THE UNIVERS ITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Aeronautical and Astronautical Engineering Aircraft Propulsion Laboratory Final Report DESIGN CONSIDERATIONS FOR ARC HEATED HYPERSONIC TUNNEL P. M. Sherman H. C. Early W. N. Lawrence UMRI Project 02953 under contract with: Mathematical Sciences Division Department of the Navy Office of Naval Research Washington 25, D. C. Reproduction in whole or in part is permitted for any purpose of the U. S. Government Jul./ 1i96o

ACKNOWLEDG.MENT This research was supported by the United States Navy under Contract No. Nonr-1224(31), Task No. NR 061-108, monitored by the Office of Naval Research, Mechanics Branch, Mathematical Sciences Division. The support of this agency is gratefully acknowledged. ii

TABLE OF CONTENTS Page LIST OF SYMBOLS iv 1. INTRODUCTION 1 2. GENERAL DESCRIPTION 2 3. OPERATING CONDITIONS 4. FACILITY COMPONENTS 7 a. Building Arrangement for Installation 7 b. Arc Chamber8 c. Nozzle 13 d. Test Section 14 e. Transition Section 14 f. Vacuum Tank 14 g. Vacuum Pumping System 15 h. Instrumentation 15 i. Diffuser 16 j. Power Supply 16 REFERENCES 22 APPENDIX A A- APPENDIX B B-l iii

LIST OF SY3BOLS A Cross sectional area a Speed of sound E0 Energy delivered to reservoir gas h Enthalpy M Mach number p Pressure Re Reynolds number T Temperature u Velocity V Volume of arc chamber 6 Isentropic exponent r Density Subscripts o Stagnation conditions oo Test section conditions * Throat conditions os Reference conditions, 1 atmosphere pressure at 273 K iv

o i-ODUCTION The rapid development of high vel ocity craft has greatly stimulated interest'in the new gas dynamic phenomena which occur at the high temperatures generated in hypersonic flighto The chemical changes which occur affect the entire flow field around a body as well as the interaction with the solid surface boundaryO There is a dearth of experimental data necessary for predicting these effectso This report deals with the initial considerations in the design and fabrication of an are heated tunnel facility to obtain such data, This tunnel is now under constructionr in order to obtain very high velocities, a great deal of energy is required. Thism in generals means that such a facility must be quasi-steady, at best. The tain advantage of the arc-heated tunnel is the possibility of obtaining high stagnat;:on temperatures at comparatively high pressures for relatively long run times. High pressures are particularly important because the extent of chemical non-equiibrium in the nozzle expansion is sensitive to pressure (for a given temperature>) 1

2. GENERAL DESCRIPTION The tunnel installation consists of a small motor coupled to a d.c. generator with a heavy flywheel, a coil, arc chamber, nozzle, test section, vacuum tank and vacuum pumps. An early artists' conception of the installation is shorn in Figure 1 and an overall layout is shown in Figure 2. The general operation is the same in principal as for any blovrdown tunnel. The arc chamber is filled with gas to the desired density. The downstream section is evacuated by means of the vacuum pumps. The small motor then brings the generator rotor and flywheel up to speed and the generator is pulsed to deliver current to the coil. When the current in the coil reaches a maximum, the circuit is interrupted so that the magnetic field of the coil collapses and an arc is initiated across the electrodes in the arc chamber. The arc heats the gas in the chamber at constant volume, to the desired. stagnation temperature and pressure. The diaphragm at the entrance to the nozzle throat then yields and the heated gas in the arc chamber is accelerated through the nozzle and test section, where it reaches a high velocity, and into the vacuum tank. Design consideration of components are discussed in section 4. 2

3. GPERAJTING CONDITIONS Unfortunately, cost is always a consideration in determining the limitations of a system. There are etwo major cost limitations in a high pressure "hot-shot" type of facility. One is the cost of delivering the electrical energy. The other is the cost of constructing a chamber for high pressures. The cost of even a small high pressure chamber increases very rapidly for pressure above 60,000 psi. The construction of a chamber for pressures over 250,000 psi becomes questionable, let alone expensive since present day alloys have a yield, at best, of below 300,000 psi. New materials or a careful pre-stressing of a series of shells present costly possibilities. A maximum pressure of 80,000 psi represented a reasonable compromise, and is therefore, one limitation on our operating conditions. The cost of supplying energy to the gas is related to the efficiency of the energy transfer process. One problem in this connection is the problem of the change in average electrical resistance of the gas with time. As the arc is initiated the gas in the arc column becomes ionized and therefore its resistance tends to be reduced. On the other hand the column tends to be reduced in cross section by a pinch effect which would tend to increase the resistance of the pinched gas. In the case of the co-axial electrode geometry the arc column also tends to be stretched out in length and rotate. This would, of course, make for an increase in resistance. There has been some experimental evidence (References 1&8) that an overall 3

average resistance of.02 ohms may be used as a very rough approximation. If the average resistance is less, a higher current will be required for the given energy transfer. [Some provision for this possibility has been made (see Appendix A).] Energy transfer to the gas of 2x1l joules appears reasonable and is therefore a second limitation on our operating conditions. With a given amount of energyr, test-section conditions depend primarily on the quantity of gas in the arc chamber and the extent the gas is expanded from reservoir to test-section. Required and limiting stagnation conditions were computed for a variety of free stream conditions. These computations were based on chemical equilibrium throughout (References 3 and 4). Isentropic quasi-steady flow was assumed. Values for the region of density above one hundred times standard were obtained by extrapolation. These values are therefore only approximate, Free stream conditions were assumed for the computation, and stagnation enthalpy computed from ho h4 + 1/2,>2. Stagnation conditions were then determined from the mollier diagram from ho and the constant entropy known from free stream conditions. From stagnation internal energy and density, limitating stagnation conditions for a maximum energy transfer of 2x106 joules and given arc chamber volumes were determined. Figure 3 is an example of computed stagnation conditions necessary for one set of test-section conditions. This graph is for TX = 270~K. Since the )Oo curves are also constant entropy curves, if Too were approximately 108~K all the constant OO curves would shift to the left 14

