - m cos B 1 = tan -1 1 m cos B, two values (Eq. conditions. nondimensional tan 1 m tan cx 3 = we have: tan a2 5 u3 .rn W 3 = relation (2.7)) (2.9) for c12 ' one by using and the other Putting between these the was found two values design parameters the first by using equal the we get m , x a and as follows: 1 m cosB (2.10) l)=cos-lJg-Tp 6 FIG.2-5. WORK COEFFICIENT$fVS. RELATIVE 1iYLiT FLOW ANGLED,. 32 Notice that a1 , x Now design help curves to choose may be,values Solving right of Figure x value vs. related of x (2.10) for for vs. together Eqs. of the B, 2-5 shows Eq. are 6, can be drawn using the and values b,)> and (2.4) for the design the value curves of X may curves of nozzle values based which Two useful values different (2.4). and (2.10) parameters. different % by Eq. angle of m . on Eq. (2.4). we get \ x = 1 m cosf3 -1 cos tan For any value of m and B, vice versa. 2.5 LOSSES AND EFFICIENCIES In cross-flow bent strips angle could cause high can be listed of flow flow blades incidence in in the nozzle (2.11) can be found, or made of curved variations in inlet Summarily the other due to skin and blade inside x are normally losses. losses open space of So small metal. hydraulic as: direction converging sheet I2 -1+1 1 1 m cos B 1 the value machines, of thin ( friction passages; the rotor; losses flow losses and change due to and mechanical losses. a> Nozzle losses For nozzle factor a factor can be used to define converging flow, so cv the which losses acts as a velocity due to skin friction correction and 33 or For the loss Appendix I, defined due to the curved will be used, the radius provides for provided passage the a hydraulic curve diameter given in is as Dh If nozzle = 4 x flow area wetted perimeter of curvature the values different values is of loss of (2.12) R then factor k the curve versus in Appendix deflection I angle R/Dh , where W2 1 % oss and is W 1 = 5 the mean water the mean values of R velocity and Dh through should the nozzle. be used Obviously to get a better ' result. b) Blade losses I> for the diameter, Hydraulic-friction flow through and using losses. blade the passages curve given The coefficient can be found in Appendix of based I. So friction on hydraulic 34 % oss subscript h diameter. "L" relative stands flow II) is due to flow direction within in Appendix As seen in Fig. 2-6, flow converges direction As seen in Fig. incidence angle "y" angle It "0". is the right-hand 40". For these is very d) cause range 2-6 jets I, the by this that will negative W is the of magnitude In this the case we the nozzle. of actual This second velocity effect set will leaving cause the maximum is half of the admission central stream line remains the admission angle is, the closer get to the work for inner surface on the second as small pass. of the angle angle the loss A is between 20* to due to this small. Efficiencies Normally defined as; the overall efficiency for a water rotor Therefore as possible. admission of admission a of blades. geometry, effect has to be kept values as for from simple the bigger of admission reasonable and change, the direction entering assumed side will the angle of hydraulic passage to one point. caused Also undeflected. and that on basis of the blade rotor in evaluated length given blades change values the different w2 velocity. Losses Losses for the can use the curve 4 L fhTxz' = turbine is effect 35 F&2-6. CONVERGING FLOW INSIDE THE ROTOR. 36 where all is nh the hydraulic the hydraulic losses efficiency across of the turbine, and covers {See also the blading. Appendix 11). 'h where AH turbine - stands inlet T between or mechanical rim friction and bearings hydraulic head of the T-I Q and the flow efficiency covers and so on and is all the defined losses as; T - Tloss T = represents Finally leakages difference and outlet. rl, where AH for The term due to disk AH - Hloss the is shaft torque. the volumetric which passes efficiency the turbine which without covers the giving any power where Q is the volume The important a turbine is to find part flow rate. of the the hydraulic evaluation efficiency. of the This efficiency term of is very 37 sensitive to the blade In order to get Eq. last section 2.6 BLADE DESIGN (2.15), in terms to the output the bending only a relatively long plates two end plates power rotor can be reinforced level smaller rotor speed. The cost higher complexity. with will be cut out the whole diameter for rotors i.e. with longer stiffer having is all transexperience the blades one would radial between Therefore volume flow like chord. the blades for rate, if a the one r-an go for and hence advantages we have chosen, no stiffer any torque small rotors. rotors of a circle. tubes, the as at each moment plates apparent joined. Therefore a specified of design in con- the blades stress, flow. and longer these turbine turbine transmission, and blades with III). mentioned the may be used to support be segments of thin-wall are so that periodic and hence For the type concerned the blades and so allow given the losses by the blades, blades crossflow in a crossflow shaft, higb carry rotor Stiffer profiles to which shaft (see Appendix head. moment due to torque a few blades to avoid all the rotor do not have a through come under the before angles &ency of the of hydraulic of two end plates mitted all effic' one has to write As mentioned designs and flow the hydraulic using sists profile is that we will plates. Therefore or made of strips higher Also shaft of the only be the blade the blades of thin sheet can 38 Zr number of blades di: inner dia. doz outer dia. L =, length of FIG.&7. rotor CROSS-FLOW TURBINE-BLADE TERMINOLOGY. 39 metal rolled around specified is "ml' which affects length, a pipe. the ratio The most of inner most design parameters which relate to outer of the other number of blades, etc., parameters. m Eqs. (See Fig., of such as on other blade (2.13a) to 2-7 blade for to be the rotor parameters, of using parameter diameter rotor effect can be found these important (2.13f) notation.) 0 5 y- = 2y - 4 = B - dO c sin y = 2 R = 0 (2.13a) s (2J3b) sin QI (2.13~) (2.13d) 2 sinTBc/2) do - di c y + dO sin cos Q/2 = 2 (2.13e) C CT = dl The solidity to the Eqs. sin of It be easier (2.13a) to (2.13f) ' (5 is defined spacing will n/Z the blades (2.13f). as the ratio on the inner-diameter to work with Let's define of the blade side the nondimensional chord of the forms rotor. of 40 and then, = Y EIc/2 27-e= (2.14a) 2A sin y = 2 sin m sin As discussed passage curvature of the blade values that values is shorter of m. 3 (l-m) (2.14e) (2.14f) ' a function section camberline and the ratios inner-to-outer and more curved the hydraulic of the ratio the variation curvature of rctor = the last passage 2-8 shows the blade ($/2 n/Z in the blade Figure (2.14d) x = of the (2.14~) 4 y X cosy 4- sin diameter sin x 5 = 0 (2.14b) B-s (centerline) deflection of over of rotor diameter blades result the angle of outer ratio, from through radius over the ratio the loss of the hydraulic of the blade. the rotor length diameter versus These curves using bigger and show 41 As mentioned passage in Section is a function the passage hydraulic angle. Bigger values us less loss. Both geometrical 2.5 the loss of the ratio R/Dh diameter 8 of R/Dh these parameters and through and is C introduced ec , where the blade and smaller parameters values Dh is deflection 8c of can be found in Eqs. the blade in give terms of (2.13) and (2.14), the blade passage as follows: but = - Dh as defined as pointed out before, deflection