Techniques of single-shot thermometry by degenerate four-wave mixing

Abstract

Proper evaluation of high-enthalpy and chemically reacting flows often requires unconventional diagnostics. Temperatures in reentry flows may exceed 10000 K within a few mean-free-paths of a shock front. This temperature rapidly drops as gas molecules dissociate into nonequilibrium species and radicals (Vincenti and Kruger, 1965). Even in flows without such harsh conditions, conventional thermometry and mass spectrometry measurements may have insufficient time and space resolution. Furthermore, these probes are intrusive, affecting the local flow field and chemical composition, e.g.,through catalysis. These problems have led to the application of laser spectroscopy and nonlinear optical techniques for the noninvasive probing of reacting fluid flows. Two of these techniques in particular have reached a fair level of maturity: coherent anti-Stokes Raman scattering (CARS) and laser-induced fluorescence spectroscopy (LIFS) (Eckbreth, 1988). CARS is a coherent optical technique which allows accurate point measurements of species concentration and temperature.Its use is limited by signal-to-noise to probing majority species. LIFS, on the other hand, is an incoherent technique which is much more sensitive than CARS and allows planar measurements, but is much less amenable to quantitative analysis. Degenerate four-wave mixing (DFWM) is a coherent nonlinear optical technique that has only recently been applied to flows of gasdynamic interest. This technique offers the promise of the quantitative accuracy of CARS (Dreier, 1990), the sensitivity of LIFS, and the capability for excellent flow-imaging (Rakestraw, 1990; Ewart, 1989). It can be applied in various ways to provide spatially resolved measurements of species concentration, vibrational populations, rotational populations (and thereby temperature), molecular diffusion rates, and other transport properties of a flowing inert or chemically reacting fluid (Fourkas, 1991). DFWM and CARS may be applied for thermometry in narrowband laser scanning experiments by measuring the ground-state rotational population distribution of a probed species to a Boltzmann distribution (Bervas, 1992). In CARS, rotational spectra are "washed out" at very high temperatures by Doppler broadening, complicating thermometry. Narrowband DFWM spectra are "Doppler-free" (Dreier, 1990), allowing laser-scanning thermometry of high temperature gases encountered, for example, in reentry-type flows. DFWM has several advantages over LIFS. The DFWM signal is coherent (laser-like) allowing efficient signal collection with very high f-number optics. This feature is especially important in flows where optical access is limited or where luminosity is high. In addition, DFWM is not inherently susceptible to quenching (Dreier. 1990), unlike LIFS, allowing the use of DFWM in many cases where LIFS cannot be used or cannot be quantitatively interpreted because of quenching. Degenerate four-wave mixing has the advantage of relative experimental simplicity. Unlike CARS, DFWM has trivial phase-matching requirements. It also requires only one laser and can be applied to atomic species. On the other hand, the interpretation of CARS signals is simpler and much more developed than that of DFWM. In some cases the choice of DFWM over CARS is a trade-off between experimental and computational difficulty. Because the cost of computing power is decreasing while the cost of lasers is relatively constant, this trade-off will continue to shift towards DFWM. This paper provides an overview of two "single-shot" resonant degenerate four-wave mixing thermometry techniques suitable for making measurements in unsteady flows or in pulsed facilities such as the T5 free piston shock tunnel. The first technique involves measuring rotational population distributions and fitting them to Boltzmann distributions to obtain rotational temperatures, and has been the conventional technique used in CARS, LIFS, and now DFWM. Single-shot thermometry by this technique requires a broad bandwidth laser to probe a number of rotational lines simultaneously (Ewart, 1990; Yip, 1992). This requirement complicates both the experimental apparatus and signal interpretation. The second technique involves time resolution of the DFWM signal. Using this novel technique, local sound speeds and transport coefficients can be inferred. The physics of this technique are discussed along with a derivation of an analytical expression for the signal generated by this technique and its experimental advantages and challenges. Other thermometry techniques, such as measuring translational temperatures via DFWM lineshapes, etc., are not included in this paper. The physical processes underlying resonant DFWM in gases are first discussed generically in order to provide insight into this phenomenon. The two techniques of thermometry are then detailed in light of these processes. Complications and experimental considerations are presented. An expression for the time-resolved DFWM thermometry signal is derived. A brief history of the analytical use of DFWM is outlined, concluding with suggestions for future directions of research.

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