Hybrid time–frequency domain dual-probe coherent anti-Stokes Raman scattering for simultaneous temperature and pressure measurements in compressible flows via spectral fitting
Jonathan E. Retter, Matthew Koll, Chloe E. Dedic, Paul M. Danehy, Daniel Richardson, Sean P. Kearney
Abstract
We demonstrate a hybrid time–frequency spectroscopic method for simultaneous temperature/pressure measurements in nonreacting compressible flows with known gas composition. Hybrid femtosecond–picosecond, pure-rotational coherent anti-Stokes Raman scattering (CARS), with two independent, time-delayed probe pulses, is deployed for single-laser-shot measurements of temperature and pressure profiles along an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mn>5</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-mm</mml:mtext> </mml:mrow> </mml:math> line. The theory of dual-probe CARS is presented, along with a discussion of the iterative fitting of experimental spectra. Temperature is obtained from spectra acquired with an early, near-collision-free probe time delay ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0</mml:mn> </mml:mrow> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:mrow> </mml:math> ) and pressure from spectra obtained at probe delays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>150</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> </mml:mrow> <mml:mn>1000</mml:mn> </mml:mrow> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , where collisions significantly impact the spectral profile. Unique solutions for temperature and pressure are obtained by iteratively fitting the two spectra to account for small collisional effects observed for the near zero probe delay spectrum. A dual-probe pure-rotational CARS system, in a 1D line-imaging configuration, is developed to demonstrate effectively the simultaneous temperature and pressure profiles recorded along the axial centerline of a highly underexpanded jet. The underexpanded air jet permits evaluation of this hybrid time–frequency domain approach for temperature and pressure measurements across a wide range of low-temperature–low-pressure conditions of interest in supersonic ground-test facilities. Single-laser-shot measurement precisions in both quantities and pressure measurement accuracy are systematically evaluated in the quiet zone upstream of the Mach disk. Precise thermometry approaching 1%−2% is observed in regions of high CARS signal-to-noise ratios. Pressure measurements are optimized at probe time delays where the ratio of the late probe delay to the Raman lifetime exceeds four ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:mrow> <mml:mo>></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4</mml:mn> </mml:mrow> </mml:mrow> </mml:math> ). The impact of low-temperature Raman linewidths on CARS pressure measurements is evaluated, and comparisons of CARS pressures obtained with our recent low-temperature pure-rotational Raman linewidth data and extrapolated high-temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Q</mml:mi> </mml:math> -branch linewidths are presented. Considering all measurements with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:mrow> <mml:mo>≥</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4.0</mml:mn> </mml:mrow> </mml:math> , measured pressures were on average 7.9% of the computed isentropic values with average shot-to-shot deviations representing a combination of instrument noise and fluid fluctuations of 5.0%.