FILE D OF THE INVENTION
The present invention generally relates to a three dimensional low pressure steam turbine moving blade device with blade profiles for axial flow steam turbine to convert thermal energy of steam into mechanical energy with high optimum stage efficiency. The three dimensional blade device is suitable for subsonic and transonic flow, and consisting of a plurality of three dimensional blade and root platform. The blades are capable of withstanding mechanical stresses arising out of energy conversion of low enthalpy entry steam and the dynamic stresses caused by the high, condenser back pressure fluctuation and also due to low steam flow condition. More particularly, the invention relates to a three-dimensional low pressure steam turbine moving blade with subsonic and transonic blade profiles for high condenser back pressure application.
BACKGROUND OF THE INVENTION
Moving blades of a low pressure steam turbine are normally mounted on the rotor in a circumferential groove, and projected outward in the flow path. The moving blades are arranged in alternating rows so that the flow of steam guided by a preceding blade row enters the succeeding moving row of blades at a desired angle. Thus, the steam properties such as temperature, pressure, velocity and moisture content change as the steam expands through the blade path. It converts the thermal energy in to mechanical energy and rotates the rotor. Blades are the most important components of a turbine in determining the turbine efficiency and consequently the heat rate of power plants.
The conventional low pressure blades are not very efficient and adequate to withstand the dynamic stresses for 0.1 bar to 0.4 bar back pressure. The subsonic and transonic flow region is defined, where the blade profile exit Mach number M (Speed/sound speed) lies within the range of 0.6-0.92 and 0.93-1.14 respectively. The conventional blades are not meeting the requirements of higher dynamic stresses for high back pressure applications.

Last-stage turbine blade is an important component of the steam turbine, which determines the overall performance of the power generation system. Hence, it is desirable to optimize the performance of these last-stage blades to reduce various aerodynamic losses and to improve the performance of the turbine. The last stage blade height is an influencing parameter for determining the aerodynamic performance of low pressure steam turbine, because it imposes high centrifugal stresses and more mechanical related difficulty. The last-stage moving blades have to meet wide range of operating conditions, aero-mechanical loads and strong dynamic forces.
Last stage blades of LP cylinder are more susceptible to damage than High pressure, Intermediate pressure and Low pressure (HP,IP & LP) drum stage blades due to the increased blade length which results in higher stress levels and a multitude of possible resonances. The high cycle fatigue strength of the blade depends on mean stress arising due to centrifugal force and alternating stress which results from unsteady forces that exist in flow field of the turbine.
The magnitude of dynamic loads increases if the last stage blades has to operate at high back pressure condition due to high mass flow, thereby increased steam flow density in these sections to meet the power requirements.
For a moving blade designed for high back pressure when operated at low pressure results into stalling in flow path and extreme unsteadiness in the saturated steam flow which makes the vibration behavior more difficult and may result into unstable vibration that occurs predominantly at fundamental mode of the blade. This high alternating stresses of the last stage blades when subjected to severe centrifugal load is responsible for fatigue failures in many cases.
Low pressure turbine modules designed for high back pressure are suitable with air cooled condenser application, generally installed where there is scarcity of water.

The blade height, mean diameter, operating speed and aerodynamic conditions are the important factors that affects the last stage blade design in both subsonic and transonic flow conditions. Damping and proper Stimulus ratio are the factors which must also be considered in the mechanical design of the blade. These mechanical and dynamic behavior of the last stage blades, as well as others, such as aero-thermodynamic properties or material selection, all influence the optimum selection of blade profile. The last-stage steam turbine moving blade for high back pressure application, therefore, requires a precisely defined profile for optimal performance with minimal losses over a wide operating range.
Low Pressure flow path steam turbine design uses modular principles and also uses the standardized profiles which is pre-engineered and well evaluated through cascade testing and CFD at design and off-design condition for development of blade geometry to the extent possible. The relevant prior patent related to the low pressure turbine blades, as known to the present inventors, are summarized hereinafter:-[1] EP 2 161 413 A2 10/03/2010 Demania, Alan Richard; Delessio, Steven Michael. [2] US 7,997,873 B2 16//08/2011 Jonathon E. Slepski, Timothy S. McMurray. [3] WO 2014/025729 A1 13/02/2014 maddaus, Alan Donn.
A steam turbine rotating blade useful for power generating unit with 4.0 square meter exhaust area is reported in Ref. [1]. The blade herein, included dovetail type root with cover which is integral part of the tip section, having overhangs on pressure side and suction side and the cover is positioned at an angle relative to the tip section with the angle ranging form 15 degrees to 35 degrees.
52 inches last Stage bucket for steam turbine with improved efficiency is reported in Ref.[2]. The airfoil shape are defined by fixed coordinate where shape lies in an envelope within +/0.25 inches in a direction normal to airfoil surface.

