A pulse shaper for the Natick Laboratories solar furnace

Solar£atrlFy,Vol. 12,pP. g5-94. PergamonPress, 196g. PrintedinGreat Britain

A PULSE SHAPER FOR THE NATICK LABORATORIES SOLAR F U R N A C E F R E D E R I C G. P E N N I M A N , ROBERT J. G O F F and J O H N M. DAVIES*

(Received 14 March 1968) Abstract- A pulse shaper has been constructed which will produce the standard nuclear weapon pulse shape in the Natick Laboratories solar furnace. An array of 16 radial vanes, each about l i f t long. is placed in the converging beam about 40 in. in front of the focus. These vanes, driven at variable speed by a specially constructed cam, control the irradiance at the target. The device operates successfully to produce pulses corresponding to the range of weapons from 25 KT to the megaton range. Over this range of speeds there is some variation in shape, especially near the peak; the difficulty arises because of the very high accelerations needed to produce this shape. Also, at long times after the peak the shape deviates from the standard, giving an exposure of about 1.9 Hat, instead of the desired 2.12 Hmtm where Hm is the maximum irradiance and t~ the time to reach that irradiance. R ~ u m ~ - Un conformateur d'impulsions a 6t6 construit pour produire la conformation d'impolsions standard d'une arme nucl6aire clans le four solaire des Laboratoires Natick. Une rang6¢ de 16 vannes radiales, de 457 mm de long chacune, est pla¢~ dans le falsceau convergent/~ environ 1016mm en face du foyer. Ces vannes, entrain6cs h vitesse variable par un arbr¢ i~cames de construction sp6ciale, rb.glent I'irradiation sur la cible. Le dispositif fonctionne parfaltement pour produire des impulsions correspondant/l la s6rie d'armes de 25 kilotonnes au rn6gaton. Pour des vitesses sup6rieurcs, il se produit des variations de forme Sl~cialement pr6s de la cr6te, la dil~cult6 provenant des acc616rations trb.s 61ev6es n6cessaires pour produire cette forme. Sur de longues l~riodes apr6s la cr/~t¢, la forme s'61oigne aussi du standard, donnant une exposition d'environ ! ,9 H . t . au lieu de la valeur d6sir6e de 2,12 H . t . , expression dans laquelle Hm indique la radiance maximale e t t . le temps n6cessalre pour atteindre cette radiance. Resumen-Se ha construido un conformador de impulsos que producir~i, en el horno solar instalado en los Laboratorios Natick, la forma de impulso standard correspondiente a armas nucleares. Un conjunto de 16 filabes radiales, cada uno de aproximadamente 1½ pies de Iongitud, es colocado en el haz convergente, aproximadamente 40 pulgadas enfrente del foco. Estos ~labes, impulsados a velocidad variable por una leva de construcci6n especial, regulan la irradiaci6n en el blanco. El dispositivo funciona eficazmente, produciendo impulsos que corresponden a la serie de armas desde 25 kilotones hasta el megat6n. Con capacidades mayores se produce alguna variaci6n de forma, especialmente cerca de la cresta, problema 6ste que se debe a las aceleraciones sumamente elevadas necesarias para producir dicha forma. Asimismo, di~rante plazos largos despu6s de la creast, la forma difiere de io standard, dando una exposici6n de 1,9 Hmtm en iugar misma.

THE NATICK solar furnace[l, 2] was built to simulate the thermal effects of nuclear weapons in order to evaluate the performance of protective clothing and other equipment used by the Army. A schematic diagram of the furnace is shown in Fig. 1. The attenuator, C, controls the steady flux at the focus, and can be adjusted to simulate the effect of distance from the explosion. Simulating the effect of weapon size is more complicated, as discussed below. The exposure times are short, from less than a second to several seconds. Essentially rectangular pulses of this range of duration are produced by shutters, F, G and H; the heavy, water-cooled shutter, F, opens relatively slowly: then the exposure shutter, H, opens to expose the sample and, finally, the limit shutter, G, closes to end the exposure. The pulse shaper to be described, E, produces a continually repeating series of pulses of the desired shape. A single pulse is selected by using shutters G and H in combination with E. *Pioneering Research Laboratory, U.S. Army Natick Laboratories, Natick, Massachusetts O1760, U.S.A. 85

86

F.G. PENNIMAN, R. J. GOFF and J. M. DAVIES

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Fig. I. The solar furnace (not to scale).

