Recovering density disturbance spectra from FLDI. Part 1

Area of Science:

• Fluid dynamics
• Optical diagnostics
• Wave phenomena

Background:

• Focused laser differential interferometry (FLDI) is sensitive to refractive index fluctuations, crucial for high-speed gas flow analysis.
• Quantitative density fluctuation measurements are essential for understanding complex flow behaviors.
• Existing methods may lack the precision or scope for detailed spectral analysis of flow disturbances.

Purpose of the Study:

• To develop and validate a spectral inversion method for recovering density disturbances from FLDI phase shift data.
• To analyze FLDI response to single- and multiple-frequency plane waves.
• To account for frequency-shifting effects in convective flows.

Main Methods:

• Analytical derivation of FLDI response to sinusoidal plane waves based on Schmidt and Shepherd's ray-tracing model.
• Numerical implementation of the FLDI instrument for validation.
• Development and validation of a spectral inversion technique, incorporating convective flow effects.

Main Results:

• Analytical FLDI response models for single- and multiple-frequency plane waves were derived and validated numerically.
• A spectral inversion method was developed and validated, demonstrating capability to recover density disturbance spectra.
• Consideration of frequency-shifting effects was integrated into the inversion process.

Conclusions:

• The developed spectral inversion method accurately recovers density disturbance spectra from FLDI measurements for specific flow conditions.
• The ray-tracing model provides a robust framework for analyzing FLDI in high-speed gas flows.
• This work lays the foundation for advanced quantitative flow diagnostics using FLDI.