ASTM E457-08(2015)

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E457 − 08 E457 − 08 (Reapproved 2015)
Standard Test Method for
Measuring Heat-Transfer Rate Using a Thermal Capacitance
(Slug) Calorimeter
This standard is issued under the fixed designation E457; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This test method describes the measurement of heat transfer rate using a thermal capacitance-type calorimeter which
assumes one-dimensional heat conduction into a cylindrical piece of material (slug) with known physical properties.
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
NOTE 1—For information see Test Methods E285, E422, E458, E459, and E511.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
E285 Test Method for Oxyacetylene Ablation Testing of Thermal Insulation Materials
E422 Test Method for Measuring Heat Flux Using a Water-Cooled Calorimeter
E458 Test Method for Heat of Ablation
E459 Test Method for Measuring Heat Transfer Rate Using a Thin-Skin Calorimeter
E511 Test Method for Measuring Heat Flux Using a Copper-Constantan Circular Foil, Heat-Flux Transducer
3. Summary of Test Method
3.1 The measurement of heat transfer rate to a slug or thermal capacitance type calorimeter may be determined from the
following data:
3.1.1 Density and specific heat of the slug material,
3.1.2 Length or axial distance from the front face of the cylindrical slug to the back-face thermocouple,
3.1.3 Slope of the temperature—time curve generated by the back-face thermocouple, and
3.1.4 Calorimeter temperature history.
3.2 The heat transfer rate is thus determined numerically by multiplying the density, specific heat, and length of the slug by the
slope of the temperature–time curve obtained by the data acquisition system (see Eq 1).
3.3 The technique for measuring heat transfer rate by the thermal capacitance method is illustrated schematically in Fig. 1. The
apparatus shown is a typical slug calorimeter which, for example, can be used to determine both stagnation region heat transfer
rate and side-wall or afterbody heat transfer rate values. The annular insulator serves the purpose of minimizing heat transfer to
or from the body of the calorimeter, thus approximating one-dimensional heat flow. The body of the calorimeter is configured to
establish flow and should have the same size and shape as that used for ablation models or test specimens.
This test method is under the jurisdiction of ASTM Committee E21 on Space Simulation and Applications of Space Technology and is the direct responsibility of
Subcommittee E21.08 on Thermal Protection.
Current edition approved May 1, 2008May 1, 2015. Published June 2008June 2015. Originally approved in 1972. Last previous edition approved in 20022008 as E457 – 96
(2002).E457 – 08. DOI: 10.1520/E0457-08.10.1520/E0457-08R15.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E457 − 08 (2015)
FIG. 1 Schematic of a Thermal Capacitance (Slug) Calorimeter
3.3.1 For the control volume specified in this test method, a thermal energy balance during the period of initial linear
temperature response where heat losses are assumed negligible can be stated as follows:
Energy Received by the Calorimeter front face 5Energy Conducted Axially Into the Slug
~ !
q 5 ρC l ΔT/Δτ 5 MC /A ΔT/Δτ (1)
~ ! ~ ! ~ !
c p p
where:
q˙ = calorimeter heat transfer rate, W/m ,
c
ρ = density of slug material, kg/m ,
C = average specific heat of slug material during the temperature rise (ΔT), J/kg·K,
p
l = length or axial distance from front face of slug to the thermocouple location (back-face), m,
ΔT = (T − T ) = calorimeter slug temperature rise during exposure to heat source (linear part of curve), K,
f i
Δτ = (τ − τ ) = time period corresponding to ΔT temperature rise, s,
f i
M = mass of the cylindrical slug, kg,
A = cross-sectional area of slug, m .
In order to determine the steady-state heat transfer rate with a thermal capacitance-type calorimeter, Eq 1 must be solved by
using the known properties of the slug material (for example, density and specific heat)—the length of the slug, and the slope
(linear portion) of the temperature–time curve obtained during the exposure to a heat source. The initial and final temperature
transient effects must be eliminated by using the initial linear portion of the curve (see Fig. 2).
