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ASTM E637-98

(Test Method)

Standard Test Method for Calculation of Stagnation Enthalpy from Heat Transfer Theory and Experimental Measurements of Stagnation-Point Heat Transfer and Pressure

Standard Test Method for Calculation of Stagnation Enthalpy from Heat Transfer Theory and Experimental Measurements of Stagnation-Point Heat Transfer and Pressure

SCOPE
1.1 This test method covers the calculation from heat transfer theory of the stagnation enthalpy from experimental measurements of the stagnation-point heat transfer and stagnation pressure.  
1.2 Advantages:  
1.2.1 A value of stagnation enthalpy can be obtained at the location in the stream where the model is tested. This value gives a consistent set of data, along with heat transfer and stagnation pressure, for ablation computations.
1.2.2 This computation of stagnation enthalpy does not require the measurement of any arc heater parameters.  
1.3 Limitations and Considerations -There are many factors that may contribute to an error using this type of approach to calculate stagnation enthalpy, including:  
1.3.1 Turbulence -The turbulence generated by adding energy to the stream may cause deviation from the laminar equilibrium heat transfer theory.  
1.3.2 Equilibrium, Nonequilibrium, or Frozen State of Gas -The reaction rates and expansions may be such that the gas is far from thermodynamic equilibrium.  
1.3.3 Noncatalytic Effects -The surface recombination rates and the characteristics of the metallic calorimeter may give a heat transfer deviation from the equilibrium theory.  
1.3.4 Free Electric Currents -The arc-heated gas stream may have free electric currents that will contribute to measured experimental heat transfer rates.  
1.3.5 Nonuniform Pressure Profile -A nonuniform pressure profile in the region of the stream at the point of the heat transfer measurement could distort the stagnation point velocity gradient.  
1.3.6 Mach Number Effects -The nondimensional stagnation-point velocity gradient is a function of the Mach number. In addition, the Mach number is a function of enthalpy and pressure such that an iterative process is necessary.  
1.3.7 Model Shape -The nondimensional stagnation-point velocity gradient is a function of model shape.  
1.3.8 Radiation Effects -The hot gas stream may contribute a radiative component to the heat transfer rate.  
1.3.9 Heat Transfer Rate Measurement -An error may be made in the heat transfer measurement (see Methods E469 and Test Methods E422, E457, E459, and E511).  
1.3.10 Contamination -The electrode material may be of a large enough percentage of the mass flow rate to contribute to the heat transfer rate measurement.  
1.4 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all of the safety problems 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.

General Information

Status
Historical
Publication Date
09-May-1998
ICS
17.200.10 - Heat. Calorimetry
Technical Committee
E21 - Space Simulation and Applications of Space Technology
Drafting Committee
E21.08 - Thermal Protection
Current Stage
Ref Project

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Replaced By
ASTM E637-05 - Standard Test Method for Calculation of Stagnation Enthalpy from Heat Transfer Theory and Experimental Measurements of Stagnation-Point Heat Transfer and Pressure
Effective Date
15-Sep-2005

