Determining Shock and Detonation Wave Propagation Time Using Wavelet Methods

The propagation speed of a shock or detonation wave in a shock or detonation tube is usually determined by a time-of-flight method by dividing the distance between two transducers with the propagation time of the disturbance signal. Some arbitrariness is inherent in determining the propagation time by this method. A new method based on Haar and Morlet wavelet transforms is reported. The method was tested against a step and a decaying spike with added noise, which are representative of shock and detonation waves. The wavelet methods can be applied to the step discontinuity provided that the SNR ratio is good. The wavelet methods worked very well for the decaying spike in the presence of noise. Nomenclature E [ ] Expected value of fs Sampling frequency nd Number of averages N Sample size TOF Time-of-flight WCCC Wavelet cross-correlation coefficient WECC Wavelet envelope correlation coefficient u ̄ Average wave propagation speed ΔL Distance between two transducers Δt Time-of-flight of a disturbance between two sensors; also, sampling period θxy Phase angle τxy Time delay σ Standard deviation ψ Wavelet function (mother wavelet) ψa,b Translated and dilated wavelet function (daughter wavelet) Ψ Fourier transform of wavelet function <> Mean ensemble valu