approximately one, i.e. a factor of approx. l10of change. Likewise, if Too were approximately 680~K all the wo curves would shift to the right approximately one. The velocity curves would not change much with change in To in this high velocity region. Figure 3 also indicates the limit on stagnation conditions for energy transfer of 2x106 joules and arc chamber volumes of 60 in.3 and 240 in.3 The 240 in.3 limitation on stagnation conditions is the same as that for the transfer of approx. 500,000 joules with the approx. 60 in,3 volume. Of course, any set of conditions below the energy limit lines could be obtained by the transfer of less energy. Figures 4 through 11 indicate the change in thermodynamic coordinates through an isentropic expansion for two sets of stagnation conditions. They are compared with an expansion based on an effective isentropic exponent of 1.2 and 1.4. These computations are based on a graphical integration and therefore are not very accurate and are quite tedius. It appears that these equilibrium conditions cannot be approximated by means of one effective isentropic exponent for the entire expansion. However, one exponent to some appropriate temperature, say 2000~K, and another for the remainder of the expansion appears feasible. For completely frozen flow the effective T would be above 1.4 due to the presence of monatomic molecules. For flow where just composition is frozen, 6 would approach 1.28 for diatomic molecules with vibrational degrees of freedom, or somewhat less where other degrees of freedom such as ionization enter. These have not been computed 5

partly because there is evidence (Reference 5) that at relatively high stagnation pressures the flow through a nozzle expansion will remain very close to chemical equilibrium* Figures 4 through 11 are based on the method described in Reference 6. This method employs the mollier diagram and a graphical integration of the steady, one-dimensional momentum equation in the form d(U2/2) = _1 dp T, a, and ) are plotted versus p. Then. is plotted versus p and graphically integrated to obtain u2/2 as a function of p. u and M are obtained from u2/2 and a respectively, and A/A*, from 0UX*U* The eu calculations for the'/ = 200 conditions are based on extrapolated values. Figure 12 is a plot of free stream Reynolds number per foot versus free stream Mach number for a few values of free stream temperature and density as parameters. These curves were computed on the same basis as Figure 3. The usual quasi-steady state blowdown tunnel expression was employed to approximate the change of stagnation conditions with time, after flow is established, An arbitrary limit of approx. 1% decay in stagnation density per millisecond of flow time was employed. This limit for our initial short nozzle represents an average of approx..3% decay in stagnation density per particle residence time in the nozzle. The decay rate is a function of the ratio of arc chamber volume to throat size as well as a function of the stagnation conditions. Setting the decay rate for a given arc chamber volume places a maximum on the 6

throat size or a minimum on the test section velocity for a given effective test-section sizeo The effective test-section area depends on the boundary layer displacement thicknesso Unfortunately there is no reliable way of determining the boundary layer displacement thickness. All present methods are of questionable accuracyo One added problem here is the extent that the nozzle wall provides effective boundary layer cooling in the short period of time involvedo For T, approx. 100 K and an effective testsection area of 1 square foot, the minimum velocity is limited to approxo 8000 ft/see At Ta, approxo 270 ~K this becomes approx. 13,000 ft/sec, Run time is usually considered from the start of the flow in the testsection to the time of flow breakdown (See Section 4 f.) From all indications, however, there is a time lag in the adverse temperature effects on the surfaces in the arc chambero sThat is, erosion or evaporation of electrodes, liner, insulation, etc. increases rapidly with elapsed run timeo GThe run time will therefore be limited by the opening of a valve in the arc chamber (See Section 4 bo). This idump valve" will limit the run time to 15 to 20 milliseconds. 40 FACILMTY COMP)WOmENMTS ao Building Arrangement for Installation The tunnel is to be installed in an addition to the Aircraft Propulsion Laboratory. The general arrangement of the layout is as shown 7

in Figure 2o A special cavity ai i d concrete pad with built in ties were constructed for the motor-generator-flywheel power supply Completely isolated concrete pads ae also included for model support and support of optical equipetnto Floor pad provision has been made for the use of a schlieren system of long focal length Support for the arc chaber is to be built into the floor~ The coiiL, electrodes aerc chamber,, nozle, and vacuum tank are on a common centerline Steel has been kept to a minimum in the vicinity of the coil to minimize magnetic losses and field distortion4 bo Arc Chamber igure 13 shows the intermn l arrangemnt of the arc chamber The XmDin considerations in the design 8are: 1) maximum inxternal pressure9 2) wrximum wal11 stress, 3) vollune 4 ) internal geonetry 5) electrode geometry, 6) nozzle-throt geometry 7) pressure seals and insulation 1) As previously indicted the design is based on a maximum internal pressure of 80Q000 psio The decision was largely a cost factort 2) The mximum wal stress occurs atce of the chamber It will always9 of course, exceed the maxinium pressure9 n matter how thick the chamber wall is Successful heat treatment of thick walls requires special alloys and these are expensive and difficult to machineo The wall thickness is determined by the maximum internal pressure, the material used and a factor of safety of 2o Thick 8

shell elasticity theory is used to determine stresses. 3) Choice of arc chamber volume is related to maximum energy transfer to gas, stagnation pressure and temperature limits, and the decay rate of stagnation conditions. For a given energy transfer, higher temperatures and pressures are possible with a smaller volumes (See Figure 3). The decay rate of stagnation conditions decreases as the volume increases. Therefore, it is desirable to have as large a chamber as possible from the one standpoint and as small a chamber as possible from the other standpoint. Once maximum stagnation pressure is determined for a given energy transfer, however, the arc chamber volume is roughly determined. This can be seen from Figure 3. For a pressure maximum of 80,000 psi and energy transfer of 2x106 Joules, an arc chamber volume of 60 in.3 was decided on as consistant with all requirements. 4) For a given volume, several arc chamber geometries are feasible. Volume to internal surface area should be a maximum for minimum loss due to heat transfer to the chamber walls. A maximum volume to surface area ratio would be obtained by a spherical chamber. However, a spherical chamber presents problems in fabrication and sealing. A cylindrical chamber was decided on to obtain axial symmetry, ease of fabrication and economy. For a cylindrical chamber a length to diameter ratio of approx. 1 is closest to the 9

