|Title of Invention||
" TRANSONIC BLADE PROFILES"
|Abstract||The present invention relates to the aerodynamic design of moving blades, pertaining to later stages of axial steam turbines where the inlet flow is nonuniform over the blade height. The claim made herein is a set of six invented transonic blade profiles which can be used to develop various type of 3D twisted blades for axial steam turbine. The aerodynamic characteristics of these 6 base profiles are evaluated herein as a function of stagger angle and pitch/chord ratios. The aerodynamic characteristics invented herein is for a group of six base profiles which are to be used for creation of three dimensional blades made of varying cross-sections and twisted over the blade height while ensuring the centers of gravity of these sections lie in a radial line. Each of the blades, sections from hub to tip is twisted differently from desired outlet angle. Thus the nomograms can be used to develop quickly a first level design of a 3D blade making use of 2D base profiles whose performance is shown in the form of nomograms.|
|Full Text||FIELD OF INVENTION
This invention relates to transonic blade profiles for development of 3D twisted blades for axial steam turbine.
BACKGROUND OF THE INVENTION
The design of 2D (referred as 2D or c) lindrical blade having identical cross-section throughout the blade span) and 3D blades are of paramount importance for power generation. Various patems, e.g. U.S patents no. 5779443 (1998). 5211703 (1993) and 5192190 (1993) refer to "stationary" blade. U.S Patent no. 5779443 deals with radially bent blade (radial shift of centers of areas of individual profiles over the blade height). The present investigation refers to design of six base profiles and construction of moving blade (by making use of these base profiles) without radial shift.
In cylindrical stages, the profiles remain same for more than one stage over their blade height without significant loss in efficiency. The inlet flow is more or less uniform over the Wad height Usually a few profiles are sufficient to create many blade rows. The present ir vention primarily concerns to moving blade of axial steam turbine stages,
where the direction of incoming flow to moving blade varies along the blade height, thus necessitating twisted blade Hence the design and manufacturing of twisted blade is costly and time consuming as it is to be done every time for varying flow condition.
Normally the conventional blades are of constant cross-section and cylindrical in shape over the blade height. At any cross section the shape of the profile remains same as shown typically in Fig. 1. I he profile or section is made of two surfaces, suction face and pressure face, each joining leading edge to trailing edge. X-axis and y-axis coincide to turbine axis and circunferential direction, respectively.
The center of gravity lies at origin of coordinate axes. The blade or profile is set at angle "betabi" or y.tg (or gamatg). also known as stagger angle with respect to U-axis. Chord is defined an axial distance of base profile measure between two farthest tangents to the profile; one at leading edge side and other at trailing edge side. The tangents are normal to the chord. Axial chord is the projected length of the profile on X-axis; hence varies with profile stagger. Inlet and exit flow angles ß1, tg and ß2. tg are fluid angles with respect to tangent (U-axis), respectively. The profile faces can be specified by various ways e.g. through discrete points (x, y co-ordinates), through a set of areas and through bezier points.
In this invention new 3D blade can be made of many such profiles (Fig. 1) but with varying shape and other parameters such as stagger angle, chord, axial chord, cross sectional areas (Fig. 2). The centers of gravity of the profiles coincide in x-y planes. The areas of cross section, stagger angles, and the ratio chord (c)/pitch (s) monotonously decrease from hub to tip, whereas pitch (=2 r/no of blades; r=radius where the profile is located) increase along the blade height. A typical sketch of such set of stacked profiles for all six sections and blade-to-blade (cascade) view are shown in Fig. 2.
OBJECTS OF THE INVENTION
An object of this invention is to propose steam turbine runner blades in low and intermediate pressure cylinders are of higher height and higher aspect ratio compared to those of high pressure cylinders. They are needed to handle forger specific volume of steam during expansion; hence designer has to use twisted or 3D blades.
Another object of the present invention is to propose a set of six original transonic blade profiles, which can be used to develop various types of 3D blades for axial steam turbine.
DESCRIPTION OF INVENTION
According to this invention there is provided a set of six transonic blade profiles comprising each a pressure face and a suction face joined at their leading and trailing edges, the cross sections being twisted over the blade height and that the centers of gravity of these sections lie in a radial line.
BRIED DESCRIPTION OF DRAWING
The nature of invention, its objective and further advantages residing in the same will be apparent from the following description made with reference to the non-limiting exemplary embodiments of the invention represented in the accompanying drawings.
