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MFM simulations of flows near walls

by

Brian Spalding and Sergei Zhubrin, CHAM Ltd, London, England


Abstract and contents

It is shown that the velocity and temperature fluctuations in fluids flowing past solid walls can be well represented by the Reynolds concept, according to which fluid is conveyed to the wall at a finite rate per unit area, and is there brought to equilibrium in respect of velocity and temperature.

With the aid:

calculations are presented, and compared with experimental data, for:
  1. the velocity and velocity-fluctuation distributions in fully-developed turbulent pipe flow;

  2. the velocity and velocity-fluctuation distributions in the same flow, with no transport equations for turbulent properties;

  3. the temperature and temperature-fluctuation distributions in the same flow, at both low and moderate Prandtl numbers;

  4. the distributions of all four of the above in flat-plate boundary flows;

  5. the temperature and temperature-fluctuation distributions in a wake behind a heated cylinder; and

  6. the temperature and temperature-fluctuation distributions in a curved square-sectioned duct.
The agreement between predictions and all experiments is satisfactory with a single value for the one arbitrary constant.

Conclusions are drawn regarding the usefulness of the Multi-Fluid Model for the simulation of wall-friction and -heat-transfer phenomena.

References are provided.


1. The velocity and velocity-fluctuation distributions in turbulent pipe flow;

Details of the simulations.

Illustrations.


2. The velocity and velocity-fluctuation distributions in the same flow, with no transport equations for turbulent properties ;

Details of the simulations.

Illustrations.


3. The temperature and temperature-fluctuation distributions in the same flow, at both low and moderate Prandtl numbers;

Details of the simulations.

Illustrations.


4. The distributions of the velocity and velocity fluctuations in flat-plate boundary flows;

Details of the simulations.

Illustrations.


5. The temperature and temperature-fluctuation distributions in a wake behind a heated cylinder;

Details of the simulations.

Illustrations.


6. The temperature and temperature-fluctuations distributions in a curved square-sectioned duct.

Details of the simulations.

  • Hydrodynamic turbulence: KEMODL
  • Number of fluids: 17
  • Coupling/splitting scheme: PM
  • Time scale: KE/EP
  • Micromixing constant: 5.0
  • Near-wall transfer rate: logarithmic-law "wall-function"

    Illustrations.


    7. Conclusions

    The results which have been presented appear to justify the following conclusions:

    1. With a single value for the micro-mixing constant CONMIX, namely 5.0, it appears to be possible to fit, with fair accuracy, experimental data for distributions of:
      • mean velocity,
      • velocity fluctuations,
      • mean temperature,
      • temperature fluctuations.
      for all the near-wall flows which have been investigated so far.
    2. The pressure-gradient source in the velocity-PDF equations has successfully enabled fully-developed flow conditions to be predicted.
    3. The computational expense of procuring population-grid-independent solutions has proved to be easily affordable.
    4. The treatment of the whole near-wall layer as a generalised "Reynolds Flux" enables the effects of a wall on the fluctuations in the interior of a flow to be accurately simulated.
    5. It has been shown that MFM can be used simultaneously with Kolmogorov-style turbulence models such as k-epsilon and LVEL. It does not however need to rely on these.

    Further applications and developments which immediately suggest themselves include:

    Click here for more about the possibilities of future development


    8. References

    HO Buhr, AD Carr and RE Baltzisher (1968)
    "Temperature profiles in Liquid Metals and the Effect of Superimposed Free Convection in Turbulent Flow", Int. J. Heat Mass Transfer, v11, p. 641-654.
    SE Elgobashi, WM Pun and DB Spalding (1977)
    "Concentration fluctuations in isothermal turbulent confined coaxial jets", Chem. Engng. Science, v32, p. 161-166.
    MH Ibragimov, VI Subbotin et al (1978)
    "Structure of turbulent flow and heat transfer mechanism in channels", Atomizdat, Moscow, USSR.
    J LaRue, PA Libby (1974)
    "Temperature fluctuations in the plane turbulent wake", Phys. Fluids, 1974, N11, p. 1956-1967.
    J Laufer (1953)
    NACA Rep., 1174.
    Y Nagano and M Tagawa (1988)
    "Statistical characteristics of Transfer Processes in Wall Turbulent shear Flow",Transport Phenomena in Turbulent Flows: theory, experiment and numerical simulations, Ed. M Hirata, N Kasagi, Hemisphere, 1988, pp. 275-288
    H Reichardt (1938)
    "Messungen turbulenter Schwankungen", Naturwissenschaften, 404
    O Reynolds (1874)
    "On the extent and action of the heating surface of steam boilers"; Proc. Manchester Lit Phil Soc, vol 8, 1874