ASTM E598-08(2015)
(Test Method)Standard Test Method for Measuring Extreme Heat-Transfer Rates from High-Energy Environments Using a Transient, Null-Point Calorimeter
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 × 10 2 MW/m2 (2.5 × 104 Btu/ft 2-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 develo...
SCOPE
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 × 10 7 Pa (atmospheric to greater than 1.5 × 10 2 atm). Measured heat-transfer rates have ranged from 5.68 to 2.84 × 10 2 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 and health practices and determine the applicability of r...
General Information
Buy Standard
Standards Content (Sample)
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:E598 −08 (Reapproved 2015)
Standard Test Method for
Measuring Extreme Heat-Transfer Rates from High-Energy
Environments Using a Transient, Null-Point Calorimeter
This standard is issued under the fixed designation E598; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
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
2. Referenced Documents
sample) using the measured transient temperature rise of a
2.1 ASTM Standards:
thermocouple located at the null point of a calorimeter that is
E422Test Method for Measuring Heat Flux Using a Water-
installed in the body and is configured to simulate a semi-
Cooled Calorimeter
infinite solid. By definition the null point is a unique position
E511TestMethodforMeasuringHeatFluxUsingaCopper-
on the axial centerline of a disturbed body which experiences
Constantan Circular Foil, Heat-Flux Transducer
the same transient temperature history as that on the surface of
a solid body in the absence of the physical disturbance (hole)
3. Terminology
for the same heat-flux input.
3.1 Symbols:
1.2 Null-point calorimeters have been used to measure high
convective or radiant heat-transfer rates to bodies immersed in
a = Radius of null-point cavity, m (in.)
both flowing and static environments of air, nitrogen, carbon b = Distancefromfrontsurfaceofnull-pointcalorimeterto
dioxide, helium, hydrogen, and mixtures of these and other the null-point cavity, m (in.)
gases. Flow velocities have ranged from zero (static) through C = Specific heat capacity, J/kg–K (Btu/lb-°F)
p
d = Diameter of null-point cavity, m (in.)
subsonic to hypersonic, total flow enthalpies from 1.16 to
1 2 4
k = Thermal conductivity, W/m–K (Btu/in.-sec-°F)
greater than 4.65×10 MJ/kg (5×10 to greater than 2×10
5 7
L = Length of null-point calorimeter, m (in.)
Btu/lb.), and body pressures from 10 to greater than 1.5×10
2 q = Calculated or measured heat flux or heat-transfer-rate,
Pa (atmospheric to greater than 1.5×10 atm). Measured
2 2
W/m (Btu/ft -sec)
heat-transfer rates have ranged from 5.68 to 2.84×10 MW/
2 2
2 2 4 2 q = Constantheatfluxorheat-transfer-rate,W/m (Btu/ft -
m (5×10 to 2.5×10 Btu/ft -sec).
sec)
1.3 The most common use of null-point calorimeters is to
R = RadialdistancefromaxialcenterlineofTRAXanalyti-
measure heat-transfer rates at the stagnation point of a solid
cal model, m (in.)
bodythatisimmersedinahighpressure,highenthalpyflowing
r = Radial distance from axial centerline of null-point
gas stream, with the body axis usually oriented parallel to the
cavity, m (in.)
flow axis (zero angle-of-attack). Use of null-point calorimeters
T = Temperature, K (°F)
at off-stagnation point locations and for angle-of-attack testing T = Temperature on axial centerline of null point, K (°F)
b
may pose special problems of calorimeter design and data T = Temperature on surface of null-point calorimeter, K
s
(°F)
interpretation.
t = Time, sec
1.4 This standard does not purport to address all of the
Z = Distance in axial direction of TRAX analytical model,
safety concerns, if any, associated with its use. It is the
m (in.)
responsibility of the user of this standard to establish appro-
2 2
α = Thermal diffusivity, m /sec (in. /sec)
3 3
ρ = Density, kg/m (lb⁄in. )
This test method is under the jurisdiction of ASTM Committee E21 on Space
Simulation andApplications of SpaceTechnology and is the direct responsibility of
Subcommittee E21.08 on Thermal Protection. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved May 1, 2015. Published June 2015. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1977. Last previous edition approved in 2008 as E598–08. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E0598-08R15. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E598−08 (2015)
4. History of Test Method ment concept was a major step in leading others to adapt this
concept to the transient measurement of high heat fluxes in
4.1 FromliteraturereviewsitappearsthatMastersandStein
ground test facilities.
(1) werethefirsttodocumenttheresultsofananalyticalstudy
of the temperature effects of axial cavities drilled from the
4.2 Beck and Hurwicz (2) expanded the analysis of Masters
backsideofawallwhichisheatedonthefrontsurface(seeFig.
and Stein to include steady-state solutions and were the first to
1). These investigators were primarily concerned with the
label the method of measurement “the null-point concept.”
deviation of the temperature measured in the bottom of the
They effectively used a digital computer to generate relatively
cavity from the undisturbed temperature on the heated surface.
large quantities of analytical data from numerical methods.
Since they were not in possession of either the computing
Beck and Hurwicz computed errors due to relatively large
powerorthenumericalheatconductioncodesnowavailableto
thermocouplewiresintheaxialcavityandwereabletosuggest
the analyst, Masters and Stein performed a rigorous math-
that the optimum placement of the thermocouple in the cavity
ematical treatment of the deviation of the transient
occurred when the ratio a/b was equal to 1.1. However, their
temperature, T , on the bottom centerline of the cavity of
b
analysislikethatofMastersandSteinwasonlyconcernedwith
radius, a, and thickness, b, from the surface temperature T .
s
the deviation of the temperature in the axial cavity and did not
The results of Masters and Stein indicated that the error in
address the error in measured heat flux.
temperature measurement on the bottom centerline of the
4.3 Howey and DiCristina (3) were the first to perform an
cavity would decrease with increasing values of a/b and also
actual thermal analysis of this measurement concept.Although
decrease with increasing values of the dimensionless time,
the explanation of modeling techniques is somewhat ambigu-
αt/b , where αis the thermal diffusity of the wall material.
ous in their paper, it is obvious that they used a finite element,
Theyalsoconcludedthatthemostimportantfactorintheerror
two dimensional axisymmetric model to produce temperature
intemperaturemeasurementwastheratio a/bandtheerrorwas
profiles in a geometry simulating the null-point calorimeter.
independent of the level of heat flux. The conclusions of
Temperature histories at time intervals down to 0.010 sec were
Masters and Stein may appear to be somewhat elementary
obtained for a high heat-flux level on the surface of the
compared with our knowledge of the null-point concept today.
analytical model. Although the analytical results are not
However,theidentificationanddocumentationofthemeasure-
presented in a format which would help the user/designer
optimize the sensor design, the authors did make significant
general conclusions about null point calorimeters. These in-
clude: (1) “., thermocouple outputs can yield deceivingly fast
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this test method.
NOTE 1—1-T (0,t)=Surface temperature (x=0) of a solid, semi-infinite slab at some time, t.
s
NOTE 2—2-T (0,b,t)=Temperature at r=0, x=b of a slab with a cylindrical cavity at some time, t, heat flux, q, the same in both cases.
b
FIG. 1Semi-infinite Slab with Cylindrical Cavity
E598−08 (2015)
response rates and erroneously high heating rates (+18%) graphically illustrated on Figs. 3 and 4. The optimum value of
when misused in inverse one-dimensional conduction solu- the ratio a/b is defined to be that number which yields the
fastest time response to a step heat-flux input and maintains a
tions.” (2) “The prime reason for holding the thermocouple
depth at R/E =1.1 is to maximize thermocouple response at constant value of indicated q˙/input q˙ after the initial time
response period. From Figs. 3 and 4, it can be seen that this
high heating rates for the minimum cavity depth.” (Note:
optimum value is about 1.4 for two families of curves for
Rand Eas used by Howey and DeChristina are the same terms
which the cavity radius, a, is held constant while the cavity
as aand bwhicharedefinedin4.1andareusedthroughoutthis
thickness, b,isvariedtospanawiderangeoftheratio a/b.This
document.) (3)Afinite length null-point calorimeter body may
is a slightly higher value than reported by earlier analysts. It is
be considered semi-infinite for:
important to note that the analytical results do not necessarily
~αt!
