Method for determining time-resolved heat transfer coefficient and adiabatic effectiveness waveforms with unsteady film cooling
AssigneeThe United States of Americas represented by the Secretary of the AirForce
InventorsJames L. Rutledge, Jonathan F. McCall
Life of this patent
Estimating the term…
Abstract
A new method for determining heat transfer coefficient (h) and adiabatic effectiveness (η) waveforms h(t) and η(t) from a single test uses a novel inverse heat transfer methodology to use surface temperature histories obtained using prior art approaches to approximate the h(t) and η(t) waveforms. The method best curve fits the data to a pair of truncated Fourier series.
Claims5
A method for determining heat transfer coefficient h and adiabatic effectiveness η waveforms h(t) and η(t) from a single test on a film cooled test article, wherein η is determined from adiabatic wall temperature Taw as a dimensionless number
- η
- =
- T
- ∞
- -
- T
- aw
- T
- ∞
- -
- T
- c
- ,
- comprising the steps of:
- (a) soak the test article to a uniform and known temperature;
- (b) expose the test article to a freestream flow at a different and known temperature;
- (c) measure spatial surface temperature Ts as a function of time over a plurality of time steps, to determine Ts(t);
- (d) calculate surface heat flux qs(t) for each time step;
- and,
- (e) find periodic Taw(t) and h(t) functions that are least squares fits to:
- qs(t)=h(t)(Taw(t)−Ts(t)),
- using truncated Fourier series as the periodic Taw(t) and h(t) functions;
- defined as:
- h
-
- (
- t
- )
- =
- h
- ^
- 0
- 2
- +
- ∑
- n
- =
- 1
- N
-
-
- (
- h
- ^
- n
-
- cos
-
- n
-
-
- π
-
-
- t
- L
- +
- h
- ~
- n
-
- sin
-
- n
-
-
- π
-
-
- t
- L
- )
- ;
- and
- ,
-
- T
- aw
-
- (
- t
- )
- =
- T
- ^
- 0
- 2
- +
- ∑
- n
- =
- 1
- N
-
-
- (
- T
- ^
- n
-
- cos
-
- n
-
-
- π
-
-
- t
- L
- +
- T
- ~
- n
-
- sin
-
- n
-
-
- π
-
-
- t
- L
- )
- .
A method for determining heat transfer coefficient h and adiabatic effectiveness η waveforms h(t) and η(t) from a single test on a film cooled test article, wherein η is determined from adiabatic wall temperature Taw as a dimensionless number
- η
- =
- T
- ∞
- -
- T
- aw
- T
- ∞
- -
- T
- c
- ,
- comprising the steps of:
- (a) soak the test article to a uniform and known temperature;
- (b) expose the test article to a freestream flow with a varying, but known temperature as a function of time;
- (c) measure spatial surface temperature Ts as a function of time over a plurality of time steps, to determine Ts(t);
- (d) calculate surface heat flux qs(t) for each time step;
- and,
- (e) find periodic η(t) and h(t) functions that are least squares fits to:
- qs(t)=h(t)(T∞(t)−η(t)(T∞(t)−Tc(t))−Ts(t)),
- using truncated Fourier series as the periodic η(t) and h(t) functions;
- defined as:
- h
-
- (
- t
- )
- =
- h
- ^
- 0
- 2
- +
- ∑
- n
- =
- 1
- N
-
-
- (
- h
- ^
- n
-
- cos
-
- n
-
-
- π
-
-
- t
- L
- +
- h
- ~
- n
-
- sin
-
- n
-
-
- π
-
-
- t
- L
- )
- ;
- and
- ,
-
- η
-
- (
- t
- )
- =
- η
- ^
- 0
- 2
- +
- ∑
- n
- =
- 1
- N
-
-
- (
- η
- ^
- n
-
- cos
-
- n
-
-
- π
-
-
- t
- L
- +
- η
- ~
- n
-
- sin
-
- n
-
-
- π
-
-
- t
- L
- )
- .
Dependencies are inferred from the claim text.