The Space Congress® Proceedings 1966 (3rd) The Challenge of Space

Mar 7th, 8:00 AM

Missile Explosion Simulation Missile Explosion Simulation

Robert O. Harper Apollo Support Department, Missile and Space Division, General Electric Company

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Scholarly Commons Citation Scholarly Commons Citation Harper, Robert O., "Missile Explosion Simulation" (1966). The Space Congress® Proceedings. 3. https://commons.erau.edu/space-congress-proceedings/proceedings-1966-3rd/session-11/3

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MISSILE EXPLOSION SIMULATION

By

Robert O. Harper Apollo Support Department Missile and Space Division General Electric Company Daytona Beach, Florida

SUMMARY

Missile propellant systems are not designed to ex­ plode. However, prototype missiles may require a range destruct command for safety reasons or even ex­ plode due to some malfunction. Digital computer sim­ ulations of missile explosions were run to provide an estimate of physical parameters which an Explosion Measurement System must measure. The computer simulations were run using the Naval Ordnance Labor­ atory "WUNDY" hydrodynamic computer code (pro­ gram) reported on herein as well as with a two dimen­ sional code. After an explosion the remotely measured data are used to determine inputs to the hydrodynamic computer code. Iterative methods are then used to fit data points currently capable of measurement and to provide values for other quantities not directly meas­ urable. Results include shock wave position as well as static pressure, dynamic pressure, particle veloc­ ity, temperature, density, and energy as functions of both elapsed time and distance from the center of the explosion.

The initial calculations were made to provide good estimates of the magnitude and rate of change of physi­ cal parameters such as temperature, pressure, den­ sity, velocity, etc., which were to be remotely meas­ ured. During the course of the study it was determined that such a digital computer simulation is also a valu­ able tool for post incident analysis.

DESCRIPTION OF SIMULATION

The physical system is described on the computer in terms of total energy content, density, size, the equations of state, etc. The Lagrangean differential equations of compressible flow are set up in finite dif­ ference form and solved in sequential time steps. »^»^ The size of each time step is internally controlled in order to provide both accurate results and economical computer running time.

Data resulting from the computer calculations may be processed through another computer program, "WUNPLT, " and automatically plotted directly from the computer output magnetic tapes. An individual looks at printed output from the basic hydrodynamic computer run, the three available forms of which are illustrated in Figures la, Ib, and Ic, and selects those curves which should be plotted. Each selected curve then requires about one minute of IBM 7044 com­ puter time and one minute of digital plotter time to produce. A typical computer run of 5000 cycles takes 30 minutes of computer time. On magnetic output tapes there are then available plots of particle velocity, density, total static pressure, dynamic pressure, and temperature as functions of distance from the center of detonation for some 250 different points in time. There are also plots available of density, particle ve­ locity, total static pressure, overpressure, and dynamic

pressure as functions of time for eight different loca­ tions as well as a plot of shock wave location versus time.

Sample curves of physical parameters versus dis­ tance from the center of detonation at selected points in time are presented in Figures 2 through 5. A sample curve of total pressure versus time for a given location is shown in Figure 6 as automatically plotted.

Provision has been made inNOL "WUNDY" to insert variable geometry rather than the flat plane, infinite cylinder, or spherical geometry previously available. This will allow computation of two-dimensional problems for analysis of a missile explosion when required by inci­ dent geometry. Normally, a simple spherical geometry will provide sufficient information about an incident. How­ ever, the criticality or nature of an incident may make a two-dimensional solution desirable. In those two- dimensional cases, the expansion ratio along a number of stream lines would be obtained photographically and en­ tered as additional statements in the geometry subroutine of the computer program. The program will accept an ad­ ditional 96 different expansion equations, but seven stream lines should be sufficient and would give about 20 data points around a contour plot. Computer time for each different stream line would be one-half hour of IBM 7044 computational time or atotalof 3-1/2 hours for the seven-line case. The equations describing expansion along each stream line are functions of the specific inci­ dent. They may be analytical expressions or numerical tables obtained from photographic records. The network for calculating the physical representation of an explo­ sion including variable geometry is illustrated in Figure 7.

There is a new equation of state (Landau- Stanyukovich) for hydrogenous materials such as TNT included in the program along with the real air and y law gas equations of state previously available. Pro­ visions for insertion of nine other basic equations of state are in the program. When sufficient experimen­ tal data on rocket propellants is available to describe their equations of state accurately, these equations should be utilized. Presently available equations of state for most propellant combinations are predictions and less useful for calculations than the experimentally verified TNT equation currently include din the program.