sphere configuration. It is desirable, however, to allow for a long "stretched out" arc so that a length to diameter ratio of ~7 1 has an advantage. The compromise of a length to diameter ratio of approx. 2 was made. ) The electrode geometry should provide for good contacts at all junctions, reasonable current density, the possibility of varying the distance between electrodes, and uniform transfer of energy. Soft copper washers and silver plated surfaces are provided to minimize contact resistance between surfaces. Electrode diameter is kept at a minimum of 1-1/2" with no section having less than that equivalent area. There is evidence (Reference 7) that with co-axial electrodes, the arc rotates, resulting in a more uniform transfer of energy and less electrode evaporation. The electrode tips are therefore concentric. They are removable to provide for altering the distance between them. 6) The subsonic section of the nozzle, and the throat section, as well as a portion of the supersonic section of the nozzle are all part of the arc chamber structure. The entrance to the throat should be smooth and gradual. A total conical angle of 20~ was chosen for this. The downstream section of the nozzle has a total angle of 15~ (See Section 4 c.). The throat section must withstand high heat transfer rates. Tungsten throat inserts are used for this purpose. These inserts are made with a straight section at the throat of the 10

order of the throat diamter. There is evidence that such a design makes for a more uniform flow. Throat size to obtain given test section conditions depends on effective test-section area. This in turn depends on boundary displacement thickness. Until are Inmo more about comiuting displaceiaent thickness, throat size for given test-section conditions cannot be determined. Throat diameters will vary betwteen approx..02" and.15" as outside limits. 7) Most materials generally used for sealing purposes extrude at a pressure of 80,000 psi. Pressure sealing the arc chamber therefore becomes a problem. Seals must be designed so that there is no place for any extruded material to go. This is also true of electrical insulation materials. Here there are some exceptions, however. One is natural mica which can be "piled up" in thin sheets for insulation in the direction perpendicular to the sheets. Another is aluminum oxide porcelain which will take a compression load of over 200,000 psi. There is also malamine-glass insulation which is quoted as takirg a compressive load of 90,000 psi. A combination of the mica and epoxy-glass has been used successfully (Reference 8)* 8) A liner for the chamber is advisable for two reasons. It facilitates moderate changes in internal size and/or geometry. It also makes possible the use of a material of high thermal and electrical conductivity for the inside surface of the chaimber. A perforated baffle is provided as part of the liner to provide somewhat of a 11

settling chamber and to smooth the fluctuations set up by the rotating arc The baffle is placed in the chamber so that there is a comparatively small volume on the downstream side to minimize pressure lag on the downstream side of the baffle. The diaphragm is placed just upstream of the throat and can be either a plastic film such as Mylar or a scribed metal disc. The Mylar probably evaporates. The scribed metal has the advantage of rupturing at a given pressure. 9) Advantage can be taken of the time lag in the contamination of the gas by oxidation, evaporation and/or erosion of metal component in the arc chamber, by venting the arc chamber after a pre-set period of time. A large fast acting valve is required for this purpose. Two possibilities are being considered for this valveo One is an explosive charge in a plastic plug, the other is a closing based on explosive bolts, In either case automatic triggering by a timing circuit is required. The hot gas will be vented vertically through the roof to minimize the problem of reaction forces. 10) The arc chamber will be mounted on rails so that it can be moved along its axis, horizontally. This makes for easy access and easy removal of the downstream section of the nozzle, 12

Co Nozzle The initial nozzle to be used is axisymmetric. An axisymmetric nozzle has the following advantages: 1) minimum throat perimeter to throat area ratio for minimum change in throat section with time, 2) smooth boundary layer growth, 3) greater flow uniformity, 4) symmetrical thermal expansion. A conical nozzle was chosen for versatility and economy for initial operation. The nozzle has a total included angle of 15~. This represents a compromise between minimizing both axial gradients in the test-section and the possibility of boundary layer separation, and minimizing boundary layer displacement thickness. The larger the nozzle angle the greater the likelihood of boundary layer separation and the larger the gradients in the test-section. The smaller the nozzle angle the longer the nozzle becomes for a given test-section area and the thicker the boundary layer in the test-section. For the high stagnation densities, the Reynolds number will be higher than the critical Reynolds number for the region in the nozzle where the flow reaches a Mach number of about 3. (Reference 9) The boundary layer will therefore probably become turbulent long before reaching the test-section region, so that even though the boundary layer is cooled it will probably be turbulent in the test-section region. 13

d. Test Section, e. Transition Section There appears to be little advantage to a straight test-section with a conical nozzle. The test-section region is therefore in the conical portion of the tunnel. The diameter at the test-section centerline is approximately 19". A conical section downstream of the test-section has provision for model mounting and instrumentation access. The nozzle and test-section are in one piece and can be removed without interferring with any model mounting. f. Vacuum Tank The vacuum section downstream of the test-section has a volume of approximately 400 cubic feet. If a diffuser is employed, the vacuum tank should be large enough so that the pressure in the tank will not increase beyond that behind the normal shock at the diffuser exit, before the end of the run. A more conservative limitation is a tank large enough so that with the maximum mass flow, the pressure in the tank does not reach the test-section exit pressure before the end of the run. Both criteria were considered in determining the vacuum tank volume, The tank is 4 feet in diameter made in two sections for easy diffuser mounting, possible future change in test-section, and economy. Double welds are used for strength with the space between them vented to the vacuum sideo This is done in order to minimize the possibility of virtual leaks from enclosed pockets. Single Army-Navy standard "0" -rings are employed for vacuum seals. Shell 14

thickness is based on ASME code with sections 3/8" and 5/16" thick. All inside surfaces are coated with low vapor pressure paint or oil to minimize the problem of removal of moisture from hygroscopic surfaces. g. Vacuum Pump To obtain proper starting of the flow through the nozzle a low pressure is required downstream of the nozzle so that the starting shocks will be swept rapidly downstream. (See Reference 10)* An analysis of the starting problem requires a compressible two-dimensional unsteady solution for which no mathematical techniques are available. Some analyses, however, have been made by means of one-dimensional method of characteristics (Reference 10). Our vacuum system is based on obtaining a pressure of approximately 1/2 micron of mercury in less than an hour. Pumping performance is indicated in Figure 14. The system consists of a small rotary pumpiLus a 10" diffusion pump with necessary by pass and valves. A safety check is provided on the system by means of a relay for automatic valve closing in case of a pressure rise. h. Instrumentation Initially "standard" instrumentation will be employed for making measurements. Both a crystal type (Kistler) and a strain gage type (Norwood) ofi pressure transducer will be enployed to obtain the stagnation chamber pressure. Variable reluctance gages will be employed to obtain lower pressures. 15