,4. B. C. D.

Heliostat Concentrator Attenuator Test chamber

E. F. G. H.

Pulse shaper Water-cooled shutter Limit shutter Exposure shutter

i. Recorders J. Timers K. Monitor

Glasstone [3] indicated that for reasonable weapon sizes, the thermal pulses from all weapons are similar in shape and except for a very short initial pulse which accounts for less than 2 per cent of the total energy, can be represented by the standard pulse shown in Fig. 2. It consists of a very rapid rise and a much slower decline. If the response of a target material depends on the irradiance, then the effects will undoubtedly

1.00

.75

H/Hm ..50

.25

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t/tin

Fig. 2. Normalized thermal pulse from Glasstone.

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A pulse shaper for the N atick Laboratories solar furnace

87

depend on the shape of the pulse. Many attempts have been made to correlate the results obtained with rectangular and shaped pulses. For example, Chen and Jensen [4], in the Fuels Research Laboratory at Massachusetts Institute of Technology, by a combination of calculation and measurement, obtained the temperature rise history in a skin simulant protected by a thin, inert protective layer. With their results, the temperature rise history due to any pulse shape could be calculated, and attempts [5] were made to find a rectangular pulse that would give the same time-temperature curve as the standard pulse. None could be found. Also, the temperature rise in an ideal, inert, opaque, semi-infinite solid was calculated for a shaped pulse [6]. Again, a rectangular pulse that would produce the same temperature rise relation could not be found. McQue[7] exposed a skin simulant protected with various reactive fabric layers to the beam of a high current carbon arc, using both rectangular and shaped pulses. Apparently with reactive materials, when a significant amount of heat is generated by combustion, the shape of the radiation pulse is not as important as with inert materials. For certain conditions, a rectangular pulse could be found that gave approximately the same temperature rise curve as given by a shaped pulse. However, the duration and energy of the rectangular pulse depended on the characteristics of the material and a satisfactory method could not be found for predetermining those characteristics. Obviously, for satisfactory simulation of nuclear weapon effects in this type of experiment. a method of producing the required pulse shape at the furnace is essential. CHARACTERISTICS OF THE STANDARD PULSE Glasstone[3] indicated some useful relations between the yield, W, of the nuclear weapon, the power, P, and the time. The time, tin. to reach maximum power, P.,. and likewise maximum irradiance, H,,,, at any distance, is given by t,,, = 0.032 W 1/2

(l)

P,, = 4 W 112

(2)

where W is in kilotons and t in seconds. The total thermal energy, Wth, is one-third the total energy, Wth = W/3.

(3)

The standard pulse is defined only for 0 < t < 10 t,,,; for that interval the exposure, Q, is given by Q

=

faOtmH dt = ttmtm f,o (HIHm) d(t/tm) = 2.12 Hmtm 0

o

(4)

where Q is the exposure in calories cm -z and H is the irradiance in cal cm -2 sec -1. The factor 2.12 is obtained by evaluating the integral numerically. The total thermal energy is given by W/3 = f o P dt = Pmtm f f P[Pm d(t/tm)

= 4 W'/2 (0"032)W '/2 _ff P/P,, d(t/t,,) =0"128 W

,, P/Pmd(t/tm)

(5)

88

since P/P,. and

F.G. PENNIMAN, R. J. GOFF and J. M. DAVIES

H/H,.,

f ~ P / P , , d(t/t,.) = 2.60

(6)

f~. H / H , , d(t/tm) -- 2.60

(7)

Q,o,.,

= J , H dt = 2"60 Hmtm .

(8)

Only about 81 per cent of the total e x p o s u r e is attained in the interval up to 10 tin; this is shown on G i a s s t o n e ' s curve of exposure vs. time. T h e rest of the pulse can probably be a p p r o x i m a t e d rather well theoretically but it is difficult to duplicate the "tail" in the laboratory and so far attempts have been limited to the interval 0
(9)

This is a fairly accurate representation near t -- 0 and t -- t,, but it deviates by about 12 per cent near t = tin~2. F r o m Eq. (9)

dH/dt ~ (H,./2) (rr/tm) sin (rrt/t,.) and

d2H/dt " = (H,./2) (rr/t,.) 2 cos (rrt/t,.).