of a jet so the jet thickness is of the blade diameter side of Dh that the flow pressure side relative velocity admission angle fairly rotor. = for side constant. aid = and the hydraulic by the inner- of Fig0 fill walls the wetted 2-7 we then perimeter the passage have guide through the the passage at the inner-diameter WIA = 'lL If flow. side a. --d 360 i as (L +2s) Only fully. have: Q the of the blade Consequently can be determined By the defining of water then pressure is 4 x (LXS) L + 2s does not and side through along passage the The reason flow of water diameter is 4 x flow -. wetted perimeter Wl and the blade's is a is the the of the rotor rotor we 42 but as m -5 di/do L Defining , then Q ci IT .Wl m d 0 360 = CI E c/s S C CT = h = c/d o and dO = these = into the relation a -7TmW 360 both 7rmW the denominator Q E a IT d2 W 360 01 then we have c’ 4--XDh = m we have: x ad 2>A 1 do and naming c’ Dh 1 do + 3% for x- do x 0 Q Dividing therefore, = 44 Dh (2.14) 0 k Substituting (Eq. 0 and the numerator by do 43 Also from Eqs. (2.14) 5 we have the +- definition of , 0 or R=tdo , Therefore or R iq <(C'cl + 2Xm) 4C' x = The parameter units of this velocity Ill c' kind Figure and the variation at values With reference factor for 58") the does not a function from of From Fig. happens of be a constant (t ur b ines diagrams). solidity. will of to Fig. range change having 2-9 we find closer I-l the maximum value 5), much with R/Dh m that in I) geometry of lower values a chosen seems to lead Bc values of of R/Dh the loss (between 41" to but is of R/Dh (values value to the versus increases. that we have and ec different we find variations for of as solidity angle for for homologous the maximum value to unity of deflection Consequently of versus (Appendix R/Dh , especially 1 to about similarity for 2-9 shows the variation R/Dh m value strongly of solidity efficient CT, passage. 44 FIG.2-8. RATIO OF BLADE RADIUS OF%R"ATURERAND ROTOR LENGTH fa OVER ROTOR OUTER DIAMETER VS. ROTOR INNER-TO-OUTER DIA. RATIO m . 8 80 6 60 2 0 0 0 ” ‘5 ,6 .7 .0 .9 II FltG.2- -9. RATIO OF RADIUS TO HYORAULTC DIAMETER R/Dh g AND DEFLECT ION ANGLE OF THE BLADE PASSAGE& VS. ROTOR INNER-TO-OUTER DIA. RATIO ml. I I ROTOR ANGLE OF I .5 FIG.2-10. I .6 NUMBER OF BLADES -1 I -7 m I .8 VS. INNER-TO-OUTER DIA. I .‘9 RATIO m. 46 The design of the rotors mechanical design of mum loss. Using 2-10 with no stiffer plates than by optimization the blades Eqs.(2.14a) to (2-14f), is more dominated to get the curves by the mini- shown in Fig. can be drawn. These curves solidity show the number and rotor of blades width is is reduced lessened increases to outer the rotor (Fig. assuming 2mm steel plate for because the throat the blade the blades of stress chord become and stiffness properties the blades), of As the number ratio. decreases material each choice although On the basis typical for longer Therefore of blades in bending. conclusion, diameter becomes 2-8). as the number more flexible (e.g. inner of blades and thickness we have let 18 as the minimum number of blades. When the number but shorter, the manufacturing become progressively in Fig. stiffness 2.7 number 2-10, give increased, difficulties for Points designs rotor small We have chosen of blades. better the workshops 60 as the inside as far can be the closed as losses curve and structural are concerned. SIZING OF A CROSS FLOW TURBINE For a machlne velocity Therefore affects is more severe- maximum desirable drawn of blades of jet of water the choice the size of this of leaving of inlet the type rotor, working under the nozzle absolute a small flow nozzle is constant fixed angle angle head, (Section the 2.4). from the nozzle being desirable. 47 As discussed be kept in Section small losses in order due to flow angle of admission absolute flow that design line (i.e. 2.5, to reduce the the blades is equal angle taken crosses the water within designed also rotor The The inlet incorporating In was 16O. on an approximately points and pass. by Banki and draining casing the in the second the rotor entrance should to 30 in our machine. in a prototype the flow of admission losses entering He used a cast line). the angle are horizontal on a horizontal the nozzle for his turbine. As we have tried our design processes, design had. metal covers; confines Rather we used a steel there the water will giving in least complexity 2.4 the drawing absolute be vertically be a main spray, frame combination complex avoid structures does not have a cast to the the to cover around will angle 30'. inlet Section of flow 2.8.) angle like framework of the structural in casing angle The nozzle a nozzle and manufacturing Banki's with the rotor be a separate That value "~11" will which part reference be 150". fixed resulted (See nozzle design. So with sheet rotor to Section Draining will downward. From the fact that the work coefficient is equal to 2.0 we have %1 = Assuming (nozzle 2Ul , a total-to-total and rotor), from Eq. efficiency (2.1) we get, of 75% for the turbine 48 0 (UC*) = 69,20 m2/s2 then u1 cl -wl The choice outer diameter :.ztween gear m/s = 13088 m/s = 9.00 m/s speed can be and what shaft 300 rpm. 5.88 of shaft As we were bearings. = This speed up ratio is are bore lower is needed than to reach speed). In future to specify bearings to run at high specifying dO We would (see general drawing like possible number of blades riveting the bent Fig. 2-10 in the the = for the velocity sliding us to a shaft speed studies the speed of because shaft a high to 1800 rpm it would be justifiable speeds. we get 0.3743m. the blades to the side and nozzle-rotor Therefore in order section the rotor limitations desirable, we would to get ends of the blades last speed bearings design drawing 2.81, on how large N = 300 rpm to join arrangement in Section the limited (generator Therefore depends to use wooden and bearing . we get sufficient m = 0.6 by rivets combiExtj.on like to the side plates to have the space plates. for Using and 24 blades. least 49 Now using results (zero Eqs. and blade incidence) (2-13a) to parameters. (2-13f) First we get from the following the velocity diagram we get B = 130" 53' = 52" 58' Y = 26" 29' R = 0.0956 m s = 0.0293 m and then 8 C C = 0.0843 we have previously chosen, Z The inner diameter = 24 m = 0.6 of the losses 20% extra and the power losses power has to be 6 Kw. Q = The length in then will 0.2246 is the generator = 0.0857 then will be m . specified The volume W A(U Ce) of the rotor rotor = di If m flow m3/s be to cover the mechanical then the output rate required shaft will be 50 I-&-L-= ~adiW L= a being O.l64 m 1 the admission angle, Once more recalling we can write the the velocity folPowing WJ C(j) triangles shown in Fig. relation = A(u Ce) + A&J ce) 1st total 2nd pass pass or = A@ Ce) - u2ce (UICe 1 but > + (U3Ce - u4y3 1 4 3 2 as we specified, u 2 $3, = u3 , u1 = , u4 CO2 = c03 = u2 = 2u 1 ' s4 = 0 and AN = 2Uf ce> total Therefore = AW Ce) 1st 2$ - Ui = 2Ui pass 2 2u$ - 5 > and = u; A@ Cal 2nd pass = m2U2 .1 - m21J: = 2-4, 51 The above relations transferred to the and only This entrance in total very the energy a value of pass 82% of is is received m = 0.6 within the pass do not affect , the the by the losses second total energy second rotor energy pass. and the the performance of much. MECHANICAL DESIGN The manufacturing processes made have been the most design. The general rotor in for in first as hydraulic losses turbine 2.8 rotor 18% of the means that the show that combination the following described