#0.3 have to give a value of indicated q˙/input q˙ =1.0 since this
L
difference can be calibrated in the laboratory. The data graphi-
4.4 Powars, Kennedy, and Rindal (4 and 5) were the first to
cally illustrated on Figs. 3 and 4 and substantiate conclusions
document using null point calorimeters in the swept mode.
drawn by the authors of Refs (3 and 4) that the calculated heat
This method which is now used in almost all arc facilities has
flux can be considerably higher than the actual input heat
the advantages of (1) measuring the radial distributions across
flux—especially as the ratio of a/b is raised consistently above
the arc jet, and (2) preserving the probe/sensor structural
1.5.All of the users of null-point calorimeters assume that the
integrity for repeated measurements. This technique involves
device simulates a semi-infinite body in the time period of
sweeping the probe/sensor through the arc-heated flow field at
interest. Therefore, the sensor is subject to the finite body
1/2
a rate slow enough to allow the sensor to make accurate
length, L, defined by L/(αt) ≤ 1.8 in order that the error in
measurements, yet fast enough to prevent model ablation.
indicated heat flux does not exceed one percent (6 and 7).This
4.4.1 Following the pattern of Howey and DiCristina, Pow- restriction agrees well with the earlier work of Howey and
ars et. al. stressed the importance of performing thermal DiCristina (3).
analyses to “characterize the response of a typical real null
4.6 Asectionviewsketchofatypicalnull-pointcalorimeter
point calorimeter to individually assess a variety of potential
showing all important components and the physical configu-
errors,.”. Powars et. al. complain that Howey & DiCristina
ration of the sensor is shown in Fig. 5.The outside diameter is
“. report substantial errors in some cases, but present no
2.36 mm (0.093 in.), the length is 10.2 mm (0.40 in.), and the
generalized results or design guide lines.” They state concern-
body material is oxygen-free high conductivity (OFHC) cop-
ing the analyses performed to support their own
per. Temperature at the null point is measured by a 0.508 mm
documentation, “In order to establish guidelines for null point
(0.020 in.) diam American National Standards Association
calorimeter design and data reduction, analyses were per-
(ANSI) type K stainless steel-sheathed thermocouple with
formed to individually assess the measurement errors associ-
0.102 mm (0.004 in.) diam thermoelements. Although no
atedwithavarietyofnon-idealaspectsofactualcalorimeters.”
thermocouple attachment is shown, it is assumed that the
The conclusions reached from the results of the thermal
individual thermocouple wires are in perfect contact with the
analyses were broken down into eight sub headings and were
backsideofthecavityandpresentnoaddedthermalmasstothe
discussed individually. Some of the conclusions reached were
system. Details of installing thermocouples in the null point
rather elementary and were previously reported in Refs (1-3).
cavity and making a proper attachment of the thermocouple
Others were somewhat arbitrary and were stated without
with the copper slug are generally considered to be proprietary
substantiating data. One specific conclusion concerns the ratio
by the sensor manufacturers. Kidd in Ref (7) states that the
of the null-point cavity radius, a, to the cavity thickness, b.
attachment is made by thermal fusion without the addition of
Whilestatingthattheoptimumconditionoccurredwhen a= b,
foreign materials. Note that the null-point body has a small
the authors of Ref (4)further state that when a=0.305 mm
flange at the front and back which creates an effective dead air
(0.012 in.) and b=0.127 mm (0.005 in.); a/b=2.4, the
space along the length of the cylinder to enhance one-
calculated heat flux will be 20% higher than the actual heat
dimensional heat conduction and prevent radial conduction.
flux. In more recent documentation using more accurate and
For aerodynamic heat-transfer measurements, the null-point
sophisticated heat conduction computer codes as well as an
sensors are generally pressed into the stagnation position of a
establishednumericalinverseheatconductionequation (6),the sphere cone model of the same material (OFHC copper).