(10)

T h e second derivative varies rapidly, changing from - 5 Hm/tm 2 at t -- 0, to 0 at t -t,./2 and then to - - 5 H,,Jt,, 2 at t = t m ; it b e c o m e s much smaller at longer times.

DESIGN AND OPERATION OF THE PULSE SHAPER The main requirement for a pulse shaper is to control the irradiance at the focus to produce a thermal pulse similar to Fig. 2 for any desired weapon size. Its shadow should not reduce the maximum irradiance excessively; it should not distort the image at the focus, and all points at the center of the sample area should be irradiated uniformly in time. T h e shaper must operate at the high temperatures within the beam without distortion or variation. A pulse shaper, designed by Lynch [8], had been installed at the furnace some time ago. It consisted of 16 radial vanes powered by a 1½h.p. motor through a variable speed transmission which turned a specially shaped cam. The cam follower moved a rack and pinion which controlled the master vane. T h e schematic of this unit is shown in Fig. 3. The vanes and gears, taken from a signaling searchlight because they were readily available at that time, were not sufficiently rugged for this use. Measurements indicated that after considerable use and wear the shape was not very satisfactory. At the same time, the motion of the existing system was studied using high-speed movies showing the action of the cam, cam follower, pinion and vanes at high and low speeds. A motion analyzer showed that the main sources of the trouble were in the vanes and gear box and that the rest of the system operated properly. Since the other systems considered possessed undesirable features, it was decided

A pulse shaper for the Natick Laboratories solar furnace .

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Fig. 3. Schematic diagram of pulse shaper. Motor E. Vanes Variable speed transmission F. Gear box Cam and follower G. Water-cooled shutter Rack and pinion H. Exposure shutter

i. J. K. L. M.

Limit shutter Microswitch Delay timer Pulse timer Starting switch

to install a new gear box and vanes on the old system. Instead of aluminum, stainless steel was used and the gears were specially made to operate in a new gear box. T h e vanes are about 17] in. long, 8¼ in. wide at the outer edge, tapering to about 1 in. wide at the central gear box and overlap about ¼in. along the edge; the central gear box is about 6 in. in dia. T h e vanes are held in a 42½ in, dia. ring mounted vertically about 40 in. in front of the focal point. At that plane, the concentrated beam has a nearly circular hole 8 in. in dia., leaving the gear box in the shadow caused by the test chamber. T h e outer edge of the beam is nearly square and about 30 in. on a side. One vane is the master; it is rotated by a gear and pinion at the outer end, outside the supporting ring, driven by a rack pushed by the cam. In turn. the master vane drives the central bevelled gear system at the hub which rotates the other 15 vanes synchronously. T h e flux through the vanes can be expressed in terms of the angle through which they have been rotated. If there is no overlap, then the flux is 0 at ~ = 0 and maximum at ~ = rd2. Neglecting the vane thickness and assuming uniform flux H = Hm(I-cos~)

(11)

and relating this to the irradiance given in Eq. (9) for 0 < t < t m

,p = COS-t(COS2rrt/2tm) cos ( m [ 2 tin) tm [1 + c o s z (Trt/2tm) ] llz

(13)

sin (~rt/2 tin) 2tin 2 [1 + COSz (m]2 tin) ]312 •

(14)

d.__~___ zr

dt d2~ = dt 2

(12)

~

At t = 0, ~p = 0 and d~/dt = ~r/(V'2 tin).

90

F . G . PENNIMAN, R. J. GOFF and J. M. DAVIES

F o r the overlapping condition, the velocity requirements are more reasonable. I f at a given distance from the center of the vane system, the vane width is L and the separation b e t w e e n center lines of two adjacent vanes is D, the flux is 0 until ¢ reaches the value L cos ~ --- D . (15) F o r the {in. overlap this value of ~ is about 14° at the circumference. T h e irradiance is given by H = Hm( 1 - L / D cos ~) (16) and with Eq. (9) = cos -1 [ D / L cos2(rr/2t/tm) ] (17) d_~_~_- 7r D sin (rr/2 t/tm) cos (rr/2 t/tm) dt tm L [ 1 - - D 2 / L z cos 4 (zr/2 t/tm)] "2 d2~ dt 2

n"2 D l - - 2 c o s 2 (Tr/2t/tm)+DZ/LZcos4 (rt/2t/tm) 2t,. 2 L [I - - D Z / L 2 cos 4 (rr/2 l/trn)] 3j2

