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Simulation Algorithm of Naval Vessel Radiation Noise Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013) Simulation Algorithm of Naval Vessel Radiation Noise XIE Jun DA Liang-long Naval Submarine Academy Naval Submarine Academy QingDao,China QingDao,China [email protected] [email protected] Abstract—Propeller cavitation noise continuous spectrum continuous spectrum caused by periodic time variation of results from noise radiated from random collapses of a large stern wake field that is caused by rotation of propellers, number of cavitation bubbles. In consideration of randomicity namely, time domain statistic simulation is made for of initial collapse of cavitation bubbles and similarity of propeller broadband cavitation noise waveform by use of frequency spectrums of various cavitation bubble radiated Monte Carlo method while taking into account the expected noises, theoretical analysis is conducted on four types of value of continuous spectrum of propeller cavitation radiated cavitation radiated noise continuous spectrum characteristics, noise only. The simulation results show that the input which shows that simulation modeling could be carried out for parameters have specific physical meaning and could be cavitation noise continuous spectrum waveform by use of controlled simply and could simulate the characteristics of Monte Carlo method based on statistics of cavitation bubble cavitation noise continuous spectrum in a better way. radius and initial collapse time. The model parameters are expected values, difference degree and randomicity of II. MODEL FOR NOISE RADIATED FROM SIMULTANEOUS cavitation bubble radius, which will be respectively used to COLLAPSE OF A LARGE NUMBER OF CAVITATION BUBBLES determine base waveform of radiated noise, similarity of various cavitation bubble noise frequency spectrums and Assumption 1: when ship is sailing under given working random collapse process of a larger number of cavitation conditions and sea conditions, the expected value of collapse bubbles. The input parameters have specific physical meaning radius within stern propeller area is R which is constant. and are controlled simply and could simulate the 0 characteristics of cavitation noise continuous spectrum in a Assumption 2: individual cavitation bubble collapse better way and therefore the simulation results could be better radius of cavitation bubble group is random variable R , matching with theoretical analysis. compliance expected value is Rayleigh Distribution of R0 Keywords-waveform simulation; continuous spectrum; propeller cavitation noise; broadband noise and radiated sound pressure pulse is R tp )( and corresponding frequency spectrum is R fP )( . I. INTRODUCTION Assumption 3: by neglecting interaction of cavitation Propeller cavitation noise is one of important radiated bubbles, the far broadband cavitation noise field radius is noise source for recognition of underwater targets which has random variable R which results from noises radiated from been studied widely by scholars at home and abroad[1-4]. cavitation bubble random collapse. Power spectrum of propeller cavitation noise consists of low Probability density distribution of cavitation bubble frequency line spectrum and continuous spectrum. Such continuous spectrum is recognized to be formed by noises collapse radius R could be inferred from assumption 2: radiated from random collapses of a large number of π 2 − R cavitation bubbles. Statistics of test data show that the πR 2 = 4R0 , R ≥ 0 (1) continuous spectrum could increase at the rate of 6- RF )( 2 e 12dB/octave in case of being lower than peak value and 2R0 could decrease at the rate of close to 6dB/octave in case of According to Rayleigh individual cavitation bubble being higher than peak value if such continuous spectrum model[5]: has a peak value in some frequency[5]. For this, frequency 1 P f = ∞ (2) domain method will be usually used for broadband cavitation R 915.0 R ρ noise continuous spectrum waveform simulation, e.g. use white noise to excite the filter with a given power spectrum In the formula above, f R is cavitation bubble bounce shapes so as to acquire broadband cavitation noise waveform frequency, P∞ is middle and far field pressure of liquid, sequence with a given continuous spectrum shape[6-8]. The ρ is liquid density; so, probability density distribution of continuous spectrum shapes could be determined by empirical formula such as Ross formula[5] or by parameter f R is: model such as Esc model[9-10]. Based on research results of predecessors, time averaging treatment is made in this paper to the time variation of Published by Atlantis Press, Paris, France. © the authors 0049 Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013) πf 