Construction of axial-flow turbine blades

Claim 2

A hollow turbine part for use in a hot fluid medium, said part having a pressure surface wall and a suction surface wall and having a leading edge and a trailing edge, said walls having a thickness distribution in the direction from said leading edge to said trailing edge such that, with changes of the temperature of said fluid, the temperature response at each portion of said walls in substantially the same as the temperature response at the other portions of said walls, whereby the temperature distribution in said walls changes substantially uniformly in response to changes in temperature of said fluid.

Claim 3

A hollow turbine part as claimed in claim 1, wherein said part is a hollow blade and wherein said thickness distribution is such that each portion of said walls has a mean temperature time constant which is substantially equal to a predetermined time constant, said mean time constant at each portion of said walls being the mean of the temperature time constants at the outer surface thereof, at the inner surface thereof and at an intermediate point between the surfaces thereof, each of said outer surface, inner surface and intermediate point time constants being determined by replacing the temperature response at said outer surface, said inner surface and said point to a step change of said fluid temperature with approximately a first order response thereto, and said predetermined time constant being substantially equal to the mean time constant at said leading edge of said blade.

Claim 4

A hollow turbine part as claimed in claim 1, further comprising means for supplying fluid cooling to at least one of said leading edge and said trailing edge to thereby lower the heat transfer coefficient thereof and modify the thickness thereof required to provide said temperature response therefor.

Claim 5

A hollow turbine blade for use in a fluid medium, said blade comprising a pressure surface wall and a suction surface wall and having a leading and trailing edge, said walls having a thickness distribution in the direction from the leading edge to the trailing edge of said blade such that the temperature response at each portion of said walls in substantially the same as the other portions of said walls with changes of the temperature of said fluid and such that the mean temperature time constant is substantially equal to the mean temperature time constant at said leading edge of said blade, said mean time constant at each portion of said walls being the mean of the temperature time constants at the outer surface thereof, at the inner surface thereof and at an intermediate point between the surfaces thereof, each of said outer surface, inner surface and intermediate point time constants being determined by replacing the temperature response at said each point to a step change of said fluid temperature with approximately a first order response thereto, said temperature response at each point being calculated from the following equations: delta T/ delta t a( delta 2T/ delta y2) where T(y,t) represents a temperature at an arbitrary position and an arbitrary time in a small element of said wall, t represents elapsed time after a sudden temperature change of said motive fluid, a represents thermal diffusivity of the blade material, and y represents the axis oriented in the blAde wall thickness direction with its origin located at the blade surface in the main air flow side; in the case of heating, the boundary conditions and initial conditions are: at y 0, Alpha gx(Tg - T(o,t)) (- lambda delta T/ delta y) y o at y l, Alpha cx(T(l,t) - Tc) (- lambda delta T/y) y l at t 0, T(y,O) To at t Infinity , T(y, Infinity ) TA - (TA - TB) y/l in the case of cooling, the boundary conditions and initial conditions are: at y 0, Alpha gx(T(o,t) - To) ( lambda delta T/ delta y) y o at y l, Alpha cx(T(l,t) - T) (- lambda delta T/ delta y) y l at t 0, T(y,0) TA - (TA - TB) y/l at t Infinity , T(y, Infinity ) To where in the boundary and initial condition equations Tg represents the recovery temperature of the fluid, Tc represents the cooling air flow temperature, To represents the temperature of the entire region kept in an equilibrium state that is realized before heating or after cooling, l represents the wall thickness and lambda represents the conductivity of the blade material, and TA and TB are: TA Tg(1 + Alpha cxl/ lambda + Alpha cx/ Alpha gx Tc/Tg)/(1+ Alpha cxl/ lambda + Alpha cx/ Alpha gx) TB Tg(1 + Alpha cxl/ lambda Tc/Tg + Alpha cx/ Alpha gx Tc/Tg)/(1+ Alpha cxl/ lambda + Alpha cx/ Alpha gx) where Alpha gx represents an effective local heat transfer coefficient on main air flow side, Alpha cx represents an effective local heat transfer coefficient on the cooling air flow side; and where, in the case of heating: T(y,t) TN + TA - (TA -TB)y/l and in the case of cooling: T(y,t) To - TN where TN represents the non-steady state term of the temperature, and is expressed as follows:

Claim 6

A hollow turbine blade for use in a fluid medium, said blade comprising a pressure surface wall and a suction surface wall and having a leading and trailing edge, said walls having a thickness distribution in the direction from the leading edge to the trailing edge of said blade such that the temperature response at each portion of said walls in substantially the same as the other portions of said walls with changes of the temperature of said fluid and such that the mean temperature time constant is substantially equal to the mean temperature time constant at said leading edge of said blade, said mean time constant at each portion of said walls being the mean of the temperature time constants at the outer surface thereof, at the inner surface thereof and at an intermediate point between the surfaces thereof, each of said outer surface, inner surface and intermediate point time constants being determined by replacing the temperature response at said each point to a step change of said fluid temperature with approximately a first order response thereto, said temperature response at each point being calculated from the following equations: delta T/ delta t a( delta 2T/ delta y2) where T(y,t) represents a temperature at an arbitrary position and an arbitrary time in a small element of said wall, t represents elapsed time after a sudden temperature change of said motive fluid, a represents thermal diffusivity of the blade material, and y represents the axis oriented in the blAde wall thickness direction with its origin located at the blade surface in the main air flow side; in the case of heating, the boundary conditions and initial conditions are: at y 0, Alpha gx(Tg - T(o,t)) (- lambda delta T/ delta y) y o at y l, Alpha cx(T(l,t) - Tc) (- lambda delta T/y) y l at t 0, T(y,O) To at t Infinity , T(y, Infinity ) TA - (TA - TB) y/l in the case of cooling, the boundary conditions and initial conditions are: at y 0, Alpha gx(T(o,t) - To) ( lambda delta T/ delta y) y o at y l, Alpha cx(T(l,t) - T) (- lambda delta T/ delta y) y l at t 0, T(y,0) TA - (TA - TB) y/l at t Infinity , T(y, Infinity ) To where in the boundary and initial condition equations Tg represents the recovery temperature of the fluid, Tc represents the cooling air flow temperature, To represents the temperature of the entire region kept in an equilibrium state that is realized before heating or after cooling, l represents the wall thickness and lambda represents the conductivity of the blade material, and TA and TB are: TA Tg(1 + Alpha cxl/ lambda + Alpha cx/ Alpha gx Tc/Tg)/(1+ Alpha cxl/ lambda + Alpha cx/ Alpha gx) TB Tg(1 + Alpha cxl/ lambda Tc/Tg + Alpha cx/ Alpha gx Tc/Tg)/(1+ Alpha cxl/ lambda + Alpha cx/ Alpha gx) where Alpha gx represents an effective local heat transfer coefficient on main air flow side, Alpha cx represents an effective local heat transfer coefficient on the cooling air flow side; and where, in the case of heating: T(y,t) TN + TA - (TA -TB)y/l and in the case of cooling: T(y,t) To - TN where TN represents the non-steady state term of the temperature, and is expressed as follows: