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AGARD Working Group 21 data base - October 1997
CASE - PCH03

FULLY DEVELOPED PIPE-FLOW RESULTS OF EXPERIMENTS AND DIRECT NUMERICAL SIMULATIONS

J.M.J. den Toonder, J.G.M. Eggels and F.T.M. Nieuwstadt Laboratory for Aero- and 
Hydrodynamics Delft University of Technology Rotterdamsweg 145, 2628 Delft, The Netherlands


Experiments with two-component laser doppler anemometry and Direct Numerical Simulations (DNS) on fully developed turbulent flow in a circular pipe.
Additional information about the experiments can be found in references  toonder95a, toonder95b and
for the DNS simulations in references 
kn:eggels93,eggels94a,kn:eggels94b}

Geometry of the domain

Experiments

Cylindrical pipe geometry with a diameter of 4 cm and a total length of 34 m. At the beginning of the pipe the flow is tripped. All experimental data are taken at a position where the flow can be considered
as a fully developed turbulent pipe flow.

DNS Calculations

Circular pipe with length L=5D, D being the pipe diameter.
The DNS calculations are done with a second order accurate finite volume code. Number of grid points in radial, tangential and streamwise directions is 96, 128 and 256, respectively. The gridspacing in viscous units in radial, tangential (at the pipe wall) and axial direction is 1.88, 8.84 and
7.03, respectively

Flow characteristics

Fully developed turbulent pipe flow.

Flow parameters

Experiments


Water at a temperature T=16.6 degrees C, rho=998.9 kg/m^3 and kinematic viscosity nu=1.09x10^{-6}m^2/s.
Reynolds number based on pipe diameter and mean flow rate $Re=24580$
Reynolds number based on pipe diameter and wall shear stress velocity Re_\tau=1382,
with wall shear stress velocity u_\tau=0.0373 m/s.
Wall position correction delta r=-2.92\times 10^{-5}m.

DNS Calculations


Reynolds number based on pipe diameter and bulk velocity $Re_b=5300$
Reynolds number based on pipe diameter and centerline velocity $Re_c=7000$
Reynolds number based on pipe diameter and wall shear stress velocity 
Re_tau=360


Inflow conditions

Not applicable. The DNS calculations use periodic boundary conditions and the
flow field in the experimental section is a fully developed turbulent flow.


Available quantities

Experiments


Axial and radial components of mean and rms velocity, skewness and flatness
as a function of r^+ and r/D.
Relative statistical errors in mean and rms velocity components and flatness
as a function of r^+ and r/D.

Turbulent shear stress tau_T=uv^+, viscous shear stress tau_V=-dU_z^+/dr^+ and non-dimensionalised production of turbulent energy P_{zz}=-\tau_T dU_z/dr 
as a function of r^+ and r/D
Relative statistical error for tau_T as a function of r^+ and r/D.

For more details see references toonder95a, toonder95b

DNS Calculations

Mean flow quantities:
  Mean (bulk) velocity: U_b=14.73 u_tau
  Centerline velocity: U_c=19.31 u_tau
  Friction coefficient: C_f=9.22 x 10^{-3}

Mean Axial velocity profile: <U_z>/u_\tau as a function of r/D

Root mean square (rms) values as function of r/D:
   Radial component of root mean square velocity: U_r_rms/u_tau
   Tangential component of root mean square velocity: U_t_rms/u_tau
   Axial component of root mean square velocity: U_z_rms/u_tau
   Root mean square pressure fluctuations: p_rms/rho u^2_tau

Reynolds stress <u_r u_z>, viscous stress -\nu d<U_z>/dr and total shear stress 
   <u_r u_z>-\nu d<U_z>/dr as a function of r/D

Higher order statistics: For the three velocity components and the pressure
fluctuations the third and fourth moments are provided as a function of r/D

Energy budgets of the Reynolds stresses <u_r u_r>,
<u_t u_t>, <u_z u_z> and <u_r u_z> with:
   TD: Turbulent diffusion
   PR: Production
   VP: Velocity pressure-gradient interaction
   VD: Viscous diffusion
   DS: Viscous dissipation
   Sum: TD+PR+VP+VD+DS

For more details see references eggels93,eggels94a,eggels94b}.
Size and present format of data

Inlet conditions: Not applicable

Symmetries: The flow field is axisymmetric and homogeneous in the axial direction.

Geometry: The geometry is a circular cylinder.


Outlet conditions: Not applicable



eggels93

Eggels, J.G.M., Westerweel, J., Nieuwstadt, F.T.M. and Adrian, R.J.,
"Direct numerical simulation of turbulent pipe flow: A comparison between simulation and experiment 
at low Reynolds number", Applied Scientific Research, Vol. 51, pp. 319-324, 1993.

eggels94a

Eggels, J.G.M., "Direct and large eddy simulation of turbulent flow in a
cylindrical pipe geometry", PhD Thesis, Delft University of Technology, Delft,
The Netherlands.


eggels94b
 
Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J.,
Friedrich, R. and Nieuwstadt, F.T.M., "Fully developed turbulent pipe flow:
a comparison between direct numerical simulation and experiment",
Journal of Fluid Mechanics, Vol 268, pp. 175-209, 1994.

toonder95a

den Toonder, J.M.J., "Drag reduction by polymer additives in a turbulent pipe
flow: laboratory and numerical experiments", PhD Thesis,
Delft University of Technology,
Delft, The Netherlands, 1995

toonder95b

den Toonder, J.M.J. and Nieuwstadt, F.T.M., "Reynolds number effects in a turbulent
pipe flow for low to moderate $Re$", submitted to Physics of Fluids, 1995.