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Convection with a First-Order Chemically Reactive Passive Scalar

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Turbulent Shear Flows 5

Abstract

Convection between horizontal, stress-free, perfectly conducting plates is examined in the turbulent regime for air. Results are presented for an additional scalar undergoing first order decay. We discuss qualitative aspects of the flow in terms of spectral and three-dimensional isosurface maps of the velocity and scalar fields. The horizontal mean profiles of scalar gradients and fluxes agree rather well with simple mixing-length concepts. Further, the mean profiles for a range of the destruction-rate parameter are shown to be nearly completely characterized by the boundary fluxes. Finally, we use the present numerical data as a basis for exploring a generalization of eddy-diffusion concepts that incorporates necessary non-local effects.

The National Center for Atmospheric Research is sponsored by the National Science Foundation

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Abbreviations

C(x,y,z,t)):

Concentration of decaying scalar

〈C〉):

Horizontal (or ensemble) average of C = 〈C〉 (z, t)

[C]):

Volume average (over periodic domain) of C

D):

Depth of convective layer

E υ ):

Kinetic energy spectrum

g):

Acceleration of gravity

ĝ):

Unit vector along g

k):

Wave number vector

k0):

Lowest k in numerical simulation

Nu):

Heat flux through lower plate in units kΔT/D

Nc(0)):

Scalar flux through lower boundary; units are same as for Nu

Nc(1)):

Scalar flux through top plate; units are same as for Nu

p):

Pressure field

r):

Position vector

Ra):

Rayleigh number gα(T(0) — T(1))/(κνD 3 )

Rc):

Critical Ra for slip boundaries 27 π4/4

Rλ):

Taylor microscale Reynolds number = 〈w 2〉/〈(∂w/∂z)2〉½ν

T(x, y, z, t)):

Temperature

〈T〉):

Horizontal (or ensemble average) of T= 〈T〉 (z, t)

T(0)):

Lower plate temperature

T(1)):

Top plate temperature

u (x, y, z, t)):

Velocity field (x, y, z)

u(x, y, z, t)):

x-component of velocity field

v(x, y, z, t)):

y-component of velocity field

w(x,y,z,t)):

z-component of velocity field

α):

Thermal expansivity

β):

Horizontal average of — ∂T/∂z

β):

C Horizontal average of — ∂C/∂z

γ):

Ratio of diffusivities for C and T, respectively

ΔT):

Temperature excess of lower plate over upper plate

Z):

Reacting scalar variance spectrum

ζ):

Fluctuation of C from its horizontal average

ε):

Fractional destruction rate of C in units of the thermal diffusion time

κ):

Thermometric diffusivity

κ c ):

Diffusivity for scalar C

ν):

Kinematic viscosity

φ 1):

Toroidal velocity variance; see (6 a)

Sw):

Velocity derivative skewness [(∂w/∂z)3]/[(∂w/∂z)2]3/2

ST,C):

Scalar mixed skewness [(∂A/∂z)2 (∂w/∂z)]/[(∂A/∂z)2] [(∂w/∂z)2]½, A = (C, T)

(x, y, z)):

Cartesian components of r

t):

Time

φ 2):

Poloidal velocity variance; see (6 b)

σ):

Prandtl number (ν/ κ)

θ):

Fluctuation of T from its horizontal average

Θ):

Temperature variance spectrum

ω):

Vorticity ∇ × u

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Authors and Affiliations

  1. National Center for Atmospheric Research, Boulder, CO, 80307, USA

    J. R. Herring & J. C. Wyngaard

Authors
  1. J. R. Herring
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  2. J. C. Wyngaard
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Strömungsmechanik, Technische Fakultät, Friedrich-Alexander-Universität, Egerlandstraße 13, D-8520, Erlangen, Fed. Rep. of Germany

    Franz Durst

  2. Department of Mechanical Engineering, Institute of Science and Technology, University of Manchester, PO Box 88, Manchester, M60 1QD, England

    Brian E. Launder

  3. Sibley School of Mechanical Aero Engineering, Cornell University, 238 Upson Hall, Ithaca, NY, 14853, USA

    John L. Lumley

  4. Mechanical Engineering Department, The Pennsylvania State University, University Park, PA, 16802, USA

    Frank W. Schmidt

  5. Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London, SW7 2BX, England

    James H. Whitelaw

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© 1987 Springer-Verlag Berlin Heidelberg

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Herring, J.R., Wyngaard, J.C. (1987). Convection with a First-Order Chemically Reactive Passive Scalar. In: Durst, F., Launder, B.E., Lumley, J.L., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71435-1_27

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  • DOI: https://doi.org/10.1007/978-3-642-71435-1_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71437-5

  • Online ISBN: 978-3-642-71435-1

  • eBook Packages: Springer Book Archive

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