A last stage blade of a steam turbine with plurality of indentations at a top portion of blade leading edge is reported in Ref.[3].
A set of six transonic blade profiles for axial steam turbine as reported in Ref.[4] for conventional low pressure turbine application.
OBJECTS OF THE INVENTION
It is therefore, an object of the present invention is to propose a three-dimensional low pressure steam turbine moving blade device with subsonic and transonic blade profiles for high back pressure application.
Another object of the present invention is to propose a three-dimensional low pressure steam turbine moving blade device with subsonic and transonic blade profiles for high back pressure application, in which the blade profiles comprises suction and pressure curve as set forth by equation 1-14.
A still another object of the invention is to propose a three-dimensional low pressure steam turbine moving blade device with subsonic and transonic blade profiles for high back pressure application, in which the device consists of original transonic blade profiles as set forth by suction and pressure curve expressed in equation 11-14, five original subsonic suction and pressure curve profile curve as set forth by equation 1-10, including leading and trailing edge radius defined by equation 15-16.
A further object of the present invention is to propose a three-dimensional low pressure steam turbine moving blade device with subsonic and transonic blade profiles for high back pressure application, comprising a plurality of moving blades each including original transonic blades as set forth by suction and pressure surface curve in equation 11-14, five original subsonic suction and pressure curve profile curve as set forth in equation 1-10, and leading and trailing edge radius defined by equation 15-16.

SUMMARY OF THE INVENTION
Accordingly, there is provided a three-dimensional low pressure steam turbine moving blade device with subsonic and transonic blade profiles for high back pressure application is provided. The blade shape is made up of smooth surface passing through optimized profiles section at radial location H defined by suction and pressure curve in accordance with equation 1-14. The x, Rle and Rte are the distances in mm. Rle and Rte defines the radius of leading and trailing edge curve of the blade profile at various location H, which smoothly joins the suction and pressure surface curve. The profile sections at H distances are joined smoothly with one another to form a complete moving blade of low pressure turbine. The moving blade stated has improved efficiency for high back pressure application by 2% over the conventional one.
The Suction and pressure curves defined by equation 1-10 are optimized profiles for subsonic flow within Low Pressure Turbine for high back pressure applications. The x,y, Rle and Rte as shown in Fig. 5 are the distances in mm. Rle and Rte defines the radius of leading and trailing edge curve of the blade profile at various location H, which smoothly joins the suction and pressure surface curves.
The Suction and pressure curves defined by equation 11-14 are optimized profiles for transonic flow within Low Pressure Turbine for high back pressure applications. The x, Rle and Rte are the distances in mm, Rle and Rte defines the radius of leading and trailing edge curve of the blade profile at various location H, which smoothly joins the suction and pressure surface curves.
BRIEF DESCRIPTION OF THE ACCOMPANY DRAWINGS
Figure 1 - Low pressure turbine rotating blade of prior art Ref [1] with exhaust area of
4 Sq.M.
Figure 2 - Last Stage bucket with 52 inches length of prior art Ref. [2]

Figure 3 - Last stage blade of a steam turbine of prior art Ref. [3] with plurality of
indentations at a top portion of blade leading edge
Figure 4 - Mach number distribution for prior art Ref.[4] at hub profile section
Figure 5 - Maridional Flow Path of Low Pressure turbine showing two last stages.
Figure 6 - Description of Blade Profile geometry
Figure 7 - 3D last stage moving blade for low pressure turbine for high back pressure
application.
Figure 8 - Mach Number distribution across blade channel a hub section
Figure 9 - Mach Number distribution across blade channel at tip section
Figure 10- Local lean and profile offset for invented design for last stage moving
blade Figure 11 - Campbell diagram for last stage moving blade Figure 12 - Goodman diagram showing the dynamic stresses for last stage moving
blade
DETAILED DESCRIPTION OF THE INVENTION
The present invention relates to a three-dimensional low pressure steam turbine moving blade device with subsonic and transonic blade profiles for high back pressure application whereas the prior art is related to low back pressure which can be achieved with water cooled condenser. Also, the prior art blades are less efficient and more susceptible to fatigue failure.
The present invention differs from the prior arts on several counts and the salient feature of the present invention vis-à-vis the prior art [1],[2],[3] and [4] is described below.
1) Prior art Ref. [1], caters to the power generation unit consisting of low pressure turbine rotating blade with exhaust area of 4 square meter whereas the present patent is related to low pressure turbine moving blade for high back pressure application with approximately 1.8 square meter area. The difference between both the geometries has been clearly vindicated in Fig. 1 and Fig.7.

