Radiation-Induced
Flows and Transport (RIFT)
(supported by
NASA Grant No. NGT5-50447)
________________________________________________________________________________________________________________________
Principal Investigator: Prof. Paul D. Ronney
Graduate Student: David B. Clayton
________________________________________________________________________________________________________________________
Research Plan and Objectives
Many gases and liquids are neither completely transparent nor completely opaque to some wavelengths of electromagnetic radiation (EMR). As a consequence, thermal energy transfer may occur within the fluid by emission and absorption of EMR, a process called "internal radiation." Because of thermal expansion and buoyancy effects, internal radiation may couple to the motion of the fluid. The study of internal radiation and its coupling to fluid flow and heat and mass transport is important in a wide variety of practical problems including glass and semiconductor processing (Salinger et al, 1993), atmospheric flows with application to global climatic change (Gille and Goody, 1964), astrophysical flows (Ruzdjak and Tandberg-Hanssen, 1989), combustion systems, plasma physics (Meerson, 1996) and heat transfer in inhabited enclosures (Tan and Howell, 1991). The purpose of this study is to examine flow-radiation interactions in gases in the microgravity environment to isolate effects which are primarily due to coupling with buoyancy-induced flow from those that are intrinsic to internally radiating fluids, and from these experiments to provide benchmark experiments that may be used to test models of radiatively-driven flow.
Based on a review of the literature on radiatively-driven flows, a set of experiments have been identified that are simple and well-characterized, are relatively straightforward to conduct, have a high probability of success, are likely to yield new scientific results, are of relevance to practical problems, and cannot be studied at earth gravity because of buoyancy influences:
1. Radiatively-affected heat transport in optically-thick media with strongly temperature- dependent radiative properties
a. Stability of steady planar and spherical temperature profiles
b. Dynamics and stability of planar and cylindrical thermal waves
Heat transport in optically-thick media with strongly temperature-dependent radiative conductivity can exhibit some unusual differences from classical thermal conduction in media with constant thermal diffusivity D. These differences include the generation of flows that would be suppressed or masked by buoyancy at one-g. The objectives are to determine the stability criterion, study nonlinear evolutions of these instabilities, and identify the governing mechanisms of instability.
Experiment: Heat transport in optically-thick media with strongly temperature-dependent radiative properties
In an optically-thick gas having a strongly temperature-dependent a and radiative conductivity lR, steady conduction profiles (for example between isothermal flat plates maintained at different temperatures) may be unstable for the following reason. If a parcel of gas receives slightly more heating than its neighbors, its temperature increases, thus a decreases and lR increases. Hence, the thermal energy would penetrate further into the gas in this particular direction. The gas motion caused by thermal expansion further augments the disturbance, stretching the disturbance into a long narrow channel of hot gas. Consequently, an initial perturbation is encouraged, possibly leading to the formation of channels of hot gas. Viscosity would tend to damp this instability, but radiative heating or cooling induces a flow with ReR ~ Pl-1. Since this number can be large for some radiating gases, the induced ReR may exceed the threshold for instability.
The objective of this part of the investigation is to determine the stability boundaries of steady temperature profiles in optically-thick media, in particular as a function of the optical thickness parameter and Planck number, t and Pl respectively. Two gases will be employed: SF6 and CH4, with varying amounts of added helium. CH4 is employed to obtain conditions (at high pressure) where the radiation pressure gradient may be strong enough to influence the flow, and thus enable a comparison of flows with and without significant radiation pressure effects. CO2 will also be used for a few tests because its Planck mean absorption coefficient changes less with temperature than that of SF6 (Dunn et al., 1982) and in this way the effect of the absorption spectra will be evaluated.