Photographs will be taken of the luminous flow field by means of a Fastax camera. This camera has been used to record at 7000 frames per second. It will also be used for future schlieren pictures. i. Diffuser Initially the diffuser will be omitted (for economy). The advantages of a diffuser apply here as in any blowdown tunnel. A conical section with an angle similar to that of the nozzle will probably eventually be used. It may be fabricated of a non-metalic material. j. Power Supply General Scheme - The power source for supplying electrical energy to the arc chamber is designed to store energy taken from the power line over a time interval of approximately 20 minutes and deliver it to the arc chamber during an interval of approximately 5 milliseconds. This energy will be stored by means of a doe unipolar generator and flywheel used in conjunction with a large inductance coil* The energy will first be stored in the flywheel over a 20 minute interval required for the flywheel to reach a speed of 10,000 rpm; then it will be transferred to the inductive energy storage coil over a 3 second interval and then transferred to the arc chamber during a 5 millisecond interval. (Reference 11). Allis-Chalmers Unipolar Generator, Flywheel, and Drive Motor - The operation of the system is schematically shown in Figure 15. The generator 16

and flywheel are driven up to speed by the electric motor. Then, the field of the generator is energized by closing S1, and the current builds up in the inductance coil. At the instant of current maximum, S2 is opened, and the current is diverted to the arc chamber. The unipolar generator has been developed by the Allis-Chalmers Company for applications requiring very large amounts of low voltage d.c. current. For pulse operation, this generator runs at 10,000 rpm and will deliver 500,000 amperes at 45 volts. The generator does not use conventional brushes but uses liquid metal to make electric contact with the spinning rotor. The liquid metal is an eutectic mixture of sodium and potasium known as NaK which is liquid at room temperature. The flywheel has a diameter of 26 incheso At 10,000 rpm, the stored kinetic energy of the flywheel and generator rotor is 20 million joules. Inductance Coil - The energy storage coil will have an inductance of 120 microhenries and a resistance of 47 microhms. The computed total circuit resistance, including the internal resistance of the generator, will be 65 microhmso This computation is based on published data regarding the resistance of bus bar connections and switch terminals. The computed energy storage in the magnetic field of the inductance is 6x106 joules at a current of 315,000 ampereso This current maximum will be reached approximately 3.2 seconds after the current starts to build up in the coil. There is some uncertainty regarding the time constant of the field winding of the unipolar generator. The rate of field build up is not accurately known under conditions where the generator is heavily loaded, and if the field time constant is longer 17

t eectd, the a current Emy be somewhat is than 315,000 Figure tl6 lS a plot of the gnerat rent as a funtion of tie. The firSt curve. biaed on the asu on tha the field buiLd up t is tgzerO 44XI >Ihe seeond curvw. e is based on the assurmtion that the genertator f:ld buIis up at anr esxonential rate vit>h a ti constant of onre seond. The dotted, portions of the tio curves represent the circuit behavior if the firing switch ere not opened at the tie of the first current maximme. The electrical behavior of this circuit can be simeJified by replacing the generator and ly9heel with an equivalent capacitance of 20.000 fara- charged to 45 volts. This is a good equivalent circuit for situations in which the rise t of the generator field i not significLato 1The rae for he oil will be supported by a structure of heavy oak tebers. A hotograph of this structure is shorn in Figure 17 though the total rrighit of the aluminum cable is only 15,000 lbs,0 the magnetic forces on this structur are quite large, and very heavy bracing is necessary to withstand thee forceS. The alunmir. bus bars connecting the coil, sGitch, and generator 111 hlave, a current-carrying cross-sectional area of 4" x 20`. The coil' lrindring vili conisLt of 26 parallel conductors of polyethyleneinsulated aluminum cable Each conductor is 29 in diater and has a cross-ectional area of 3,000,000 circular milso Appendices A and B describe design criteria and method of calculation of transient loa current.o 18

Switch - An optimumn switching system for transferring the coil current into the arc chamber will need to interrupt a current of 300,000 amperes and withstand voltages up to 20 kilovolts within about a millisecond after the current is transferred. This is a very special switching requirement which canno b t be met by commercially available switch gear. This switching problem can be greatly sirplified if the arc inside the chamber is initiated by a heavy shorting wire (bar) which bridges the electrodes during the switching process. Hoowever, the vaporization of a shorting bar adds a substantial amount of contamination of the gas in the arc chambers and it will be desirable to develop a switching arrangement which will permit the arc to be initiated with a minimum of gas contamination due to vaporized metalo Present plans are to accomplish the switching in a 3-stage process which will use 2 switches and a fuse all connected in parallel. The #1 switch will be very heavy and massive and will carry most of the current during the 3 second charging intervalo When this heavy #1 switch is opened, the current will beee transferred to a lighter faster acting swith wch which will carry the current for perhaps 1/10 second so that the heavy #1 switch has time to get completely open and deionized. The relatively light #2 switch will be opened by compressed air and by magnetic forces, It is expected that the opening time of #2 switch can be limited to about 2 milliseconds, The #2 switch will be shunted by a high voltage fuse which will carry the current for about 1 to 3 milliseconds before blowing and opening the circuit and thus diverting the current into the arc chamber. 19