Figure 8 shows the variation of debris radius and shock radius with percent yield and time for the Titan mC detonation. Where the shock wave cannot be observed and measured directly, useful data may be obtained from measurement of the debris radius out until the shock wave velocity approaches mach 3 (mach 2.5 for 25-percent yield, mach 2.95 for 50-percent yield, and mach 3.2 for 78.5-percent yield). Shortly after the time corresponding to this velocity, the debris reaches its maximum expansion and begins to contract, losing its direct relationship with the shock wave. For veloci­ ties of shock wave above mach 3, the variation due to per­ cent yield may be largely eliminated by hand calculations

540

prior to selecting input conditions for a computer run to duplicate an incident. Table I shows the re­ sults of three such preliminary calculations using three measured debris radii and corresponding times from a 25-percent yield detonation of a Titan ETC. The first assumed percent yield in these calculations rapidly converges on the true value, oscillating slightly about it in the process. The calculation procedure is as follows:

Assume that a Titan me detonated and that the radius of explosion products (Rep) was measured as 30.20 meters at 17,329 microseconds. We first as­ sume any percent yield, say 78.5percent (7.245 x 1010 ergs/gm) from which we get Rs/Rep = 1.094555 at the measured Rep and, in turn, calculate the radius of shock (Rs) as 39.6229 meters. From the measured time of 17,329 microseconds and calculated Rs = 39.6229,

we obtain an energy release of 1.172784 x 1019 ergs (^280 tons TNT) or 24 percent (2.2128 xlO10 ergs/gm).

Next, using the 24 percent calculated as our assumed percent yield and the measured Rep of 30. 20 meters, we get Rs/Rep = 1.128242 and, in turn, calculate Rs =40.8424 meters. From the measured time of 17,329 microseconds and calculated R =40.8424 meters, we obtain an en­ ergy release of 1.2265366 x 10 19 ergs (*293 tons TNT) or 25.1 percent (2.31422 x 1010 ergs/gm).

The 25.1-percent yield obtained is used as the as­ sumed percent yield for the next iteration and the proc­ ess is continued until a satisfactory fit to this and other measured data is obtained. In this way, much com­ puter time will be saved and only those computer itera­ tions absolutely needed will be calculated for the com­ plete detonation.

PROBLEM MOt. WUNDY 303 TITAN 3 C 50 D C 584 TOMSCYCLF TIME(SFC) NEXT TJME^TFP TOTAL FNFR1Y JPT1905 1.75142E-09 7.3312PE-05 fl.02681E 29 36

18 SFP 64

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Figure 4. Titan EIC, 50

Figure 5. Titan me, 50 Percent, Density versus Radius, 0 to 75 Meters

544

10*-

STRTION 1L3X/RP1195 LB. TEST

10* '— 10* 10* 10-'

TIKE - SECCNDS

Figure 6. Sample of Automatic Plot of Output Data Figure 7. A Variable Geometry Calculation Network Shortly After Detonation

I ' Shock Radius, 25% Yield

Shock Radius, 50% YieldShock Radius, 78. 5% Yield

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300Radius (meters)

Figure 8 . Variation of Debris Radius and Shock Radius versus Time for Titan IEEC Detonation

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Table I. Calculation of Shock Radius from Explosion Products Radius for Titan TEC (25-Percent Yield)

Measured

R ep(meters)

*17.59

*30.20

*57.42

Time (microseconds)

5704

17329

42583

Assumed Percent

Yield

78.5 23.0 25.1 78.5 24.0 25.1 78.5 24.0 25.1

CalculatedR /R s ep

1.052811 1.065848 1.065355 1.094555 1.128242 1.127562 1.180275 1.230635 1.229618

Calculated

Rs(meters)

18.5189 18.7483

| 18.7396 |39.622940. 8424

| 40.8178 |67.7714 70.6631

| 70.6047 |

Calculated Percent

Yield

23.0 25.1 25.0 24.0 25.1 25.0 24.0 25.1 25.0

Actual Rs(meters)

| 18.74 |

| 40.82 |

| 70.61 |

REFERENCES

1. One-Dimensional Hydrodynamic Code for Nuclear- Explosion Calculations NOLTR62-168 (DASA-1518).

2. Notes on the Equations UsedinWUNDYNOLTN-5421.

3. R.D. Richtmyer, Difference Methods for Initial- Value Problems, Interscience, 1957.

4. K.P. Stanyukovich, Unsteady Motion of Continuous Media, Pergamon Press, 1960.

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