FIELD OF INVENTION
This invention relates to a runner blade for low specific speed Francis turbine.
BACKGROUND
Conventionally the reaction hydraulic turbine consist of spiral casing (or scroll case), stay vane, guide vane, runner and draft tube in that order. Runner also known as impeller is the only rotating passage. Mixed flow hydraulic turbine where the runner inlet flow is radial and runner exit flow is predominantly axial in direction is known as Francis turbine. The runner which is characterised by a large number of blades (usually 11-19), equally spaced circumferentially around the turbine axis; coverts hydraulic energy (water head) into mechanical energy. It is called reaction turbine by definition if the pressure drop across the runner alone is more than 60% of the pressure drop occurring across the total water path (spiral casing to draft tube). Francis turbines with various kind of water path are used in practice for a range of specific speed ns, m=70-400 rpm, and head range H=50-500 m; or alternatively for a range of unit discharge q11 = 150-1350 litre/second, and unit speed nll= 40-130 rpm. The hydraulic efficiency n (or eta) for prototype runner is expected to be in the range of 90-95%. A runner is designed to be site specific i.e. for a limited range of unit discharge q11: design unit discharge +100 lps and fixed unit speed nil based on runner diameter (D), machine speed (n) rpm and rated head H (m); to provide efficient and cavitations free characteristics. The characteristic dimensions are defined as
Unit speed; nil = (n*D)/VH
Unit discharge; q11 = q/(D2 H)
Specific speed; ns, m = nPkw/H5/4
Hydraulic efficiency; eta or n = 1000*Pkw/(rho*g*q*H)
Where q is discharge in Ips (=litre/second), Pkw is power developed (in KW) by the turbine rho (998.2) and g(9.81) are water density and acceleration due to gravity.
A typical turbine characteristics are plotted as shown in Fig. 1A of the
accompanying drawings showing efficiency iso-contours el, e2...............optimum
guide vane openings al, a2.... as function of unit discharge qll and unit speed n11.Note:
Guide vane openings:ale2 >e3 >e4
For a unit design speed, say n11, d a turbine is designed to deliver q11, d at operative point 'O' (Fig. 1A). Usually the turbine is expected to operate around point 'O' within ql 1, d±100 Ips efficiently. With the years of operation, the head deteriorates significantly, hence operating point shift to lesser efficient location say R. The point R is at higher discharge and at slightly higher n11 at lower efficiency point, resulting into lesser turbine power. New hydro power plant needs huge investment hence designer seeks for renovation and modernization of existing plant with minimum investment. Retrofitting runner is an obvious cost-effective first choice. The aim of the invention is to develop a new runner which has got optimum efficiency near new operating point R (Fig. IB), and suit existing water path and retaining stationary components of hydraulic paths (viz. Spiral casing, guide vane, draft tube and stay vane).
George E, Meeker & Willem Jansen have described turbine having 2 or more runner blades each having a Cork Screw configuration (U.S. Pat No. 5, 997,242; Dec 7, 1999). One wicket gate configuration for hydraulic turbine is proposed by A Gokhman (U.S. Pat 5,441, 384; Aug. 15, 1995). David G. Homes et.al has proposed blade configuration for Francis runner for improved cavitation-free performance (U.S. Pat No. 4,379,757;Oct. 30, 984). Benno Buchelt has proposed a blade for Kaplan turbine (U.S. Pat No. 6, 007, 297, Dec 28, 1999). The reported work by Kurokawa et.al (US Pat No. 6,217,285 Bl, Apr 17, 2001)
and Strycek et.Al (US Pat No. 3,964,841; Jun 22,1976) concern with the design of centrifugal blower, fan and pump for flow discharge as output. They are not meant for turbine application where power is output. The work by Billdal et.Al (US pat No. 6,135,716, Oct 24, 2000) proposed impeller for turbine with leaning of leading and trailing edges with respect to hub and shroud; respectively, in the direction of rotation. Harada et.al (US Pat No. 6,338,610 Bl; Jan 15, 2002) propose impeller for discharge as output with secondary flow loss reduction as goal by providing leaned blade. Nishikawa (US Pat No. 4,274,810; Jun 23, 1981) proposed blade for fan application. Centrifugal compressor for discharge as output is proposed by Seleznev.at.al. (US Pat No. 3, 973,872; Aug 10, 1976). Swearingen (US Pat No. 30,610,775; Oct 5, 1971) is for impeller to work with flow motion in gaseous medium entrained with liquid and solid particles. Kugel (US Pat No. 2, 042, 064, May 26, 1936), Kalpan (US Pat No. 1, 509,653; Sep 23, 1924) and Konda M (US Pat No. 3,440,969; Apr 29, 1969) deal with various construction features of runners for centrifugal flow machines. The present invention relates to design of new runner blade consisting of blade profiles with reduced plan angle for retrofit work to existing mixed flow machines (Francis turbine) water paths, to suit deteriorated head.
