The objective of this effort was to experimentally verify a dynamic gas temperature measurement system in laboratory experiments. The dynamic gas temperature measurement system verification program is described. A brief description of the sensor geometry and construction is followed by a discussion of the probe heat transfer analysis and subsequent compensation method. The laboratory experiments are described and experimental results are discussed. Finally, directions for further investigation are given

Elmore, D. L.

Robinson, W. W.

Watkins, W. B.

English

NASA Technical Reports Server

N89--1288 4,
FURTHER DEVELOPMENT OF THE
DYNAMIC GAS TEMPERATURE MEASUREMENTSYSTEM*
D. L. Elmore, W. W. Robinson, W. B. Watkins
Pratt & Whitney Engineering Division
INTRODUCTION
The objective of this effort was to experimentally verify a dynamic gas
temperature measurement system in laboratory experiments. In previous work
(Ref. I) a measurement system was developed for gas turbine combustor exhausts,
with special emphasis placed on dynamic response to enable determination of
fluctuating components. The measurement probe was demonstrated to have greater
than one hour life in a jet engine combustor, and very long (>5 hours) life in
an atmospheric burner. Under the current program the measurement and
compensation methods were verified by comparing the results obtained by the
compensated dynamic sensors with those of a fine-wire resistance thermometer of
intrinsically high frequency response. Two signal sources were used: I) a
rotating wheel which alternately directed hot and cold gas streams at the
sensors and 2) an atmospheric pressure kerosene/air burner. A commercially
available optical fiber thermometer was tested for dynamic response in the
burner experiment.
The following sections describe the dynamic gas temperature measurement
system verification program. A brief descriptio_ of the sensor geometry and
construction is followed by a discussion of the probe heat transfer analysis
and subsequent compensation method. The laboratory experiments are described
and experimental results are discussed. Finally, directions for further
investigation are given.
PROBE DESCRIPTION
The dynamic temperature probe concept is shown in Figure 1. The probe
employs two thermocouples of different wire diameters positioned in close
proximity. The thermoelements are large enough in diameter that frequency
response above a few Hertz is limited by thermal inertia. When the
thermocouples are exposed to the same instantaneous temperature and velocity in
the gas stream, the difference in thermal responses will be governed by
convective effects (proportional to wire diameter) and conductive effects
(proportiona) to specific heat, thermal conductivity and wire length). Many
previous studies (Refs. 2 and 3) used thermoelements of sufficiently large
(_I00) length-to-diameter ratio that conduction effects may be neglected, and
compensations were based on first-order convective time constants. The present
sensor, however, is designed for engine hot-section applications, and the
*Work pecformed under NASA Contract NAS3-24228
51
https://ntrs.nasa.gov/search.jsp?R=19890003513 2020-03-20T04:37:04+00:00Z
4smaller le_gth-_o-_iameter ratios required for structural adequacy necessitates
inclusion of transient conduction effects in the compensation method.
A novel feature of each thermocouple is the beadless, butt-welded
thermoelement. The beadless construction allows the sensor to be modelled as a
cylinder in crossflow, which simplifies the model considerably. ISA type B
(Pt/6Rh - Pt/3ORh) thermocouples were used for the burner tests and type K
(chromel-alumel) thermocouples were used for the rotating wheel tests.
PROBE THERMAL ANALYSIS AND COMPENSATION METHOD
The energy conservation equation describing convective and conductive heat
transfer to the thermocouples is
dTw _ 4hq d2Tw (1)
dt PwCpwd (Tg - Tw) + _
The thermoelement and support wires were modelled with the nodal breakup shown
in Figure 2, and equation (i) is implemented in this model in finite difference
form to describe the temperature versus time history of the wire. Material
properties for the two t/c legs are averaged in these calculations. To
determine the thermocouple response to a given gas stream frequency component,