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ASTM E637-98 - Standard Test Method for Calculation of Stagnation Enthalpy from Heat Transfer Theory and Experimental Measurements of Stagnation-Point Heat Transfer and PressureASTM E637-98 - Standard Test Method for Calculation of Stagnation Enthalpy from Heat Transfer Theory and Experimental Measurements of Stagnation-Point Heat Transfer and Pressure
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ASTM E637-98 - Standard Test Method for Calculation of Stagnation Enthalpy from Heat Transfer Theory and Experimental Measurements of Stagnation-Point Heat Transfer and Pressure
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E 637 – 98
Standard Test Method for
Calculation of Stagnation Enthalpy from Heat Transfer
Theory and Experimental Measurements of Stagnation-Point
Heat Transfer and Pressure
This standard is issued under the fixed designation E637; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The enthalpy (energy per unit mass) determination in a hot gas aerodynamic simulation device is
a difficult measurement. Even at temperatures that can be measured with thermocouples, there are
many corrections to be made at 600 K and above. Methods that are used for temperatures above the
range of thermocouples that give bulk or average enthalpy values are energy balance (see Practice
E341), sonic flow (1, 2), and the pressure rise method (3). Local enthalpy values (thus distribution)
may be obtained by using either an energy balance probe (see Method E470), or the spectrometric
technique described in Ref (4).
1. Scope 1.3.3 Noncatalytic Effects—The surface recombination
rates and the characteristics of the metallic calorimeter may
1.1 This test method covers the calculation from heat
give a heat transfer deviation from the equilibrium theory.
transfer theory of the stagnation enthalpy from experimental
1.3.4 Free Electric Currents—The arc-heated gas stream
measurements of the stagnation-point heat transfer and stagna-
mayhavefreeelectriccurrentsthatwillcontributetomeasured
tion pressure.
experimental heat transfer rates.
1.2 Advantages:
1.3.5 Nonuniform Pressure Profile—Anonuniformpressure
1.2.1 Avalue of stagnation enthalpy can be obtained at the
profile in the region of the stream at the point of the heat
location in the stream where the model is tested. This value
transfer measurement could distort the stagnation point veloc-
gives a consistent set of data, along with heat transfer and
ity gradient.
stagnation pressure, for ablation computations.
1.3.6 Mach Number Effects—The nondimensional
1.2.2 This computation of stagnation enthalpy does not
stagnation-point velocity gradient is a function of the Mach
require the measurement of any arc heater parameters.
number.Inaddition,theMachnumberisafunctionofenthalpy
1.3 Limitations and Considerations—There are many fac-
and pressure such that an iterative process is necessary.
tors that may contribute to an error using this type of approach
1.3.7 Model Shape—The nondimensional stagnation-point
to calculate stagnation enthalpy, including:
velocity gradient is a function of model shape.
1.3.1 Turbulence—The turbulence generated by adding en-
1.3.8 Radiation Effects—Thehotgasstreammaycontribute
ergy to the stream may cause deviation from the laminar
a radiative component to the heat transfer rate.
equilibrium heat transfer theory.
1.3.9 Heat Transfer Rate Measurement—An error may be
1.3.2 Equilibrium, Nonequilibrium, or Frozen State of
madeintheheattransfermeasurement(seeMethodsE469and
Gas—The reaction rates and expansions may be such that the
Test Methods E422, E457, E459, and E511).
gas is far from thermodynamic equilibrium.
1.3.10 Contamination—The electrode material may be of a
large enough percentage of the mass flow rate to contribute to
1 the heat transfer rate measurement.
This test method is under the jurisdiction of ASTM Committee E21 on Space
1.4 This standard does not purport to address all of the
SimulationandApplicationsofSpaceTechnology,andisthedirectresponsibilityof
Subcommittee E21.08 on Thermal Protection.
safety concerns, if any, associated with its use. It is the
Current edition approved May 10, 1998. Published July 1998. Originally
responsibility of the user of this standard to establish appro-
published as E637–78. Last previous edition E637–97.
priate safety and health practices and determine the applica-
The boldface numbers in parentheses refer to the list of references appended to
this method. bility of regulatory limitations prior to use.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E637–98
TABLE 1 Heat Transfer and Enthalpy Computation Constants
2. Referenced Documents
for Various Gases
2.1 ASTM Standards:
1/2 1/2 1/2 1/2
K , kg/(N ·m ·s) K ,(N ·m ·s)/kg
i M
E341 Practice for Measuring PlasmaArc Gas Enthalpy by Gas
3/2 1/2 3/2 1/2
(lb/(ft ·s·atm )) ((ft ·s·atm )/lb)
Energy Balance
−4
Air 3.905 3 10 (0.0461) 2561 (21.69)
E422 Test Method for Measuring Heat Flux Using a −4
Argon 5.513 3 10 (0.0651) 1814 (15.36)
3 −4
Carbon dioxide 4.337 3 10 (0.0512) 2306 (19.53)
Water-Cooled Calorimeter
−4
Hydrogen 1.287 3 10 (0.0152) 7768 (65.78)
E457 TestMethodforMeasuringHeat-TransferRateUsing
−4
Nitrogen 3.650 3 10 (0.0431) 2740 (23.20)
a Thermal Capacitance (Slug) Calorimeter
E459 TestMethodforMeasuringHeat-TransferRateUsing
a Thin-Skin Calorimeter
0.5
E469 Method for Measuring Heat Flux Using a Multiple-
K q˙ b D/U !
~
M oo Eq3
4 H – H 5 (2)
F G
e w 0.5
Wafer Calorimeter
~b D/U !
~P / R! oo x 50
t
E470 Method for Measuring Gas Enthalpy Using Calori-
Where the “modified” Newtonian stagnation-point velocity
metric Probes
gradient is given by:
E511 Test Method for Measuring Heat Flux Using a
Copper-Constantan Circular Foil, Heat-Flux Gage
2 0.5
~4 @~g21! M 12#
oo
~b D/U ! 5 (3)
oo x 50 F 2 G
3. Significance and Use
g M
oo
3.1 The purpose of this test method is to provide a standard
calculation of the stagnation enthalpy of an aerodynamic
A potential problem exists when using Eq 3 to remove the
simulation device using the heat transfer theory and measured
“modified” Newtonian velocity gradient because of the singu-
values of stagnation point heat transfer and pressure. A
larity at M =0. The procedure recommended here should be
oo
stagnation enthalpy obtained by this test method gives a
limited to M > 0.1
oo
consistent set of data, along with heat transfer and stagnation
where:
pressure for ablation computations.
−1
b = stagnation-point velocity gradient, s ,
D = hemispherical diameter, m (or ft),
4. Enthalpy Computations
U = freestream velocity, m/s (or ft/s),
`
4.1 This method of calculating the stagnation enthalpy is
(bD/U ) = dimensionless stagnation velocity gradi-
` x=0
based on experimentally measured values of the stagnation-
ent,
pointheattransferrateandpressuredistributionandtheoretical
K = enthalpy computation constant,
M
1/2 1/2 3/2 1/2
calculation of laminar equilibrium catalytic stagnation-point
(N ·m · s)/kg or (ft ·atm ·s)/lb, and
heat transfer on a hemispherical body. The equilibrium cata-
M` = the freestream Mach number.
lytic theoretical laminar stagnation-point heat transfer rate for
For subsonic Mach numbers, an expression for (bD/U )
` x=0
a hemispherical body is as follows (5):
for a hemisphere is given in Ref (6) as follows:
R bD
q 5 K ~H – H ! (1)
53–0.755 M ~M ,1! (4)
Πi e w S D
x 50 ` `
P
U
t
`
where:
For a Mach number of 1 or greater, (bD/U ) for a
` x=0
q = stagnation-point heat transfer rate, W/m (or Btu/
hemisphere based on “classical” Newtonian flow theory is
ft ·s),
presented in Ref (7) as follows:
P = model stagnation pressure, Pa (or atm),
t
R = hemispherical nose radius, m (or ft),
8@~g21!M 2 12#
bD g21
`
H = stagnation enthalpy, J/kg (or Btu/lb),
S D 5H F1 1
e
x 50
U 2 2
~g11!M
`
`
H = wall enthalpy, J/kg (or Btu/lb), and
w
1 0.5
K = heat transfer computation constant.
i g21
g21!M 2 12
@~ #
`
4.2 Low Mach Number Correction—Eq 1 is simple and
G J (5)
2gM 2 ~g21!
`
convenient to use since K can be considered approximately
i
Avariation of (bD/U ) with M and g is shown in Fig.
constant(seeTable1).However,Eq1isbasedonastagnation-
` x=0 `
1.The value of the Newtonian dimensionless velocity gradient
point velocity gradient derived using “modified” Newtonian
approaches a constant value as the Mach number approaches
flow theory which becomes inaccurate for M <2.An
oo
infinity:
improved Mach number dependence at lower Mach numbers
can be obtained by removing the “modified” Newtonian
bD g21
5 4 (6)
exprssion and replacing it with a more appropriate expression S D x 50,M→` Œ S D
U g
`
as follows:
and thus, since g, the ratio of specific heats, is a function of
enthalpy, (bD/U ) is also a function of enthalpy.Again, an
` x=0
iteration is necessary. From Fig. 1, it can be seen that
Annual Book of ASTM Standards, Vol 15.03.
Discontinued, see 1983 Annual Book of ASTM Standards, Vol 15.03. (bD/U ) for a hemisphere is approximately 1 for large
` x=0
E637–98
FIG. 1 Dimensionless Velocity Gradient as a Function of Mach Number and Ratio of Specific Heats
Mach numbers and g=1.2. K is tabulated in Table 1 using 4.4 Velocity Gradient Calculation from Pressure
M
(bD/U ) =1 and K from Ref (5). Distribution—The dimensionless stagnation-point velocity
` x=0 i
4.3 Mach Number Determination: gradient may be obtained from an experimentally measured
4.3.1 TheMachnumberofastreamisafunctionofthetotal pressure distribution by using Bernoulli’s compressible flow
enthalpy, the ratio of freestream pressure to the total pressure, equation as follows:
p/p ,thetotalpressure, p ,andtheratiooftheexitnozzlearea
g21
t t
1 1
0.5
1 2 p/p ! g
U @ ~ #
totheareaofthenozzlethroat, A/A8.Fig.2(a)andFig.2(b)are t
5 (7)
S D
g21
U
reproduced from Ref (8) for the reader’s convenience in `
0.5
g
@1 2 ~p /p ! #
` t
determining Mach numbers for supersonic flows.
4.3.2 The subsonic Mach number may be determined from