error in indicated heat flux is shown to be considerably higher
4.7 The value of the lumped thermal parameter of copper is
than 20% and is highly time dependent.
not a strong function of temperature. In fact, the value of
1/2
(ρC k) for OFHC copper varies less than three percent from
p
4.5 The latest and most comprehensive thermal analysis of
room temperature to the melting point, 1356 K (1981°F); (see
the null-point calorimeter concept was performed by Kidd and
Fig. 6). Thermal properties of OFHC copper are well docu-
documented in Refs (6 and 7). This analytical work was
mented and data from different sources are in good agreement
accomplished by using a finite element axisymmetric heat
(8). Most experimenters use the room temperature value of the
conduction code (7). The finite element model simulating the
parameter in processing data from null-point calorimeters.
null-point calorimeter system is comprised of 793 finite ele-
ments and 879 nodal points and is shown in block diagram 4.8 The determination of surface heat flux as a function of
form in Fig. 2. Timewise results of normalized heat flux for time and temperature requires a digital computer, programmed
different physical dimensional parameters (ratios of ato b) are to calculate the correct values of heat-transfer rate. Having the
E598−08 (2015)
FIG. 2Finite Element Model of Null-Point Calorimeter
FIG. 3Null-Point Calorimeter Analytical Time Response Data
measured null-point cavity
...
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: E598 − 08 E598 − 08 (Reapproved 2015)
Standard Test Method for
Measuring Extreme Heat-Transfer Rates from High-Energy
Environments Using a Transient, Null-Point Calorimeter
This standard is issued under the fixed designation E598; 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 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 × 10
2 4 5 7
MJ/kg (5 × 10 to greater than 2 × 10 Btu/lb.), and body pressures from 10 to greater than 1.5 × 10 Pa (atmospheric to greater
2 2 2 2 4 2
than 1.5 × 10 atm). Measured heat-transfer rates have ranged from 5.68 to 2.84 × 10 MW/m (5 × 10 to 2.5 × 10 Btu/ft -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 and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
E422 Test Method for Measuring Heat Flux Using a Water-Cooled Calorimeter
E511 Test Method for Measuring Heat Flux Using a Copper-Constantan Circular Foil, Heat-Flux Transducer
3. Terminology
3.1 Symbols:
a = Radius of null-point cavity, m (in.)
b = Distance from front surface of null-point calorimeter to the null-point cavity, m (in.)
C = Specific heat capacity, J/kg–K (Btu/lb-°F)
p
d = Diameter of null-point cavity, m (in.)
k = Thermal conductivity, W/m–K (Btu/in.-sec-°F)
L = Length of null-point calorimeter, m (in.)
2 2
q = Calculated or measured heat flux or heat-transfer-rate, W/m (Btu/ft -sec)
2 2
q = Constant heat flux or heat-transfer-rate, W/m (Btu/ft -sec)
R = Radial distance from axial centerline of TRAX analytical model, m (in.)
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 Dec. 1, 2008May 1, 2015. Published January 2009June 2015. Originally approved in 1977. Last previous edition approved in 20022008 as
E598 – 96 (2002).E598 – 08. DOI: 10.1520/E0598-08.10.1520/E0598-08R15.
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
E598 − 08 (2015)
r = Radial distance from axial centerline of null-point cavity, m (in.)
T = Temperature, K (°F)
T = Temperature on axial centerline of null point, K (°F)
b
T = Temperature on surface of null-point calorimeter, K (°F)
s
t = Time, sec
Z = Distance in axial direction of TRAX analytical model, m (in.)
2 2
α = Thermal diffusivity, m /sec (in. /sec)
3 3
ρ = Density, kg/m (lb ⁄in. )
4. History of Test Method
4.1 From literature reviews it appears that Masters and Stein (1) were the first to document the results of an analytical study
of the temperature effects of axial cavities drilled from the backside of a wall which is heated on the front surface (see Fig. 1).
