Blades of an axial turbine

A method for manufacturing a turbine blade, the method comprising:

• designing a turbine blade by:
• receiving, at one or more processors, initial geometrical and aerodynamic information of the turbine blade, the turbine blade comprising a blade airfoil attached to a rotor disk by utilizing a blade root, the blade airfoil subdivided into a plurality of airfoil slices, the plurality of airfoil slices stacked along a longitudinal axis of the blade airfoil;
• determining, by the one or more processors, an area of maximum stress on the turbine blade by performing, by the one or more processors, a stress analysis on the turbine blade;
• obtaining, by the one or more processors, the maximum amount of stress within the determined area of maximum stress;
• obtaining, by the one or more processors, a safety factor by dividing material yield stress of the turbine blade by the obtained maximum amount of stress;
• and
• performing, by the one or more processors, a first plurality of operations responsive to the safety factor being less than 1.5 and the determined area of maximum stress occurring at the junction of the blade airfoil and the blade root, the junction of the blade airfoil and the blade root comprising an area on the blade airfoil equal to 15% of the blade airfoil length away from the junction of the blade airfoil and the blade root, the first plurality of operations comprising:
• creating a fillet at the junction of the blade airfoil and the blade root by creating a fillet at the junction of the blade airfoil and the blade root, the fillet comprising a radius in a range of 15 millimeters;
• and
• increasing respective thickness of each airfoil slice of the plurality of airfoil slices with a distance from the junction of the blade airfoil and the blade root equal to 15% of the blade airfoil length by increasing respective thickness of each airfoil slice of the plurality of airfoil slices by an amount of 800 microns;
• performing, by the one or more processors, a second plurality of operations responsive to the safety factor being less than 1.5 and the determined area of maximum stress occurring at an area on the blade between 15% and 100% of the blade airfoil length away from the junction of the blade airfoil and the blade root, the second plurality of operations comprising at least one of:
• increasing respective thickness of a respective airfoil slice within the determined area of maximum stress;
• decreasing the maximum stress by:
• shifting respective locations of upper airfoil slices along respective chord lines of the upper airfoil slices by calculating a respective distance between a respective surface center of each respective upper airfoil slice of the upper airfoil slices and the surface center of the airfoil slice within the area of maximum stress and minimizing the respective distance by shifting respective locations of the upper airfoil slices along respective chord lines of the upper airfoil slices, the upper airfoil slices comprising airfoil slices of the plurality of airfoil slices located above the respective airfoil slice within the area of maximum stress;
• and
• changing respective twist angles of the upper airfoil slices by an amount of 4° relative to respective initial twist angle for each airfoil slice of the plurality of airfoil slices, the respective initial twist angle for each airfoil slice of the plurality of airfoil slices comprising a respective angle between an arbitrary reference coordinate system and a line connecting a proximal end of each slice of the plurality of airfoil slices to a distal end of each slice of the plurality of airfoil slices;
• performing, by the one or more processors, a third plurality of operations responsive to the safety factor being equal to 1.5, the third plurality of operations comprising at least one of:
• determining natural frequencies and mode shapes of the turbine blade by performing, by the one or more processors, a modal analysis on the turbine blade at a working speed of the turbine;
• determining occurrence of frequency resonance within the turbine blade for up to the first three natural frequencies by utilizing Campbell diagram;
• performing, by the one or more processors, a fourth plurality of operations responsive to the frequency resonance occurring at n<10 and only the first frequency comprising the resonance, the fourth plurality of operations comprising at least one of:
• increasing the radius of the fillet by 50%;
• increasing respective thicknesses of proximal airfoil slices of the blade airfoil by an amount of 400 microns, the proximal airfoil slices comprising airfoil slices equal to 15% of the blade airfoil length away from the junction of the blade airfoil and the blade root;
• and
• decreasing respective thicknesses of distal airfoil slices of the blade airfoil by an amount of 400 microns, the distal airfoil slices comprising airfoil slices at distances between 15% and 100% of the blade length away from the junction of the blade airfoil and the blade root, respective thickness of each airfoil slice of the plurality of airfoil slices decreasing linearly from the junction of the blade airfoil and the blade root to a tip of the turbine blade;
• performing, by the one or more processors, a fifth plurality of operations responsive to the frequency resonance occurring at n<10 and only the second frequency comprising the resonance, the fifth plurality of operations comprising at least one of:
• changing respective twist angles of the plurality of airfoil slices by an amount linearly increasing from −2° to 2° from a proximal end of the blade airfoil to a distal end of the blade airfoil, the proximal end of the blade airfoil comprising the junction of the blade airfoil and the blade root, the distal end of the blade airfoil comprising the tip of the turbine blade;
• and
• shifting respective locations of the upper airfoil slices along respective chord lines of the upper airfoil slices;
• performing, by the one or more processors, a sixth plurality of operations responsive to the frequency resonance occurring at n<10 and both the first and the second frequencies comprising the resonance, the sixth plurality of operations comprising at least one of:
• shifting respective locations of the upper airfoil slices along respective chord lines of the upper airfoil slices;
• and
• increasing the radius of the fillet by 50%;
• calculating reduced frequency number for two modes of pure bending and pure torsion, the reduced frequency number defined by:
• K
• =
• 2
• ⁢
• π
• ⁢
• c
• ⁢
• ω
• V
• ∞
• wherein, K denotes reduced frequency, c denotes chord length, ω denotes natural frequency, and V∞ denotes impact velocity of a fluid at a leading edge of the blade;
• performing, by the one or more processors, a fifth plurality of operations responsive to calculated K being between 0.3 and 0.5 for the pure torsion mode and calculated K being less than 0.8 for the pure bending mode, the fifth plurality of operations comprising at least one of:
• adjusting the safety factor at a value equal to 1.5 by shifting respective locations of the upper airfoil slices along respective chord lines of the upper airfoil slices;
• increasing the radius of the fillet by 50%;
• increasing respective thicknesses of proximal airfoil slices of the blade airfoil by an amount in of 400 microns, the proximal airfoil slices comprising airfoil slices at most 15% of the blade airfoil length away from the junction of the blade airfoil and the blade root;
• and
• decreasing respective thicknesses of distal airfoil slices of the blade airfoil by an amount of 400 microns, the distal airfoil slices comprising airfoil slices at distances between 15% and 100% of the blade length away from the junction of the blade airfoil and the blade root, respective thickness of each airfoil slice of the plurality of airfoil slices decreasing linearly from the junction of the blade airfoil and the blade root to a tip of the turbine blade;
• and
• manufacturing the turbine blade by utilizing the designed turbine blade.