where the velocity ratio may be calculated along the body
Fig. 3 (see also Test Method E511). An iteration is necessary
from the stagnation point. Thus, the dimensionless stagnation-
todeterminetheMachnumbersincetheratioofspecificheats,
point velocity gradient, (bD/U ) , is the slope of the U/U
g, is also a function of enthalpy and pressure.
` x=0 `
and the x/D curve at the stagnation point.
4.3.3 Theratioofspecificheats, g,isshownasafunctionof
entropy and enthalpy for air in Fig. 4 from Ref (9). S/R is the 4.5 Model Shape—The nondimensional stagnation-point
velocitygradientisafunctionofthemodelshapeandtheMach
dimensionless entropy, and H/RT is the dimensionless en-
thalpy. number. For supersonic Mach numbers, the heat transfer
FIG. 2 (a) Variation of Area Ratio with Mach Numbers
E637–98
FIG. 2 (b) Variation of Area Ratio with Mach Numbers (continued)
FIG. 3 Subsonic Pressure Ratio as a Function of Mach Number and g
relationship between a hemisphere and other axisymmetric radiant energy are the hot gas stream itself or the gas heating
blunt bodies is shown in Fig. 5 (10). In Fig. 5, r is the corner device, or both. For instance, arc heaters operated at high
c
radius, r isthebodyradius, r isthenoseradius,and q˙ isthe pressure (10 atm or higher) can produce significant radiant
b n s,h
stagnation-point heat transfer rate on a hemisphere. For sub- fluxes at the nozzle exit plane.
sonic Mach numbers, the same type of variation is shown in 4.6.2 The proper application requires some knowledge of
Fig. 6 (6). the radiant environment in the stream at the desired operating
4.6 Radiation Effects: conditions. Usually, it is necessary to measure the radiant heat
4.6.1 As this test method depends on the accurate determi- transfer rate either directly or indirectly.The following is a list
nation of the convective stagnation-point heat transfer, any of suggested methods by which the necessary measurements
radiant energy absorbed by the calorimeter surface and incor- can be made.
rectly attributed to the convective mode will directly affect the 4.6.2.1 Direct Measurement with Radiometer—
overall accuracy of the test method. Generally, the sources of Radiometers are available for the measurement of the incident
E637–98
FIG. 4 Isentropic Exponent for Air in Equilibrium
FIG. 6 Stagnation-Point Heat Transfer Ratio to a Blunt Body and
FIG. 5 Stagnation-Point Heating-Rate Parameters on
a Hemisphere as a Function of the Body-to-Nose Radius in a
Hemispherical Segments of Different Curvatures for Varying
Subsonic Stream
Corner-Radius Ratios
radiant flux while excluding the convective heat transfer. In its The basic radiometer view angle should be 120° or greater.
simplest form, the radiometer is a slug, thin-skin, or circular This technique allows for immersion of the radiometer in the
foil calorimeter with a sensing area with a coating of known test stream and direct measurement of the radiant heat transfer
absorptance and covered with some form of window. The rate. There is a major limitation to this technique, however, in
purpose of the window is to prevent convective heat transfer that even with high-pressure water cooling of the radiometer
from affecting the calorimeter while transmitting the radiant enclosure, the window is poorly cooled and thus the use of
energy.Thewindowisusuallymadeofquartzorsapphire.The windows is limited to relatively low convective heat transfer
sensing surface is at the stagnation point of a test probe and is conditions or very short exposure times, or both.Also, stream
located in such a manner that the view angle is not restricted. contaminants coat the window and reduce its transmittance.
E637–98
4.6.2.2 Direct Measurement with Radiometer Mounted in
Cavity—Thetwolimitationsnotedin4.6.2.1maybeovercome
by mounting the radiometer at the bottom of a cavity open to
the stagnation point of the test probe (see Fig. 7). Good results
can be obtained by using a simple calorimeter in place of the
radiometer with a material of known absorptance. When using
this configuration, the measured radiant heat transfer rate is
used in the following equation to determine the stagnation-
point radiant heat transfer, assuming diffuse radiation:
q˙ 5 q˙ (8)
r r
1 2
a F
2 12
FIG. 8 Circular Cavity Configuration (see Eq 8)
where:
q˙ = radiant transfer at stagnation point,
r
levels is difficult. There are many schemes that could be used
q˙ = radiant transfer at bottom of cavity (measured),
r
to measure incident radiant flux indirectly. One such would be
a = absorptance of sensor surface, and
the measurement of the radiant flux reflected from a surface in
F = configuration factor.
the test stream. This technique depends primarily on the
For a circular cavity geometry (recommended), F is
accurate determination of surface reflectance under actual test
ConfigurationA-3 of Ref (11) and can be determined from the
conditions. The surface absorptance and a measurement of the
following equation:
surfac
...