While experiments on buoyant flow coupled to gas radiation have been conducted at earth-gravity for a long time, only one “laboratory” study (i.e., excluding astrophysical observations) of radiation-driven flow in an environment free from buoyancy influences has been performed. In work not yet submitted for archival publication, the PI and a graduate student conducted, with support from a 2-year Annual NRA grant, very simple experiments in the NASA-Glenn 2.2 second drop tower. A pressure vessel was filled with SF6 gas and a buoyantly stable temperature gradient was created in the gap between two flat horizontal parallel plates (Fig. 2), the upper one electrically heated and the lower thermoelectrically cooled. In this way a steady temperature gradient was created in the essentially quiescent gas at 1g. Judicious use of baffles and insulation minimized the buoyant flow off of the top plate that would otherwise influence the flow in the test section even after µg began. The thermal field and flow was assessed from images taken by a shearing interferometer system (Fig. 3). After dropping the apparatus, a flow developed in the test section when the chamber contained SF6 (Fig. 1). Very steep gradients and possibly a fingering-like instability can be seen. The same behavior is seen to lesser extent with CO2 (not shown). When the chamber contained N2 (not shown) only decaying flows were observed, indicating that only radiatively-active gases can generate such a flow. This was found even at the same earth-gravity Rayleigh number (Ra) defined as g(DT/T)L3/nD, where L is the plate spacing and n the kinematic viscosity, indicating that the decaying weak buoyant convection present before the drop was not responsible for the observed flow.
The previous section discussed the stability of steady temperature profiles. Some unusual unsteady transport effects are possible in media with D ~ Tn when n > 0. When subject to a heat source, such a medium exhibits “thermal waves,” whose temperature reaches the ambient value (To) at a finite distance (z) from the source. This is unlike the classical constant-D (D being the thermal diffusivity) similarity solution to the unsteady heat conduction equation, where T reaches To only as z ® Ą. In planar geometry, for a constant heat flux the thermal wave propagates at a nearly constant rate for large n. In contrast, for the classical constant-D case the velocity of the isotherms decreases rapidly with time. These results are qualitatively similar for planar, cylindrical and spherical geometry, though in the latter cases the wave progresses more slowly. Because in ionized gases lR ~ T5/2, thermal waves are found in the ionized gases generated by nuclear explosions, supernova explosions, and laser irradiation of thermonuclear fusion pellets (Milhalas and Milhalas, 1984). Thermal waves have not been studied in conventional laboratory experiments, because few substances other than plasmas have sufficiently large n to make the effect highly pronounced. It is possible to study thermal waves in the microgravity environment using an optically-thick radiating gas having Pl << 1. In this case most heat transfer is by radiative rather than molecular conduction, and the radiative thermal diffusivity DR ~ T4/aR. For a gas such as SF6 with aR ~ aP ~ T-2, DR ~ T6. Hence, for some optically thick gases lR and DR may be very strongly temperature-dependent and thermal waves might be observed.
It is plausible that thermal waves in radiatively-active gases could be rendered unstable as well. It is well known from combustion literature (Williams, 1985) that a planar front propagating in a gas at a constant rate will be unstable to hydrodynamic disturbances if the density of the gas behind the front is lower than that ahead of the front. This is called the Darrieus-Landau (DL) instability. It arises because small perturbations of the front which are curved toward (away from) the high-density gas will induce divergence (convergence) of the streamlines ahead of the front, thereby increasing (reducing) the local pressure which encourages the perturbation to grow. A similar behavior could be expected to occur in thermal waves due to their similar character. Unlike a study of planar thermal waves, this proposed study of the stability properties requires mg conditions; otherwise buoyant forces would overwhelm any instability. Consequently, the objective of this set of experiments is to test for the existence of unsteady thermal waves and to determine their stability at mg.
Methodology
To successfully accomplish the proposed experiments, two apparatuses are required: (I) for experiment 1a and 1b (planar), a modified Rayleigh-Bénard apparatus; and (II) for experiment 1a (spherical) and 1b (cylindrical), an isothermal sphere or heated wire in the center of a gas-filled box.