These investigators were primarily concerned with the deviation of the temperature measured in the bottom of the cavity from the
undisturbed temperature on the heated surface. Since they were not in possession of either the computing power or the numerical
heat conduction codes now available to the analyst, Masters and Stein performed a rigorous mathematical treatment of the
deviation of the transient temperature, T , on the bottom centerline of the cavity of radius, a, and thickness, b, from the surface
b
temperature T . The results of Masters and Stein indicated that the error in temperature measurement on the bottom centerline of
s
the cavity would decrease with increasing values of a/b and also decrease with increasing values of the dimensionless time, αt/b ,
where α is the thermal diffusity of the wall material. They also concluded that the most important factor in the error in temperature
measurement was the ratio a/band the error was independent of the level of heat flux. The conclusions of Masters and Stein may
appear to be somewhat elementary compared with our knowledge of the null-point concept today. However, the identification and
documentation of the measurement concept was a major step in leading others to adapt this concept to the transient measurement
of high heat fluxes in ground test facilities.
4.2 Beck and Hurwicz (2) expanded the analysis of Masters and Stein to include steady-state solutions and were the first to label
the method of measurement “the null-point concept.” They effectively used a digital computer to generate relatively large quantities
of analytical data from numerical methods. Beck and Hurwicz computed errors due to relatively large thermocouple wires in the
axial cavity and were able to suggest that the optimum placement of the thermocouple in the cavity occurred when the ratio a/b
The boldface numbers in parentheses refer to the list of references at the end of this test method.
NOTE 1—1-T (0,t) = Surface temperature (x = 0) of a solid, semi-infinite slab at some time, t.
s
NOTE 2—2-T (0,b,t) = Temperature at r = 0, x = b of a slab with a cylindrical cavity at some time, t, heat flux, q, the same in both cases.
b
FIG. 1 Semi-infinite Slab with Cylindrical Cavity
E598 − 08 (2015)
was equal to 1.1. However, their analysis like that of Masters and Stein was only concerned with the deviation of the temperature
in the axial cavity and did not address the error in measured heat flux.
4.3 Howey and DiCristina (3) were the first to perform an actual thermal analysis of this measurement concept. Although the
explanation of modeling techniques is somewhat ambiguous in their paper, it is obvious that they used a finite element, two
dimensional axisymmetric model to produce temperature profiles in a geometry simulating the null-point calorimeter. Temperature
histories at time intervals down to 0.010 sec were obtained for a high heat-flux level on the surface of the analytical model.
Although the analytical results are not presented in a format which would help the user/designer optimize the sensor design, the
authors did make significant general conclusions about null point calorimeters. These include: (1) “., thermocouple outputs can
yield deceivingly fast response rates and erroneously high heating rates ( + 18 %) when misused in inverse one-dimensional
conduction solutions.” (2) “The prime reason for holding the thermocouple depth at R/E = 1.1 is to maximize thermocouple
response at high heating rates for the minimum cavity depth.” (Note: R and E as used by Howey and DeChristina are the same
terms as a and b which are defined in 4.1 and are used throughout this document.) (3) A finite length null-point calorimeter body
may be considered semi-infinite for:
αt
~ !
# 0.3
L
4.4 Powars, Kennedy, and Rindal (4 and 5) were the first to document using null point calorimeters in the swept mode. This
method which is now used in almost all arc facilities has the advantages of (1) measuring the radial distributions across the arc
jet, and (2) preserving the probe/sensor structural integrity for repeated measurements. This technique involves sweeping the
probe/sensor through the arc-heated flow field at a rate slow enough to allow the sensor to make accurate measurements, yet fast
enough to prevent model ablation.