2) The prior art Ref. [2] is of last Stage bucket with 52 inches length whereas the present invention is of low pressure turbine moving blade with leading and trailing edge height 325 & 368 mm respectively. The difference between both the geometries has been clearly shown in Fig. 2 and Fig. 7.
3) The prior art Ref [3] is of last stage blade of a steam turbine with plurality of indentations at a top portion of blade leading edge, whereas present invention consist of low pressure moving blade with no such type of indentation.
4) The prior art Ref. [1] & [2] geometry having low pressure rotating blade with dovetail type ‘T’ root whereas the present invention consist of low pressure moving blade with 'T' root.
5) The prior art Ref. [1] & [2] geometry consists of is of low pressure rotating blade with integral shroud whereas the present patent having low pressure moving blade of freestanding type.
6) The prior art Ref. [2] geometry include a mid-blade connection point positioned between blade root and blade tip used to couple adjacent buckets, whereas present invention does not require such connection point. Even without such connection point for mechanical coupling the dynamic characteristic are quite good for the present invention. This helps in the reduction in the cycle time for manufacturing.
7) The prior art Ref. [2] geometry is presented in Cartesian co-ordinates for the turbine bucket at various radius location, whereas the present invention the 3D blade geometry made up of smoothly joined surface with suction, pressure, leading and trailing edge curve and in form of 5th order polynomials and they are parameterized. In the prior art Ref. [1] & [3] geometry is not defined neither in terms of coordinates nor in terms of parameterized form.
8) Prior art Ref. [4] is related to transonic profiles for low pressure turbine blade and can be used to develop 3D low pressure turbine blades is suitable for

conventional low pressure blading with low back pressure, whereas present invention refers to low pressure moving turbine blade consists of optimized subsonic and transonic profiles.
9) Prior art Ref. [4] has shown the Mach number distribution for the hub profile section as shown in Fig, 4. The suction and Pressure surface Mach number distribution intersects very earlier from the trailing edge which will results into high separation and secondary losses, In the present invention the profile is optimized to minimize for profile and secondary losses, the surface Mach number distribution at hub section for the present invention is shown in Fig. 8.
The flow in the LP steam turbine is extremely complex due to presence of transonic flow, interaction of rotating and non-rotating blades with upstream wakes. Also due to boundary layer, shock interaction, development of secondary vortices and inherently unsteady flow.
The present invention presents a moving blade shape of low pressure turbine blade for high back pressure application. The present embodiment provides many advantage over conventional low pressure blading, which includes improved aerodynamic performance by 2% greater than the conventional low pressure blading at design point. Also, off-design performance of the low pressure moving blade having improved efficiency by approximately 2.8 % over a range of 0.1 to 0.4 bar back pressure condition.
Fig. 5 shows the meridional flow path view of the last two stages low pressure turbine section that at include moving blade 1 & 2 with circumferentially grooved T root 4 & 5 and guide blade 3 with sealing arrangement 6 & 7. A plurality of moving blade is mounted in the rotor groove which are mechanically coupled at the root and axially positioned between adjacent blade rows. The passage between the moving blades row defines the path for a portion of steam flow.
Fig. 7 shows the prospective view of last stage blade for low pressure turbine with

high back pressure. This moving blade includes a blade portion that includes a trailing edge and a leading edge, wherein steam flows from leading edge 1 to trailing edge 3, which also includes a first concave surface 2 and a second convex surface 4. First surface 2 and second surface 4 are connected axially at trailing edge 1 and leading edge 3, and extend radially between a rotor blade root 5 and a rotor blade tip 6. A blade chord distance L is a distance measured from leading edge 1 to trailing edge 3 at any point along a radial length H of moving blade.
In the exemplary embodiment, the leading edge height is approximately 325 mm and trailing edge height is approximately 368 mm. Although the leading and trailing edge height described herein 325 & 368 mm respectively, it will be understood that these length may be any suitable length depending on the desired application. Root 5 includes a T type used for coupling moving blades to a rotor, and a blade platform 7 that determines the flow path passage through each moving blade. In the exemplary embodiment, T root 5 is a straight entry that engages within a circumferential groove in in rotor.
Last stage moving blade is designed with a series of profile section taken at radial distance H to define the blade shape. A profile section can be defined as the cross section view of the blade (Fig. 6). The shape of blade determines the aerodynamic characteristic of the blade.
Pressure and Mach number distribution, flow separation, channel width change, profile smoothness, profile loss, allowable stresses and manufacturability are some of the aerodynamic and structural parameters that influence the final shape of the blade profile section.
The two dimensional and three dimensional aero foils are analysed for aerodynamic performance using streamline curvature code and Computational Fluid Dynamics (CFD). The aerodynamic performance parameters such as profile loss, profile loss coefficient, flow deflection, surface Mach number distribution are evaluated during 20

2D cascade analysis. The low pressure turbine moving blade for high back pressure application having improved loading characteristic with respect to conventional shown in Fig 8 & 9 for hub and tip section respectively.
Section 1 Curve - Pressure Surface (H=0 mm)
y= -1.65866863 +0.52193062*x - 0.005497999998* x˄2+7.967641087*10˄-6*x˄3
- 5.71317589*10"-8 x"'4 + 7.417644579*10"-11 x˄5 .… Eq. 1
Section 1 Curve - Suction Surface (H= 0 mm)
y=4.6751845* + 1.72606959* x - 0.034460975* x˄2 + 0.00038939276* x˄3-
2.67123984*10˄-6 x˄4˄ + 6.64262365*10˄-9 x˄5 Eq. 2
Section 2 Curve - Pressure Surface (H. 57.82 mm)
y = -1.52795865* + 0.44633346* x - 0.0051291271* x˄2 - 0.000035054511* x˄3 +
4.0045589598*10˄-7 x ˄4 -1.64647237*10˄-9x˄5 Eq. 3
Section 2 Curve - Suction Surface (H= 57.82 mm)
y = 3.67449152* + 1.50387659* x - 0.030166024* x˄2 + 0.00029351544* x˄3-1
1.92007317* 10˄-6 x˄4 + 4.379266488* 10˄-9 x˄5 … Eq. 4
Section 3 Curve-Pressure Surface (H. 115.65 mm)
y = -1.39984947* + 0.32116147* x - 0.0059843094* x˄2 - 0.000038045844* x˄3 +
4.32205952*10˄-7 x˄4 - 2.014822610*10˄-9x˄5 Eq. 5
Section 3 Curve - Suction Surface (H= 115.65 mm)
y = 2.51678309* + 1.20038719* x - 0.027048562* x˄2 + 0.00026437904* x˄3-
1.96826865*10˄-6 x˄4 + 4.86137362*10˄-9 x ˄5 Eq. 6
Section 4 Curve - Pressure Surface (H= 173.47 mm)
y = -1.28609274* + 0.11196778* x- 0.0050091044* x˄2 - 0.000078652944* x˄3 +

8.75296579*10˄-7 x ˄4 - 4.60329134*1 0˄-9x˄5 Eq. 7
Section 4 Curve• Suction Surface (H= 173.47 mm)
y = 1.80461724* + 0.81368724* x - 0.020105579* x˄2 + 0.00014152823* x˄3 -
1.23138045*10˄-6 x"4 + 2.89025927* 10˄-9 x˄5 Eq. 8
Section 5 Curve• Pressure Surface (H= 231.29 mm)
y = -1.25788427* - 0.13081172* x - 0.0045904774* x˄2. - 0.00013036122* x˄3 +
1.70428691*10˄-6 x˄4 - 1.087525603* 10˄-8x˄5 Eq.9
Section 5 Curve - Suction Surface (H. 231.211 mm)
y=1.53561526* + 0.391448046* x - 0.010574574* x˄.2. - 0.000093500135* x˄3+
7.29972751*1 0˄-7x˄4 -3.67372119*10˄-9x˄5 ….Eq.10
Two optimized transonic suction and pressure profile curves is represented by the equation 11 to 14.
Section 6 Curve - Pressure Surface (H=289.11 mm)
y=-1.42790356* -0.41164055* x - 0.0072201921 * x˄2 -0.00011941299* x ˄3 +
1.78162836*10˄-6x˄4 - 1.39467199*1 0˄-8x˄5 …Eq. 11
Section 6 Curve - Suction Surface (H = 289.11 mm)
y= 1.51040140* + 0.026552949* x - 0.0061652291 * x˄2 - 0.00018457579* x˄3-
5.34823531 *1 0˄-7 x˄4 + 1.38763622*1 0˄-8 x˄5 … Eq. 12
Section 7 Curve - Pressure Surface (H= 346.94 mm)
y= -1.659159837* -0.74695329* x -0.0112213294* x˄2 - 0.000031670870* x˄3+
3.339099729*1 0˄-7 x˄4 - 6.81691028*1 0˄-9x ˄5 … Eq. 13
Section 7 Curve -Suction Surface (H=346.94 mm)
y= 1.66072397* -0.37849476* x+0.012756407* x˄2 - 0.0011973675* x˄3+