Apparatus (I) (Fig. 2), produces steady planar temperature profiles in a gas confined between parallel plates confined in a pressure vessel. This apparatus (except for the thermal wave experiment modification) has already been built, tested, and operated in the drop tower package as shown in Fig. 3. For the unsteady thermal wave experiments (modified apparatus I), both plates would be thermoelectrically cooled and a very thin heating foil would be placed in the center of the gap. This symmetry ensures that the actual heat flux for each thermal wave is known, i.e., half the total heat input. Metal foils of 25 µm thickness are commercially available that would have a response time of the order (25 x 10-6m)2/(3 x 10-6 m2/sec) » 2 x 10-4 sec, which is much smaller than the radiative time scales of interest. The heat flux can be determined by measuring the voltage drop across the foil and the current passing through it.
Apparatus (II) (Fig. 4a) is simply an electrically heated wire or sphere (Fig. 4b) with an internal electrical heating element placed in the center of a gas-filled box. The size of the pressure vessel will be at least 10 times the sphere diameter. The heated-wire portion of this apparatus has already been built, tested, and operated. For sphere experiments, the sphere radius will be larger than a-1 so that the system is optically thick even at the smallest relevant scale. The mass of the sphere, which will be made of a conductive material, will be minimized to obtain rapid heating at the beginning of the test.
Two types of diagnostic measurements will be made: thermal properties and imaging. The thermal properties will be used to verify the 1-d transport equations, to quantify spatial and temporal deviations from steady and/or 1-d profiles and to quantify the amplitude and temporal spectrum of the disturbances. Thermal properties will be measured by thermocouples and radiometers. Imaging will provide qualitative information on overall flow and thermal structures and provide quantitative 2-d maps of the density field where practical.
For all experiments, fine-wire thermocouples (50mm) will be placed at several locations within the gas. Since their size is much smaller than the spatial scales of interest, their influence on heat transport should be negligible. In addition, their response time (»50ms) is sufficient to study the relatively slow radiative processes of interest. Both wide-angle radiometers mounted flush with a wall and narrow-angle shielded radiometers will be employed, so that both the overall radiant energy and the radiant energy along a line of sight can be evaluated. The thermocouple and radiometer data are collected with analog-to-digital converters and on-board microcomputers.
Since all of the gases proposed for use are transparent at visible wavelengths, it is possible to use a laser shearing interferometer system (Liu and Ronney, 1997) because these techniques are sensitive to changes in gas temperature, which affects the density and index of refraction of the gas. The imaging system consists of a He-Ne laser, adjustable beam expander, mirrors, shearing plate and a ground-glass diffuser screen. A field of view of 5 cm in diameter or larger is possible depending on the size of the beam expander. This system has been used repeatedly in drop tower experiments with great success (see Fig. 3). In all cases, standard video framing rates are adequate because of the slow evolution times of these experiments. As in previous drop-tower experiments, a fiber-optic link to ground-based VCRs will be used.
At earth gravity, the characteristic time scales of radiation-driven flow in gases are much longer than those of buoyancy. For example, at 1 atm and 1000K, the ratio of the radiation time scale divided by the buoyancy time scale for CO, CO2, and SF6 is about 36, 45, and 17, respectively. To make these ratios less than 0.1 to reasonably neglect buoyancy would require g < 1.5 x 10-4go, 1.0 x 10-4go, and 4.5 x 10-4go, respectively. This clearly indicates the need for low-gravity conditions in drop tower experiments because aircraft experiments cannot meet these g requirements. The time needed for these experiments would be no longer than 2 seconds and would therefore be within the capabilities of drop tower facilities at the NASA Glenn Research Center.
The design of the experiments proposed here requires assessment of the relations between a number of time and length scales. The important time scales are the buoyancy-induced transport time scale (tb) for large temperature differences ~ (D/g2)1/3, the conduction/viscous time scale tc ~ (a2D)-1 and the radiation time scale (tr) ~ rCp/(4aPsT3). The relevant length scales include (D2/g)1/3 for buoyancy-induced transport, aP-1 or aR-1 for radiation and (Dtr)1/2 = a-1Pl1/2, which is the smallest scale at which conventional thermal conduction does not smooth out radiatively-driven instabilities. The basic requirements for a meaningful experiment are (A) to suppress buoyancy influences, tb >> tr; (B) to observe radiatively-driven nonuniformities (Dtr)1/2 << aP-1 or aR-1, which is equivalent to Pl-1/2 << 1; (C) for an optically-thin experiment t << 1 and for an optically-thick experiment t >> 1; (D) to witness the evolution of the phenomenon of interest during the drop test, tr must be less than the available duration of µg; and (E) the radiation time scale must be longer than the buoyant time scale at one-g (tr > tb(g=1)), otherwise it is not necessary to employ µg experiments.
