1.4 1.3 1.2
.9 .8 .7 .6 .5
.I
M (x)
-44- 1. 10 in. 2
ln both cases the exit area/throat area ratios are almost the same (1. 093 and 1. 10).
3. 4 Thermal Pulse Heater
3. 4. 1 The alternatives. The most critical point in the evolu- tion of the experiment was the development of a device which would
produce ten1.perature fluctuations in the gas flow at a specified frc- quency and a detectable amplitude. This device also had to meet the requirement that it would not produce noise or auxiliary signals that would interfere with the correct operation of the instrumentation.
Also, it must not be excessively costly or hazardous, and should be such that it could be coupled with a gas bleed or expansion device that would cancel the pressure caused by the heating action, thus resulting in the production of a pure entropy wave.
The following schemes '..Vere considered: (i) spark gap heater, (ii) resistance wire heater, (iii) chemical heater, (iv) laser device.
Scheme (iv) was completely out of the question since the laser output needed would be of the order of a megawatt because of poor energy transfer characteristics from the laser light to the gas. }vioreover, the laser would be prohibitively costly.
Scheme (iii) was unfeasible because a controlled high-fre- quency combustion process was judged to be unattainable. Scheme
(i) had two drawbacks, the first being that it would require a huge bank of high-voltage capacitors (making it economically unfeasible);
the second and prime prohibitive factor, however, would be that the electrical noise and gas ionization produced would most probably
nullify proper operation of instrmnentation such as hot wire anemorr:e- ters, cold wire resistance thern101neter s, and piezoelectric trans- ducers.
The electrical resistance heater appeared to be the most promising alternative, and it was selected for development. It would not be prohibitively costly to build, it would not produce electrical noise that would saturate electronic instrumentation, nor would it need hazardous power sources such as kilovolt power sup plies. How- ever, the one drawback of the resistance heater is its gross ineffi- ciency,which will be explained below.
3. 4. 2 Heater design and performance. The heater was mod- elled by an array of current-carrying wires immersed in a gas flow.
To produce a temperature fluctuation in the wires, a periodic rec- tangular voltage waveform was impressed upon the wires. A rectan- gular voltage waveform \vas selected because of the relatively simple design required for the high power pulse generator needed to pro- duce this voltage.
The differential equation governing the wire temper atLue is:
dT w
cw err- =
I ( 2 t )R 1 -h A1 ( T - T )
c w co
where T = wire temperature w
T00
=
gas free stream temperature I(t)=
wire currentR1
=
wire resistance A1=
wire surface area C=
heat capacity of wirew
( 3. 7)
-46-
h - heat transfer coefficient of wire, evaluated at mean fihn c
temperature
This equation is considered in detail in Appendix C and is solved for the case of a rectangular power wave of period T and duty cycle
0
a.1 T 0
• It is then found that the maximum wire temperature fluctua- tion for a given power input occurs for
o.
1
=
~. Then an array of parallel wires is considered with total heat transfer area AT in a gas mass flow ofm .
The end result of the calculation is that the ratio0
of the temperature fluctuation in the gas,
T ,
and the average wire gtemperature rise, T -T , is given as a function of the square wave w 00
period,
where
T·
o·T -T w 00
c p
=
=
aH/2
2e }
e ~ -1
specific heat at constant pressure T
~
=
C 0 /h A.w c 1
( 3. 8)
To illustrate the behavior of equation (3. 8), numerical values for the actual heater in the experiment will be used. The heater de- sign is a compromise between size, electrical power requirements, and durability.
A diagram showing the construction of the thermal pulse heat- er is given m fig. 3. 13. The heater consists of 15 banks of 25 paral- lei strands of. 004-inch diameter 80-20 nichrome wire. The strands
Typical Heater Bank (Actual Size)
+
Terminal 1/16" Diam. Brass Rod 25 Nichrome Wires .004" Diameter 1/8" Thick Phenolic Strip...
2 1/8" Pulse Heater Assembly 15 Banks Spaced .005" ApartFig. 3.13 Thermal Pulse Heater Construction
...,.
-48-
are soldered at each end to a 1/ 16-inch diameter brass rod. The rods are spaced 2 3/4 inches apart and mounted on 1/8-inch thick phenolic strips. The strips are spaced. 005 in. apart using brass shirn
spacers. The small gaps formed by the shims are used for the bleed compensation system, to be described later. The banks are connected electrically in series.
Numerical values for use in equation (3. 8) are based on . 004 in.
wire diameter, 2. 7 5 in. wire length, a gas flow of l. 04 lbin/ sec at M
=
0. 2 with flow properties evaluated at 64°F and 3 atm pressure.Two iterations were made to determine mean film temperature and wire temperature. The results of the calculations are shown in figs.
3. 14, 3. 15, and 3. 16.
Figure 3. 14 shows
(T -
T )/T
as a function of square wave w 00 gfrequency. This graph immediately reveals the gross inefficiency of the heater: for frequencies at and above 400Hz, the wire t:empera- ture must be hundreds of degrees centigrade just to produce a l °C temperature fluctuation in the gas. Figure 3. 15 presents this concept in a more quantitative display. Note that as a gas temperature fluctu- ation of 5°C is required, the nichrome is pushed towards its melting temperature. Another point to be considered is the electrical power requirement. The combined wire resistance of the heater is 5 oluns.
If V is the square wave voltage, the average wire temperature T w is related to V by:
hA(T -T )
w 00 (3. 9)
A plot of this relationship for the heater designed for the experiment is given in fig. 3. 16. Note that 275 volts produces a Tw of 280°F.
800
tOO
~00
200
0
200
eoo
FREQUENCY CH~)
Fig. 3.14 Wire Heater Temperature-Frequency Response Function
1000 F
2400
1600
1200
800
400
-50-
~00
Design Operating Point at 400 HZ
00 1000
F
FREQUENCY (Hi!)
Fig. 3.15 Heater Wire Average Temperatures Required to Produce Gas Temperature Fluctuations of Various Amplitudes and Frequencies
~00
250
200
ISO
too
50
100 200 ~00
EXPERIMENT OPEF'<.A1"1NG POINT