Investigation of measurement sensitivities in cross-correlation Doppler global velocimetry

• Calculation of CRLB minimum velocity estimation variance in CC-DGV.
• Monte Carlo simulations to quantify effects of varying test conditions and velocities.
• Best performance is found for small frequency step size and high vapor modulation depth.

Cross-correlation Doppler global velocimetry (CC-DGV) is a flow measurement technique based on the estimation of Doppler frequency shift of scattered light by means of cross-correlating two filtered intensity signals. The signal characteristics of CC-DGV result in fundamental limits for estimation variance as well as the possibility for estimator bias. The current study assesses these aspects theoretically and via Monte Carlo signal simulations. A signal model is developed using canonical numerical functions for the iodine absorption cell and incorporating Poisson and Gaussian signal noise models. Along with consideration of the analytical form of the Cramér–Rao lower bound, best practices for system settings are discussed. The CC-DGV signal processing routine is then assessed by a series of Monte Carlo simulations studying the effect of temperature mismatch between flow signal and reference detector cells, velocity magnitude, and discretization error in the frequency modulation. A measurement bias was observed; the magnitude of the bias is a weak function of the cell temperature mismatch, but it is independent of the flow velocity magnitude. The measurement variance was found to approach the Cramér–Rao lower bound for optimized conditions. A cyclical bias error resulting from the discrete nature of the laser frequency sweep is also observed with maximum errors of ±1.0%±1.0% of the laser frequency scan step size, corresponding to peak errors of ±0.61±0.61 m s−1 for typical settings. Overall, the signal estimator is found to perform best for matched cell temperatures, small frequency step size, and high velocity regimes, where the relative bias errors are collectively minimized.