dominant arrangement under parameters drawing, and an isometric view Different parts pages. which the in turbine is to be the mechanical scheme of the nozzle of the machine are submitted of the machine are briefly as follows: Rotor The turbine has a squirrel-cage-shaped and 165 mm long. is The optimum rotor, 380 mm 0-D. speed under the design each blade being simply head of 10 m 300 rev/min. It has 24 blades, Blades can be rolled on the general side plates of 2 mm galvanized arrangement with The rotor the bearing out rivets goes through (Part 14). (Part has no drive housing which drawing). which the steel sheet They are joined segment. (see Part to the rotor 12). Power is shaft. rotates rotor a circular with bearing transmitted the rotor, supports only through and the shaft the rotor 11 52 t-1 _----I -+ F I 11 I! IiY E-R0 TOR COMBINA TION OF CROSS- FL0 R/RBINE 54 ISOMETRIC VIEW OF CROSS-FLOW MACHINE 55 Bearings The bearfng steel pipe, rotor side is weided plates Bearings there this It works wear Chain with which of circular is fixed oil-impregnated wood. the maximum permissible and simplicity Furthermore as in dry to the 13). low cost applications. 'j piece it speed makes it does not conditions. It Although for suitable need lubrication. requires no seal 15). In our design the bearing rotates .a on the wooden bearing and increasing with the rotor, the bearing so equalizing life. transmission chain which and gear transmitted i s welded derailleur to tihe bearing gear housing is generator fixed (Part by means to the s speed gives circular 21). speed of 1800 rev/min. is used which hub and set is used for The unnecessary an 18-tooth and a circular gears, A 52-tooth to the ratio A chain of about six to generator. gear and only the rotor has a constant combination turbine from and gears. A complete the plate (Part for its The generator rotor) rivets in wet as well of bicycle from a short are made of a special Power is plate is to a circular of bearing, low-speed (Part which are some limitations kind for housing, is fixed the gears gear plate of five in (being with to the gear chain second the speed gear driven set step are for bore, The latter a bicycle up (Part replaced by a 52-tooth a central set, cogs gear 22). by spacers on the the same as one of circular plate is 56 be fixed with step (Part the generator a 36-tooth The last 23). an oil Chapter machine In order that not bath would do further to increase two chains be installed around the life speed-up chain this the chain. makes it as the difficult see in final choice, transmission system. and sprockets, Therefore to machine As you will on its be used. by side turbine be selected of the in for chain. improvements in parallel side this the not we have be provided in second and must be fixed level should transmission to incorporate the gear has 17-teeth condition The two-step 4 this used for For the power shaft. a good lubrication so we did gear being we recommend two sprockets should on each shaft, Housing The housing It has a fixed door servicing. It with completely section a removable section is which (Part 32), covers placed has a lifting two simple made of thin handle latches galvanized most of the in the back and is (Parts rotor of sheet (Part the fastened steel. 31), turbine, to the and for fixed 34 and 35). Frame The frame generator size is mounting may vary totally is made of angles, a steel when using plate different welded welded together. to short legs (Part 38). generators The and its Nozzle The nozzle (Part different 41). is The flow output completely made of steel can be changed powers. This is and set possible plates, on different by chaning welded together valves the angle for of 57 flap (Part to the 42). flap The semi-circular has holes for never Warning: channel different (Part 43) which is welded settings. change ---the flow while the turbine & -in operation As the system of flow while the piping before which can result this changing the and the 2.9 a change "water-hammer" in valve before to the shut-off After setting, the nozzle. position the valve must gently. of installing has not been studied, cost of the a surge-tank because it would as a shock increase the size turbine, EVALUATION OF EFFICIENCIES Knowing hydraulic method the size efficiency given in the of different of the last efficiency is the parts turbine = the Following the 76% total-to-total efficiency prediction, so the design is of the energy by drain into rl t-s turbine we get: to our loss of the can be found. sections 'h This almost position,, head, damage. has. to be a gate reduced flap high can cause in serious there The possibility absorber a relatively is working must be slowly be opened under the turbine To avoid The flow works flow = 60% acceptable, account and is very Taking we get, close the effect 58 If efficiency a mechanical of 90% is of 94% and a generator efficiency assumed then rl t-sm = 56.5% rl t-su = 51% and (See Appendix 2010 II.) RADIAL-INFLOW PARTIAL-ADMISSION WATER TURBINE Description This flow type and axial of is a potential simply rectangular cross section portions of 80". The rotor fastened at one end only,around in its inward radial distributes cross- are rolled out the passes and subsequently of sheet the rotor through is flow in each one being metal circumference enters distributor the circumference, The flow motion, plane, the axial to the of a spiral-shaped which inner blades as cantilevers. radially the of consists opposite disk alternative types. The turbine with turbine of with the blades deflected two an arc and are the turbine a swirling while to leave still the in rotor direction. Flow Control This type the volsume flow velocity consequently through as described to the diagrams would the turbine the whole range rotor gives under keep their would work of power. the possibility constant head. design-point at its of controlling Therefore geometry design-point the and efficiency ROTATABLE SLEEVE BLADES SPIRAL NOZZLE BLADES FIG.&-11. RADIAL-INFLOW PARTIAL-ADMISSION WATER TURBINE. 60 The control the angle sleeve of the flow This of admission. between rotor could be easily could could be brought fixed sleeve to vary more or less the admission by reducing be done by installing and distributor. which achieved a rotatable The sleeve would alignment with into have ports ports on a area. Dimensions For specified of this type 450 rpm. ing head would have a diameter with However, problems on the 2). problem To solve 340 mm would speed this inner side which the the spiral the draining problem reduce the axial (5.5 there would at be drain- rotor. rotor diameter geometry of brings and size by increasing width kw) a turbine 220 mm when turning of the rotor of the is output of about size increasing Unfortunately, another (10 m) and power the the rotor out (see Fig. diameter to to 55 mm and the to 300 rev/min. This would require (55 mm). To keep the dimension of the spiral a spiral fluid distributor velocity would in of the spiral the same width small, the radial have to be increased. Conclusions A rectangular result (in entry we are working, turbine cross For the port). dimensions unattractive. section of the order range as large We have not of specific as this taken of 60 x 200 mm would speed make the the design in which radial further. inflow Chapter 3 DESIGN OF AXIAL-FLOW TURBINES 3.1 DESCRIPTION In this flow chapter turbines design machines with rotor all then blades, to the reaction for water flows some simple We have ratio axial- chosen which to enables the blading. through a set the circumference passes the rotor The turbine tailwater. to design hub-to-tip-diameter blades around is to the problem. high Principally, (installed the task as a solution us to use untwisted 3.2 * of nozzle blades of the hub disk), blades and through can be designed into the the diffuser as an impulse or a machine. ADVANTAGES These designs The design type. processes plastic if of these they are will give and off-design machines simpler machines besides have comparable machines advantages provides to be mass produced with the Banki easy manufacturing (i.e. sand casting and molding). The blades which should are made of molded, accurate profiles performance. is higher than of the transmission and a lower can also be used as a drive the generator. or cast and consequently Moreover that extruded the shaft Banki gear-up motor type ratio plastic a better speed design in these and therefore will to drive a be needed. other These machines FIG.S-1. INLET AND OUTLET VELOCITY DIAGRAMS 0FAX.IAL-FLOW TURBINE STAGE. 