a sinusoidal temperature variation a(t) is used as a boundary condition on the
nodes exposed to the gas stream, and several cycles of gas stream temperature
are iterated. The true dynamic response of the wire is obtained when peak
response amplitudes change less than 0.1% from one-half-cycle to the next.
Comparisons between parametric modelling and experimental data are
required in the compensation scheme to determine an in situ value of hg and the
resulting compensation spectrum. This method is described as follows. Let the
calculated thermocouple and gas stream temperature dynamic amplitudes be
denoted by 0i (f) and a(f), respectively, where i = I for the smaller
thermocouple and i = 2 for the larger thermocouple. Gas stream signal a(t) is
used as a boundary condition for nodes 0-9 and wire temperatures Oi (t) are
calculated at discrete frequencies fn, over a practical frequency bandwidth
(usually 4 to 30 Hz). At each frequency fn signal amplitude ratio is
determined:
Oi(fn)/a(fn) (2)
Note that _(fn)/a(fn) forms a portion of the linear compensation spectrum in
the practical bandwidth; this spectrum may be extended to cover the bandwidth
of interest. Calculations are repeated for several values of the aerodynamic
parameter (Figure 3a)
0.48K9 Prl/3 u_I/2_ (3)
F- (_)½ Pw Cpw
which provides aerodynamic scaling between the two different diameter
thermocouples (Ref. 1). Note that F is proportional to an Hilpert equation
(Ref. 4) form of heat transfer coefficient hg for a cylinder in crossflow:
52
PwCpw F = 0.48K 9 prl/3 Re1/2 (4)
hg - d_ d
Variation of F, therefore, corresponds to a variation in hq. At constant
values of F the ratio of the small and large diameter thermocoOple responses
at given frequencies yields a calculated transfer function Hc (fn) (Figure 3b).
Hc(fn) = _2(fn)/81(fn) (5)
The experimental portion of the compensation method includes recording of
the two-wire probe signals, digitizing and converting to temperature using
appropriate calibration curves. Temperature versus time waveforms 8i, E(t) are
Fourier transformed to yield 8i, E(f) and division of 82 by 81 yields an
experimental transfer function HE (f). Experimental and theoretical transfer
functions are compared; where the two match at the discrete frequencies in the
practical frequency bandwidth, experimental F's are then averaged, the
calculated 82(f)/ 81(f) associated with the average F is identified, thereby
identifying the calculated 81(f)/a(f), the compensation spectrum gain, and
_(f), the compensation spectrum phase, for the smaller thermocouple. The
calculated compensation spectrum is used over the bandwidth of interest (0-i
KHz). The compensated gas stream temperature spectrum is calculated by
dividing the experimentally-measured frequency spectrum by the calculated
thermocouple compensation spectrum.
a(f) = 8i,E(f)/(Si(f)/a(f))c (6)
These concepts have been reduced to practice in dynamic temperature sensor
compensation software. Fortran coding is used and the program is operational
on IBM computers with execution time of about 4 minutes per case.
EXPERIMENT
The rotating wheel experiment is shown in Figure 4. A drive assembly
consisting of electric motor and shaft was used to rotate a wheel plate which
had 8 holes on a 20.32 cm (8 inch) bolt circle diameter. Heated and ambient
temperature air was supplied to two tubes mounted close together on one side of
the rotating wheel and in-line with the holes' bolt circle diameter. As the
wheel rotated the holes passed the two air supply tubes and allowed hot and
cold air pulses to flow. A bifurcated manifold was placed on the opposite side
of the rotating wheel in-line with the supply tubes to collect the hot
(568K(563F)) and cold (289K(60F)) pulses and feed them into a transition
section which became a single circular tube. Hot and cold air pulses were
thereby delivered to the sensors mounted immediately downstream of the single
circular tube. The wheel was rotated to produce a 250 Hz narrowband signal.
Chromel-alumel thermocouples were used in the dynamic temperature sensor, and
an analog-compensated 6.4Mm (.00025 inch) diameter fine wire resistance
thermometer was used as reference sensor.
An atmospheric pressure combustor with flowfield containing large
