Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T22:11:21.906Z Has data issue: false hasContentIssue false

Turbulent mixing of passive and chemically reacting species in a low-speed shear layer

Published online by Cambridge University Press:  12 April 2006

R. G. Batt
Affiliation:
Engineering Sciences Laboratory, TRW Space and Defense Systems Group, Redondo Beach, California 90278

Abstract

A series of experiments has been conducted in a low-speed wind tunnel in which measurements were performed in a two-dimensional turbulent shear layer experiencing the mixing of both a passive and a chemically reacting species. The low-temperature air in the jet's primary flow was seeded with dilute concentrations of N2O4 so that the dissociation reaction N2 + N2O4 [harr ] 2NO2 + N2 occurred in a near-equilibrium manner within the mixing layer owing to the turbulent mixing properties and the imposed temperature gradient. Mean and fluctuating values of velocity, temperature and NO2 concentration were measured up to axial distances of 25 in. for jet velocities of 23 and 50ft/s (Rex [les ] 7 × 105) and for three primary temperatures (252, 273 and 305°K). Velocity and temperature measurements were performed with hot-wire probes, whereas a fibre optics light sensor probe was used to measure NO2 concentrations. Local correlations between species and other fluid properties were obtained by positioning a hot-wire sensor within the light gap of the fibre optics probe and simultaneously recording output signals from both probes. A relatively complete set of turbulent statistics was measured for the non-reacting shear layer, including such results as temperature/species correlations, probability densities, filtered and unfiltered moving-frame velocities, skewness and flatness factors, spectra, velocity and temperature integral scales, intermittency factors for velocity, temperature and passive species, and conventional intensities. Some typical results from the investigation are as follows: the turbulent Schmidt and Lewis numbers were 0·5 and 1·0 respectively; the correlation between passive NO2 concentration and temperature was approximately 0·95; dramatic changes consistent with equilibrium chemistry occurred in NO2 concentration profiles with chemical reaction; velocity, temperature and concentration spectra were comparable over a 2½-decade range in wavenumber (k−2); spectra, probability densities, time-trace data and smoke-seeded shear-layer photographs indicate that, for axial locations x = x0 [ges ] 18·5 in. and for speeds u1 [ges ] 23ft/s, undisturbed edge fluid rarely penetrates completely across the mixing region. Although not specifically addressed during the current study, measured results herein suggest that the turbulent motion for the present shear layer is characterized more by random and/or three-dimensionality effects than by large-scale two-dimensional coherent structures, as has been observed recently in other shear-layer investigations.

