Abstract
The probability distributions of the velocity incidence are presented. The analysis is performed in one or two points and the duration of the greatest events is taken into account. The length scaling is given by various positions and the spacings of the probes in a cross section. The flow investigated is a boundary layer submitted to a positive pressure gradient and with self-preserved profiles for mean and conventional turbulent properties.
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Abbreviations
- A(t) or A t :
-
instantaneous incidence: tan−1(V(t)/U(t)) ≡ A + a(t)
- a :
-
coefficient of the relation
- a :
-
coefficient of the relation U 0 = (X − X 0 )a
- C f :
-
friction factor: τ p /0.5 ϱU 2 0
- G :
-
clauser factor:
- G :
-
clauser factor: (H 12 −1)H 12 (C f /2)1/2
- H 12 :
-
form factor: δ 1 /δ 2
- L :
-
threshold for A(t)
- N :
-
probability to observe one event by the two probes (def in the paper)
- P :
-
probability to observe one event by one probe
- pdf :
-
probability density function
- R :
-
Reynolds number basedon δ = U 0 δ/v
- S :
-
skewness factor (for \(g: g^3/{(g^2)^{3/2}})\)
- T :
-
flatness factor (for g: \(g: g^4/{(g^2)^{2}})\)
- X :
-
longitudinal coordinate
- Y:
-
transverse coordinate
- U :
-
longitudinal mean velocity
- U 0 :
-
longitudinal free stream mean velocity
- V :
-
transverse mean velocity
- U(t), V(t):
-
instantaneous velocities, U(t)=U + u(t), V(t)= V+ v(t)
- β :
-
−(δ 1 /τ p )/U 0 (dU 0 /dX)
- δ :
-
boundary layer thickness
- δ 1 :
-
displacement thickness:\(\int^{\delta}_{0}(1-U/U_o)\text dy\)
- δ 2 :
-
momentum thickness:\(\int^{\delta}_{0}(1-U/U_o)(U/U_o)\text dy\)
- Δy :
-
distance between two X-wire probes in a cross section
- v :
-
kinematic viscosity
- τ p :
-
wall friction
- ψ(t):
-
pseudo fluctuating incidence: tan−1(v(t)/u(t))
- ´:
-
R.M.S. value
- —:
-
time average
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Zougari, H., Charnay, G. (1989). Statistical Characteristics of the Velocity Incidence in a Decelerated Boundary Layer. In: André, JC., Cousteix, J., Durst, F., Launder, B.E., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73948-4_15
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DOI: https://doi.org/10.1007/978-3-642-73948-4_15
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