63 3.3 ANALYSIS Similar can write to the analysis Euler's specifications together h01 But if rotor equation is AH 0 - = the different cross-flow turbine, we velocity-triangle 3-l). ulcel total - u2ce2 hydraulic (3.1) l head difference ac'ross the then h01 - h02 where Appendix n is tt the = total-' AHog %t (3.2) co-total efficiency of the turbine (see II). The three and reaction blading to relate (Fig. h02 the shown for parameters: which flow specify are defined the respectively coefficient, type of the velocity coefficient diagram and as follows: cX @ work (3.3a) -T- - u2ce2 UICel qJ z (3.3b) u2 m R E %l l--=r-- + 532 (3*3c) 64 The analysis case where outlet C X is done for remains constant Now for of the rotor. be chosen, hence values A good approach type with different angle to the rotor (i.e. R and 9). of from "ol" I/J, $ and constant a velocity and to vary can can be specified. of different is triangle to machines to keep the the inlet two rtfher of this flow parameters we have g AHo u = %t YJ of shaft the usual to the nozzles R of reaction and (3.3b) Now, choice inlet each design to the design degrees From (3.2) the mean diameter,for . (3.4) speed gives us the mean diameter 60 U IT @J-) (3.5a) = dt+dh 2 (3.5b) rate will be & = dm = and d and mass flow where W is m the output W A(U Ce) power (3.6) of the turbine. 65 The annulus area then will be . Aa where p diameters is = (3.7) the density. the annulus Aa area before high to be able value for this we try ratio and hence ce) are found. (3.5ai gives u9L9a Zq. (3,5bj and (3.8) If the 3.4 be - d; Then the ratio of hub to tip blades. triangle (3.4), shaft diameter A reasonable gives (3.6) speed dh and is not the . can be determined we can find dh/d, us the value and (3.7) of mean diameter. to optimize of hub and tip (3.8) us the value Of terms 0.8. of velocity Eq. in j to keep the around from ratio has to be chosen will to use untwisted is Now, a choice AU we know that = $ (d: As mentioned enough, Also d, values of and using Then using Eqs. . acceptable the dh/dt of a new shaft speed ratio. DESIGN OF BLADES Figure 3-2 shows procedure. To find information I and curves relations approximate the blade angles given the terminology from used in this flow in Reference curves given angles (2). in Ref. design we may use the The following (2) with a good two 66 b- BLADE WIDTH r 0 LEADING EDGE /' \ FLOW INLET \ \ \\\ \ \ t FLOW OUTLET ANGLE /3r MADE OUTLET AXLE & STAGGER A!JGLE DEVIAT ION ANGLE6 'NG EDGE FiG.3-2. RLADE TER!lIrJOLOGY. L 1 67 for accuracy, incidence and deviation angles. (3.9) 60-X 2 0.08 + ( 300.1 6 8_ = c/s c Please see Fig. formulae. In Eq. for 3-2 information These two formulae eC so the blade = 6, + Mind angles B2 Suggested or blade ec (3.101, = values re It will are on parameters useful turning + 6, (3.10) angle + used in above in preliminary is equal design. to 6 be B,i-6 for leading and trailing = (0.03 to o.os>c = (0.02 to O.Ol)C edge radii are 68 The design angle "A" solidity and an optimum can be estmated width-to-chord = from Fig. t C from Eqs. for value the blades for is solidity by the Zweiffel to choose o . a stagger The optimum criterion for the value of ratio; b s also procedure cos2c12(tgal 2.5 + tgcx2) (3.11) 3-2, = (3.12) cos (3.12) x and (3.11) we find o , cl=;. In steam and gas turbines the number of the blades reasonable value In our concerned. number of for are normally chord case, the blades the dimensions as far as blades which gives of determined short, and by choosing as vibration are the blades a and stresses are a good choice for us a reasonable blade passage the seems to be a good approach. Then finding blade 3.5 shapes by trying the dimensions different of the blades curves for we can find the blade the profile. SIZING OF THE MACHINES Single-stage axial-flow turbines are normally named on the 69 basis of their velocity types of velocity triangle The design total-to-total designed method procedure with given the turbine specifications hydraulic a) turbine are will efficiency. Finally be calculated using can then power for of the generator power. 5,5 Kw. output the be optimized. from 10% extra for power So the and 10 m. head, Design of an impulse Assumptions velocity-diagram (implicit gives The design be designed a value Then the machine will 5Kw. electrical will of the III. to guess turbine. the efficiency to get itself the and most common and 50%-reaction. to the estimated in Appendix In order impulse in each case is for respect machine Two possible are: efficiency be designed the triangles. are a total-to-total specifications in an impulse an acceptable absolute direction, velocity from Fig. leaving = efficiency of: machine), nozzle to minimize AH0 machine work Also the rotor leaving Ho1 - Ho2 losses = coefficient and flow angle). is of 0.80 of 20 coefficient we will to be in therefore and of 0.8 specify that (which the the axial we have, 10 - $ 3-3 we have, Fig. 3.3. IMI'CLSE VELOCITY DIAGRAM Substituting for the last two relations into Eqr. (3.4) U we have: u rl g Hcl = ++$ applying numerical values u = n we have 5.90 (at mean diameter); m/S so A(UCe) Then from Eq. = $U2 = 69.75 (3.6) the volume-flow Q lpnn A Ibaa from = a2 = 68.2O = O" = 51.34O = 51.34O and I B, \ B2 rate 0.0791. m3/s the velocity OL1 i m2/s2 diagram is . and rearranging 71 and c1 w1 c2 The choice = 3.54 = 7.38 m/s m/s speed has to be done with a) the value 0.8; which The minimum number at 1800 rev/min by almost all With is 24 teeth. regard for sprocket This 80 teeth then wili be d = m for the big 0.2087 m value the value diameter ratio ratio available on the generator sprocket is recommended of shaft should speed lead to teeth. to the above discussion gives diameter a l/2"-pitch Therefore the hub-to-tip number for to the ,of two standard us 1800 rev/min of teeth manufacturers. by specifying an available gives regard of hub-to-tip and b) a combination can be found spinning rotor w2 be around shaft. rev/min = m/s considerations: sprockets gotten 13.26 of the shaft following should = sprocket, a shaft speed of 540 The dimensions of the 72 and dt dh = 0.2347 m = 0.1827 m blade The ratio separately diameter Nozzle design. for ratio is then 0.78 which is in an this machine and rotor as they blades should have different be designed flow inlet and angles. First for information given having solidity tried 0,026O m range. Blade cases = of hub-to-tip acceptable outlet height nozzle blades: in Ref. (2) best-looking profiles with blade and inlet angle, angle other (3.9) A9 