Abstract
The measured mean velocity profiles at the various stations along a conical diffuser (8° total divergence angle) were found to consist of log regions, half-power law regions and linear regions. The describing coefficients for the inner half-power law region (which followed a rather narrow log region) differed from the standard values due to the axi-symmetric geometry and lack of moving equilibrium of the flow as it attempted to adjust to a varying adverse pressure gradient. However, these coefficients (like those for the linear region) correlated with the local wall shear stress and the kinematic pressure gradient.
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Abbreviations
- A, B :
-
coefficients in logarithmic law velocity distribution (Eq. (1))
- C, D :
-
coefficients in half-power law velocity distribution (Eq. (5))
- Di :
-
inside diameter of feed pipe (10.16 cm)
- d p :
-
outer diameter of Preston tube
- E, F :
-
coefficients in linear law velocity distribution (Eq. (10))
- P s :
-
local static pressure
- R :
-
local radius of diffuser, (D i /2) + x w sin 4°
- Re :
-
Reynolds number, D i U b /v
- U :
-
local mean velocity in the x w direction
- U b :
-
cross-sectional average mean velocity (x-direction) in feed pipe
- U c :
-
mean velocity at the diffuser centerline
- u * :
-
local friction velocity
- u + :
-
dimensionless local mean velocity, U/u *
- χ:
-
axial distance along diffuser centerline (measured from inlet to diffuser) Fig. (2)
- χw :
-
distance along diffuser wall (measured from inlet to difusser (Fig. 2)
- y w :
-
distance from wall in direction orthogonal to wall (Fig. 2)
- y + :
-
dimensionless position, y w u */v
- α:
-
kinematic (axial static) pressure gradient, (1/g9) dP s/dx
- δ* :
-
displacement thickness (Eq. (4))
- Δ:
-
dimensionless pressure gradient parameter, x v/(u*) 3
- χ:
-
Von Karman constant (0.41)
- ϱ:
-
density
- ν:
-
kinematic viscosity
- τ:
-
shear stress
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Trupp, A.C., Azad, R.S. & Kassab, S.Z. Near-wall velocity distributions within a straight conical diffuser. Experiments in Fluids 4, 319–331 (1986). https://doi.org/10.1007/BF00266297
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DOI: https://doi.org/10.1007/BF00266297