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Standard Test Method for Measuring Extreme Heat-Transfer Rates from High-Energy Environments Using a Transient, Null-Point Calorimeter

SIGNIFICANCE AND USE
5.1 The purpose of this test method is to measure extremely high heat-transfer rates to a body immersed in either a static environment or in a high velocity fluid stream. This is usually accomplished while preserving the structural integrity of the measurement device for multiple exposures during the measurement period. Heat-transfer rates ranging up to 2.84 × 102 MW/m2 (2.5 × 104 Btu/ft2-sec) (7) have been measured using null-point calorimeters. Use of copper null-point calorimeters provides a measuring system with good response time and maximum run time to sensor burnout (or ablation). Null-point calorimeters are normally made with sensor body diameters of 2.36 mm (0.093 in.) press-fitted into the nose of an axisymmetric model.  
5.2 Sources of error involving the null-point calorimeter in high heat-flux measurement applications are extensively discussed in Refs (3-7). In particular, it has been shown both analytically and experimentally that the thickness of the copper above the null-point cavity is critical. If the thickness is too great, the time response of the instrument will not be fast enough to pick up important flow characteristics. On the other hand, if the thickness is too small, the null-point calorimeter will indicate significantly larger (and time dependent) values than the input or incident heat flux. Therefore, all null-point calorimeters should be experimentally checked for proper time response and calibration before they are used. Although a calibration apparatus is not very difficult or expensive to fabricate, there is only one known system presently in existence (6 and 7). The design of null-point calorimeters can be accomplished from the data in this documentation. However, fabrication of these sensors is a difficult task. Since there is not presently a significant market for null-point calorimeters, commercial sources of these sensors are few. Fabrication details are generally regarded as proprietary information. Some users have developed me...
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1.1 This test method covers the measurement of the heat-transfer rate or the heat flux to the surface of a solid body (test sample) using the measured transient temperature rise of a thermocouple located at the null point of a calorimeter that is installed in the body and is configured to simulate a semi-infinite solid. By definition the null point is a unique position on the axial centerline of a disturbed body which experiences the same transient temperature history as that on the surface of a solid body in the absence of the physical disturbance (hole) for the same heat-flux input.  
1.2 Null-point calorimeters have been used to measure high convective or radiant heat-transfer rates to bodies immersed in both flowing and static environments of air, nitrogen, carbon dioxide, helium, hydrogen, and mixtures of these and other gases. Flow velocities have ranged from zero (static) through subsonic to hypersonic, total flow enthalpies from 1.16 to greater than 4.65 × 101 MJ/kg (5 × 10 2 to greater than 2 × 104 Btu/lb.), and body pressures from 105 to greater than 1.5 × 107 Pa (atmospheric to greater than 1.5 × 102 atm). Measured heat-transfer rates have ranged from 5.68 to 2.84 × 102 MW/m2 (5 × 102 to 2.5 × 104 Btu/ft2-sec).  
1.3 The most common use of null-point calorimeters is to measure heat-transfer rates at the stagnation point of a solid body that is immersed in a high pressure, high enthalpy flowing gas stream, with the body axis usually oriented parallel to the flow axis (zero angle-of-attack). Use of null-point calorimeters at off-stagnation point locations and for angle-of-attack testing may pose special problems of calorimeter design and data interpretation.  
1.4 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, health, and environmental practices and determine the appli...