Opening a circuit of this type has been acco li shed at lower current levels in previous work at the University of Michigan. This previous work involved currents of about 5,000 amperes, and the t fuse voltage would rise to 50 kilovolts in less than a millisecond. The fuse elenent consisted of a #18 copper wire inside a thick 1/4" ID. fiberglass tube filled with oil. It is expected that this fuse technique using mult1ple fuse elements connected in parallel can be extended to the present application. Under certain conditions the arc may not be successfully initiated in the arc chamber. To prepare for this possibility, two safety precautions are being provided. An overvoltage spark gap across the terminals of the energy storage coil will be adjusted to breakdown and short-circuit the coil at a maximum voltage of approximately 20 kilovolts. This overvoltage spark gap will be of extra heavy construction so that the elctrodes will not burn away if most of the stored energy is dumped into this arc. Another hazard is that the stored energy may be dissipated in the fuse box, and thereby generate a substantial explosion. The fuse will be located inside a thick walled concrete box filled with sand. One side of this box will consist of a plywood panel which will break in case of an explosion and vent the gas and sand outside the building. The heavy Il switch does not appear to involve any unusual design problems. For the!2 fast acting, mechanical switch a variety of designs have been considered. After evaluating various alternative designs, it has been decided to build this switch i the form of a metal di:sk which 20

forms a low resistance short circuit across the end of a coaxial line. The shorting disk will be clamped in place by an explosive bolt assembly, and a 100 psi air tank will supply air pressure inside the coaxial line. When the switch operates, the bolt explodes, and the air pressure and magnetic force accelerate the shorting disk forward. The air flow assists in restraining the tendency of an arc to form across the switch terminals. Sequence Timer - The firing of the tunnel will be carried out by an automatic timing mechanism. This sequence timer will program the following events: (1) applying pulsed pressure to the liquid metal (NaK) current collector system of the generator, (2) energizing the field of the generator to initiate the build up of current in the energy storage coil, (3) providing signals for starting recorders and triggering oscilloscopes, (4) opening the mechanical switches in the charging circuit, (5) energizing the suicide field reducing circuit on the generator, and (6) operating the dunp valve which removes the residual gas in the arc chamber after the useful running time of the tunnel has been completed. 21

REFERENCES l. Perry, R. W. ana MacDermott, W. N., "Development of the Spark-Heated, Hypervelocity, Blowdown Tunel-Hotshotf, AEDC-TR-58-6, June 1958. 2. Turner, T. E., "Design of Lockheed Spark-Heated Wind Tunnel", LMED-48467, March 1959. 3. Hilsenrath, J. and Beckett, C. W., "Table of Thermodynamic Properties of Argon-Free Air to 15,i00K" - 5EDCTN-561, September 1956. 4. Feldman Saul, "Hypersonic Gas Dynamic Charts for Equilibrium Air", AVCO, January 1957. 5. Hall, J. G. and Russo, A. Lo, "Studies of Chemical Nonequilibrium in Hypersonic Nozzle Flows", presented at Combustion Institute Meeting, Western States Section, Los Angeles, November 2-5, 1959. 6. Bird, G. A., "Some Methods of Evaluating Imperfect Gas Effects in Aerodynamic Problems", Royal Aircraft Establishment, January 1957,AD-139148. 7. Harris, W. G., "The Boeing Eight Inch Model Hotshot Wind Tunnel", D2-4711, September 1959. 8. Rohtert, R. E., Chief of Wind Tunnels, McDonnell Aircraft Co. - private communication. 9. Reshotko, Eli, "Stability of the Conrressible Laminar Boundary Layer" Guggenheim Aeronautical Laboratory, Memo. No. 52, January 15, 1960. 10. Glick, H. S., Hertzberg, A., Smith, W. E., "Flow Phe nomena in Starting a Hypersonic Shock Tunnel", AEDC-TN55-16, March 1955 1I. Early, H. C. and Walker, R. C., "Economics of Multimillion-Joule Inductive Energy Storage", Communication and Electronics, No. 3, July 1957. 22

APPENDIX A Design Criteria for the Energy Storage Power Source - Choosing the optimum design parameters for the power supply requires a knowledge of (1) the amount of energy to be delivered to the gas, (2) the rate of heat loss from the gas, (3) the efficiency of converting stored electrical energy to internal energy of the gas, and (4) the voltage and current characteristics of the arc as a function of gas temperature and pressure, Reasonable estimates are available as to the energy requirements. Estimates as to the voltage and current characteristics of the arc are based on extrapolations of arc characteristics under substantially lower pressures and temperatures. Because of this uncertainty, it is desirable to provide a maximum amount of flexibility in the design of the power supply. Additional flexibility will also be obtained by providing for possible modifications of the electrode geometry inside the arc chamber. The choice of design values for the power supply was to a certain degree dictated by the characteristics of the Allis-Chalmers Model 2112 unipolar generator which was the only suitable choice commercially available. The generator peak current rating of 500,000 amperes places an upper limit on the pulse current obtainable from the power supply. The flywheel kinetic energy storage of 20,000,000 joules places a second limiting condition on the design of the system. In considering the optimum design of the inductance coil to operate with this generator, it was necessary to consider the relative importance of maximum energy storage vs. maximum current. A-i

Calculations indicate that an energy storage of approximately 6 megajoules in the coil at 315,000 amperes could be obtained with a total circuit(d.c.) resistance of 65/tohms and an inductance of 120/h. Of this 65/Aohms total, 47,/phms will be in the coil and the remaining 18/.ohms is the estimated resistance of the rest of the circuit including the switch and the internal resistance te neror we e erna essnce of the generator is not known with any certainty, and if the actual resistance should be in error by 10 or 20cohms, the wind tunnel design objectives could still presumably be met. On the other hand, a coil design which would attempt to utilize the full 500,000 armpere capability of the generator would involve more risk because (l) the total circuit resistance would need to be so low that any error in estimates would be very serious; (2) the inductance would be reduced by more than 50 per cent, and this could not be increased except by building a new coil; and (3) the time and cost of developing a 500,000 ampere switching system are substantially greater than for a 300,000 ampere system. It was decided to go ahead with the 300,,000 ampere design and build an inductance coil with a six-turn winding. If it is determined in the future that it is very important to go to higher currents, then one or two turns can be removed. Removing one turn will decrease the inductance by approximately 30 per cent and increase the peak current by about 20 per cent. If it is assumed that the arc load behaves as a linear resistance of.02 ohms, the six-turn, 120ch coil has a discharge time constant of 6xlO03 seconds. In the event that the arc resistance is less than the above figure and the discharge time is undesirably long, it may be desirable to use a A-2

