Model-based review of Doppler global velocimetry techniques with laser frequency modulation

Abstract

Optical measurements of flow velocity fields are of crucial importance to understand the behavior of complex flow. One flow field measurement technique is Doppler global velocimetry (DGV). A large variety of different DGV approaches exist, e.g., applying different kinds of laser frequency modulation. In order to investigate the measurement capabilities especially of the newer DGV approaches with laser frequency modulation, a model-based review of all DGV measurement principles is performed. The DGV principles can be categorized by the respective number of required time steps. The systematic review of all DGV principle reveals drawbacks and benefits of the different measurement approaches with respect to the temporal resolution, the spatial resolution and the measurement range. Furthermore, the Cramér-Rao bound for photon shot is calculated and discussed, which represents a fundamental limit of the achievable measurement uncertainty. As a result, all DGV techniques provide similar minimal uncertainty limits. With Nphotons as the number of scattered photons, the minimal standard deviation of the flow velocity reads about 106m/s/Nphotons, which was calculated for a perpendicular arrangement of the illumination and observation direction and a laser wavelength of 895nm. As a further result, the signal processing efficiencies are determined with a Monte-Carlo simulation. Except for the newest correlation-based DGV method, the signal processing algorithms are already optimal or near the optimum. Finally, the different DGV approaches are compared regarding errors due to temporal variations of the scattered light intensity and the flow velocity. The influence of a linear variation of the scattered light intensity can be reduced by maximizing the number of time steps, because this means to acquire more information for the correction of this systematic effect. However, more time steps can result in a flow velocity measurement with a lower temporal resolution, when operating at the maximal frame rate of the camera. DGV without laser frequency modulation then provides the highest temporal resolutions and is not sensitive with respect to temporal variations but with respect to spatial variations of the scattered light intensity. In contrast to this, all DGV variants suffer from velocity variations during the measurement. In summary, the experimental conditions and the measurement task finally decide about the ideal choice from the reviewed DGV methods.