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ASTM E511-07(2020)(Test Method)
Standard Test Method for Measuring Heat Flux Using a Copper-Constantan Circular Foil, Heat-Flux Transducer

SIGNIFICANCE AND USE
3.1 Fig. 1 is a sectional view of an example circular foil heat-flux transducer. It consists of a circular Constantan foil attached by a metallic bonding process to a heat sink of oxygen-free high conductivity copper (OFHC), with copper leads attached at the center of the circular foil and at any point on the heat-sink body. The transducer impedance is usually less than 1 V. To minimize current flow, the data acquisition system (DAS) should be a potentiometric system or have an input impedance of at least 100 000 Ω.  
3.2 As noted in 2.3, an approximately linear output (versus heat flux) is produced when the body and center wire of the transducer are constructed of copper and the circular foil is constantan. Other metal combinations may be employed for use at higher temperatures, but most (4) are nonlinear.  
3.3 Because the thermocouple junction at the edge of the foil is the reference for the center thermocouple, no cold junction compensation is required with this instrument. The wire leads used to convey the signal from the transducer to the readout device are normally made of stranded, tinned copper, insulated with TFE-fluorocarbon and shielded with a braid over-wrap that is also TFE-fluorocarbon-covered.  
3.4 Transducers with a heat-sink thermocouple can be used to indicate the foil center temperature. Once the edge temperature is known, the temperature difference from the foil edge to its center may be directly read from the copper-constantan (Type T) thermocouple table. This temperature difference then is added to the body temperature, indicating the foil center temperature.  
3.5 Water-Cooled Transducer:  
3.5.1 A water-cooled transducer should be used in any application where the copper heat-sink would rise above 235 °C (450 °F) without cooling. Examples of cooled transducers are shown in Fig. 2. The coolant flow must be sufficient to prevent local boiling of the coolant inside the transducer body, with its characteristic pulsations (“chugging”) of t...
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1.1 This test method describes the measurement of radiative heat flux using a transducer whose sensing element (1, 2)2 is a thin circular metal foil. These sensors are often called Gardon Gauges.  
1.2 The values stated in SI units are to be regarded as the standard. The values stated in parentheses are provided for information only.  
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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM E458-08(2020)(Test Method)
Standard Test Method for Heat of Ablation

SIGNIFICANCE AND USE
4.1 General—The heat of ablation provides a measure of the ability of a material to serve as a heat protection element in a severe thermal environment. The parameter is a function of both the material and the environment to which it is subjected. It is therefore required that laboratory measurements of heat of ablation simulate the service environment as closely as possible. Some of the parameters affecting the heat of ablation are pressure, gas composition, heat transfer rate, mode of heat transfer, and gas enthalpy. As laboratory duplication of all parameters is usually difficult, the user of the data should consider the differences between the service and the test environments. Screening tests of various materials under simulated use conditions may be quite valuable even if all the service environmental parameters are not available. These tests are useful in material selection studies, materials development work, and many other areas.  
4.2 Steady-State Conditions—The nature of the definition of heat of ablation requires steady-state conditions. Variances from steady-state may be required in certain circumstances; however, it must be realized that transient phenomena make the values obtained functions of the test duration and therefore make material comparisons difficult.  
4.2.1 Temperature Requirements—In a steady-state condition, the temperature propagation into the material will move at the same velocity as the gas-ablation surface interface. A constant distance is maintained between the ablation surface and the isotherm representing the temperature front. Under steady-state ablation the mass loss and length change are linearly related.
   where:
  t  =  test time, s,   ρo  =  virgin material density, kg/m3,   δL  =   change in length or ablation depth, m,   ρc  =   char density, kg/m3, and   δc  =   char depth, m.  This relationship may be used to verify the existence of steady-state ablation in the tests of charring ablators.  
4.2.2 Exposure T...
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1.1 This test method covers determination of the heat of ablation of materials subjected to thermal environments requiring the use of ablation as an energy dissipation process. Three concepts of the parameter are described and defined: cold wall, effective, and thermochemical heat of ablation.  
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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM E341-08(2020)(Practice)
Standard Practice for Measuring Plasma Arc Gas Enthalpy by Energy Balance