3.3.2 In order to calculate the initial response time for a given slug, Eq 2 may be used. This equation is based on the idealization
of zero heat losses from slug to its holder.
l ρC 2
p
τ 5 ln (2)
R 2
kπ q indicated
S D
q input
where:
k = thermal conductivity of slug material, W/m·K
q = q that would be measured at the back-face of the slug by Eq 1, W/m
indicated
q = constant q at the front-face of the slug beginning at τ = 0, W/m
input input
3.3.3 Although the goal of good slug calorimeter design is to minimize heat losses, there can be heating environments, such as
very high heat fluxes, where even a good slug calorimeter design cannot meet the recommended 5 % maximum heat loss criterion
of 6.1. Also, this criterion only deals with heat losses measured during the cooling phase, not losses during the heating phase, which
“Thermophysical Properties of High Temperature Solid Materials,” TPRC, Purdue University, or “Handbook of Thermophysical Properties,” Tolukian and Goldsmith,
MacMillan Press, 1961.
Ledford, R. L., Smotherman, W. E., and Kidd, C. T., “Recent Developments in Heat-Transfer Rate, Pressure, and Force Measurements for Hotshot Tunnels,”
AEDC-TR-66-228 (AD645764), January 1967.
E457 − 08 (2015)
FIG. 2 Typical Temperature–Time Curve for Slug Calorimeter
can be greater than the cooling losses. Under these circumstances, significant heat losses from slug to holder during the heating
phase, as well as other possible decaying processes such as a drop in surface catalycity, can cause the Temperature-Time slope to
decrease significantly more than can be accounted for by the increasing heat capacity with temperature of the Copper slug alone,
making it important that the slope be taken early in the process before the losses lower the slope too much, introducing more error
to the downside on the heat flux calculated (see Fig. 3). The degree of losses affect the exact position where the best slope begins
to occur, but typically it should be expected at about time τ = τ calculated by Eq 2 for q /q = 0.99, which value of τ
R indicated input R
is abbreviated as τ . Fig. 2 and Fig. 3 assume that “heat source on” is a step function. This is an idealization, but the reality
R0.99
can be significantly different. For example, in some cases a calorimeter may experience a higher heat flux prior to reaching its final
position in the heat source, which can cause the initial maximum slope to be higher than what is wanted for the calculation of the
heat flux at the final position. Therefore, it is important to note that “zero” time, to which τ is added to determine where to
R0.99
start looking for the desired slope, is when the calorimeter has reached its final position where it is desired to measure the heat
flux. Therefore, choosing the best place to take the slope can be very important. Should more accurate results be required, the losses
form the slug should be modeled and accounted for by a correction term in the energy balance equation.
3.3.4 For maximum linear test time (temperature–time curve) within an allowed surface temperature limit, the relation shown
as Eq 3 may be used for a calorimeter which is insulated by a gap at the back face.
τ 5 0.48 ρl C ΔT /q˙ (3)
~ !
max,opt. p frontface
where:
ΔT = the calorimeter final front face temperature minus the initial front face (ambient) temperature, T .
front face o
3.3.5 Eq 3 is based on the optimum length of the slug which can be obtained by applying Eq 4 as follows:
Childs, P. R. N., Greenwood, J. R., and Long, C. A., “Heat flux measurement techniques,” Proceedings of the Institution of Mechanical Engineers, Vol 213, Part C, 1999,
pp. 664–665.
Kirchhoff, R. H., “Calorimetric Heating-Rate Probe for Maximum-Response-Time Interval,” American Institute of Aeronautics and Astronautics Journal, AIAJA, Vol
2, No. 5, May 1964, pp. 966–67.
E457 − 08 (2015)
FIG. 3 Temperature–Time Curve when Heat and Other Items are Significant During Heating Phase
l 5 3 k ΔT /5q˙ (4)
opt. front face c
3.4 To minimize side heating or side heat losses, the body is separated physically from the calorimeter slug by means of an
insulating gap or a low thermal diffusivity material, or both. The insulating gap that is employed should be small, and
recommended to be no more than 0.05 mm on the radius. Thus, if severe pressure variations exist across the face of the calorimeter,
side heating caused by flow into or out of the insulation gap would be minimized. Depending on the size of the calorimeter surface,
variations in heat transfer rate may exist across the face of the calorimeter; therefore, the measured heat transfer rate represents
an average heat transfer rate over the surface of the slug.
3.5 Since interpretation of the data obtained by this test method is not within the scope of this discussi
...