Fig. 1. Profile Geometry Definition
Fig. 2. Stacked Profiled and a Cascade
Fig. 2A. Base Profile: Typical Points
Fig. 2B. Base Profile: Coordinates of Typical Points
Fig. 3. Base Profiles: c 100b J r
Fig. 4. Base Profiles: cl00BJ r
Fig. 5. 3D View of a Typical Blade
Fig. 6. Nomogram (beta2ax): Profile 1 of cl00blr
Fig. 7. Nomogram (zeta): Profile 1 of cl00b-lr
Fig. 8. Nomogram (beta2ax): Profile 2 of cl00blr
Fig. 9. Nomogram (zeta): Profile 2 of c 100b 1 r
Fig. 10. Nomogram (beta2ax): Profile 3 of cl00blr
Fig. 11. Nomogram (zeta): Profile 3 of c 100b 1 r
Fig. 12. Nomogram (beta2ax): Profile 4 of cl00blr
Fig. 13. Nomogram (zeta): Profile 4 of cl00blr
Fig. 14. Nomogram (beta2ax): Profile 5 of cl00b lr
Fig. 15. Nomogram (zeta): Profile 5 of c 100b 1 r
Fig. 16. Nomogram (betaZax): Profile 6 of cl00blr
Fig. 17. Nomogram (zeta): Profile 6 of 100b 1 r
Fig. 18 Hub Profile: Grid & Iso-Mach Contours
Fig. 19 Hub Profiles: Grid & Iso-Mach Contours
Fig. 20 Hub & lip Profile: Surface Pressure Distribution
Fig. 21 Hub Profile: Surface Maeh no. Distribution
Fig. 22 Comparison of 2D CFD and 3D CFD Study
GEOMETRY AND FLOW FEATURES;
Usually the flow in low pressure cylinder and 3D moving blade used for the steam expansion through the cylinder have the following common features
1. Inlet flow any ß1.tag at hub is more acute than that at tip side
2. Exit Mach number at hub is lower than that at the tip
3. Maximum centrifugal stress is at hub, hence larger area of hub profile.
4. Higher solidity at hub for mechanical strength, hence the blade profile at hub has lower pitch/chord ratio compared to profiles at the tip side.
5. Exit flow is transonic.
6. Hub profile is more cambered than tip profile to account flow turning.
7. Blade is usually tapered to maintain nearly equal gap between upstream and downstream blade rows; from hub to tip.
8. Exit flow angle P2,tg at tip is more acute than that at the hub side.
Invented Base Profile: The invented base profile are Bezier generated ones
and typically described by typical points (fig 2A).
Point Pl= the location of minimum x-coordinate (xmm.) Point P2= the location of minimum y- coordinate. At leading edge side (ymnl) Point P3 = the location of maximum y-coordinate. On suction face (ymxl) Point P4= the location of maximum y-coordinate. On pressure face (ymx2)
Point P5= the location of maximum x-coordinate (xmx)
Point P6= the location of minimum y-coordinate. At trailing edge side (ymn2)
Point P7= the location of center of gravity. x=0, y=0.0
Base chord = xmy-xmn=100 (reference)
The date file containing a series of 6 base profiles (Fig. 3 and 4) is designated as cl00lr. The file consists of 6 sets of profile each with 91 points on each of the two surfaces; suction and pressure surfaces. The file cl00-lr contains first the profile with higher camber followed by profiles with lower camber.
Bach of the base profiles has base chord length as 100 units. The coordinates can be scaled up or down as per the need. The center of all porfile area lies at point (0.0,0.0). The percentage ratio of maximum blade thickness to base chord varies approximately 18.3, 15.5, 12.8. 10.2, 7.9 and 7.7 from first to last line. Fig 2B provides the coordinates of 6 typical points of each of the 6 profiles.
A typical view of 3D blade using profiles of cl00lr for a sample set of stagger angle and chord is shown in Fig. 5.
Analysis based on two-dimensional (2D) Computational Fluid Dynamics
(CFD): The initial setting angle for this base profile is y,tag *90.0 deg. Each of the 6 base profiles staggered to values desired for 3D blade formation is analyzed for a set of
pitch/chord ratio at transonic Mach on M2 =0.9. The aerodynamic performance is computed by a 2D CFD (Computational Fluid Dynamic) solver and database is created in the form of aerodynamic characteristics (namograms).
Cascade performance of individual profiles is simulated by a CFD solver using air as fluid medium with the rat'o of specific heats k-14.
Energy loss coefficient zeta or ^ defined as
ζ =1 [ 1 -(p2/po2) _k-1.]/ 1 -(p2/po 1) k-1 |
where p2 is mass -averaged static pressure at the outlet, pol and po2 are
mass averaged stagnation pressure at the inlet and exit of the cascade.
Outlet flow angle (beta2ax) is computed as function of pitch/chord ratio and stagger angle (gamatg). Similarly energy loss efficient (zeta) is found as function of pitch/chord ratio and stagger angle (gamatg). Note : Beta2ax =-ß2,tag-90.0; Betalax= 90- ßl,tg, degree.
