Abstract

This study focuses on comparing the accuracy of existing analytical models for heat flux measurement using a copper slug calorimeter in high-temperature environments. Two analytical models, the no loss model, with simpler calculations by ignoring heat loss, and the slug loss model, which incorporates heat loss for greater accuracy, are evaluated. A novel measurement approach, combining finite element analysis (FEA), optimization techniques, and experimental data, was developed to provide a robust framework for this comparison. The new method was tested by comparing its results with those obtained from the two existing models. The heat flux values were 237.181 W/cm2 for the no loss model, 252.95 W/cm2 for the slug loss model, and 254.97 W/cm2 from the proposed approach (numerical estimation method). The results demonstrated that the proposed approach aligns more closely with the slug loss model, suggesting its suitability for accurate heat flux measurement in high-temperature environments and its utility as a tool for comparing analytical methods. These findings provide valuable insights for choosing appropriate models in various heat flux measurement applications.

References

1.
Sankar
,
G.
,
Chandrasekhara Rao
,
A.
,
Seshadri
,
P. S.
, and
Balasubramanian
,
K. R.
,
2016
, “
Techniques for Measurement of Heat Flux in Furnace Waterwalls of Boilers and Prediction of Heat Flux—A Review
,”
Appl. Therm. Eng.
,
103
, pp.
1470
1479
.
2.
Drake
,
S. J.
,
Martin
,
M.
,
Wetz
,
D. A.
,
Ostanek
,
J. K.
,
Miller
,
S. P.
,
Heinzel
,
J. M.
, and
Jain
,
A.
,
2015
, “
Heat Generation Rate Measurement in a Li-Ion Cell at Large C-Rates Through Temperature and Heat Flux Measurements
,”
J. Power Sources
,
285
, pp.
266
273
.
3.
Liu
,
T.
,
Montefort
,
J.
,
Stanfield
,
S.
,
Palluconi
,
S.
,
Crafton
,
J.
, and
Cai
,
Z.
,
2018
, “
Analytical Inverse Heat Transfer Method for Temperature-Sensitive-Coating Measurement on a Finite Base
,”
Int. J. Heat Mass Transf.
,
118
, pp.
651
662
.
4.
Ram Prabhu
,
M.
,
Balaji
,
C.
,
Sundararajan
,
T.
, and
Chacko
,
M. J.
,
2021
, “
Estimation of Aerodynamic Heating on Scramjet Inlets and Validation With Measurements
,”
ASME J. Therm. Sci. Eng. Appl.
,
14
(
1
), p.
11010
.
5.
Wang
,
C.
,
Jiao
,
H.
,
Anatychuk
,
L.
,
Pasyechnikova
,
N.
,
Naumenko
,
V.
,
Zadorozhnyy
,
O.
,
Vikhor
,
L.
,
Kobylianskyi
,
R.
,
Fedoriv
,
R.
, and
Kochan
,
O.
,
2022
, “
Development of a Temperature and Heat Flux Measurement System Based on Microcontroller and Its Application in Ophthalmology
,”
Meas. Sci. Rev.
,
22
(
2
), pp.
73
79
.
6.
Nawaz
,
A.
,
Gorbunov
,
S.
,
Terrazas-Salinas
,
I.
, and
Jones
,
S. M.
,
2012
, “
Closed Gap Slug Calorimeter for Plasma Stream Characterization
,”
43rd AIAA Thermophysics Conference
, NASA Ames Research Center Document ID 20120016016,
New Orleans, LA
,
June 25–28
.
7.
Jayaprakash
,
C.
,
Kumar
,
P. P.
,
Srinivas
,
J.
, and
Manjunath
,
P.
,
2016
, “
Development of Copper Slug Calorimeter for Heat Flux Measurements
,”
Proceedings of the Asian Congress on Gas Turbines (ACGT)
, ACGT Paper No. 2016-064,
Mumbai, India
,
Nov. 14–16
.
8.
Vadivel
,
M.
,
Bhalaji
,
G. R.
, and
Raam
,
C.
,
2016
, “
Experimental Calibration of Heat Flux From Copper Slug Calorimeter in High Speed Combustor
,”
Int. J. Mod. Eng. Res.
,
6
(
12
), pp.
12
16
.
9.
Matsui
,
M.
,
Shinmi
,
K.
,
Komurasaki
,
K.
, and
Arakawa
,
Y.
,
2008
, “
Enthalpy Distributions of Laser Driven High Enthalpy Wind Tunnel
,”
26th AIAA Aerodynamic Measurement Technology and Ground Testing Conference
, AIAA Paper No. 2008-4133,
Seattle, WA
,
June 23–26
, p.
4133
.
10.
Hightower
,
T.
,
Olivares
,
R. A.
, and
Philippidis
,
D.
,
2008
, “
Thermal Capacitance (Slug) Calorimeter Theory Including Heat Losses and Other Decaying Processes
,”
Thermal and Fluids Analysis Workshop (TFAWS)
, NASA Ames Research Center Document ID 20090008662,
San Jose, CA
,
Aug. 18–22
.
11.
Nawaz
,
A.
,
Gorbunov
,
S.
,
Terrazas-Salinas
,
I.
, and
Jones
,
S.
,
2012
, “
Investigation of Slug Calorimeter Gap Influence for Plasma Stream Characterization
,”
43rd AIAA Thermophysics Conference
, AIAA Paper No. 2012-3186,
New Orleans, LA
,