shorting switch across the electrodes to "chop off the tail" of the discharge pulse. Choice of Conductor Size and Coil Dimensions - The total weight of aluminum used in the coil windings and bus bar connections was determined from economic considerations and the law of diminishing returns. Because of the very low duty cycle, the ohmic heating of the conductor is unimportant, and the use of extra parallel conductors serves only to reduce circuit resistance and increase the efficiency of energy transfer. The 26 parallel aluminum conductors used in the six-turn coil weigh 15,000 pounds and cost approximately $9,000. Extra expenditure to decrease the coil resistance would have increased the energy storage and peak current capability. However, the same increase in performance could be obtained at about the same cost by increasing the size of the flywheel. The choice of 15,000 pounds of conductor in the coil appears to represent a reasonable balance between the cost of the doc. generator and the cost of the inductance coil as discussed in Reference 11. In choosing the type and size of conductor, a comparison of costs indicated a substantial saving in using aluminum instead of copper. The use of 2" diameter 3,000,000 circular mil cable is advantageous compared to the use of a smaller size cable in that less space is lost in insulation and the more compact winding has a higher ratio of inductance to resistance. Still larger cable, up to 5,000,000 circular mils, could also have been obtained, and this was seriously considered. It was decided that the increased A-3

difficulty in handling larger cable and in obtaining terminations of sufficiently low resistance would offset any advantages. In order to minimize the high voltage insulation problem, all the 26 conductors have one common terminal on the inside (small radius) surface of the coil and another common terminal on the outside (large radius) surface of the coil. Aluminum clamping posts for terminating the inner ends of the coil winding can be seen in the photograph Figure 17. For design purposes, it is assumed that voltage spikes as high as 20 kv may be encountered. The voltage between any two adjacent turns will be only 1/6 of this total. An overvoltage protector spark gap will be used to protect the system against excessive voltages. Since there may be arc-over conditions where several megajoules of stored energy has to be dissipated, arcing horns will be used to protect the gap from melting. The gap and horns will be located so that the magnetic field of the coil will act to move the arc along the horns. If preliminary tests indicate that an arc reaching the ends of the horns does not have enough voltage to re-ignite at the gap, this design will require modification. The ratio of a.c. resistance to d.c. resistance of an inductance coil can be substantially reduced by (l) enameling the individual strands of the conductor, (2) transposing the winding in such a manner that all the parallel conductors have the same flux linkages and hence the same d during the discharge. These refinements are of particular importance in the design of 60 cycle electrical equipment where the efficiency of power transformation is important, and power loss presents a cooling problem. In the design of A-4

the present inductance coil, heating is not a factor and the loss of stored energy (of the order of 10 per cent) due to high a.c. resistance does not justify the added expense of using enameled wire and transposing the windings. Enameled aluminum wire costs two to three times the cost of bare aluminum wire and the problems associated with transposing the windings are complicated by the high magnetic forces on all the conductors. The winding has a radial depth of 27 inches, an axial length of 31 inches and an average diameter of 120 inches. For a given length of wire, the optimum geometry of a winding for maximum inductance is when the radial thickness and the axial length of a winding are equal and 0.66 times the average diameter. The present coil has an inducatance of 95% of the inductance that could have been obtained by using the maximum inductance geometry. However, the larger diameter design has the advantage that the magnetic pinch force tending to compress the windings and stress the terminals is substantially reduced. Also the a.c. resistance loss due to parasitic eddy currents in the conductors is less than in the maximum inductance geometry. A-5

APPENDIX B Calculation of Transient Load Current of Generator - During the 20 minute interval required to run the generator and flywheel up to full speed, there is of course no electrical load on the generatoro After the desired rotational speed has been reached, the build up of current in the generator and coil could be initiated by closing a switch in this circuit. However, such a switch would be very heavy and expensive and would have significant resistanceo Hence, it is advantageous to omit the switch and initiate the load current by energizing the field winding of the generatoro The output voltage of the generator is given by the simple relation E =K n () where 0 = the total magnetic flux n = rotational speed, taken here in revolutions per seco K = constant of proportionality If the flux were to rise instantaneously, the voltage would be a step function, and the circuit could then be analyzed as a function of speed and currento In fact, under these conditions, the generator will behave exactly as if it were a 20,000 farad capacitor, and the analysis follows the conventional analysis for a series RL circuit. Such an analysis has been carried out and is plotted in the first curve on Figure 160 However, the field windings are inductive, and when the voltage is applied to the field winding, there is a time lag before the field current, B-I

as the flux, reaches peak value. The exact manner in which the flux rises is a difficult problem in flux diffusion through iron and other conductors. The rate of flux rise is a function not only of the applied voltage but also of the load current the generator is delivering. The manufacturer estimates that the field will rise in the order of a second, although this has not been verified experimentally for large load currents. This is not negligible compared to the two second tine constant of the energy storage coil. If it is assumed that the field flux will rise on an exponential path with a time constant of one second, the differential equations describing the voltage, current, and speed relations are given below. First, the loop voltage equation is L t + R i = K 0 n (2) and if it is assumed that = Om (1 - e-t/) (3) where V is the time constant of the flux rise, here taken as one second, then by the conservation of energy, the total initial energy, W, at any later time must be the sum of stored inductive energy, the integral of the ohmic power losses and the remaining kinetic energy in the generator. Thus W = L i2 4 R i2d t + 1 I W2 (4) 2 2 where c= 2 2 n n I = moment of inertia of the generator and flywheel. Since the total energy is constant, the time derivative is zero. B-2

Differentiating equation (4) after substituting in terms of n instead of cJ yields dW O = L i t + R i + (2 )2 I n n(5)'at: d~dtdt Since the speed is decreasing (dn/dt< 0), the last term is negative, which may be interpreted as meaning that the power into the coil, plus the power into heat, is the power out of the generator. If the voltage equation (2) is multiplied by current, it becomes a power equation also. i L -+ iR i = i K n (6) Subtracting (5) from (6) yields the differential relation between speed and current. iK n= - (2 )2n dn (7) or - (2St)2 I dn K.. dt (7a) If the flux 0 is independent of time, equation (7a) can be rewritten as ~ (2 I J d t =.- n (8) and equation (2) becomes L dt +R + +{ ) t i d t = 0 (9) If the coefficient of the last term is arbitrarily written as (K 2 _ -_ (2 )2 I - C, the relation to the standard RLC series circuit is immediately obvious. By way of comparison, the equivalent value of this capacitance is about B-3

