Abstract
A formalism previously used in the context of deformable porous media and turbulent/ nonturbulent intermittent flows is restated here. The behavior of the intermittency function derivatives at the interface gives rise to surface integrals over the latter. The conditioned equations of continuity, momentum, energy, vorticity, and conservation of a scalar are derived for the turbulent and irrotational zones. Surface integrals with a precise physical meaning enter the conditioned equations. They can be interpreted as entrainment of mass, momentum, energy and scalar, and as direct interactions between the turbulent and irrotational regions. Use is made of the experimental conditioned measurements for: (i) the plane wake behind a heated flat plate, and (ii) the heated turbulent round jet; the profiles of entrainment of mass and the combination of direct interactive force and entrainment of momentum are calculated. These derived profiles are compared with models proposed by previous investigators.
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Abbreviations
- C:
-
Molecular flux of scalar through the interface, Eq. (41)
- D:
-
Orifice diameter for the jet
- dS:
-
Interface surface infinitesimal element
- E:
-
Entrainment of mass per unit mass, Eq. (17)
- F:
-
Mean force per unit mass of turbulent on irrotational zones
- f1, f2, f3, f4 :
-
Self-preserving functions defined by Eqs. (51)–(64)
- fγ :
-
Interface crossing rate
- g, h2 :
-
Self-preserving functions defined by Eqs. (54) and (63)
- I:
-
Intermittency function
- K:
-
Entrainment of total kinetic energy, Eq. (30)
- l(x):
-
Half-width of the wake based on velocity defect
- M:
-
Average entrainment of momentum, Eq. (21)
- n:
-
Normal to the interface pointing towards the turbulent zone
- P, Q:
-
Any fluid mechanical variables
- p:
-
Pressure
- q:
-
Molecular scalar flux vector
- r:
-
Radial coordinate for the jet
- r1/2 :
-
Half-radius of the jet based on velocity
- S(x, t):
-
Surface of the turbulent/nonturbulent interface
- T:
-
Scalar
- Tm :
-
Maximum value of T at a section of the jet
- t:
-
Time
- UJ :
-
Jet exit velocity
- Um :
-
Maximum value of the mean velocity at a section of the jet
- U0 :
-
Free stream velocity for the wake
- Us :
-
Velocity defect at the centerplane of the wake
- u:
-
Velocity vector
- us :
-
Interface velocity
- u, v:
-
x and y (or r) velocity components
- V:
-
Elementary control volume
- ve :
-
Modulus of the velocity of advance of the interface relative to a fluid element at the same point
- W:
-
Mechanical work done by the turbulent fluid upon the irrotational fluid
- w:
-
Tangential velocity component for the jet
- x:
-
Position vecto
- x, y:
-
Streamwise and normal coordinates
- γ:
-
Intermittency factor
- δm :
-
Momentum thickness of the boundary layer at the trailing edge of the plate
- δij :
-
Kronecker delta
- η:
-
Similarity variable
- Θ:
-
Mean entrainment of scalar T
- μ:
-
Viscosity of the fluid
- v:
-
Kinematic viscosity of the fluid
- ρ:
-
Density of the fluid
- σij :
-
Viscous stress tensor
- ф:
-
\(\frac{{\sigma _{ij} }}{\rho }\frac{{\partial u_i }}{{\partial x_j }}\) in the kinetic energy equations
- ωi :
-
Vorticity component
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© 1979 Springer-Verlag Berlin Heidelberg
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Dopazo, C., O’Brien, E.E. (1979). Intermittency in Free Turbulent Shear Flows. In: Durst, F., Launder, B.E., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows I. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46395-2_2
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DOI: https://doi.org/10.1007/978-3-642-46395-2_2
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