OBJECTS OF THE INVENTION
An object of the present invention is to propose a new runner blade with 9 profile sections suitable to meet new unit discharge and speed more efficiently than the known art.
Another object is to propose an efficient runner blade to fit with existing water path, i.e. retaining crown, skirt, inlet and outlet boundaries.
Still another object of this invention is to propose a new runner is better than prior art runner for higher unit discharge and higher unit speed in terms of efficiency; and lower pressure minima.
Yet another object of this invention is to propose a runner which is more suitable for retrofit job at deteriorated available head than prior art or existing runner.
BRIEF DESCRIPTION OF INVENTION
According to this invention there is provided a runner blade for Low Specific Francis turbine comprising a group of nine blade profiles covering from crown, the first profile, to the skirt, the ninth profile, each blade profile made up of a concave curve, known as pressure curve and a convex curve known as suction curve, both jointed at two ends, one known as leading edge at the flow inlet side and the second known as trailing edge at the flow exit side, wherein radial width of profile of (non-dimensional is made with respect to runner diameter dl) i.e. (rmx-rmn)/dl from 0.275 to 0.159; plane angle Gmx- 6mn within the range from 38.152 to 36.735 degrees and the chord length L of profile (normalized with respect to runner diameter dl) i.e. L/Dl within the range from 0.293to 0.199 from crown to skirt and for side blade axial span (non-dimensional with respect to runner diameter dl) i.e. Znorm=Zmx-Zmn/d1 varies between 0.102 to 0.123 and the said blade can be utilized for new job for geometrically similar water path characterized such that the setting angles of guide vane openings within the range of 12 to 15 degrees and at the specific speed of the turbine within the range from 83 to 98 rpm., the efficiency of the turbine being increased by 0.7% over the existing ones.
The runner passage consists of flow domain bounded by inlet crown or hub (1) and skirt (2) (also known as ring, band or tip). The flow domain has an array of blades equi-spaced circumsferentially and extending between and interconnecting crown (1) and skirt (2). The runner rotates about the turbine center line by the action of flow causing thrust on the blade surfaces. Water path is characterized by the dimensions D, the runner inlet diameter.
The runner is expressed in global Cartesian coordinate axis (x,y,z system; z aligned with turbine axis positive toward i.e., guide van side). The water path is divided into a set of quasi-streamlines (r,z system; r=(x2+y2). Each streamlines is a projected view on (r,z) plane of blade profile. In (x,y) plane the blade profile look like aerofoil sections having thicker and rounded leading edges at inlet and thinner, sharp trailing edges at outlet.
The runner consists of blade profiles with lower chord (about 15%) than that form prior art (existing runner). Invented profiles are slightly thinner (about 5%) with lower plane angle 0mx-0mn (about 10°) with respect to prior art (note: 0=tan1 (-y/x). Prior art runner has S-shaped profiles.
DESCRIPTION WITH REFERENCE TO ACCOMPANYING DRAWINGS
The nature of invention vis-a-vis prior art will be apparent from the following description made with reference to non-limiting exemplary embodiments of the invention represented in the accompanying drawings:-
Fig. 1A Typical universal characteristics of a Francis Turbine
0= design point R= at derated head ale2>e3>e4- Hydraulic efficiency. Suffix: d = at design H r = at revised H q11 = unit discharge, lps. n11 = unit speed. I cl, Ic2 = Iso-efficiency contours.