2 bubbles. Fig 1b is result of simulation analysis which is π 2 − R0 fR 2 exactly the same to theoretical analysis above. = 0 4 f R , f ≥ 0 (3) F() fR 3 e R 2 fR Expected value of cavitation radius is R0 , power spectrum of broadband synthetic noise radiated from simultaneous collapse of a large number of cavitation bubbles compliant with Rayleigh Distribution. a. Base power spectrum ∞ 2 2 = S()()() f F fRR P f dfR 0 2 πf 2 2 R0 (4) ∞ π − fR 4 f 2 = 0 R e PR () f dfR 0 3 b. Power spectrum of synthetic noise 2 fR Figure 1. Simulation results of simultaneous collapse under the same In formula (4), S() f is broadband synthetic noise waveform structure frequency spectrum. B. Different structures of various cavitation bubble A. The same structure of various cavitation bubble waveform waveforms From formula (2), the cavitation bubbles collapse time is Because the sound pressure pulse peak value is positively in positive proportion to cavitation bubbles radius in the 2/3 proportional to R , in case of only relative amplitude to be same area of liquid; so, the cavitation bubbles of different considered, it is as follows: radius will have different collapse times which will then result in differences between various cavitation bubble = 2/3 PR ()() f R P1 f (5) radiated noise spectrums. It is worked out from formula (2) and (4): In formula (5), P1() f represents cavitation bubble π 2 2 frequency spectrum when R=1, hereinafter called base − R 2 ∞ πR 2 frequency spectrum. The corresponding power spectrum is = 4R0 (9) S() f e PR () f dR called base power spectrum and the corresponding waveform 0 2R2 is called base waveform. 0 It could be worked out as follows from formula (2): The formula above shows that the broadband synthetic noise power spectrum radiated from simultaneous collapse of 1 P∞ R = (6) cavitation bubbles of different radius is modulus square of ρ 0.915 f R weighted sum of noise spectrum radiated from cavitation Infer with formula (5) and (4): bubbles of different radius. The time scale factor is used in 2 simulation to describe the effect of time length of cavitation πf 2 2 R0 ∞ π − 2 P∞ f R 2 2 bubbles collapse on the variation of waveform. Therefore, = 2/3 0 4 f R S( f ) 1.3( ) e dfR P1 () f (7) ρ 0 2/9 δ 2 f R variance of time scale factor can be used to describe the 2 difference of noise spectrum PR () f radiated from πf 2 2 R0 ∞ π − cavitation bubbles of different radius which is called degree P∞ fR 2 = 2/3 0 4 f R Set C 1.3( ) e dfR ,C is of difference. The larger the degree of difference is, the ρ 0 2/9 2 fR smaller the similarity of broadband synthetic noise power spectrum and base power spectrum is, or vice versa. Fig 2 is constant, and it is worked out as follows: simulation result that is worked out from formula (9). The 2 2 S()() f= C P f (8) digits in the fig are cavitation bubble radius. a and b are 1 simulation results in case of δ being smaller, and c and d are The analysis process above shows that the broadband δ synthetic noise power spectrum radiated from simultaneous simulation results in case of being larger. The simulation collapse of a large number of cavitation bubbles of different results verify the correctness of theoretical analysis above. radius will be exactly the same to base power spectrum in Meanwhile, formula (9) shows that the larger the cavitation terms of shapes in case amplitude normalized frequency bubble radius R is, the larger the radiated noise pressure spectrums of various cavitation bubbles radiated noise are weight coefficient and the larger the contribution to total the same. Constant C represents proportional coefficient of sound field is if R0 is given. The larger the R0 is, the total noise energy radiated from cavitation bubbles of smaller radiated sound pressure weight coefficient is and the different radius to radiated energy of each unit of cavitation smaller the contribution to the total sound field is. Published by Atlantis Press, Paris, France. © the authors 0050 Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013) 0.85 radiated from cavitation bubbles that collapse randomly in a 0.6 large number and at different times can be expressed as: 2 0.8 πR2 ∞ − ∞ 2 πR 2 − ω = 4R0 j t0 S() f e P1() f e dt0 dR 0 2 −∞ 2R0 a.Power spectrum of noise radiated from cavitation bubbles of different 2 πR 2 radius in case of δ =10 − ∞ πR 2 ∞ − ω = 4R0 j t0 e dR P1() f e dt0 0 2 −∞ 2R0 ∞ 2 − ω = C P() f ej t0 dt (12) 1−∞ 1 0 π 2 b.Power spectrum of synthetic noise in case of δ =10 − R ∞ πR 2 In formula (12), constant = 4R0 . C1 e dR 0.8 0.55 0 2 0.5 0.3 2R0 It is known from formula (12) that the cavitation bubbles that are different in radius and identical in waveform structure have energy contributions to the broadband c.
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