Type
Research Article
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alber, I. E. & Batt, R. G. 1976 Diffusion limited chemical reaction in a turbulent shear layer. A.I.A.A. J. 14, 7076.Google Scholar
Batt, R. G. 1975 Some measurements on the effect of tripping the two-dimensional shear layer. A.I.A.A. J. 13, 245246.Google Scholar
Batt, R. G., Kubota, T. & Laufer, J. 1970 Experimental investigation of the effect of shear flow turbulence on a chemical reaction. A.I.A.A. Paper no. 70–271.Google Scholar
Becker, H. A., Hottel, H. C. & Williams, G. C. 1967 The nozzle-fluid concentration field of the round, turbulent free jet. J. Fluid Mech. 30, 285303.Google Scholar
Bilger, R. W. 1976 The structure of diffusion flames. Combust. Sci. Tech. 13, 155170.Google Scholar
Boehman, L. I. 1967 An investigation of momentum and mass transport properties in isoenergetic flows. Illinois Inst. Tech. Rep. ARL 67–0058.
Bradbury, L. J. S. 1965 The structure of a self-preserving turbulent plane jet. J. Fluid Mech. 23, 3164.Google Scholar
Bradshaw, P. 1966 The effect of initial conditions on the development of a free shear layer. J. Fluid Mech. 26, 225236.Google Scholar
Bradshaw, P. 1967 Irrotational fluctuations near a turbulent boundary layer. J. Fluid Mech. 27, 209230.Google Scholar
Bradshaw, P., Ferriss, D. H. & Johnson, R. H. 1964 Turbulence in the noise-producing region of a circular jet. J. Fluid Mech. 19, 591624.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.Google Scholar
Bush, W. B., Feldman, P. S. & Fendell, F. E. 1976 On diffusion flames in turbulent shear flows; modeling reactant consumption in a mixing layer. Combust. Sci. Tech. 13, 2755.Google Scholar
Castro, I. P. & Bradshaw, P. 1976 The turbulence structure of a highly curved mixing layer. J. Fluid Mech. 73, 265304.Google Scholar
Champagne, F. H., Pao, Y. H. & Wygnanski, I. J. 1976 On the two-dimensional mixing region. J. Fluid Mech. 74, 209250.Google Scholar
Chandrsuda, C., Mehta, R. D., Weir, A. D. & Bradshaw, P. 1977 Effect of free-stream turbulence on large structure in turbulent mixing layers. Submitted to J. Fluid Mech.Google Scholar
Chung, P. M. 1969 A simplified statistical model of turbulent chemically reacting shear flows. A.I.A.A. J. 7, 19821991.Google Scholar
Corrsin, S. & Uberoi, M. S. 1949 Spectra and diffusion in a round turbulent jet. N.A.C.A. Rep. no. 1040.Google Scholar
Davies, P. O. A. L. 1966 Turbulence structure in free shear layers. A.I.A.A. J. 4, 19711978.Google Scholar
Davies, P. O. A. L., Fisher, M. J. & Barratt, M. J. 1963 The characteristics of the turbulence in the mixing region of a round jet. J. Fluid Mech. 15, 337367.Google Scholar
Demetriades, A. 1968a Turbulent front structure of an axisymmetric compressible wake. J. Fluid Mech. 34, 465480.Google Scholar
Demetriades, A. 1968b Turbulence measurements in an axisymmetric compressible wake. Phys. Fluids 11, 18411852.Google Scholar
Drmotakis, P. E. & Brown, G. L. 1976 The mixing layer at high Reynolds number: largestructure dynamics and entrainment. J. Fluid Mech. 78, 525560.Google Scholar
Donaldson, C. Dup. & Varma, A. K. 1976 Remarks on the construction of a second-order closure description of turbulent reacting flows. Combust. Sci. Tech. 13, 5579.Google Scholar
Fiedler, H. E. 1974 Transport of heat across a plane turbulent mixing layer. Adv. in Geophys. 18, 93109.Google Scholar
Fiedler, H. E. 1975 On turbulent structure and mixing mechanism in free turbulent shear flows. In Turbulent Mixing in Nonreactive and Reactive Flows. A Project Squid Workshop, pp. 381410. Plenum.
Forstall, W. & Shapiro, A. H. 1950 Momentum and mass transfer in coaxial gas jets. J. Appl. Mech. 17, 399408.Google Scholar
Forthmann, E. 1934 Ing. Arch. 5, 4261.
Giauque, W. F. & Kemp, J. D. 1938 The entropies of nitrogen tetroxide and nitrogen dioxide. J. Chem. Phys. 6, 4052.Google Scholar
Gibson, M. M. 1963 Spectra of turbulence in a round jet. J. Fluid Mech. 15, 161173.Google Scholar
Glasstone, S. 1946 Textbook of Physical Chemistry, 2nd edn. Van Nostrand.
Grant, H. L. 1958 The large eddies of turbulent motion. J. Fluid Mech. 4, 149190.Google Scholar
Hall, T. C. & Blacet, F. E. 1952 Separation of the absorption spectra of NO2 and N2O4 in the range of 2400–5000 Å. J. Chem. Phys. 20, 17451749.Google Scholar
Hinze, J. O. 1959 Turbulence, 1st edn. McGraw-Hill.
Ikawa, H. & Kubota, T. 1975 Investigation of supersonic turbulent mixing layer with zero pressure gradient. A.I.A.A. J. 13, 566572.Google Scholar
Jones, B. G., Planchon, H. P. & Hammersley, R. J. 1973 Turbulent correlation measurements in a two-stream mixing layer. A.I.A.A. J. 11, 11461150.Google Scholar