SIGNIFICANCE AND USE
3.1 The purpose of this practice is to measure the total or stagnation gas enthalpy of a plasma-arc gas stream in which nonreactive gases are heated by passage through an electrical discharge device during calibration tests of the system.  
3.2 The plasma arc represents one heat source for determining the performance of high temperature materials under simulated hyperthermal conditions. As such the total or stagnation enthalpy is one of the important parameters for correlating the behavior of ablation materials.  
3.3 The most direct method for obtaining a measure of total enthalpy, and one which can be performed simultaneously with each material test, if desired, is to perform an energy balance on the arc chamber. In addition, in making the energy balance, accurate measurements are needed since the efficiencies of some plasma generators are low (as low as 15 to 20 % or less in which case the enthalpy depends upon the difference of two quantities of nearly equal magnitude). Therefore, the accuracy of the measurements of the primary variables must be high, all energy losses must be correctly taken into account, and steady-state conditions must exist both in plasma performance and fluid flow.  
3.4 In particular it is noted that total enthalpy as determined by the energy balance technique is most useful if the plasma generator design minimizes coring effects. If nonuniformity exists the enthalpy determined by energy balance gives only the average for the entire plasma stream, whereas the local enthalpy experienced by a model in the core of the stream may be much higher. More precise methods are needed to measure local variations in total enthalpy.
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1.1 This practice covers the measurement of total gas enthalpy of an electric-arc-heated gas stream by means of an overall system energy balance. This is sometimes referred to as a bulk enthalpy and represents an average energy content of the test stream which may differ from local values in the test stream.  
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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM E457-08(2020)(Test Method)
Standard Test Method for Measuring Heat-Transfer Rate Using a Thermal Capacitance (Slug) Calorimeter

SIGNIFICANCE AND USE
4.1 The purpose of this test method is to measure the rate of thermal energy per unit area transferred into a known piece of material (slug) for purposes of calibrating the thermal environment into which test specimens are placed for evaluation. The calorimeter and holder size and shape should be identical to that of the test specimen. In this manner, the measured heat transfer rate to the calorimeter can be related to that experienced by the test specimen.  
4.2 The slug calorimeter is one of many calorimeter concepts used to measure heat transfer rate. This type of calorimeter is simple to fabricate, inexpensive, and readily installed since it is not water-cooled. The primary disadvantages are its short lifetime and relatively long cool-down time after exposure to the thermal environment. In measuring the heat transfer rate to the calorimeter, accurate measurement of the rate of rise in back-face temperature is imperative.  
4.3 In the evaluation of high-temperature materials, slug calorimeters are used to measure the heat transfer rate on various parts of the instrumented models, since heat transfer rate is one of the important parameters in evaluating the performance of ablative materials.  
4.4 Regardless of the source of thermal energy to the calorimeter (radiative, convective, or a combination thereof) the measurement is averaged over the calorimeter surface. If a significant percentage of the total thermal energy is radiative, consideration should be given to the emissivity of the slug surface. If non-uniformities exist in the input energy, the heat transfer rate calorimeter would tend to average these variations; therefore, the size of the sensing element (that is, the slug) should be limited to small diameters in order to measure local heat transfer rate values. Where large ablative samples are to be tested, it is recommended that a number of calorimeters be incorporated in the body of the test specimen such that a heat transfer rate distribution across...
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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 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM E3057-19(Test Method)
Standard Test Method for Measuring Heat Flux Using Directional Flame Thermometers with Advanced Data Analysis Techniques

