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Hydrodynamic stability of boundary layers with surface mass transfer

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Abstract

The linear stability of the flat plate boundary layer with surface blowing and suction is investigated by the application of numerical techniques. Complete neutral stability curves, critical Reynolds numbers and wave numbers, and other stability characteristics are determined for a wide range of surface mass transfer intensities. The critical Reynolds number, based on the displacement thickness, is found to vary from 59 to 32500 between the extreme limits of blowing and suction that are investigated. Comparisons are made between the present results and available linear stability information for boundary layers with surface mass transfer and with free-stream pressure gradients. The universal stability bound of Joseph is evaluated and compared with the corresponding numerically exact neutral stability curve.

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Abbreviations

c :

complex wave velocity, normalized by u ∞

F :

reduced stream function, (3)

H :

shape factor, (8)

Re :

Reynolds number; Re δ=u ∞ δ/ν; Re 1=u ∞ δ 1/ν; Re 2=u ∞ δ 2/ν

U :

dimensionless velocity, u/u ∞

u :

streamwise velocity component

u ∞ :

free-stream velocity

v :

transverse velocity component

v w :

blowing or suction velocity at plate surface

x :

streamwise coordinate

Y :

dimensionless coordinate, y/δ

Y c :

location of critical layer

y :

transverse velocity component

α :

wave number; αδ=αδ; α 1=αδ 1

δ :

boundary layer thickness, (6a)

δ 1 :

displacement thickness, (6b)

δ 2 :

momentum thickness, (6c)

η :

similarity variable, (3);η δ, η 1, and η 2 defined in (7)

ν :

kinematic viscosity

φ :

amplitude of disturbance

ψ :

stream function

c:

critical condition

References

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Author information

Authors and Affiliations

  1. Drexel University, Philadelphia, Pa., USA

    F. K. Tsou

  2. University of Minnesota, Minneapolis, Minn., USA

    E. M. Sparrow

Authors
  1. F. K. Tsou
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  2. E. M. Sparrow
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Tsou, F.K., Sparrow, E.M. Hydrodynamic stability of boundary layers with surface mass transfer. Appl. Sci. Res. 22, 273–286 (1970). https://doi.org/10.1007/BF00400533

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  • DOI: https://doi.org/10.1007/BF00400533

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