20,000 farads. The solution of equation (9) is relatively simple. However, if the flux is not a constant but is given as a function of time as in equation (3), then while equation (7a) is valid, equation (8) is not. It is possible to differentiate equation (7a) and substitute back into the voltage equation (2) yielding a single differential equation in n. The equation, while linear, does not have constant coefficients. To add to the difficulty, the singular points of the differential equation are essential singularities, and, thus, will not yield to a power series solution. A numerical solution must be obtained, however, which yields the current as a function of time. Using three equations, L di R K 0 L —+RI=KKn dt 0= (1 - t) and W L i2 R i2d t + I (2 )2 n2 2 2 2 a simultaneous solution for current and speed was obtained. The current has been plotted in Figure 16. There is not much difference in the peak value of coil current whether the flux rises rapidly or in about one second. The reason for this is that most of the energy dissipation occurs when the current is near maximum value. During the time when the flux is low, the current is also low, so that the net result is that energy loss is low. For example, at 1.5 seconds, half the time to reach the peak current, less than 5 per cent of the total energy has gone into heating. By the time that the B-4

current reaches peak value, about 60 per cent of the energy has gone into heating. If the assumption of a one second time constant for the flux rise is valid, the time delay of flux rise is not too important. Its primary effect is to extend the time necessary to reach peak current, but it does not cause appreciable energy loss. If, however, the rise time is substantially longer, a high current switch between the generator and the coil may be required. B-5

.: I. - I I I "I... I11 II...:I —,I I,.~~~~~ 1,..1 1, ~~~~~~~~: I:: i~ I.. ~~~ II..I - ~~~~~~ 1. I - ~~~~~,.I I II -.-~:'i:I:-: -:... 1.-..I.1, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I - ~ ~ ~ ~ ~ ~ -,,:-:': I~~~~~~~~~~~~:::: I::. ~~~~~~~~~~~ I' I..-I ~-I'l I,:::::":::::,-:,:"~ ~ - I I.I I I I1'II 11.1 I -.1 I ~ I'', ~III,11::',,:.I: I I' l.., I' l I.. - I_ I i;: 1:,. I I':I:,I:I~~~ ~ —-.1 1.. I.I.. ~~~~'.'' I I.. I ~~~~.I. I - I,,. - I.:: - I I II:. ~ ~ ~..... I I I:,~: l~ l~li::i, I::,:: I:I.I I I IIIii: I. I I:i::i::::::: i I " ~ ~ - ~ ~, - I - 1 -. ~~~~~:::.':':::~ ~:;,: I II::`.a. I I. I I --,.:.:. I I.l. ~i I - I II: II I, I.,: -:u:i:: II: I I ~~~~~~-.11%.,::... I: II:::::I I::i:'.. -'':.~ ~ ~ J:: I I II. I I I, 1 I 1 1-1, I I:.:' II III.. I 1 1. I::: (-1 -: II -'. I 1 I: - I:- I II: I,I I I, I 1..1.I.II ~~-. 1...II I,I -:.: 1:: I:i:: I I... II Iii.I IIIii~I. I, I, ~ ~ ~ I~., - I'', I I I:i I I: I"~~I - I..I. I::i-::,:,....:-I II.. ~ ~ ~ ~ 11-1 I. 1... I I 1,iilii i:'.'B' -';,;;;:':::::~,,,, - ~''..::::I1.I::: I ~ I. ~, 11~11., I I I I I I I: I...I,..::,,.,:.I.iI -''., - 1,., -. I I I I - 1,.. I.1 - ~~~~~~ ~ ~ ~~~~ ~~::: -.I1. I,1..1 ~ I1I ~ I. -... ~~. ~II. 1I.. ~ - 111'....' I'l ~.,11.:. I ~ I.I..II ~~I. I I. 1.. I.. ~~~~~~~~~~~~~~. - II. ~~~~~~~~~.. I I~~~~~.:.. I I I ~~~~~~~~~.I,,::I... ~~~~~~~~~~~~~.~~~1.".:,~~~~~~~~,: -:-:_~~~~~~~~~~, II I:i:: I iI: "Cs II.rII,,.I''... I'llII..I I' l'I, ~ I. -, 1, ~... 1 111 - 11 I I''..II I"-~~~~..1.: I II -. I 11I%.- -:::-::':I. I..I IIII1I I..,, 11.~~~~~~~~~~~~~I:....', ~ ~ ~ ~ ~ ~ ~:i I ~.I-. - I SI ~.iI. r I -. ~~~~~~:j.,.. I, - I I I I " -..I i:.,: 1.: I.,I I I I.... I:,,:., l.I.. ~ ~...~I I III I.I I I I. III I I;I;I., II I...l, ~ 1IIt: I-:~I~.1I.. ~ ~ I-. I. II... -I I 1; I.I., I.. -I::,.II III I.,. I..:I la =,1I: ~ I.I ~ IIII...I~~III..II.1....3 ~~I 11I. I.1 ~. ~....1. II. II.~I I.1.1, I ~...,;;:::::.I. II ~. ~:::.-'. ~'.I-, III: I.I II:II ~.: I,.1,.Il~1,PII71I.y... III ~.., ~ I ~ I::%'::,.1I I,:.::,:I:: I. I...