(18)

(19)

A plot of ~ and its derivatives vs. time, for 0 < t < t m with D / L -- 0.97, shows that increases smoothly from 0.25 rad. at t = 0 to rr/2 rad. at t = t m ; d~/dt is 0 at t = 0, increases rapidly and smoothly to a m a x i m u m value of about 2/t,, rad. sec -1 at about 0.3 tm and then decreases smoothly to 0 at t = tin; d2¢/dt " has a very high positive value at t = 0, decreases rapidly and smoothly to 0 when the velocity is m a x i m u m and then decreases m o r e slowly to a minimum value of about - 5~tin2 rad. sec -2 at t = tin. O u r concern is mostly for this time region b e c a u s e the changes o c c u r more rapidly then. F o r the rest of the exposure, i.e. for t > t,,, the changes o c c u r more slowly and methods that are satisfactory for the beginning of the pulse can accomplish the slower changes more easily. Controlling the pulse shape for say the last half of the duration, as precisely and reproducibly as desired, is still difficult; very small deviations in the cam shape, play in the gears and vibration cause relatively large deviations. it b e c o m e s m o r e complicated to extend this analysis to the whole system, i.e. to integrate along the vane and to include all the vanes. A c c o u n t must be taken of the vane thickness and the non-uniformity of the flux; the flux is essentially zero o v e r some of the area. T h e specific cam design was mainly empirical. T h e irradiance at the focus was m e a s u r e d as a function of the position of the rack driving the m a s t e r vane and the c a m shape to give the desired variation in that irradiance was determined graphically, taking into account the combination of the cam and follower riding it. T h e c a m is driven directly by a variable speed transmission which can be set from inside the test chamber; the speed can be controlled o v e r the range from 2 to 40 r.p.m. T h e vanes open and close continuously, giving a series of pulses; a single pulse is selected by opening and closing the water-cooled shutter and the exposure and limit shutters through a switch on the cam and a time delay circuit. Figure 4 is a photograph of the system. PERFORMANCE AND CALIBRATION T o evaluate the s y s t e m ' s performance, the irradiance at the focus was m e a s u r e d with a l P40 gas phototube protected by a metal shield with a i / 16 in. dia. aperture at the center. A piece of white high-temperature tape was put o v e r the aperture to reduce the intensity and diffuse the light on the phototube. T h e output was recorded with a

Fig. 4. Photograph of the pulse shaper, in place, showing the driving motor, cam, rack, pinion and central gear box.

[Facing page 90]

A pulse shaper for the Natick

Laboratories

solar furnace

91

Consolidated Eiectrodynamics Corporation amplifier type 1-155, and recorder type 5-124 using a 7-363 galvanometer which has a flat (___5 per cent) frequency range of 0 - 1 0 0 0 Hz. The galvanometer records for various transmission speeds from 10-35 r.p.m, are shown in Figs. 5-9. There are differences in the shapes for the various speeds, for example, a change from a single to a double peak near the maximum, and other changes in the interval before 3 tin. These are due to rapid changes in speed of rotation required at various times during the pulse. In this work the following method was adopted for comparing experimental curves with the standard pulse: 1. First, H,, for the experimental curve is determined. For a smooth curve this is relatively easy to do but it is obvious from the examples in Figs. 5-9 that there will generally be some difficulty. Moreover, it is desirable to select the value of rim that will give the best fit using the procedure described below and. accordingly, it is necessary to carry out this procedure for several choices of H,,. 1.0

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Fig. 5. S h a p e d p t l l s e . 10 r . p . m . . 2 . 4 4 M T t,,, = 1.58 s e c , s h a p e f a c t o r , 1.88.

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HIHm

0

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Fig. 6. S h a p e d p u l s e . 15 r . p . m . . 4 6 8 K T t,,, ~ 0 . 6 9 s e c , s h a p e f a c t o r 1-91.