amplitude (several hundred degrees) temperature fluctuations was used as source
in the second experiment (Figure 5). An 1159K (1626F) mean temperature test
point compared dynamic temperature sensors, a fine wire (12.7_m(.0005 in.)
diameter) resistance thermometer and compensated optical fiber thermometer
responses in the 0-I KHZ bandwidth. An 1655K (2519F) mean temperature point
53
compareddynamic temperature sensor and optical fiber thermometer responses in
the samebandwidth. ISA type B thermocouples were used in the dynamic
temperature sensor.
RESULTS
A 20 Hz rotating wheel test point was used to derive the F for the 250 Hz
test point compensation. Compensated6.4Mm (.00025 inch) resistance
thermometer and 76_m (.003 inch) thermocouple spectra are shownin Figure 6.
Compensatedtime-domain waveshapesare comparedin Figure 7. The 76_m
thermocouple has been compensatedapproximately 28db at the fundamental
frequency; the resistance thermometer, however, required O.9db of compensation
due to its inherently higher response.
Figure 8 comparescompensated76_m (3 mil) and 127Mm (5 mil)
thermocouples and 12.7Mm (.0005 mil) resistance thermometer spectra for the
atmospheric burner 1159K(1626F) test point. The compensatedthermocouples
differ by 10%or less over the 0-1 KHzbandwidth, whereas the 12.7_m
resistance thermometer is between37 and 56%lower than the 127_m
thermocouple. The amplitude spectrum of the resistance thermometer is shownin
Figure 9. Note that a difference of 56%at I KHzbetween the compensated127Mm
t/c and 12.7Mm resistance thermometer represents about 1.5K/_.
Figure 10 is the transfer function between the uncompensatedoptical fiber
thermometer and the compensated76_m thermocouple for the 1159K(1626F) test
point. Figure 11 showsthe percentage difference of line amplitudes between
the compensatedoptical fiber thermometer and compensated76Mm (3 mil)
thermocouple. Qualitatively similar results were obtained in a second burner
test at 1655K(2519F) as shownin Figures 12 and 13.
CONCLUDING REMARKS
The dynamic gas temperature measurement system offers measurement
capabilities previously unavailable for gas turbine engines. Structural
adequacy of the probes demonstrated in previous work is now more meaningful in
combination with measurement fidelity verification. The method can potentially
be adapted to transient engine acceleration combustor exit temperature
measurements, associated blade and vane cooling flow temperature measurements
during transients, as well as used for measurement of steady-state engine
dynamic gas temperature signals.
Directions for further work in this measurement technique include
fine-tuning and optimization of the basic method as well as extending the work
to investigate some fundamental aspects of heat transfer.
i° Measurement uncertainty contribution, both precision and bias, should be
determined for each source in the experiment and compensation method,
including the fine-wire thermometer standard. The need is to optimize
thermoelement diameter ratio and frequency range for determining r, and
to improve the experimental setup and other factors to minimize
uncertainty in the compensated gas stream measurement. Such an
uncertainty analysis would involve propagation of uncertainties for
$4
.1
.
time-dependent quantities, and would require combining uncertainties in
both time and frequency domains.
The finite-difference model should be extended to include material
properties for both halves of the thermoelement. Use of average
properties simplifies the model with compromise to uncertainty in the
compensation method. The average properties versus individual properties
change would determine the corresponding measurement uncertainty
contribution, and allow cost versus complexity trade-offs to be made for
the compensation scheme.
The variation of r with frequency should be investigated. The F values
used in this work were averaged over the practical working bandwidth.
Investigation of frequency dependent F effects were beyond the scope of
this work.
Values of hg implicit in r should be determined explicitly according to
equation (4). The measurement technique developed here offers a novel
possibility for measuring hg for a cylinder in crossflow in a combustion
stream.
a _-
Cp =
d =
D =
f =
H(f) =
h =
K =
M =
p :
Pr =
Re =
T =
t =
U =
X
=