ind 6 angles are i I and (3.10) = 19.25" = 5*09O 19.25O = 72.29O B2 curves staggers we have: . but this and profiles, for an optimum of 45" are suggested. then B1 = through different profile,) From Eqs. The blade for the same deflection of 1,5 and a stagger several by looking value (We gave the 73 To choose the number of the blades From the spacing. -b = cos 45 = 1.5 C -C S (See Fig. above specifications = to specify the we have 0,71 3-21,) In this case a different number 15 blades seemed to be a good number sectional area prefer we have for the blades to have blades with cross-sectional area). With the above of blades as it (as we want bigger specification gives were tried, a reasonable to use plastic chordal length nozzle blade Finally cross- blades, we and hence more sizes are as follows: = 0.0434 m C = 0.0651 m b = 0.0462 m = 0.0025 m = 0.0005 m S m rt 9 In the same way calculations done. for The results blade sections. are tabulated for in Table the rotor 3-1, blades Also were see Fig. 3-4 B; NOZZLE BLADES ROTOR BLADES o oo 51.3 6; Z 68.2 15 51.3 16 TABLE 3-l: CT AC AOind 8O 1.5 45 19.25 5.09 19.25 1.5 30 5.13 6.27 56.34 IMPULSE TURBINE BRING B; S C b 73.29 43.4 65.1 57.57 40.7 61.6 B; 0 rR rt 46.2 2.5 0.5 12.4 53.35 2.5 0.5 21.8 2 DIMENSIONS (DIMENSIONS IN mi) 75 NOZZLE BLADES ROTOR BLADES - FIG.304. . ---- _ BLADE SECTIONS OF THE AXIAL-FLOW IMPULSE TURBINE. 76 Evaluation in Appendix each loss of efficiencies, III and information parameter Nozzles blades the blades N Pt X Pt X ar X 2.48 0.97 1.13 0.10 4.2 7.20 9.04 0080 1.12 0.10 1.2 20.20 rl given the value N pr Substituting for about to the method of can be found. TABLE 3-2: equation we got respect Pb X Rotor With BLADES LOSS FACTORS the numerical and assuming values for 1 mm. radial the parameters clearance for in the the rotor we have, = r) t-t The assumed value to the optimum for 80.6% rltt of the that flow mechanical 90% then II diffuser blades down to .75 of its n t-s if was 80%; therefore, we are close enough design. Then from Appendix specify . efficiency the machine = we can find after the value other rotor when it efficiencies. will leaves reduce We the velocity the rotor so, 75% is 95% and generator and the unit efficiencies efficiency will be; equal to 77 Mechanical of design. the mechanical description the about 11 t-sm = 71.0% rl t-su = 64.1% It is not design in different general-arrangement The machine seen. chain and sprocket is combination. -- bush gives a feature Also (even all ins ,c+Lled a smooth center blades the inner will In the next drawing pages can be by means of descriptions are for the bush allows the center-section blades section. has high-accuracy transmit (see blades (Part (Part drawing 1, Part 12) with 13) are molded flow hubs of the to the nozzles. bush to the duct (Part 15). surrounding This the rotor, efficiency. us to use low-c<.st housing tribe the rotor-thrust-bearing materials (Part li) 15 blades, into The nose up-stream in a plastic surface increase plastic The diffuser to the for nozzle 14) euides rustable) details a short 1800 RPM generator The rotor (Part this the only section combination rotor, which be given. Further the These are Therefore and turbine This diffuser as bearings blades all as follows: The up-stream and the downstream nozzle will to he made of plastic. has 16 blades. act parts transmission. Rotor-nozzle which report. to run a 5Kw., given to describe this drawing individualiy components necessary 22). force 73 L 79 80 The bushing molded is fixed to the upstream between fixed the flanges end (i.e. of Parts to the bushing are front the is similarly flanges *' through bearing. small holes Housing adaptor. water pipe turbine the rotor blading is in the bushing. blading with the end After resin -Is also adhesive. fastened to The diffuser adhesive. to a flanged front enables of bushing, clamped between Water flows the nose and lubricates to the back bearing has three the The center downstream individual section, us to connect and the water. the through hub. The upstream and flange. with flows The housing together. itself in to the bushing Then some water It clamped projections are lubricated in and frame.-- are bolted is The nozzle slots by structural bearings in the which 22 and 23. the hole front fastened fastened of Parts The rotor in 21 and 22. of the nozzle the hub of the nozzles blading size), by square-cross-section the blades The nose in be means of a flange nozzle These match up with of each blade. assembly to the housing Part turbine section section sections 21, is actually to a standard (Part (Part which 10" 22) encloses 23) is an the the outlet collector. sheets Different parts welded to steel facilities from cast for iron. of the housing flanges. sand casting, can be made of rolled However, Parts if there 21 and 22 would are steel local be better made 81 The frame The turbine through of (Part is bolted to the the housing the 25) is made of steel frame back frame plate (Part supports the Transmission system. Power is output by the meansof shaft has four in slots the bore on its the of As the disk transmit output only transmitted stub which plate the (Part match bolts (Part 26) shown in Figure from disk together. flange The upper These are a coupling loosely tovque, rotor 2, to the 31). This up with small disk teeth shaft. in contact and no bending with the rotor it moment or thrust can force, to the shaft. (Part 33) which flange bearing leaking tapered shaft i- b fixed into 32) is supported to the housing seal in by a flange back plate the drain bearing by bolts. side, which The prevents the bearing. bearing bush and a nut the right (Part has a rubber The ball in the with flange locking bearing, washer, together keeps the with a shaft in position. In order combination (Parts rotor welded some of the 24). generator. circumference is The output water using angles to raise the rotor of two sprockets 34 and 35). chain (bicycle chain). rotor and generator The chain is speed used with used in The sprockets shafts, to the generator respectzvely. this a tooth system ratio is speed a of four standard have 80 and 24 teeth l/2" on the 52 We do not in this case. loading recommend the use of standard To transmit five them up to their bicycle sprockets kw at a speed of 1800 kPM would maximum strength and would leave be no safety margin. To fix the larger (Part 36) is bushing hammering Using to the installed the turbine will This lower turbine is rotor shaft done to avoid than five at a power a split taper any need for a meter work before at its less than five kw, the by the means of a value the best kw level has to be reduced at least turbine to the on the shaft. in powers To run the flow used. or pressing the unit sprocket turbine efficiency inlet. Obviously when it is run fully the output loaded. Different by installing result some kind for users would Design turbine. as for increase not find of a reaction This section is impulse results will turbines are also the of this machine in were studied, size and complexity. possibilities but all power cases I feel attractive. machine concerned with design of the calculations machine. tabulated drawing these The principles the controlling of mechanism in a significant that b) possibilities Therefore be presented. In fact same, so to avoid it is not only of a 50% reaction are exactly the assumptions the repeating submitted as it structure axial the same and of both the mechanical is quite similar 83 to impulse given in machine. But a short the following and nozzle specify rotor a work of the blades will coefficient and reaction The absolute will axial direction. guess for velocity machine is have the same cross absolute is that section. flow angle its We to the both leaving then be in the the The first the total-to-total diagram efficiency calculation B2 % U A(UC6) Q = 68.2“ = O*O" = 8.84 = 78 . 