SIGNIFICANCE AND USE
5.1 Need for Heat Flux Measurements:  
5.1.1 Independent measurements of temperature and heat flux support the development and validation of engineering models of fires and other high environments, such as furnaces. For tests of fire protection materials and structural assemblies, temperature and heat flux are necessary to fully specify the boundary conditions, also known as the thermal exposure. Temperature measurements alone cannot provide a complete set of boundary conditions.  
5.1.2 Temperature is a scalar variable and a primary variable. Heat Flux is a vector quantity, and it is a derived variable. As a result, they should be measured separately just as current and voltage are in electrical systems. For steady-state or quasi-steady state conditions, analysis basically uses a thermal analog of Ohm's Law. The thermal circuit uses the temperature difference instead of voltage drop, the heat flux in place of the current and thermal resistance in place of electrical resistance. As with electrical systems, the thermal performance is not fully specified without knowing at least two of these three parameters (temperature drop, heat flux, or thermal resistance). For dynamic thermal experiments like fires or fire safety tests, the electrical capacitance is replaced by the volumetric heat capacity.  
5.1.3 The net heat flux, which is measured by a DFT, is likely different than the heat flux into the test item of interest because of different surface temperatures. An alternative measurement is the total cold wall heat flux which is measured by water-cooled Gardon or S-B gauges. The incident radiative flux can be estimated from either measurement by use of an energy balance [Keltner, 2007 and 2008 (16, 17)]. The convective flux can be estimated from gas temperatures and the convective heat transfer coefficient, h [Janssens, 2007 (18)]. Assuming the sensor is physically close to the test item of interest; one can use the incident radiative and convective fluxes from the...
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1.1 This test method describes the continuous measurement of the hemispherical heat flux to one or both surfaces of an uncooled sensor called a “Directional Flame Thermometer” (DFT).  
1.2 DFTs consist of two heavily oxidized, Inconel 600 plates with mineral insulated, metal-sheathed (MIMS) thermocouples (TCs, type K) attached to the unexposed faces and a layer of ceramic fiber insulation placed between the plates.  
1.3 Post-test calculations of the net heat flux can be made using several methods. The most accurate method uses an inverse heat conduction code. Nonlinear inverse heat conduction analysis uses a thermal model of the DFT with temperature dependent thermal properties along with the two plate temperature measurement histories. The code provides transient heat flux on both exposed faces, temperature histories within the DFT as well as statistical information on the quality of the analysis.  
1.4 A second method uses a transient energy balance on the DFT sensing surface and insulation, which uses the same temperature measurements as in the inverse calculations to estimate the net heat flux.  
1.5 A third method uses Inverse Filter Functions (IFFs) to provide a near real time estimate of the net flux. The heat flux history for the “front face” (either surface exposed to the heat source) of a DFT can be calculated in real-time using a convolution type of digital filter algorithm.  
1.6 Although developed for use in fires and fire safety testing, this measurement method is quite broad in potential fields of application because of the size of the DFTs and their construction. It has been used to measure heat flux levels above 300 kW/m2 in high temperature environments, up to about 1250 °C, which is the generally accepted upper limit of Type K or N thermocouples.  
1.7 The transient response of the DFTs is limited by the response of the MIMS TCs. The larger the thermocouple the slower the transient response. Res...

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ASTM E2683-17(Test Method)
Standard Test Method for Measuring Heat Flux Using Flush-Mounted Insert Temperature-Gradient Gages

SIGNIFICANCE AND USE
5.1 The purpose of this test method is to measure the net heat flux to or from a surface location. For measurement of the radiant energy component the emissivity or absorptivity of the surface coating of the gage is required. When measuring the convective energy component the potential physical and thermal disruptions of the surface must be minimized and characterized. Requisite is to consider how the presence of the gage alters the surface heat flux. The desired quantity is usually the heat flux at the surface location without the presence of the gage.  
5.1.1 Temperature limitations are determined by the gage material properties, the method of mounting the sensing element, and how the lead wires are attached. The range of heat flux that can be measured and the time response are limited by the gage design and construction details. Measurements of a fraction of 1 kW/m 2 to above 10 MW/m2 are easily obtained with current gages. With thin film sensors a time response of less than 10 μs is possible, while thicker sensors may have response times on the order of 1 s. It is important to choose the gage style and characteristics to match the range and time response of the required application.  
5.1.2 When differential thermocouple sensors are operated as specified for one-dimensional heat flux and within the corresponding time response limitations, the voltage output is directly proportional to the heat flux. The sensitivity, however, may be a function of the gage temperature.  
5.2 The measured heat flux is based on one-dimensional analysis with a uniform heat flux over the surface of the gage. Measurements of convective heat flux are particularly sensitive to disturbances of the temperature of the surface. Because the heat-transfer coefficient is also affected by any non-uniformities in the surface temperature, the effect of a small temperature change with location is further amplified as explained by Moffat et al. (2) and Diller (3). Moreover, the smaller the gage s...
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1.1 This test method describes the measurement of the net heat flux normal to a surface using gages inserted flush with the surface. The geometry is the same as heat-flux gages covered by Test Method E511, but the measurement principle is different. The gages covered by this standard all use a measurement of the temperature gradient normal to the surface to determine the heat that is exchanged to or from the surface. Although in a majority of cases the net heat flux is to the surface, the gages operate by the same principles for heat transfer in either direction.  
1.2 This general test method is quite broad in its field of application, size and construction. Two different gage types that are commercially available are described in detail in later sections as examples. A summary of common heat-flux gages is given by Diller (1).2 Applications include both radiation and convection heat transfer. The gages used for aerospace applications are generally small (0.155 to 1.27 cm diameter), have a fast time response (10 μs to 1 s), and are used to measure heat flux levels in the range 0.1 to 10 000 kW/m2. Industrial applications are sometimes satisfied with physically larger gages.  
1.3 The values stated in SI units are to be regarded as the standard. The values stated in parentheses are provided for information only.  
1.4 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.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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