Lecture on Francis Turbine. by Dr. Shibayan Sarkar Department of Mechanical Engg Indian Institute of Technology (ISM), Dhanbad
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1 Lecture on Francis Turbine by Dr. Shibayan Sarkar Department of Mechanical Engg Indian Institute of Technology (ISM), Dhanbad
2 Turbines: Francis (1849) di, Qo Ri ɵ Ra Stay ring Spiral casing π Q = v d 4 o i i v = K gh i v R = R + d π Q= Q o π a i i
3 Draft Tube: Static pressure (P/γ+Z) gradually decreases when water glides over the runner blades. Water coming out of the runner posses large amount of Kinetic energy and pressure at runner, which is less than atmospheric pressure. (1) It makes possible to install the turbine above tail race without loss of head () The pressure at the exit of the draft tube is atmospheric. () Avoid cavitation, arrest separation of water. Apply Bernouli s theory at runner exit () and exit of draft tube (4) P v P4 v4 Z Z4 hf γ + g + = γ + g + + hf = head loss through draft tube..eq (1) Apply Bernouli s theory at free surface () and exit of draft tube (4) Entry at runner /exit from guide vane (1) Exit from runner () P v P v γ g γ g Z = + + Z4 P4 γ P γ = + Z Z4 ( )..eq () Replacing the above value to eq (1) P P v v 4 = ( Z Z) hf γ γ g g P P v v 4 = hs hf γ γ + g g Same, as difference is negligible..eq ()..eq (4)..eq (5) Z hs Z Datum Air Z4 P atm Static suction head dynamic suction head
4 Draft Tube: (4) Static pressure (P/γ+Z) at runner (at the level of ) is less than atmospheric pressure by an amount equal to the static and dynamic suction head. V /g (5) Velocity of water at of runner is very high (-15% of net working head, for high specific speed it is 45% in case of kaplan turbine), by employing draft tube recovers this wasted KE is utilized which increases efficiency of the turbine. (6) Prevent splashes of water coming out of the runner. 4º D Prevent possibility of flow separation η dt =90%, angle less than 8º Above tail race level.5 to D Below Tail race level 0.5 to 1D less excavation, head loss at bend, η dt =85% Increase area of water exit, increase whirling action, suit for helical flow, η dt =85% η dt Length minimum and less excavation, head loss at bend, η dt =60% Efficiency of the draft tube is expressed as ( V V4 ) hf g = V g actual conversion of Kinetic Head into Pressure Head = Kinetic Head at of the draft tube Sometimes friction loss is expressed as h f ( V V4 ) = k g, k = const
5 Governing Mechanism
6 Velocity Diagram V 1 Vr u Vr1 V Slow runner Vr Relationship: V 1 u V Fast runner Vr1 Vr V r1 u u 1 = + Runners are classified according to the speed, as per their shape and velocity triangle Vr u V 1 V Rotation Vr1 Medium runner Vr V r1 u1 u Hpr = + V1 V Vr V r1 u1 u He = + + Centrifugal head (CFH) Outward flow: u >, CFH +ve, V r increases at Inward flow: >u, CFH -ve, V r decreases at Degree of Reaction (R) change in pressure energy inside the runner (Hpr) = change in total energy inside the runner (He) Vr 1 v β v f v w D / φ u Guide vane α v 1 v w1 D 1 / v f1 Vr = Vr 1 v 1 = velocity of fluid at = velocity of the vane at v r1 = relative velocity of fluid at α = angle between the direction of the fluid and the direction of motion of the vane, guide blade angle v w1 = velocity of whirl at = angle made by v r1 with direction of motion at, vane angle at v 1 = velocity of fluid at v f1 = velocity of flow at v w = velocity of whirl at v f = velocity of flow at β = angle between v with the direction of motion of vane at ϕ = angle made by v r with direction of motion of vane at, vane angle at
7 Francis Turbine Equations Working Proportions: (1) Ratio to width to diameter (n )= b1/d1 = 0.1 to 0.45, for slow runner flow is predominantly radial and exit is axial () Speed ratio (Ku) = 1 gh = 0.6 to 0.9 () Flow ratio (kf) = V / f 1 gh = 0.15 to 0.0 (4) Coeff of velocity (kv)= 1 gh = 0.97 to 0.99 Design Parameters: Head (H), running speed (N), Power output (P) is required size of the runner and its vane angle is to be find out. (1) Assume probable value of η h, η o, n and ratios (Ku, kf, kv) () Workout the mass or volumetric flow rate, where shaft power P = η o γqh Key Term: Without whirl V w =0 v v f1 Negligible blade thickness 1 Kv 1 =K =1 Radial =90º w1 Radial exit β=90º; V=Vf No blade friction Vr1=Vr () Flow opening area A 1 = πd 1 b 1 -Zt 1 b 1, =πd 1 b 1 K 1 where Z is number of blades, t 1 is thickness of runner at, b 1 = width of the runner at, and K 1 is vane thickness coeff = approx 0.95 (4) Flow velocity V f1 = Q/ πd 1 b 1 K 1, by continuity equation Q= Rotation πd 1 b 1 K 1 V f1 = πd b K V f (5) u1=πdn/60 (6) Work done by turbomachine = ρq( Vw1± Vwu), (7) Hydraulic Efficiency (η v h ) assuming radial exit = V w1 /gh [V w is zero] Vr = Vr (8) Head supplied to turbine = Work Done or head utilized at runner + Kinetic β 1 vhead f φ at exit H i = p 1 /ρg+v 1 /g ρq( Vw v u 1u1± Vwu) V w Ht = + again gross head Hg = Ht hl whereas for pump ρ gq g + D 1 t 1 b 1 Vr 1 D α b H p = Hg hl
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