IB Existing and suggested typical Iso-efficiency contours.
IC3 = prior art Iso efficiency contours.
IC4 = Iso efficiency contours for new runner.
n11 = unit speed
q11 = unit discharge, lps.
O = design point
R = at derated head.
2A Meridional passage of a runner (r-z coordinate system)
1 = inlet
2 = crown or hub
3 = Guide vane side
4 = Turbine axis
5 = Draft tube side
6 = outlet
7 = streamline
8 = skirt or hand or tip D = diameter.
2B Meridional passage and Quasi-streamlines
9 = crown
10 = Two faces of a profile
11 = skirt.
3 Runner profiles from prior art (x-y coordinate system)
1 = Leading edges
2 = crown profile
3 = skirt profile
4 = Trailing edges
5 = Prior Art Existing Runner with 9 profiles
6 = Leading edge enlarged.
Fig. 4A Invented runner profiles (x-y coordinate system)
7 = Crown profile
8 = Skirt profile
9 = Leading edge enlarged.
Fig. 4B Geometry Description of invented profiles.
r = sqrt (X*X+Y*Y)
O = a tan (-y/x)
Ata; r = rmx
Atb; z = zmx, 0 = 0 mx
Atd; r = rmn
A+c; z = zmn, 0 = 0 mm
d1= runner diameter rnorm = (rmx-rmn)/dl znorm = (zmx-zmn)/dl
(Table Removed)
Fig. 5 Crown profile section (prior art and invented)
Fig. 6 Mean profile section (prior art and invented)
Fig. 7 Skirt (band) profile section (prior art and invented)
Fig. 8 Three dimensional view of the invented blade (x-y-z coordinate system).
1 = Leading edges
2 = Suction Face
3 = Pressure Face
4 = Trailing edges.
Fig. 9 Pressure loading over the crown section (Prior art profile and Invented profile)
Fig. 10 Pressure loading over the skirt section (Prior art profile and
invented profile)
Fig. 11A CFD simulation of surface pressure distribution (skirt not shown)
Fig. 11B CFD simulation of surface pressure distribution (crown, skirt 8B blade).
GEOMETRY AND FLOW FEATURES:
New runner blade (Fig.4) have 9 profile sections to suit quasi-streamline (Fig. IB) and existing water part (Fig. 1A). There are 19 blades circumferentially equally spaced around the turbine axis and rotating with design rpm.
Each of the sectional profile is made of two unique curves: pressure curve (lower one) and suction curved (top one)' each starting from leading edge (at inlet flow side) and ending at trailing edge (at exit flow side). The characteristics of nine invented profiles and shown in Fig. 4B' in term of the parameters:
1. rnorm=(rmx-rmn)/d1
2. Znorm=(Zmx-Zmn)/d1
3. L/d1
4. Өmx
5. Өmn
Where rmx=Maximum value of r rmn=Minimum value of r zmx=Maximum value of z zmn=Maximum value of z Өmx=Maximum value of Ө Өmn=Minimum value of Ө
Note with reference to Fig. 4B:
r=Polar radius =  (x2-y2)
Ө=tan1 (-y/x) or atan (-y/x)
Sec= Profile section number (1 to 9; 1 for crown, 9 for skirt)
(x,y,z)= Cartesian co-ordinate system
(r,z)=Meridional plane
(x,y)= blade-to-blade plane
dl or D= runner diameter
L=Profile length [ (zb-zc)2+ (rb-rc)2]
Suffix b, c refers to point at zmx and zmn.
The invented blade profile has monotonous variation (either increasing or decreasing) of geometrical parameters of radial width of profile (non-dimentional made with respect to runner diameter di) i.e. (rmx-rmn)/ di from 0.275 to 0.159):
Plane angle 0mx- 0mn (from 38,152 to 36, 735 degrees) and chord length L of profile (normalized with respect to runner diameter di)i.e. L/ di, is with in the range from 0.293 to 0.199 from crown to skirt.