LIST OF SYMBOLS
gas stream temperature amplitude at frequency f
heat capacity
thermocouple element diameter
thermocouple support wire diameter
frequency
transfer function
convective heat transfer coefficient
thermal conductivity
Mach number
gas pressure
Prandtl number = CPK_Z
Reynolds number
Temperature
time
velocity
wire length coordinate
thermal diffusivity = PCp
aerodynamic parameter defined in Equation (3)
viscosity
phase shift of thermocouple response with respect to gas temperature
at frequency f
densit)
thermocouple response
55
C
E
i
n
T
W
g
Subscripts
calculated
experimental
I, 2 denoting smaller and larger thermocouples, respectively
frequency index
theoretical; total gas properties
wire
gas
lo
J
1
.
REFERENCES
Elmore, D. L., Robinson, W. W., and Watkins, W. B., "Dynamic Gas
Temperature Measurement System," NASA CR-168267, Final Report for NASA
Contract NAS3-23154. See also ISA Transactions 2__44,No. 2, pp. 73-82.
Dils, R. R., and Follansbee, P. S., "Wide Bandwidth Gas Temperature
Measurements in Combustor and Combustor Exhaust Gases," Instrumentation in
the Aerospace Industry, Vol. 22, Proceedings of the 22nd International
Instrumentation Symposium, San Diego, Calif., 1976, pp. 307-328.
Yule, A. J., Taylor, D. S., and Chigier, B. A., "On-line Digital
Compensation and Processing of Thermocouple Signals for Temperature
Measurement in Turbulent Flames," AIAA 16th Aerospace Sciences Meeting,
16-18 January 1978, Paper No. 78-3.
Eckert, E. R. G., and Drake, R. M., Heat and Mass Transfer, 2nd Edition,
1959, McGraw-Hill, New York, p. 242.
56
/-Laser butt weld
76 I_m Type B-_ / (no bead)
254 t_m Type B
v,ew  i 
Alumina Itl
View C probe body --'/l_ I
@
Sec B-B
.2.3.41Tri.8,1#.mrs, /, )
/ IXt I
IL._ ,_ '_'- j_T_x)O_
Fig. 1 Dynamic Temperature Sensor
Concept
Fig. 2 Nine-Node Finite Difference
Model
ei
8
f(Hz)
ml_ /-r_
4 30 f(Hz)
Fig. 3A Parametric Calculation Of
@i(f)/a(f)
Fig. 3B Ratio @2/g I For Several Values
Of r
57
ORIGINAL. PAGE IS
OF POOR QUALITY
Fig. 4 Rotating Wheel Experiment @ Fig. 5 Atmospheric Pressure Burner
Experiment
Decibels - 10.00
30.00 --
i 23%
2_oo i/"3°° 0 28% /"-76_m
10,00
,I ] , _ /
-30.00 -- '_'L._
6.4 pm resistance
thermometer
- 50oo I I 1 1 I
000 4000 80.00 120.00 16000 200.00
Frequency (Hz) , 101
thermocouple
15000
,,o0 2
Dynamic
temperature 0.00
(K)
-75.00
15000
0000 0003
64 tJm res=stance
thermometer --_
76pro thermocouple J
= ; ', !
0006 0009 0012 0.015
Time (se_l
Fig. 6 Rotating Wheel Experiment
Compensated 76_m And 6.4Hm
Sensor Power Spectral Densities
Fig. 7 Rotating Wheel Experiment
Compensated 76_m And 6.4_m
Sensor Wave-Forms
58
30.00 37% 100 Hz
i6% 200 Hz
[_I 7% 1 kHz
_ 10% 56% o
400 Hz _"_'_L
400 Hz I ' ....
0.00 - ,,_'_,'_127 pm (5rail)
12 7 IJmresistancethermometer}_, "v_t_476 pM (3rail)
-10.00 I I I Ir_ I
0 400 800 1200 1600 2000
Frequency(Hz)
Temperature
RMS K/SQRT (Hz)
20
15
10
0 400 800 1200 1600
Frequency (Hz)
I
20OO
Fig. 8 Atmosphereric Pressure Burner
Compensated Thermocouples And
Resistance Thermometer Power
Spectral Densities
Fig. 9 Resistance Thermometer Linear
Spectrum
-10
-20
Gain -30
(dB) -40
-50
-- .. /-- _ -6 dB/octave
'_,_ /--_ 12Hz
_ f-- - -3 dB/octave
/--- _ 150 Hz
- _6 dB/octave
( _ PSD OFT
Gain = 20 log 10 \j-pS_ c-o-om-_/C )
I I I
10 100 1000
Frequency (Hz)
200 --
150 --
Difference
(% of 100 --
reading)
50--
0
Temperature 20 [-K RMS/ \,'_z 0
1
10 100 1000
Frequency
10 100 1000
Frequency(Hz)
Fig. 10 Transfer Function Between
Uncompensated Optical Fiber
Thermometer And Compensated
76_m Thermocouple (II59K(1626°F)
Test Point)
Fig. ii Differences Between Optical
Fiber Thermometer And 7E_m
Thermocouple Amplitudes (1159K
(1626°F) Test Point)
59
-10
-20
-30
Gain
(dB) -40
-50
-60
- _,/- _ -6 riB/octave
- - -3 riB/octave -j' _ //'-
Gain 20tog ,0i_s_PZS_/c _
I
10 100 1000
Frequency (Hz)
-6 dB/octave
1ooI-
Difference(%of 500f-reading)
-50
1
Temperature 20
K RMS/k/'Hz O[
1
10 I O0 1000
10 100 1000
Frequency (Hz)
Fig. 12 Transfer Function Between
Uncompensated Optical Fiber
Thermometer and Compensated
76pmThermocouple (1655K(2519°F)
Test Point)
Fig. 13 Differences Between Optical
Fiber Thermometer and 76_m
Thermocouple Amplitudes
(1655K(2519°F) Test Point)
6O


Further development of the dynamic gas temperature measurement system

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