08 m2/s2 = 0.0704 m3/s = 9,52 = Wl = C2 A suitable dh/dt Cx shaft is is 85%. The result of the is: m/s 3 =w2 1 accpetable differences turbines. flow rotor 50% reaction of one,and to be the same for impulse of the paragraphs. The significance rotor description speed for or J/Kg m/s = 3.54 above 720 RPM,. Therefore; m/s results which can give an 84 d m dt dh blade height = 0.2345 = 0.2615 = 0.2075 = 0.027 5-lfdt = Blade be used for between of bladings a stagger From the 0.79 nozzle number of m For simplicity design. both m and rotor the blades for of 45", I.5 blades for criterion (Eq. = O.&l, = cosx= S blading. nozzle section But because and the For preliminary be different. -b rotor-blade the nozzle will Zweiffel the of differences rotor, design and 16 blades (3.11)) for rotor will the solidity let's select for the rotor. blades we have also -b c Then blade Z S 0.71 dimensions b will . be as follows (Table 3-3): C AR0 in 6 0 C B1 B2 re rt NOZZLE BLADES 15 48.76 39.3 55,3 20.0 6.4 94.6 20 74.6 2.5 0.5 ROTOR BLADES 16 45.76 39.3 55.3 20.0 604 94.6 20 74.6 2.5 0.5 TABLE 3-3: REACTION-TURBINE BLADE DIMEKSIONS. 85 NOZZLE BLADES ROTOR BLADES - FIG.3-6. -. -. BLADE SECTIONS OF THE AXIAL-FLOW REACTION TURBINE. 86 The blade cross-sections Evaluation Appendix given of different sb Npr Npt NOZZLES 4.15 1.0 1.12 ROTOK 4048 1.03 0012 be found, tip which then design that is design absolute to-static the value that are as 'ar ' 0.1 4.0 8.75 0.1 4.0 9.27 clearance for the rotor efficiency can 85.6% is close diffuser velocity will enough to the first guess, so 95% mechanical as before blades when leaving will diffuse the flow to the rotor, then the total- be, rl t-s are assumed Upt of total-to-total = this efficiency If coefficients in acceptable. we specify of its given is, For preliminary if loss 1. to 1,5 mm radial r7t-t the the method LOSS FACTORS OF REACTION-MACHINE BLADING Specifying on the 3-5. 3-4: TABLE 3-4: half 'Using of efficiencies. the values III, in Table blade are shown in Fig. = efficiency then 83.6% and 90% generator the machine and the unit efficiency efficiencies are, 87 = rl t-sm Mechanical design. impulse and reaction details about mentlon the differences of this machine turbine itself this reaction generator, altogether). the and give that sizes blades better T-$ su = 71.5% mechanical the same. will design be given, of the in of the units and axial diffusion, but which other than turbine, there (turbine, diffuser no further The output impulse size, on both Therefore and performance. bigger total The diffuser increase in size slightly in are machine is more than is , The general machines difference longer 79.4%. in results speed and the is not much frame this to and machine are in a few points in efficiency. The transmission is used with and rotor ratio two sprockets shafts, respectively. is having 2.5 and the same size 24 and 60 teeth chain on the (l/2") generator Ghapter 4 DISCUSSION ON ADVANTAGES OF DIFFERENT TYPES As seen in had individually from parameters in machines are All Therefore cost The crossflow locally areas turbine which the processes molding, Technology molders cross-flow which could which Program provide In that turbine it is of being improvements are turbines should the under intermediate axial-flow processes the be preferred industries be of processes but in industry manufactured in industrial To satisfy might needed to be discussed. be made are mostly case encouraging may be of great have The type etc.), is maintenance. manufactured fabrications, of machine. need more sophisticated goals (i.e. of the to choose in the developing such as plastic importance. The amount of labor cross-flow being to farms. and casting, Adaptation and service to need skilled But axial-flow turbine the turbine possibilities and/or and shipped have parts plastic countries. both to farms. which of the best not Looking the price requirements such as sheet-metals turbines processes designed gives prototypes country, under of maintenance the choice areas and shipped made centrally processes type studied and some disadvantages. and manufacturing in farming each of the the vieC: of a developing to be made and the important chapters, the manufacturing turbine, going last some advantages at the problem the the which much higher has to be put than into making each what has to be done for the 90 axial-flow type. because The axial-flow of automation machines and their smaller would size probably be cheaper when produced in large numbers. Comparison high of speed of the and cross flow reaction generator, in chain and sprockets bath even for the low speed of cross-flow becoms necessary. A big cost. be similar for scale production axial types. machines the impulse to the and lower forces for cross but initial otherwise two-step construction will scale transmission cost is investments for the seems likely production. cost will transmission to For large be much more costly the material it Therefore machine. more expensive small flow reaction the chain of each of the units of the is because is small the the up ratio transmission and its a far of the price units This gear lubricated, flow turbine The rest all a lower over speed we have chosen the axial because portion generator an advantage a simple.- and be well last unattractive, shows that, are entailed. not mkes it is provides of generator in an oil long as it so that For the kind of the turbines machine machines, electrical must work the structures for than the axial molds the flow and dyes are required. Finally there is often the efficiencies surplus requiring a lower channels, values water water flow and so forth. of the machines While differ. flow available a high will therefore require efficiency less costly machine pipes, 91 The following table shows the efficiencies of the different machines. Cross-Flow Turbine Axial-Flow Impulse Turbine Axial-Flow Reaction Turbine 85% t-t 76% 80% t-s 60% 75% 83.5% 71% 79.5% 64% 71.5% t-sm 56.5% t-su 51% Key : t-t E total-to-total t-s 2 total-to-static efficiency of turbine blading t-sm Z total-to-static efficiency of machine (shaft t-su E total-to-static efficiency of unit efficiency Based on all the best 4,l solution of turbine considerations we chose blading power) (electrical the power) reaction machine as chapter has some to the problem. IMPROVEMENTS ON REACTION MACHINE The preliminary questionable design features. much as possible. shown in Here we try Following are the last tc improve some items on that which it design as seems necessary to cover. By looking this nozzle chapter at the general-arrangement (DRN, No, AF301), combinaticns in the two schemes drawing difference can be seen. between submitted the rotor- in 92 This improved design rotor. The atvlospheric central hole pressure to the other side covered friction and give on sliding with melt.) in the rotor water supplied adaptor new adapter enables The smaller tube The oil lubricating bath in settling angle size for performance. 