Kolpin, M. A. 1964 The flow in the mixing region of a jet. J. Fluid Mech. 18, 52954.Google Scholar
Lawrence, J. C. 1956 Intensity, scale and spectra of turbulence in mixing region of free subsonic jet. N.A.C.A. Rep. no. 1292.Google Scholar
Lee, J. & Brodkey, R. S. 1963 Light probe for the measurement of turbulent concentration fluctuations. Rev. Sci. Instrum. 34, 10861090.Google Scholar
Lees, L. & Hromas, L. 1962 Turbulent diffusion in the wake of a blunt-nosed body at hypersonic speeds. J. Aero. Sci. 29, 976993.Google Scholar
Libby, P. A. 1976 On turbulent flows with fast chemical reactions. Part III: Two dimensional mixing with highly dilute reactants. Combust. Sci. Tech. 13, 7998.Google Scholar
Liepmann, H. W. & Laufer, J. 1947 Investigation of free turbulent mixing. N.A.C.A. Rep. no. 1257.Google Scholar
Lin, S. C. 1966 A bimodal approximation for reacting turbulent flows. I. Description of the model. II. Example of quasi-one-dimensional wake flow. A.I.A.A. J. 4, 202216.Google Scholar
Lin, S. C. & Hayes, J. E. 1964 A quasi-one-dimensional treatment of chemical reactions in turbulent wakes of hypersonic objects. A.I.A.A. J. 2, 1214–1222.
Mayer, E. & Divoky, D. 1966 Correlation of intermittency with preferential transport of heat and chemical species in turbulent shear flows. A.I.A.A. J. 4, 19952000.Google Scholar
Moore, D. W. & Saffman, P. G. 1975 The density of organized vortices in a turbulent mixing layer. J. Fluid Mech. 69, 465473.Google Scholar
Nye, J. O. & Brodkey, R. S. 1967 Light probe for measurement of turbulent concentration fluctuations. Rev. Sci. Instrum. 38, 2628.Google Scholar
O'Brien, E. E. 1971 Turbulent mixing of two rapidly reacting chemical species. Phys. Fluids 14, 13261331.Google Scholar
Oh, Y. H. & Bushnell, D. M. 1975 Influence of external disturbances and compressibility on free turbulent mixing. Aerodynamic analysis requiring advanced computers. N.A.S.A. Special Publ. no. 347, pp. 341376.Google Scholar
Patel, R. P. 1973 An experimental study of a plane mixing layer. A.I.A.A. J. 11, 6771.Google Scholar
Phillips, O. M. 1955 The irrotational motion outside a free turbulent boundary. Proc. Camb. Phil. Soc. 51, 220229.Google Scholar
Proudian, A. P. & Feldman, S. 1965 A new model of mixing and fluctuations in a turbulent wake. A.I.A.A. J. 3, 602609.Google Scholar
Ragsdale, R. G. & Edwards, O. J. 1965 Data comparisons and photographic observations of coaxial mixing of dissimilar gases at nearly equal stream velocities. Lewis Res. Center, N.A.S.A. Tech. Note D-3131.
Rosensweig, R. E. 1959 Measurement and characterization of turbulent mixing. Ph.D. thesis, M.I.T.
Rosensweig, R. E., Hottel, H. C. & Williams, G. C. 1961 Chem. Engng Sci. 15, 111133.
Roshko, A. 1976 Structure of turbulent shear flows: a new look. A.I.A.A. J. 14, 13491357.Google Scholar
Spalding, D. B. 1976 Mathematical models of turbulent flames; a review. Combust. Sci. Tech. 13, 325.Google Scholar
Spencer, B. W. & Jones, B. G. 1971 Statistical investigation of pressure and velocity fields in the turbulent two-stream mixing layer. A.I.A.A. Paper no. 71–813.Google Scholar
Sunyach, M. 1971 Contribution à l’étude des frontières d’écoulements turbulents libres. Sc.D. thesis, Université Claude Bernard de Lyon.
Sunyach, M. & Mathieu, J. 1969 Mixing zone of a two-dimensional jet. Int. J. Heat Mass Transfer 12, 16791697.Google Scholar
Sutton, E. A. 1968 Chemistry in pure-air hypersonic wakes. A.I.A.A. J. 6, 18731882.Google Scholar
Sutton, G. W. & Camac, M. 1968 Wake-temperature turbulent fluctuation decay rates deduced from O2 radiation. A.I.A.A. J. 6, 24022410.Google Scholar
Torr, H. L. 1962 Mass transfer in dilute turbulent and non-turbulent systems with rapid irreversible reactions and equal diffusivities. A.I.Ch.E. J. 8, 7078.Google Scholar
Townsend, A. A. 1949 Momentum and energy diffusion in the turbulent wake of a cylinder. Proc. Roy. Soc. A 197, 124140.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.
Webb, W. H. & Hromas, L. A. 1965 Turbulent diffusion of a reacting wake. A.I.A.A. J. 3, 826837.Google Scholar
Wegener, P. P. 1959 Supersonic nozzle flow with a reacting gas mixture. Phys. Fluids 2, 264275.Google Scholar
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417432.Google Scholar
Winant, C. D. & Browand, F. R. 1974 Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.Google Scholar
Wygnanski, I. & Fiedler, H. 1969 Some measurements in the self-preserving jet. J. Fluid Mech. 38, 577612.Google Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327361.Google Scholar