June 25–28
.
12.
Bazgir
,
A.
, and
Zhang
,
Y.
,
2024
, “
Harnessing Deep Learning to Solve Inverse Transient Heat Transfer With Periodic Boundary Condition
,”
ASME J. Therm. Sci. Eng. Appl.
,
16
(
12
), p.
121001
.
13.
Qin
,
F.
,
He
,
Q.
,
Gong
,
Y.
,
An
,
T.
,
Chen
,
P.
, and
Dai
,
Y.
,
2022
, “
The Application of FEM-BEM Coupling Method for Steady 2D Heat Transfer Problems With Multi-scale Structure
,”
Eng. Anal. Boundary Elem.
,
137
, pp.
78
90
.
14.
Guo
,
W.
,
Li
,
Y.
,
Li
,
Y.-Z.
,
Tian
,
S.
, and
Wang
,
S.
,
2016
, “
Thermal-Structural Analysis of Large Deployable Space Antenna Under Extreme Heat Loads
,”
J. Therm. Stress
,
39
(
8
), pp.
887
905
.
15.
Li
,
X.
,
Ren
,
L.
,
Xu
,
Y.
,
Shi
,
J.
,
Chen
,
X.
,
Chen
,
G.
,
Huang
,
H.
,
Guo
,
S.
, and
Tang
,
Y.
,
2021
, “
Simulation Analysis of 2D Finite Element Axial Transient Temperature Distribution of HTS Cable
,”
IEEE Trans. Appl. Supercond.
,
31
(
5
), pp.
1
6
.
16.
Wang
,
Y.
,
Li
,
X.
,
Liu
,
D.
, and
Liu
,
Y.
,
2021
, “
Analysis of Two Calculation Methods of Heat Flux Based on Slug Calorimeter
,”
IEEE Sens. J.
,
21
(
2
), pp.
1287
1293
.
17.
Qian
,
G.-L.
,
Hoa
,
S. V.
, and
Xiao
,
X.
,
1997
, “
A Vibration Method for Measuring Mechanical Properties of Composite, Theory and Experiment
,”
Compos. Struct.
,
39
(
1
), pp.
31
38
.
18.
Kowalik
,
M.
,
Pyrzanowska
,
J.
,
Piechal
,
A.
,
Blecharz-Klin
,
K.
,
Widy-Tyszkiewicz
,
E.
,
Suprynowicz
,
K.
, and
Pyrzanowski
,
P.
,
2017
, “
Determination of Mechanical Properties of Rat's Artery Using Optimization Based Method and Ogden's Model
,”
Mater. Today: Proc.
,
4
(
5
), pp.
5849
5854
. .
19.
Tang
,
J.
,
Xie
,
W.
,
Wang
,
X.
,
Chen
,
Y.
, and
Wu
,
J.
,
2022
, “
Study of the Mechanical Properties of Near-Space Airship Envelope Material Based on an Optimization Method
,”
Aerospace
,
9
(
11
), p.
655
.
20.
NIST Chemistry WebBook
,
2024
, “
NIST Standard Reference Database 69
,” https://webbook.nist.gov/cgi/inchi?ID=C7439921&Type=JANAFG&Plot=on#Refs, Accessed November 12, 2024.
21.
Shomate
,
C. H.
,
1954
, “
A Method for Evaluating and Correlating Thermodynamic Data
,”
J. Phys. Chem.
,
58
(
4
), pp.
368
372
.
22.
ASTM International
,
2015
,
Standard Test Method for Oxyacetylene Ablation Testing of Thermal Insulation Materials (ASTM E285)
, 8th ed.,
ASTM International
,
West Conshohocken, PA
.
23.
Vojvodich
,
N. S.
,
1969
, “
Hypervelocity Heat Protection-A Review of Laboratory Experiments
,”
J. Macromol. Sci.
,
3
(
3
), pp.
367
394
.
24.
Manjhi
,
S. K.
, and
Kumar
,
R.
,
2020
, “
Comparative Performance of K, E, and J-Type Fast Response Coaxial Probes for Short-Period Transient Measurements
,”
ASME J. Therm. Sci. Eng. Appl.
,
13
(
3
), p.
031029
.
25.
Matweb
,
2024
, “
The Online Materials Information Resource of Copper (Cu)
,” https://www.matweb.com/search/DataSheet.aspx?MatGUID=9aebe83845c04c1db5126fada6f76f7e&ckck=1. Accessed November 14, 2024.
26.
ASTM International
,
2015
,
Standard Test Method for Measuring Heat-Transfer Rate Using a Thermal Capacitance (Slug) Calorimeter (ASTM E457)
, 8th ed.,
ASTM International
,
West Conshohocken, PA
.
27.
Zhu
,
X. X.
,
Yang
,
Q. T.
, and
Wang
,
H.
,
2018
, “
Improvement of Heat Insulation Structure in the Slug Calorimeter and Test Analysis
,”
J. Exp. Fluid Mech.
,
32
(
6
), pp.
34
40
.
28.
Huang
,
H.-C.
, and
Usmani
,
A. S.
,
2012
,
Finite Element Analysis for Heat Transfer: Theory and Software
,
Springer Science & Business Media
,
London
.
29.
Goyal
,
V.
, and
Goyal
,
V.
,
2022
,
Solutions to Engineering Problems Using Finite Element Methods
,
Advanced Engineering Instructional Services
,
Alpharetta, GA
.
30.
Nelder
,
J. A.
, and
Mead
,
R.
,
1965
, “
A Simplex Method for Function Minimization
,”
Comput. J.
,
7
(
4
), pp.
308
313
.
31.
Martin
,
H. T.
,
Cortopassi
,
A. C.
, and
Kuo
,
K. K.
,
2017
, “
Assessment of the Performance of Ablative Insulators Under Realistic Solid Rocket Motor Operating Conditions
,”
Int. J. Energy Mater. Chem. Propuls
,
16
(
1
), pp.
1
22
.
32.
MathWorks
, “LOWESS Smoothing,” https://se.mathworks.com/help/curvefit/lowess-smoothing.html, Accessed July 30, 2024.
You do not currently have access to this content.