!U;! I NETIC COUPLING l l F ___ Jrl l | _~4. FLYWHEELl 5. UNIPOLAR GENERATOR ___;| | | ~~~~~7. BUS - BARS Ill| 8. SWITCH 9.| POWER SUPPLY II CONTROL I | i —_L~-*1 210. ARC CHAMBER 2I. NOZZLE' ~^^ ~ ~ ~~ 2 NETIC COUPLING 3. SPEED INCRECASE GEARBOX 4. FLVWHACUUM PUMPEEL 5. UNIPOLAR GENERATDS 6. COIL 7. BUS - BARS |IB. SWITCH / l________________ _ _ =_9. POWER SUPPLY I: CONTROL' 0O. ARC CHAMBER II. NOZZLE 12. TEST SECTION 13. VACUUM TANK 8 FT 14. VACUUM PUMP.... ISOLATED PADS r____________________ _. ___ _ _ _-. --— = - -DOORWAYS FIG (2)

10000'I. --.. 60 CU. IN.. 240 CU. IN. el /^/240 U.iN. o 0 1000 0o u E 10O L cT co 0oF 01) Ct nt w 0 0 z 2 Too=, 270 OK 100 Eo 2 X 106 JOULES 1,0,/ s 8.042 X 10-2 LB/CU. FT. I0 4000 5000 6000 7000 8000 9000 10000 11000 12000 To IN OK FIG (3)

10000 TEMPERATURE VS PRESSURE FOR AN ISENTROPIC 8000 - EXPANSION FROM to a 100 ATM To = 10000 K! ^ */ 4000 / 7^/ 4000 00/ 2000 - \.a <.\ 0., I: _ I, -5 10-4 -3 -2 1 oo2 -o3 10 10 10 10 10 10 10 10 P (ATM) FIG (4)

6000 TEMPERATURE VS PRESSURE FOR AN ISENTROPIC 5000 E- XPANSION FROM / Po* 200 ATM To = 6000 K / 4000 7 /7/ / / 2000 / // // / 3*/ /' 1000 ~0~~~ -I I.. 1 10-4 10o3 1o'2 10 1 10 102 103 10 P (ATM) FIG (5)

22000 20000 - - EQUILIBRIUM r - 1.2 18000 16000 r 14000 - w 12000 - I. -10000 - 8 \ 8000 6000 - VELOCITY VS PRESSURE 4000 FOR AN ISENTROPIC EXPANSION FROM 2000 P- Po 100 ATM To = 10000 *K 0 I I I I I 10'5 1 0'4 1 0'3 10'2 1 I 10 102 Io3 104 P (ATM) FIG (6)

16000 14000 -- EOUILIBRIUM ~ ~- =_ l 12000 =1.4 w 10000 I,8000 - 3 6000 - VELOCITY VS PRESSURE 4000 FOR AN ISENTROPIC EXPANSION FROM 2000 f- f 200 ATM To = 6000 OK 10-4 10 3 102 101 1 10 102 10 104 P (ATM) FIG (7)

20 1 8 MACH NUMBER VS PRESSURE FOR AN ISENTROPIC 1 6 EXPANSION FROM \ \ \ t~~~~~Po I100 ATM 14 \ To = 10000 OK I 0 8 6 4 2~~~~~~2 0 1 0-5 I 0-4 I 0'3 10 i2 10o-1 10 102 10 P (ATM) FIG (8)

20 18 M\ \ACH NUMBER VS PRESSURE FOR AN ISENTROPIC 16 EXPANSION FROM \o = 200 ATM 14 - To = 6000 OK 2 - -N I 0 8 4 2 0 1 10 l0 10"4 10 3 0o-2 1 I0 102 103 104 P (ATM) FIG (9)

20 I 8 MACH NUMBER VS A/A* / FOR AN ISENTROPIC / / I 6 EXPANSION FROM/ / to I100 ATM / 4 To = 10000 K / / 12 -( 0/ / / l 10) 6 4 2 0 I,' I, I,-, -I, —-I, —, I1 0 102 103 104 15 10 A /A FIG (10)

20 I 8 MACH NUMBER VS A/A* FOR AN ISENTROPIC 1 6 EXPANSION FROM o 200 ATM 14 - To =6000 "K /, / / / 12 - /7 I0 - / 7I 8 7 7 0o 102 3 4 05 o6 A /A* FIG (I i)

I6 \ p' FREE STREAM RE VS M FOR CHEMICAL EQUILIBRIUM AND Eo = 2 X 106 JOULES 0~~~ I 05 0~~~~~~~ ]-:r \ 0 ^ V ~~~~ 44 A- 10~~~~~~~~~~~~~ 0 24 10 12 14 16 18 20 22 24 26 M co FI G (12)

ARC CHAMBER INTERNAL ARRANGEMENT DUMP PORT OUTER ELECTRODE DIAPHRAGM I /\NNER ELEC_^^/TROD ///E// _ M10D_ ^Ro _ADUE COPPER ^^^^^^^~F RPERFORATEDO BAFFLE CHECK VALVE AND INLET PORT PRESSURE V///A r-^COPPER TRANSDUCER INSULATION FIG (13)

I0 102. z 10 I ~ -- I0 \ 10-6 ANTICIPATED PERFORMANCE OF VACUUM SYSTEMS BASED ~-7 ~ UPON 400 CU. FT. VOLUME 0-8 - I OI I 10 20 30 40 50 1 2 MINUTES St —- HOURS PUMP DOWN TIME FIG (14)

COIL SI UNIPOLAR — ~ s- FIELD GENERATOR SUPPLY FLYWHEEL I ARC CHAMBER DRV DRIVE MOTOR SCHEMATIC OF POWER SUPPLY FIG (15)

350 300 250 (2) _ / / 200 I 150 \ K: / / COIL CURRENT s: I / /RISE CHARACTERISTICS (I) INSTANTANEOUS RISE 100 - / IN GENERATOR FLUX (2) EXPONENTIAL RISE OF FLUX WITH A TIME CONSTANT OF ONE SECOND 50 W / = 20 X 106 JOULES V = 42.6 VOLTS N 10000 RPM i~ ~~~~~/ / y^~~L = 120,4H R 65 4(OHMS 0 0 1.0 2.0 3.0 4.0 TIME (SECONDS) FIG (16)

Fig. 17

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DISTRIBUTION LIST (Concluded) Australian Weapons Research Institute of Aerophysics Establishment University of Toronto c/o Defense Research and Development Toronto, Canada Representative Attn' Dr. G. N. Patterson, Director Australian Joint Service Staff P. 0. Box 4837 Division of Mechanical Engineering Washington 8, D.C. National Research Foundation Ottawa, Canada Hydronautics, Inc. Attn: Dr. J. Lukasiewicz 200 Monroe Street Rockville, Maryland Dr. Y. V. G. Acharya, Assistant Attn: Messrs. P. Eisenberg, Director M. P. Tulin National Aeronautical Laboratory Palace Grounds, Jayamahal Road Bangalore-1, India

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