Cross-Wavelet Techniques for Estimating Uncertainty in Propagating Shocks and Detonations

  • F. K. Lu
  • A. A. Ortiz
Conference paper


The speed of a propagating shock or detonation wave is a parameter for characterizing impulse facilities and for understanding detonation phenomena, amongst others. The propagation speed determined by the time-of-flight (TOF) method, also known as the time delay method, is

$$ U = \Delta x/\Delta t (1) $$
where Δx is the distance between two transducers over which the wave passes by in a time interval of Δt. While this method is well established, it is arbitrary as can be seen in Fig.1 where different pairs of data points can be used to form Δt. The spread in the rise time depends on a number of factors, such as the size of the transducer, whether the transducer is recessed, viscous effects, high-frequency ringing and the data sampling rate. The arbitrariness in selecting the two points does not allow the method to provide an objective estimate of the uncertainty despite its simplicity. The estimate becomes increasingly unreliable if the error of the time estimate is comparable to ΔT. This may occur if the transducers are closely spaced or if the sampling rate is low. For the same record length, increasing the sampling rate does not fundamentally overcome this difficulty although it may reduce the uncertainty in the ΔT estimate.


Detonation Wave Shock Tube Continuous Wavelet Transform Haar Wavelet Morlet Wavelet 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • F. K. Lu
    • 1
  • A. A. Ortiz
    • 1
  1. 1.Aerodynamics Research Center, Mechanical and Aerospace Engineering DepartmentUniversity of Texas at ArlingtonArlingtonUSA

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