4.2 Off-Design the profiles are also reduce pressure is possible turbine the and velocity can not last by the and aid The lubricant in the machine force and diffuser which the holo-s reduces the chain of 38" and their best through system's rotor on the plates. the back of the the transmission The blade surfaces the the axial of plastic in the improved and valve the the high kinds us to connect conditions increases upstream equalizing sheets hub and grooves from hence between on the the rotor and reducing (For of these force through rotor, stainless-steel life, Lubrication The front of the even the best of holes is thin hydrostatic is bypassed surfaces a long surfaces less of the rotor The sliding rotor. hubs are they pressure on the two sides on the provides is stator changed. hub. The to 8" diameter piping. the cost. turbine provides and sprockets, good and hence life. changed. shapes The new blades are also optimized have a for the Performance The type of use a gate valve assumption is that flow installed the control we recommend for the machine one m. ahead of the machine. turbine is going to be run under is to The basic fairly steady 180 I60 i20 loo 80 60 40 20 0 zoo 0 400 600 SHAFT SPEE’ FIG.401. 800 1000 1200 1400 R. CHARACTERISTIC CURVES OF REACTION MACHINE FOR CONSTANT FLOW RATE. r6 02 J 00 a 0 v 40 45 50 FLOW RATE FIG.4-2. 0 55 60 65 70 m3,lrn CE.ARACTERISTIC CURVES OF REACTION MACHINE IN CONSTANT SPEED. 75 95 loads. slight Therefore changes the in required frequency More sophisticated big increases machine in size unattractive Based on this systems and price assumption curves and based on predictions. the method to have a high degree on the machine and be acceptable. to control the of the machine, turbine which will cause makes the co customers. are shown in Figures using can be set up to 5% would turbine cated power given the 4-1 characteristic and 4-2. These The off-design in Reference of accuracy. curves (3), curves of the are theoretical performance which is predi- has been found APPENDIX I TABLE OF PARTS AND WORKING DRAWINGS Following reaction machine. numbers all provided. process given information under under the complete Each drawing Special which about each part information the part on material, should "Remarks." For the case of complicated or sr;bparts "B, (1 I, C," for etc., after 'axial-flow are submitted the master reaction working drawings has a reference the heading sections stands are of the modified number. can be found type Using from the parts, drawings which are marked turbine.") reference table of manufacturing be made, or sub-drawings, part's these for are additional by letters number. "A," (AF300 98 TABLE OF PARTS AND LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS PART- KUM~ER ,I I NAME OF PART NUMBER REQ'D MATERIAL REMARKS AF311 I, FRONT ADAPTOR 1 CAST IRON AF312 ( MIDDLE SECTION 1 CAST IRON HOLES OF FLANGES SHOULD BE ALIGNED DRAIN CHUTE 1 STEEL SEE SUBDRAWINGS BACK PLATE 1 1 OMM PLATE FRONT FLANGE 1 1 5MM PLATE CURVED PLATE 1 8MM PLATE SIDE PLATE 2 5MM PLATE FRONT PLATE 1 5MM PLATE AF313 'AF313A AF313B AF313C AF313D AF313E I / . . . contl'nued TABLE OF PARTS AND LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS(Continued) NUMBER ! REQ'D 1 NAME OF PART NOSE AF314(1 AF314(2 1 ;;;if 1 AF316A AF316B AF316C I STATOR BLADING I AF317 3 11 NOZZLE AND ROTOR BLADE SECTION : AF3l8A AF318B DIFFUSER BLADING AF319 DIFFUSER-BLADE SECTION AF320 BUSH SEE AF317 FOR BLADES PROFILE. 1 ROTOR BLADING REMARKS SEE ADJACENT TABLE FOR PROFILE COORDINATES 1 I 1 MATERIAL GLASS-FIBER-REINFORCED POLYESTER THERMOSET POLYESTER RESINS 30% GLASS BY WT. THE 1.5MH STAINLESS-STEEL SHEET SHOULD BE JOiNED TO SLIDING SURFACE BY METALBONDING. EPOXY. SEE ADJACENT TABLE FOR BLADE PROFILZ. 1 GLASS-FIBER REINFORCED POLYESTER THERMOSET POLYESTER RESINS 30% GLASS BY WT. THE 1.5MM STAINLESS STEEL SHEET SHOULD BE JOINED TO SLIDING SURFACE BY METALBONDING EPOXY. SEE ADJACENT TABLE FOR BLADE PROFILE. 1 GLASS-FIBER REINFORCED POLYESTER THERMOSET. POLYESTER RESINS 30% GLASS BY WT. . ..continued TABLE OF PARTS AND I LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS (Continued) NUMBER PART j NAME OF PART NU%EER i IREQ'D MATERIAL AF321A 1 SLOTTED DISK 1 ALUM1NW AF321B ' 2 HARD STEEL 1 STAINLESS STEEL -AF322 KEY 1 SHAFT ,1 1 HUB ASSEMBLY AF323A HUB HOUSING 1 CAST STEEL AF323B FRONT CAP 1 1.5MM STEEL SHEET AF323C BALL BEARING 1 M.R.C. BEARING 206-SX ADAPTER AND NUT G-Y AF323D SEAL 1 GARLOCK 78, 0542 REMARKS EQUIVALENT STANDARD PARTS WITH THE SAME SIZE CAN ALSO BE USED. COMP NO. 26448-35 DES. GRP. D. AF323E* i (3/16"~32)~5/16" BOLT ROUND HEAD 3 I I . ..continued *no drawing; standard component TABLE OF PARTS kND LIST CT DRAWINGS OF REACTION TURBINE COMPONENTS(Continued) PART NUMBER NAME OF PART NUMBER REQ'D MATERIAL REMARKS AF324 BIG SPROCKET 1 BROWNING 4OP60 TYPE 4 BUSHING Pl NO. OF TEETH 60 PITCH l/2" PITCH CIRCLE DIA. 9.554” FOR TYPE 40 CHAIN AF325 SMALL SPROCKET 1 BROWNING 4024 NO. OF TEETH 24 PITCH l/2” PITCH DIA. CIRCLE 3.831” FOR TYPE 40 CHAIN AF326* CHAIN 1 BROWNING NO. 40 l/2" PITCH NO. 40 A.S.R.C. -I-- . ..continued *no drawing; standard component - TABLE OF PARTS AND LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS(Continued) ! PART 1 NAXE OF PART - -_-I f1 II NUKBER REQ'D I FRAME 1 SIDE ANGLES TOP ANGLE 1 AF327C # TOP PLATE 1 AF327D j AF327D 1 1, BAR j 1I AF327E ]1 ri,“,DATION FOUNDATION PLATE j AF328 I / I OIL BATH j AF329 ' OIL-BATH STEEL 2+2 II i ! I 1 80X80X8 L 2 80X80X8 L 1 80MM PLATE 2 40x8 FLATBAR ;4 1OMM PLATE 2 OFF AS DRAWN OPPOSITE HAND I COVER REMARK!! MATERIAL I 2 AND 3MF1STEEL SHEETS I SEAMWELDED 2MM STEEL SHEET I . ..continued TABLE OF PARTS AND LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS(Continued) NUMBER REQ'D ,_-- NAIVE OF PART 8 ; AF330* I I I f i1 AF331A*i j 1 GENERATOR I j 1 i (5/8"~12)~2 AF331B *[ 5/8"x12 / AF331Cj 5/8" 1 AF332A"I (l/2%12) j AF332B*/ 1/2"x12 1 AF332C*[ I I I l/2" l/2" l-1/2" NUT LOCK WASHER HEXAGON HEADED 4 AF333C *j 9/16" PLAIN WASHER 4 9/16" LOCK WASHER BOLT 4 _ -- 4 ALIGNMENT-PIN 4 AF335A"I (3/8%16) 1 AF335B*/ 3/8" AF335C*! (3/8'k16) 2" BOLT PLAIN WASHER I HEXAGON HEADED 1 WING NUT compcnent HARD STEEL 2 -standard I 4 4 I I*no drawing; HEXAGON HEADED 4 BOLT (9/16"xl2)xNUT *I VOLTS 20 LOCK WASHER AF333B* AF334 4 POLE, 5KW, 115/230 21.7 AMP. 60 CYCLE 1800 R.P.M. 1 PH. 20 NUT (9/16"xl2)x2" , WiNCO INC. SERIES 5KS4G-3 20 BOLT AF333A*; A:Z33D*/ REMARKS MATERIAL . ..End 105 I 106 f co 107 WI 108 109 =: 0 CURVED PLATE 111 112 s 1 113 7 - 114 0.0 2.5 5.0 7.5 10.0 15.0 20.0 25.0 30.0 35.0 40.0 50.0 60.0 70.0 80.0 90.0 ZE 120:o 130.0 140.0 150.0 160.0 2xax 25:5 31.5 36.0 45.0 51.0 56.5 62.0 66.0 70.0 77.0 82,O 87.0 91.5 95.0 98.0 100.0 101.5 102.5 103.0 103.5 104.0 115 I - 116 117 II 118 I OS 119 m 7 I ROTOR BLADING_ A 121 Yc mm 0.0 1.0 2.5 3.75 5.0 6.25 10.0 12.5 15.0 17.5 20.0 22.5 25.0 30.0 32.5 35.0 37.5 38.75 40.0 41.25 42.5 43.5 44.5 45.5 46.5 47.5 48.75 50.0 Xt mm I t mm 0.0 E5 2:o 3.0 6.0 E5 4:75 129:: 15.0 18.0 21.0 24.0 27.0 30.0 31.5 33.0 36.0 37.5 39.0 42,O 45.0 S5 10.0 11.5 12.5 13.25 13.85 14.0 13.85 13.25 12.6 12.0 11.25 10.5 9.12 8.62 7.75 6.75 x5 210 0.0 E 51:o 54.0 57.0 60.0 -!l 0.0 0.76 0.86 i-y8 1:43 1.76 2.02 2.52 3.28 3.78 4.13 4.34 4.34 4.43 4.59 4.54 4.28 4.13 4.03 3.53 2.83 2.17 0.0 123 cu Lc 0 - 124 125 t /’ I r, \ ‘t X R/=1.0 mm Rf=0.2 mm mm t mm 0.0 0.0 0.69 K5 0:75 1.5 0.84 1 , Of, 1.52 1.96 2.38 2.74 3.30 3.73 4.05 4.28 4.43 4.50 4.47 4.33 4.08 3.37 3.31 2.84 2.33 1.79 1.25 0.73 0.28 0.0 i-i 6:0 1E 15:o 18.0 21.0 24.0 27.0 30.0 33.0 36.0 39.0 42.0 45.0 48.0 51.0 54.0 57.0 60.0 126 -- 127 128 129 i SHAFT 220 I II I HUB HOUSING (1 of 2 132 133 134 “I 135 a 136 137 - -I 138 ? Tr ------m--A------ e--m--- ‘, -. t I --v-----------i -- FRAME (plan view) 2 of 2 -a------. ---- 140 I I I I I I I I I I I I I I I I 402 -i I Q 00 TOP ANGLE I 142 I I I I I I a I8 144 \ Y 8G9 ‘1 \ \ \ \ \ 145 35 I I 0I ALIGNMENT-PIN -- APPENDIX II FRICTION LOSS IN NONCIRCULAR CONDUITS Pressure section due to flow bend can be found where is drop K is the loss cross-section angle K and the of the bend The hydraulic radius pressure in of D h' terms where factor E/D L is then fh cross- flow of hydraulic as well velocity and diameter of the as the deflection I-l), is defined as; ' due to friction loss can also be expressed as: the length of the conduit of hydraulic be defined Re average 4 x flow area wetted perimeter drop on the basis should the of the bend, diameter ADh 5 and then v is a factor (Fig, a non-circular from; factor, the mass density. through diameter. is fh and using Fig. E/D I-2. 