Research Papers

Estimating Over Temperature and Its Duration in a Flat Plate With Sudden Changes in Heating and Cooling

[+] Author and Article Information
Chien-Shing Lee

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907-2045
e-mail: cslee@purdue.edu

Tom I-P. Shih

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907-2045
e-mail: tomshih@purdue.edu

Kenneth Mark Bryden

Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: kmbryden@iastate.edu

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 3, 2015; final manuscript received December 9, 2015; published online February 9, 2016. Editor: Kenneth C. Hall.

J. Turbomach 138(6), 061007 (Feb 09, 2016) (12 pages) Paper No: TURBO-15-1291; doi: 10.1115/1.4032306 History: Received December 03, 2015; Revised December 09, 2015

When the operating condition of a gas turbine engine changes from one steady-state to another, the cooling must ensure that the solid's temperatures never exceed the maximum allowable throughout the transient process. Exceeding the maximum allowable temperature is possible even though cooling is increased to compensate for the increase in heating because there is a time lag in how the solid responds to changes in its convective heating and cooling environments. In this paper, a closed-form solution (referred to as the 1D model) is derived to estimate the over temperature and its duration in a flat plate subjected to sudden changes in heating and cooling rates. For a given change in heating rate, the 1D model can also be used to estimate the minimum cooling needed to ensure that the new steady-state temperature will not exceed the maximum allowable. In addition, this model can estimate the temperature the material must be cooled to before imposing a sudden increase in heat load to ensure no over temperature throughout the transient process. Comparisons with the exact solutions show the 1D model to be accurate within 0.1%. This 1D model was generalized for application to problems in multidimensions. The generalized model was used to estimate the duration of over temperature in a two-dimensional problem involving variable heat transfer coefficient (HTC) on the cooled side of a flat plate and provided results that match the exact solution within 5%.

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Fig. 1

Schematic of the problem used to develop the 1D model

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Fig. 2

Temperature profiles in the plate during the first time domain

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Fig. 3

Temperature profiles in the plate during the second and third time domains

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Fig. 7

Evolution of the maximum temperature in the plate as a function of time for ∅ = 0, 0.25, 0.5, and 0.75

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Fig. 6

Evolution of the temperature in the plate as a function of time for ∅ = 0, 0.25, 0.5, and0.75

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Fig. 8

Schematic of the 2D problem

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Fig. 4

Duration of transient process

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Fig. 5

Duration of over temperature predicted by the exact solution and by the 1D model

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Fig. 10

Dimensionless temperature at x = 0 as a function of Fourier number and dimensionless initial temperature

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Fig. 9

Dimensionless surface temperature on the heated side of the plate as a function of the Biot numbers on the cooled and heated sides under steady-state conditions

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Fig. 11

Dimensionless temperature at x=0 as a function of the Fourier number and the Biot number, Bi1

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Fig. 12

Dimensionless temperature at x=0 as a function of the Fourier number and the Biot number, Bi2

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Fig. 13

Time constant as a function of thermal resistance and capacitance for time domains II and III



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