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F, G . P E N N I M A N ,

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a n d J. M. D A V I E S

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Fig. 7. Shaped pulse, 20 r.p.m., 153 K T t~, = 0.40 sec, shape factor 1.Sg 1,0

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4

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Fig. 8. Shaped pulse, 25 r.p.m., 82. I K T zm = 0.29 sec, shape factor I .gfl t.C

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Fig. 9. Shaped pulse. 35 r.p.m.. 23.8 K T

t,~ --- O. 16 s e c , s h a p e factor 1.89.

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A Pulse Shaper for the Natick Laboratories Solar Furnace

93

2. With H s chosen, tm must be determined. Even with a good smooth curve, H changes so slowly that it is not possible to determine the starting time nor the time of the maximum with sufficient precision by appearance and some indirect method must be used. A study of the standard pulse shows that at H = 0.625 Hm, t = 0"55 tm and t = !"55 tin. The width of the pulse at this relative irradiance level is 1 t,~ and from the values of 0.55 and 1.55, the position of the peak can now be located fairly accurately. 3. With these values, that is, Hm and tin, the standard curve can be drawn. This procedure was carried out for the experimental curves shown in Figs. 5-9, in each case trying various values of Hm and selecting the curve of best fit to the experimental curve by appearance, weighting the region near the peak more heavily than the rest. The resulting standard pulse is shown for each curve. The factor 2.12 in Eq. (2) can be called a shape factor since it is determined by the shape of the curve. Integration of the experimental curves in Figs. 5-9 by planimeter shows deviations from that value as listed in Table I. For all yields, the values are very close to the average value of 1.89 but this value differs from 2.12 by 0.23 or - 1 0 per cent. This means that the total energy in the pulse up to 10 t,~ is - 7 3 per cent of the Table 1. Variation of the shape factor with yield Cam speed (r.p.m.)

Yield (W(KT))

Shape factor

10 15 20 25 35

2440 468 153 82 24

1.88 1.91 1-88 1-90 1.89 av. 1.89

value for the whole pulse carried to infinite time, as compared with - 81 per cent for the standard curve. If this deviation is taken into account in using the pulse shaper, the effect is probably not very important. The present pulse shaper duplicates the standard pulse fairly well for weapon yields ranging from - 2 5 KT to ~2½ MT. There are short time deviations from the smooth irradiance curve and changes in shape near the peak for various yields, and the shape factor is 1.89 as compared to 2-12. Since the thermal effects for most materials are more sensitive to exposure than to irradiance, these deviations are not likely to cause serious difficulty. DISCUSSION

In a nuclear explosion, the temperature and the size of the fireball v ry with time. To duplicate the pulse exactly, both the intensity and wavelength distribution must be varied. Practically, the variation in wavelength distribution is very difficult to accomplish as discussed by Drew [9] and very likely for most uses it is not necessary. The standard pulse represents essentially the average of measurements on a number of weapons made with a radiometer with a flat black receiving surface. With such a surface, the result is a measure of the total energy received and includes the effect of variation

94

F.G.

P E N N I M A N , R. J. G O F F and J. M. D A V I E S

in temperature on the intensity. Unless the optical properties, that is, the reflectance. absorptance and transmittance, of the sample vary rapidly with wavelength, much more so than is generally the case for samples of interest, a properly changing flux from a constant temperature source duplicates the effects of the weapon well enough for most purposes. The present device seems to be satisfactory for current uses; if more precise shapes are needed, some possibilities that have already been studied will be considered further. REFERENCES [ I ] J, M. Davies and E. S. Cotton. Design of the quartermaster solar furnace. Solar Energy 1, 16 (19.57). [2] E. S. Cotton. W. P. Lynch, W. Zagieboylo and J. M. Davies. Image quality and use of the US Army quartermaster solar furnace. United Nations Conference on New Sources of Energy. Rome. Italy. August 196 I. [3] S. Glasstone. The Effects of Nuclear Weapons, Revised Edn. US Government Printing Office, April 1962. [4] N. Y. Chen and W. Paul Jensen. Heat transfer through thermally irradiated dry cloth. Fuels Research Laboratory. Massachusetts Institute of Technology. Tech. Rep. No. 6, 8 July 1958. [51 J. M. Davies. Not published. [6l J. M. Davies. Not published. [7] B. McQue, Not published. [8] W. P. Lynch, Not published. [9l G. G. Drew, Feasibility study of pulse shaping for a solar furnace. Sohlr Energy 9 217 (196.5).