The mathematical model and data acquisition of an underwater explosion.

Badara, Nicolae ; Dobref, Vasile ; Tarabuta, Octavian 等

Abstract: This report presents the triangulation of the underwater explosion source.

The analysis is based on the time-delay measurement the underwater acoustic wave, deriving the range and the direction to the underwater source of explosion. The mathematical model is simulated for different values of the time-delay at three sensors. It was built a practical demonstrator, which gave the possibility to verify in real environment the mathematical model.

Keywords: Underwater explosion, triangulation, data acquisition.

1. INTRODUCTION

The hydro-acoustic sensors are placed in the A, B, C points, at [d.sub.0] range; the event takes place in O point. We trace a perpendicular in P point.

The wave will cover the range FB in the time [T.sub.b], which is [T.sub.B] = [t.sub.2] - [t.sub.1], where [t.sub.2] is the time when the wave came in the B point, so FB = [T.sub.B x v, where v is the speed of waave in the water, speed known either from the hydro-acoustic prognosis or approximated at 1450m/s.

The wave will cover the range EC in the time [T.sub.C], which is [T.sub.C] = [t.sub.3] - [t.sub.1], where [t.sub.3].

Is the time when the wave came in the point C, so [E.sub.C] = [T.sub.C] x v.

We can write the following relations:

[(OP).sup.2] = [(OA).sup.2] - [(PA).sup.2] [(OP).sup.2] = [(OF + FB).sup.2] - [(AB + PA).sup.2] (1) [(OP).sup.2] = [(OE + EC).sup.2] - [(AB + BC + PA).sup.2] (2)

The unknown of the system are: OP, OA, PA.

Knowing the sides, in OPA triangle, sin A = OP/OA So the range and the direction are determinates. We observe that if the event is in the left of the hydro-acoustic sensors line, the wave came firstly in point C.

In this case:

[(OP).sup.2] = [(OC).sup.2] - [(PC).sup.2](3) [(OP).sup.2] = [(OF + FB).sup.2] - [(CB + PC).sup.2] (4) [(OP).sup.2] = [(OE + EC).sup.2] - [(CB + BC + PC).sup.2](5)

The unknown of the system are: OP, OC, PC. Knowing the sides, in OPC triangle, sin C = OP/OC. Result PA:

PA = |[(FB).sup.2] + 2| x OA x |FB - [(AB).sup.2]|/2 x AB (6)

OA = 2 x [(FB).sup.2] + 2 x [(AB).sup.2] - [(EC).sup.2]/2 x EC - 4 x FB

[FIGURE 1 OMITTED]

Where AB is the range between the sensors, AB = [T.sub.B] x v, EC = [T.sub.C] x v, with [T.sub.B] = [t.sub.2] - [t.sub.1] and [T.sub.C] = [t.sub.3] - [t.sub.1], [t.sub.1], is the time when the signal was received by the sensor from the A point, [t.sub.2] is the time when the wave came in the B point, [t.sub.3] is the time when the wave came in the C point.

The results of the simulation are presented down. The source programs are given in the table 1.

2. THE COMPOSITION OF THE DEMONSTRATOR

2.1. The underwater module

The underwater unit is realized in the following composition:

1. The hydro-acoustic module, containing a number of three identical subassemblies

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

2. The concentration data and serial transmission module

This module contains three serial cards and one command card. The connection between hydro-acoustic modules and the concentration data module is realized through a submarine special cable which assures the transmission of energy supply from the concentration data module to the sensors and of the received signal by the sensors to the concentration and serialization transmission module.

The general structure of the piezo-ceramic low frequency hydro-acoustic transducer (flex tensional) with symmetric circular section is presented in figure nr. 3. The low frequency hydro-acoustic transducer (flex tensional) is realized in the following structure:

1--The body of the transducer, made by a case from dielectric material which allows the assemblage of the bimorph elements and of the electrodes, adequate connected. The piezo-ceramic element is realized from a composition of zirconium oxides, titan and lead, as basic elements, obtained by pressing and synthesize. The element is polarized at 30 kV c.c. /cm voltage.

2--The bimorph element, made by two piezoelectric discs of circular section, of high frequency, mechanic joined; the flex tensional transducer includes two bimorph transducers;

3--The join electrodes, which assure the electric connection of the bimorph elements with the electric circuit;

4--The external connection band.

3. The low frequency amplifier

The low level signal in the passing band of the hydro-acoustic sensor is amplified in an adequate amplifier physical realized on a structure of two electronic modules joined between, as a sandwich.

4. The digitizing and serializing card

The data from the three hydro-acoustic modules are transmitted as an analogical signal to the concentration and serializing module. This module contains three serializing data cards and a command and control card. The command and control orders are received from an adequate card which orders all the electronic conversion and serializing modules.

Specific is the fact that the serial data from the card are introduced at the IDATA entrance of the other card, so at the entrance in line it will be only a data source, but which came from three hydro-acoustic sensors.

[FIGURE 4 OMITTED]

2.2 The serializing command and control card

The digitizing and serializing card command and control orders are received from the command and control card by the transmission of adequate signals presented in figure nr. 7.

The role of this card is to produce the command signals at the proper moment, which should assure:

--The synchronize and reset of the CAN;

--The command of loading the data from the CAN in the parallel-series registers;

--The clock the parallel-series moving.

The experiment was verified in the basin of the Naval Academy from Constanta (Romania). Experimental recorders have presented in figure 4.

3. CONCLUSIONS

1. In all records it appears a fundamental of low frequency at 300 Hz.

2. The wave form presents two maximum amplitude areas created by the sensors saturation.

4. REFERENCES

Mazzone, L. & Lorenzelli, P. Target localization with multiple sonar receivers, SACLANT UNDERSEA Researc center report, SR-317, 2000.

Jackson, J. & Ir Mohammad, A.,J. Nonlinear FSI due to underwater Explosion, Department of Mechanical Engineering, Clemenceau University, Clemenceau, S.C. 29631, 2000.

Gradinaru, V., Hydroacustic Basis, Ed. Ex Ponto, Constanta, Romania 2004, ISBN 973-644-346-9.

Security Program of Romanian Space Agency, Monitorising System of underwater explosions, No. 43/2005.11.10, Bucharest, Romania.

[TABLE 1 OMITTED]