The proposed experiments would employ the NASA-Glenn 2.2 second tower to obtain µg conditions. Apparatuses I and II conform to the space, weight, and power limitations of this facility. The time needed for these experiments, say 10tr, would be on the order of 1 second and are within the capabilities of the 2.2 second drop tower. Thus, studies of radiation-driven flow are ideal for short-duration µg experiments because the characteristic time scales of the phenomena are short (typically a few seconds) but the time scales for buoyant influences at earth gravity are even shorter (typically tens of milliseconds).
A complementary modeling study will be pursued which will include both linear stability analysis and detailed numerical computations. The purpose of the modeling study is to determine if the mechanisms of instability proposed here are qualitatively and quantitatively consistent with the experimental results. Our existing FLUENT computational fluid dynamics package will be employed to enable solutions that incorporate realistic data for the transport coefficients. Accurate modeling of the radiative heat transfer will be accomplished with our detailed numerical model for radiation emission/absorption using the Statistical Narrow Band / Discrete Ordinates method developed for combustion problems. This coupling of FLUENT with the radiation solver is straightforward since radiation merely introduces a heat source/sink term into the energy equation, and our versions of FLUENT are already configured for this coupling in the context of our prior combustion studies. A wider range of Planck number, optical thickness, temperature ratio between the plates, etc. can and will be considered since the computations are not restricted to limiting cases such as small Pl. Moreover, complex geometries including edge effects can and will be incorporated into the computations. See Fig. 5 below for a representative image obtained from FLUENT. The image shows CO2 gas between two aluminum plates where the top plate is held at 600K and the bottom plate is held at 300K. The P-1 radiation model is employed along with no-slip boundary conditions at the top and bottom plates. By holding the left and right edges at a constant pressure, the gas is allowed to flow in and out due to the disturbances caused by the thermal radiation. Although this is a crude first approximation at modeling radiation-driven flow it shows the capability of the FLUENT software package for such applications.
Proposed Schedule and Milestones
First Year
References
Dunn, D. S., Scanlon, K. and Overend, J. (1982). The absolute intensities of the binary combination bands in the infrared spectrum of SF6. Spectrochimica Acta 38A, 841.
Gille, J., Goody, R. (1964). Convection in a radiating gas. J. Fluid Mech. 20, 47.
Liu, J. B., Ronney, P. D. (1997). Modified Fourier Transform Method for Interferogram Fringe Pattern Analysis. Appl. Opt. 36, 6231.
Meerson, B. (1996). Nonlinear dynamics of radiative condensations in optically thin plasmas. Revs. Mod. Phys. 68, 215.
Milhalas, D., Milhalas, B. W. (1984). Foundations of Radiation Hydrodynamics, Oxford University Press, New York.
Ruzdjak, V., Tandberg-Hanssen, E., Eds. (1989). Dynamics of Solar Prominences, Springer, Berlin.
Salinger, A. G., Brandon, S., Aris, R., Derby, J. J. (1993). Buoyancy-driven flows of a radiatively participating fluid in a vertical cylinder heated from below. Proc. Roy. Soc. (London) A442, 313.
Tan, Z., Howell, J. R. (1991). Combined radiation and natural convection in a two-dimensional participating square medium. Int. J. Heat Mass Trans. 34, 785.
Williams, F. A. (1985). Combustion Theory, 2nd ed., Benjamin-Cummins, Menlo Park, CA.
Figures:
|
|
|
|
|
|
|
|
|
|