147 the Obviously as, v Dh E 7 can be found and F $- friction Re and p 148 0.20 i 0.15 1 VALUES OF R/a 0 FIG. 20 I 7. DEFLECTION ANGLE LOSS FACTOR FOR BENDS.(ASCE,J.HYDRAULIC DIV.,NOV. 65) e. 0.004 CI * 0.003 --- -IO3 IO4 IO5 Re = VII/v FIG, 2. FRECTlON FACTOR f VS. Re. FOR DIFFERENT e/D. H.Y.Choi, Heat,Mass and Momentum Transfer P 58 1 IO7 (W.M.Rohsenew and 149 APPENDIX III EFFICIENCIES The total-to-total ?J This efficiency is defined turbine output power enthalpy drop from inlet total and temperature to outlet total E tt of a turbine definition of efficiency is concerned as pressure pressure with the blading hydraulic losses. The total-to-static defined pressure Turbine output enthalpy drop and temperature concerns the amount = - t-s efficiency turbine by drain flow For a turbine efficiency disk as, plus friction and other TJ m is losses. total static going losses an overall can be defined mechanical power from inlet to outlet of energy the internal as a machine of the machine rl t-sm where of a turbine is as, n This efficiency of out pressure of the the blading. total-to-static which should That include the is -rltsxrlm the mechanical efficiency of the machine and defined 150 T -T loss T 'i,' where T stands for shaft For a turbo-generator should also be taken % = - Then the overall II-1 unit the efficiency account which output electrical input mechanical efficiency rl t-su See Fig. into torque. E of is energy work the unit l nt,sXrlmxll g . of the generatar will be defined as; 151 HYDRAULIC LOSSES ENERGY LEP,VI% TtfE TURBIiIE TO TAIL-MTER FIECHANICAL LOSSES GENERATOR LOSSES OUTPUT ELECTRICAL PONER (GENERATOR) FIG. 1 -- SCHEME OF LOSSFS Ii! GlATER TIJRRO-GENERATORS. APPENDIX IV PERFORMANCEESTIMATION OF AXIAL-FLOW TURBINES There axial-flow are several ways to evaluate The method turbine. straightforward is based by H.R.M. and H.J.A. Craig of Mechanical given here which on the method Enginetring, the efficiency given of an seems very in the paper Cox and published in the Volume 1970-71. 185 32/71, written Institution THE METHOD For an axial-flow Group two groups.. of the nozzle friction, 1 losses and rotor leakages, 1 losses. turbine factors is convenient based on relative X n secondary and losses X r etc. are for blade = the group velocities. 153 losses are due to disk only with group as 1 losses 1 losses as loss Therefore, w2 + Xr $ the sum of loss the nozzle and secondary can be defined outlet c2 Xn $ into be concerned efficiency to evaluate can be divided 2 losses work done in blading done in blading + group Group 1 losses where and group Here we will blading losses due to profile blading, l-lt-tb 2 work It are etc. Therefore stage, factors and rotor, due to profile respectively. and -. 154 Then to take account the losses we have to multiply the area ratio Ar Evaluation defined . due to tip the value of loss leakage and etc. of blading into efficiency by as follows; Rotor blade swept annulus area E The blade ‘. area factors loss factor X and secondary P defined as loss xP = x pb 'pi is the sum of profile loss Xs , where former factor Npr Npt + mp, Each one of these are + (Axp)s,e defined the factor one is + (ax 1 Pm as: X Pb 5 basic profile loss N Pi 5 loss correction factor due to incidence N Pr = loss - correction factor due to high N Pt 5 loss correction factor due to trailing Reynolds Number edge Wp) t z profile loss factor increment due to trailing iAx > p s/e - profile radius loss factor increment dtle to back surface E profile loss factor increment due to high (oxp lrn edge Mach number 155 This method can acceptably turbines of the kind case for design-point N Pi would Each of these Figs. III-2 blade opening = P x pb Npr Npt design form + axial-flow concerned (mpjrn for water In this with. , (fip)s,e will X P and be (axpIt can be found using curves Number is given defined in on the as; *2O2 E 7 for the or terminology The secondary-loss where xS is The Reynolds to 111-B. III-1 and III-8, report and the simple parameters Re See Fig. this preliminary be zero X that be used for 5 factor the secondary-loss (Ns+qb I x clol V of the blades, can be found factor using XS (Xsjb where ('s)b E basic secondary-loss z (Ns$i/b- secondary-loss ratio. factor is Figures defined III-7 as 156 Fig. 1. Turbine blade and velocity triangle 16 I __ 10 20 :i Fluid Inlet at mln.rdcl ,cont,!!on 40 F:il:O !Iw 50 60 CiJ: - ET :N;LE -B speed ccnc bon) Fig.2 . Lift parameter, 70 FL notation I orgee loss cn 90 157 I I I -G-l 0 01 I I 0.2 I c3 I I I I '24 05 06 07 0.8 RATIO-I-~ . Fig.3. .- . ., s%33 for average profiles , / J 05 5s I / / I I I I I I I I I I I MODIFIED Fig.4. LIFT 1 I / ! I 5 20 I 2 C0c:~crt.o~ rc:,o m ratio !! i p: 25 Y 5 Contraction ri I CGEFc.Z EYT - Basic profile ;x:s,%: loss r VI TRAMr; E3;E Tr!'CKSESS Fig. 5 .Traiiing TC PITPI R;T.G -tc/s edge thickness losses 158 REYNOLDS li.NE_~ Fig.6, Profile Rz,, -based against loss ratio on biade o~enq Reynolds number effect --.._ L 7 / /’ ---I 25 33 -,b/h 4or------ -35 /F c: I// t 45 bit, -- / , 50 - sj / I !5 NVLQSE ASPECT RATIO -b/h Fig. 7. Secondary loss-aspec: ratio factor ( 55 98 10 SQUARE OF 1-F. FF:A-iJE YECN VE:SC:TY RATIO ACROSS 3LA: ‘.; -et tie x~ry~ou!~e? bcc:o;i:# Fig. 8. Secondary loss-bask loss factor 159 LIST OF SYMBOLS area blade angle width of flow the blades velocity, chord of absolute the blade diameter friction factor g acceleration due to gravity H hydraulic h blade h enthalpy i incidence angle K head-loss factor L length lil mass flow N rotational 0 opening head height rate speed of the blades pressure volume flow rate radius S spacing T torque of the blades . ..continued 'LIST OF SYMBOLS(continued) U blade tangential velocity W relative Z number of blades ci angle of absolute velocity B angle of relative velocity A deop or rise 6 deviation velocity, flow of a vaiable angle efficiency turning angle stagger or setting angle mass density CT solidity flow coefficient work coefficient w speed of revolution (angular * * velocity) * 161 SUBSCRIPTS annulus hub inlet leading edge m mean value n nozzle 0 outlet P profile r rotor t tip X axial 0 and radial direction stagnation inlet direction property to the blade out of blade tangential direction * * * 163 REFERENCES (1) Horlock, J.H. Axial Flow Turbines. Robert E. Kreiger Publishing Co., Huntington, New York, 1973. (2) Dunavent, J. C.,and Erwin, J. R. Investigation of Related Series of Turbine Blade Profiles in Cascade. National Advisory Committee for Aeronautics, Washington, NACA. TN3802. i3) Craig, H. R. M., and Cox, H. J. A. Performance Estimation of -Axial Flow Taurbines. The Institution of Mechanical Engineers (Thermodynamics and Fluid Mechanics Group), Volume 185 32/71, 1970-71.

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