Research Papers: Combustion and Reactive Flows

Estimation of Thermal Barrier Coating Surface Temperature and Heat Flux Profiles in a Low Temperature Combustion Engine Using a Modified Sequential Function Specification Approach

[+] Author and Article Information
Ryan N. O'Donnell

International Center for Automotive Research,
Department of Automotive Engineering,
Clemson University,
4 Research Drive,
Greenville, SC 29607
e-mail: rodonne@g.clemson.edu

Thomas R. Powell

International Center for Automotive Research,
Department of Automotive Engineering,
Clemson University,
4 Research Drive,
Greenville, SC 29607
e-mail: trpowel@g.clemson.edu

Zoran S. Filipi

International Center for Automotive Research,
Department of Automotive Engineering,
Clemson University,
4 Research Drive,
Greenville, SC 29607
e-mail: zfilipi@clemson.edu

Mark A. Hoffman

International Center for Automotive Research,
Department of Automotive Engineering,
Clemson University,
4 Research Drive,
Greenville, SC 29607
e-mail: mhoffm4@clemson.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 22, 2016; final manuscript received October 26, 2016; published online January 10, 2017. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 139(4), 041201 (Jan 10, 2017) (9 pages) Paper No: HT-16-1101; doi: 10.1115/1.4035101 History: Received February 22, 2016; Revised October 26, 2016

A modified form of the sequential function specification method (SFSM) is developed with specific consideration given to multiple time scales in an effort to avoid overregularization of the solution estimates. The authors extend their approach to solve the inverse heat conduction problem (IHCP) associated with the application of thermal barrier coatings (TBC) to in-cylinder surfaces of an internal combustion engine. Subsurface temperature measurements are used to calculate surface heat flux profiles. The modified inverse solver is validated ex situ using a custom fabricated radiation chamber. The solution methodology is extended in situ to evaluate temperature data collected from a single-cylinder research engine operating in homogeneous charge compression ignition (HCCI) mode. Crank angle resolved, thermal barrier coating surface temperature and heat flux profiles are produced—enabling correlation of thermal conditions at the gas-wall boundary with engine performance, emission, and efficiency metrics.

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Grahic Jump Location
Fig. 1

A simplified one-dimensional thermophysical system with known back-side boundary condition and interior temperature measurement locations. Subdivision further highlights the “inverse” and “direct” regions.

Grahic Jump Location
Fig. 2

One-dimensional representation of experimental system. A fast response heat flux probe measures temperature at two independent locations—one subsurface (T1) and one at the backside boundary (T2). The TBC layer applied to the surface of the probe creates a composite system. Inverse techniques will enable estimation of the (unknown) surface heat flux via subsurface temperature information.

Grahic Jump Location
Fig. 3

Piecewise estimate of a continuous function. Note: The estimate assumes constant values of q between times steps. Also, the time step (tn1 − tn) has been deliberately exaggerated. In general, a much finer time step is achieved, resulting in more accurate approximations of the continuous function q(t).

Grahic Jump Location
Fig. 4

Detailed overview of fast-response heat flux probe

Grahic Jump Location
Fig. 5

Operational schematic of the radiation chamber. A radiative heating element generates a constant heat flux on the order of 0.5 Mw/m2. A rotational chopping wheel periodically interrupts the heat source—generating a square heat flux pulse train. The apparatus supports multiple sensors, enabling direct comparison of various temperature profiles and temperature processing methodologies.

Grahic Jump Location
Fig. 6

Phase-averaged and filtered sub-TBC temperature trace from the radiation chamber. The 95% confidence region is only slightly larger than line thickness.

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Fig. 7

Ex situ temperature response for uncoated and TBC probes. The “delay” associated with the peak temperature value of the TBC trace is directly attributable to the diffusive time delay tα.

Grahic Jump Location
Fig. 8

Successful minimization of the objective function S (as defined by Eq. (6)) yields similar measured and modeled temperature profiles at the sensor location: (a) “direct” and “inverse” solutions to the surface heat flux, (b) the SFSM estimate is bounded by its uncertainty and the associated surface temperature profiles are also provided (c). Notice the dramatic increase in temperature swing magnitude for the TBC surface—this is a direct consequence of the order of magnitude decrease in thermal conductivity of the coated probe versus its metal counterpart.

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Fig. 9

Engine orientation and subsequent location of in situ temperature probes. Data from the pulley side probe is used in this paper.

Grahic Jump Location
Fig. 10

Phase-averaged and filtered sub-TBC temperature trace from the experimental engine during fired operation at 1200 RPM. The 95% confidence region is slightly larger than that found in the radiation chamber—the likely result of increased noise contamination and cyclic variability.

Grahic Jump Location
Fig. 11

“Direct’ and “inverse” estimates of the surface heat flux for 1200 RPM (11.7 mg/cycle of fuel) and 1600 RPM (10.5 mg/cycle of fuel). The associated surface temperature profiles are also provided. The magnitude of the temperature swing at the TBC surface is significantly increased relative to the metal (i.e., uncoated) probe's profile.




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