The value of 6mn being Zero; the variation of plan angles 8mx-9mn is identical with that of 0mx. The geometrical parameter of blade; axial span (non-dimensional with-respect to runner diameter di) i.e. z norm= (zmx-zmn)/di varies between 0.102 and 0.123; with peak value is at and 6th and 7th sections (Fig.4B).
Pictorial views of typical 3 profiles (Crown, mean and skirt) for prior art and invented ones are shown in Figs. 5,6 and 7. The assembled three-dimensional view of blade (made of 9 profiles) is shown in Fig.8. The blade is made by stacking these 9 invented profiles joining the profile curves linearly.
PERFORMANCE SIMULATIN BY COMPUTATIONAL FLUID DYNAMICS (CFD)
The performance of invented blade as well as prior art with existing water path is simulated by CFD for given machine rpm (500) with water as fluid medium' for various guide vane openings. Two typical results depicted pressure loading for a tg=13° over the crown section and over the skirt are shown in Figs. 9 and 10;respectively. X-axis shows the normalized meridional distance over the profile (0 to 1.0; 0.0 at leading edge and 1.0 at trailing edge). Y-axis refers to surface pressure in N/m2. The inlet flow angle with respect to tangential direction is a tg=13°. Two inferences can be drawn from Figs. 9 and 10. The minimum pressure values are less negative in case of invented profiles indicating.
better cavitational characteristics. Typical results for discharge= 13650 kg/s, rpm=500 are as follows (The head and efficiency values are based on runner water path with appropriate correction make for stationary component losses):
ICase α tg=12°
(Table Removed)
II Case α tg=13°
(Table Removed)

III Case α tg=14°
(Table Removed)

IV Case α tg=15°
(Table Removed)

The prior art blade was to operate around a point say 'O' where ql 1=197.68 and nl 1=57.93.Due to aging of hydroset the available head H reduced such that the operation shifted to a point 'R' where q11=205.41 and n11=60.19 and efficiency is lower by 0.5%. It is obvious from the cases I-IV that invented blade for existing water path suit well for higher unit discharge and speed as needed for deteriorated head condition. The invented blade is more efficient and shows better cavitational characteristics for a range of ns, m=83-98. Figs. 9 and 10 shows better pressure loading throughout the profile length.
Figs. 11A and 11B shows typical pressure fringe plots over the runner as obtained by CFD simulations.

WE CLAIMS :-
1. A runner blade for Low Specific Francis turbine comprising a group of nine blade profiles covering from crown, the first profile, to the skirt, the ninth profile, each blade profile made up of a concave curve, known as pressure curve and a convex curve known as suction curve, both jointed at two ends, one known as leading edge at the flow inlet side and the second known as trailing edge at the flow exit side, wherein radial width of profile (non-dimensional is made with respect to runner diameter dl) i.e. (rmx-rmn)/dl from 0.275 to 0.159; plane angle 6mx- 9mn within the range from 38.152 to 36.735 degrees and the chord length L of profile (normalized with respect to runner diameter dl) i.e. L/Dl within the range from 0.293to 0.199 from crown to skirt and for side blade axial span (non-dimensional with respect to runner diameter dl) i.e. Znorm=Zmx-Zmn/dl varies between 0.102 to 0.123 and the said blade can be utilized for new job for geometrically similar water path characterized such that the setting angles of guide vane openings within the range of 12 to 15 degrees and at the specific speed of the turbine within the range from 83 to 98 rpm., the efficiency of the turbine being increased by 0.7% over the existing ones.
2. The runner blade as claimed in claim 1, wherein the profile to profile have monotonous variations, either increasing or decreasing of geometrical parameters for radial width of profile.
3. A runner blade for low speed Francis turbine substantially as herein described and illustrated with the accompanying drawings.
4. A low specific speed Francis turbine having a runner blade as claimed in any of the claims 1 to 2.