Figs 6 to 17 are the invented aerodynamic characteristics (nomograms) for 6
base profiles listed as cl00lr. The variants are as follows:
Profile 1: s/c=5-0.8; gamatg=65-75 deg; betalax=30; M2=0.9
Profile 2: s/c=0.5-0.8; gamatg=60-70 deg; betalax=30; M2=0.9
Profile 2: s/c=0.5-0.8 gamatg=60-70 deg; betalax=30; M2=0.9
Profile 4: s/c=0.6-0.9 gamatg=55-65 deg; betalax=30; M2=0.9
Profile 5: s/c=0.6-0.9 gamatg-40-50 deg; betalax=10; M2=0.9
Profile 6: s/c=0.8-l.l; gamatg-25-35 deg; betalax=10; M2=0.9
The effects of M2 is limited if M2=0.8-1.1; and effect of betalx is also limited if variation is about 10 degrees on either side of above quoted values. These results (nomograms) are useful for firsl level design, which can be improved by 3D CFD study. Some general interference from the nomograms are to be noted:
1. As gamatg increase, zeta decreases at fixed pitch/chord s/c.
2. As gamtrag iiHtfeases, beta2ax increase at fixed pitch/chord ratio s/c.
3. As s/c ratio increases, beta2ax increased at fixed gamatg
4. As s/c ratio increases, zeta decreases at fixed gamatg for profiles 1,2,3
5. As s/c ratio increases, zeta increases at fixed gamatg for profiles 4, 5, 6
6. Higher the profile camber, higher the loss; hence profile 1 has high zeta.
3D-Blade Design A number of 3D blade shapes can be designed knowing profile-wise stagger angle, which gives the desired outlet angle and loss; and also making use of profile-wise scaling factor to suit blade taper from hub to lip to suit steam flow path design. The profile rotation (stagger) as well as scaling is done with respect to center of
area (center of gravity: e.g.) of each profile. Scaling implies profile blow up and blow down keeping e.g. same; thus same scale factor in x and U (or y) directions of the profile.
A computer program "blade3d" developed by the inventor performs the above job; i.e. stacking about e.g. and sealing of profile; just by specifying the file name containing profiles i.e. cl00bir. gamatg and scale factor profile-wise; as well as radius of radius of profile section in blade height. Fig. 5 shows a 3D blade for gamatg= 70.65, 60.55, 50. 45 for hub to tip profiles at radii= 500, 520, 540. 560. 580, 600 mm and scaling factor as 0.5 common for all 6 profiles with a set of base profiles designated by the data file name cl 00b 1 r.
Analysis based on three-dimensional (3D) computational Fluid Dynamics (CFD): It may be noted above the profile-wise orientation is made using nomograms based on 2D CFD analysis. Geometrical shape of a 3D blade is made by logic discussed in earlier section by using computer software *'blade3d". Thus, the first level of design for a 3D blade is ready which need to tested and refined, if necessary by making use of 3D CFD software or experiment
A typical 3D blade for a typical flow condition resembling low pressure power turbine first stage is constructed with gamatg == 69, 66, 62, 55, 43, 29 and scale = 0.353, 0.353, 0.352, 0.352, 0.353, 0.290 for profiles 1 to 6; respectively. The above stagger angles and nomograms for s/c amounting to no blade z=67 for radii=200, 213, 226, 252, 265; gave the outlet angles as needed by a typical existing steam flow path design.
Three dimensional flow analysis by a CFD solver was carried out for this moving blade row. Figs 18and 19 show the grid and Iso-Mach contours for typically two profiles; hub and tip. Surface pressure distribution and Mach number distribution with respect to axial flow direction, say z, are shown in Figs 20 and 21. A suction peak midway between the middle and end of the suction surface is visible. The profile appear to be aft-loaded. the comparison of outlet flow angles as computed by 2D CFD and 3D CFD is shown in Fig. 22. The comparison is satisfactory.
1. A set of six transonic blade profiles comprising each a pressure face and a suction face joined at their leading and trailing edges, the cross sections being twisted over the blade height and that the centers of gravity of these sections lie in radial line.
2. Transonic blade profiles as claimed in claim 1 wherein the base profiles are Bezier generated ones and typically described by typical points (Fig. 2A).
Point Pl=the location of minimum x-coordinate (xmm)
Point P2= the location of minimum y-coordinate. At leading edge side
Point P3- the location of maximum y-coordinate. On suction face
Point P5=the location of maximum x-coordinate (xmx)
Point P6=the location of minimum y-coordinate. At trailing edge side
Point P7= the location of center of gravity. x=0, y=0.0.
Base chord=xmx-xmn=100 (reference)
3. A set of six transonic blade profiles as claimed in claim 1 wherein the
base profiles are as shown in Fig. 2B.
4. A set of six transonic blade profiles as claimed in claim 1 wherein the centers of gravity of the profiles coincide in x-y planes.
5. A set of six transonic blade profiles as claimed in claim 1 wherein the areas of cross section, stagger angles, and the ratio chord (c)/pitch(s) monotonously decrease from hum to tip, whereas pitch (=2 r/no of blades; r=radius where the profile is located) increases along the blade height.
6. A set of six transonic blade profiles substantially as herein described and illustrated in the accompanying drawings.
|Indian Patent Application Number||653/DEL/2004|
|PG Journal Number||13/2010|
|Date of Filing||31-Mar-2004|
|Name of Patentee||BHARAT HEAVY ELECTRICALS LIMITED|
|Applicant Address||BHEL HOUSE, SIRI FORT,NEW DELHI-110 049, INDIA|
|PCT International Classification Number||F01D 5/00|
|PCT International Application Number||N/A|
|PCT International Filing date|