0.000015631309* x˄4-7.06053865*1 0˄-8x ˄5 … Eq. 14
The leading and trailing edge is defined by the equation 15 to 16. The trailing edge radius confirms the strength and vibration requirement criteria for design as well as off-design condition.
Leading Edge Radius
Rle = -0.0019x + 3.3585 ……………………………………….…… Eq. 15
Trailing Edge Radius
Rte = -0.0017x + 3.2347 ……………………………………….…… Eq. 16
The pressure surface 2 (Fig. 7) and suction surface 4 (Fig. 7) are determined by the stated equation 1 to 16 in order to maintain the smooth surface along the radial length H (Fig.7) of moving blade. Point, tangent and curvature continuity has to be ensured for the entire curve during manufacturing to maintain the surface continuity.
Fig. 10 shows the applied local lean, it eliminates secondary tosses in the hub area and also decreases the pressure gradient in radial direction. Local lean is defined as the local angle made by the line passing through centre of gravity of two adjacent profiles with the radial line passing through the centre of gravity of hub profile and angle placement of profiles centre of gravity in radial direction. In addition, use of local lean an additional x and y shift in centre of gravity of profile located from section 2 to section 7 with respect to profile located at section 1 is provided to take the advantage in static and dynamic stress induced during the operation. This local lean and shift in profile centre of gravity defines the 3D shape of the blade.
After the blade is manufactured the vibration characteristic is fixed and any change in shape can change the vibration characteristic in undesired way. Profile chord is important criteria to ensure structural integrity during operation. Moving blade for high back pressure stages herein having optimized chord for wide range of operation. In

order to maintain the intended performance of blade, shape of blade may be modified subjected to determine the modified behaviour through computer analysis. The
analysis determine the optimum amount of mass required to achieve level of dynamic stress. Modifying blade by removing the mass increase the natural frequency of blade and adding mass decreases the natural frequency of blade. Change in profile' shape may also alter the dynamic response of the blade.

WE CLAIM
1. A three-dimensional low pressure steam turbine moving blade device with subsonic and transonic blade profiles for high back pressure application, the device comprising:-a plurality of free standing moving blade constructed spaced apart circumferentially from each other about an axis of a turbine wheel and having tips, and means for continuously coupling at the root, wherein each of the moving blades having a suction profile curve, pressure profile curve, leading edge radius and trailing edge radius of the moving blades are constructed in correspondence to the technical relationships indicated in the equations 1,2, 15 and 16 respectively.
2. The device as claimed in claim 1, wherein each of the moving blades is having a suction profile curve, pressure profile curve, leading edge radius and trailing edge radius configured in accordance with the technical relationships expressed in equations 3,4, 15 and 16 respectively.
3. The device as claimed in claim 1, wherein each of the moving blades is having a suction profile curve, pressure profile curve, leading edge radius, and trailing edge radius constructed in accordance with the technical relationships expressed in equations 5,6,15 and 16 respectively.
4. The device as claimed in claim 1, wherein each of the moving blades is having a suction profile curve, pressure profile curve, leading edge radius and trailing edge radius configured in accordance with the parametric relationships expressed in the equations 7,8, 15 and 16 respectively.
5. The device as claimed in any of the preceding claims, wherein each of the moving blades having a suction profile curve, pressure profile curve, leading

edge radius and trialing edge radius configured in accordance with parametric relationships indicated the equations 9, 10, 15 and 16 respectively.
6. The device as claimed in any of the preceding claims, wherein each of the moving blades having a suction profile curve, pressure profile curve, leading edge radius and trailing edge radius in constructed accordance with the technical relationships indicated in equations 11, 12, 15 and 16 respectively.
7. The device as claimed in claim 1, wherein each of the moving blades having a suction profile curve, pressure profile curve, leading edge radius and trailing edge radius constructed in accordance with the relationships expressed in equations 13, 14, 15 and 16 respectively.
8. The device as claimed in any of the preceding claims, wherein the leading and trailing edge radius of each of the moving blades of the device is constructed in accordance with the technical relationships expressed in equations 15 and 16 respectively
9. The device as claimed in any of the preceding claims, wherein profile can be generated with direct scaling according to claim 1 to 7.
10. The device as claimed in any of the preceding claims, wherein the local lean and offset of profile as mentioned in claim 1, 2, 3, 4, 5, 6, 7 & 8 in accordance with Fig 10.