4.4.1 Following the pattern of Howey and DiCristina, Powars et. al. stressed the importance of performing thermal analyses to
“characterize the response of a typical real null point calorimeter to individually assess a variety of potential errors, .”. Powars
et. al. complain that Howey & DiCristina “. report substantial errors in some cases, but present no generalized results or design
guide lines.” They state concerning the analyses performed to support their own documentation, “In order to establish guidelines
for null point calorimeter design and data reduction, analyses were performed to individually assess the measurement errors
associated with a variety of non-ideal aspects of actual calorimeters.” The conclusions reached from the results of the thermal
analyses were broken down into eight sub headings and were discussed individually. Some of the conclusions reached were rather
elementary and were previously reported in Refs (1-3). Others were somewhat arbitrary and were stated without substantiating
data. One specific conclusion concerns the ratio of the null-point cavity radius, a, to the cavity thickness, b. While stating that the
optimum condition occurred when a = b, the authors of Ref (4) further state that when a = 0.305 mm (0.012 in.) and b = 0.127
mm (0.005 in.); a/b = 2.4, the calculated heat flux will be 20 % higher than the actual heat flux. In more recent documentation
using more accurate and sophisticated heat conduction computer codes as well as an established numerical inverse heat conduction
equation (6), the error in indicated heat flux is shown to be considerably higher than 20 % and is highly time dependent.
4.5 The latest and most comprehensive thermal analysis of the null-point calorimeter concept was performed by Kidd and
documented in Refs (6 and 7). This analytical work was accomplished by using a finite element axisymmetric heat conduction code
(7). The finite element model simulating the null-point calorimeter system is comprised of 793 finite elements and 879 nodal points
and is shown in block diagram form in Fig. 2. Timewise results of normalized heat flux for different physical dimensional
parameters (ratios of a to b) are graphically illustrated on Figs. 3 and 4. The optimum value of the ratio a/b is defined to be that
number which yields the fastest time response to a step heat-flux input and maintains a constant value of indicated q˙/input q˙ after
the initial time response period. From Figs. 3 and 4, it can be seen that this optimum value is about 1.4 for two families of curves
for which the cavity radius, a, is held constant while the cavity thickness, b, is varied to span a wide range of the ratio a/b. This
is a slightly higher value than reported by earlier analysts. It is important to note that the analytical results do not necessarily have
to give a value of indicated q˙/input q˙ = 1.0 since this difference can be calibrated in the laboratory. The data graphically illustrated
on Figs. 3 and 4 and substantiate conclusions drawn by the authors of Refs (3 nd 4) that the calculated heat flux can be considerably
higher than the actual input heat flux—especially as the ratio of a/b is raised consistently above 1.5. All of the users of null-point
calorimeters assume that the device simulates a semi-infinite body in the time period of interest. Therefore, the sensor is subject
1/2
to the finite body length, L, defined by L/(αt) ≤ 1.8 in order that the error in indicated heat flux does not exceed one percent (6
and 7). This restriction agrees well with the earlier work of Howey and DiCristina (3).
4.6 A section view sketch of a typical null-point calorimeter showing all important components and the physical configuration
of the sensor is shown in Fig. 5. The outside diameter is 2.36 mm (0.093 in.), the length is 10.2 mm (0.40 in.), and the body material
is oxygen-free high conductivity (OFHC) copper. Temperature at the null point is measured by a 0.508 mm (0.020 in.) diam
American National Standards Association (ANSI) type K stainless steel-sheathed thermocouple with 0.102 mm (0.004 in.) diam
thermoelements. Although no thermocouple attachment is shown, it is assumed that the individual thermocouple wires are in
perfect contact with the backside of the cavity and present no added thermal mass to the system. Details of installing thermocouples
in the null point cavity and making a proper attachment of the thermocouple with the copper slug are generally considered to be
proprietary by the sensor manufacturers. Kidd in Ref (7) states that the attachment is made by thermal fusion without the addition
of foreign materials. Note that the null-point body has a small flange at the front and back which creates an effective dead air space
E598 − 08 (2015)
FIG. 2 Finite Element Model of Null-Point Calorimeter
FIG. 3 Null-Point Calorimeter Analytical Time Response Data
along the length of the cylinder to enhance one-dimensional heat conduction and prevent radial conduction. For aerodynamic
heat-transfer measurements, the null-point sensors are generally pressed into the stagnation position of a sphere cone model of the
same material (OFHC copper).
E598 − 08 (2015)
FIG. 4 Null-Point Calorimeter Analy
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.