engineering innovation

engineering innovation

Thin-Filament Velocimetry

ISSI

TFV of a Flame

Thin-Filament Velocimetry and Pyrometry

Larry P. Goss, William L. Weaver and Darryl D. Trump

Innovative Scientific Solutions, Inc.

and

James R. Gord

AFRL/PRSC

A novel technique employing a thin ceramic filament has been developed for the simultaneous measurement of temperature and velocity in combusting flowfields. The technique utilizes the optical analog of hot-wire anemometry for velocimetry and blackbody emission for thermometry. The energy flux from a laser is employed to heat a section of 14-m -SiC filament, and the temperature relaxation of the filament is tracked by its graybody emission. Heat-transfer coefficients are measured directly, allowing gas properties to be determined. A modified-King's-Law Nusselt-number correlation was found to yield the best agreement with experimental results. A fully explicit time-dependent model was employed for numerical fitting of the experimental velocity results. Profiles of a premixed propane-air flame were obtained and compared with LDV measurement results.

INTRODUCTION

In previous studies by the authors, the graybody emission from a thin -SiC filament was utilized to investigate the temperature profiles of premixed and diffusion flames. [1-6] The -SiC filament is commercially available, has a diameter of 14 m, and displays low thermal conductivity along the filament axis, making it ideal for spatial determination of temperature profiles.

Because of the small size of the filament, it responds quickly to temperature (and velocity) changes in its surroundings; its high emissivity (0.88), which is constant over a wide temperature range, allows quantitative conversion of filament-emission intensity to gas temperature. The technique known as Thin-Filament Pyrometry has been applied in several studies involving non-sooting laminar, [1] turbulent, [2-6] and sooting flames. [7] The thermal properties of the filament have been modeled (steady state) in two earlier studies, [8-9] and a full non-steady, time-dependent heat-transfer model has also been developed. [7] Because of the strong dependence of the filament response on Reynolds number and the thermal properties of the flowfield, velocity as well as temperature information can be obtained from the filament emission.

The advantages of this technique over the use of conventional hot-wire-anemometer probes is that both temperature and velocity can be determined simultaneously and that the technique can be applied to combusting flowfields. [10] The authors previously investigated the velocimetry capabilities of the thin filament in the case of a laminar air jet. [11]

Three separate approaches to obtaining velocities by heating the filament with a laser source were examined: 1) steady state, 2) impulse (square wave), and 3) sinusoidal. The response of the laser-heated filament was modeled using an explicit time-dependent model; in the present study this model was modified for numerical fitting of experimental decays. The present study represents the first application of the combined thin-filament velocimetry and pyrometry techniques in a combusting environment.

Experimentally, the energy flux of a laser is used to heat a small section of the filament, the emission from which is observed by an InGaAs detector and converted to filament temperature and velocity. In the impulse-flux-heating case (square wave) utilized in this study, the relaxation of the temperature to that of the ambient surroundings after heating by the laser is tracked to determine the gas velocity. The velocities obtained by the Thin-Filament Velocimetry (TFV) technique in a premixed propane-air flame and those obtained by a conventional Laser Doppler Velocimetry (LDV) instrument are compared.

THEORY AND MODEL

(1)

where k is the thermal conductivity of the filament, T is the filament temperature, T gas is the temperature of the surrounding gases, T ref is a reference temperature, x refers to the distance along the axis of the filament, is the density of the filament, h is the convective heat-transfer coefficient, d is the diameter of the filament, is the Stefan-Boltzmann constant, is the emissivity of the filament, is the laser flux used to heat the filament, and C is the heat capacity of the filament.

The expression presented in Equation 1 assumes that the energy balance of the filament is coupled with the exact transport solutions for the surrounding fluid only through the heat-transfer coefficient. All fluid properties are included in the calculation of h and do not appear explicitly in the filament energy balance. Radiation, absorption, and emission from surrounding gases or soot are neglected because of the additional requirements to model the surrounding fluid and combustion processes. In addition, it is assumed that no temperature gradient exists within the differential section of the filament.

Equation 1 was used as the basis for an explicit, finite-difference numerical calculation of filament temperature as a function of time. The heat-transfer coefficient was calculated using a Nusselt-number correlation and could be varied as a function of position and time to correspond to spatial and time dependent velocity profiles. Gas-temperature and external-energy-flux terms could also be varied as a function of position and time.

Equation 1 can be rearranged for calculating the heat-transfer coefficient, h , from the temperature of the filament and of the surrounding gas as a function of time and position

(2)

If a correlation is employed for the relationship between Nusselt number and Reynolds number, it is possible to calculate the velocity of a fluid flowing in the direction perpendicular to the filament. Such a correlation is the experimentally obtained modified King's-Law correlation of the Nusselt number for convective flow across a cylinder when the Reynolds number is between 0 and 44, as given by

(4)

Rearranging Equation 4 and solving for temperature yields

(5)

where

(6)

is the convective time constant of the filament for a given gas temperature and velocity. Equation 6 shows that the convective time constant is a function of filament properties (i.e., density, heat capacity, and diameter--all of which are assumed to be constant in this study), and gas properties through the heat-transfer coefficient, h . The convective time constant is a maximum for low temperature/low velocity and a minimum for high temperature/high velocity.

RESULTS

For evaluation of the TFV technique in cold flow, a series of measurements was made on a 6-mm-diameter nitrogen laminar jet. The velocity measurements were made 2 mm above the jet exit and covered a wide range of flow conditions (0.5 - 25 slpm). Velocities obtained using the TFV technique were compared with those obtained using an LDV instrument. The results are shown in Figure 1. In this figure the velocity obtained with the TFV technique is plotted as a function of that obtained with the LDV instrument under each flow condition. The experimentally observed slope of 1.012 for the resulting line indicates close agreement between the results from the two velocimetry techniques.

For evaluation of the TFV technique under flame conditions, a premixed propane-air flame (0.3 slpm propane, 5.2 slpm air) was chosen for study because of the small change in gas properties which occurs between products and reactants. The choice of gas is important when velocity measurements are to be made since both the kinematic viscosity and the thermal conductivity of the gas affect the observed rate of cooling (or heating) of the filament. A comparison of results obtained with the LDV and TFV instruments for the centerline profile of the flame is shown in Figure 2. The agreement between the results achieved with the two techniques is quite good.

The TFV technique was used for simultaneous spatial profiling of the values of temperature and velocity of the premixed propane-air flame. A 7 x 12 point two-dimensional grid was adopted for studying the flame. Starting at a location 1 mm above the exit of the 10-mm-diameter tube, a 2-mm radial/6-mm axial grid was used to profile the flame. Because of the symmetry of the flame, only one-half of the flame was profiled. Figure 3(a) displays an overlay of the velocity contour and temperature image of the flame. For this figure the acceleration of the velocity field resulting from the high-temperature zones can be clearly seen. Figure 3(b) shows an overlay of the temperature contour and velocity image of the flame. The height of the cold inner cone is evident, along with the flame velocity acceleration with temperature.

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References:

1. V. Vilimpoc, L. P. Goss, and B. Sarka, Opt. Lett. 13 , 19 (1988).

2. T. H. Chen, J. Propul. Power 8 , 46 (1992).

3. T. H. Chen and L. P. Goss, AIAA-89-0156 .

4. R. W. Davis, E. F. Moore, W. M. Roquemore, L.-D. Chen, V. Vilimpoc, and L. P. Goss, Combust. Flame 83 , 263 (1991).

5. F. Takahashi and L. P. Goss, in Twenty-Fourth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, PA, 1992), pp. 351-359.

6. K. Hsu, L. Chen, V. Katta, and L. Goss, AIAA-93-0455 .

7. L. P. Goss, T. H. Chen, V. Vilimpoc, M. E. Post, D. D. Trump, and B. Sarka, AIAA-90-0156 .

8. V. Vilimpoc and L. P. Goss, in Twenty-Second Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, PA, 1988), p. 1907.

9. L. P. Goss, V. Vilimpoc, B. Sarka, and W. F. Lynn, Trans. ASME, J. Eng. Gas Turbines Power 111 , 46 (1989).

10. L. P. Goss, W. L. Weaver, D. D. Trump and J. R. Gord, AIAA-94-0495 .

11. L. P. Goss, J. R. Gord, D. D. Trump, and M. E. Post, AIAA-93-0518 .

* This work was supported, in part by USAF Contract F33615-90-C-2033.