Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

non-buoyant axisymmetric jet issuing steadily from an orifice into a semi-infinite stationary environment and a buoyant jet in the
same environment. The work is a continuation of Basu and Mansour.
Author
Reynolds Averaging; Large Eddy Simulation; Direct Numerical Simulation; Mathematical Models; Plumes; Turbulence
20010022652 Stanford Univ., Center for Turbulence Research, Stanford, CA USA
Dynamic Wall Modeling for LES of Complex Turbulent Flows
Wang, Meng, Stanford Univ., USA; Annual Research Briefs - 2000: Center for Turbulence Research; December 2000, pp.
241-250; In English; See also 20010022631
Contract(s)/Grant(s): N00014-95-1-0221; No Copyright; Avail: CASI; A02, Hardcopy; A03, Microfiche
Large-eddy simulation (LES) of wall-bounded flows becomes prohibitively expensive at high Reynolds numbers if one
attempts to resolve the small but dynamically important vortical structures (streaks) in the near-wall region. The number of grid
points required scales as the square of the friction Reynolds number, which is nearly the same as for direct numerical simulation
(DNS). To circumvent the severe near-wall resolution requirement, LES can be combined with a wall-layer model. In this
approach, LES is conducted on a relatively coarse grid designed to resolve the desired outer flow scales. The dynamic effects of
the energy-containing eddies in the wall layer (viscous and buffer regions) are determined from a wall model calculation, which
provides to the outer flow LES a set of approximate boundary conditions, often in the form of wall shear-stresses. Wall models
which supply wall stresses to the LES are also called wall stress models. The simplest wall stress models are analogous to the wall
functions commonly used in Reynolds-averaged Navier-Stokes (RANS) approaches except that they are applied in an instantaneous
sense in time-accurate calculations. The wall function provides an algebraic relationship between the local wall stresses
and the tangential velocities at the first off-wall velocity nodes. This approach was first employed in a channel flow simulation
by Schumann, who assumed that the streamwise and spanwise velocity fluctuations are in phase with the respective surface shear
stress components. A number of modifications to Schumann’s model have been made by, for example, Grotzbach and Werner and
Wengle to eliminate the need for a priori prescription of the mean wall shear stress and to simplify computations, and by Piomelli
et al. to empirically account for the phase shift between the wall stress and near-wall tangential velocity due to the tilting of nearwall
eddies. The algebraic wall stress models mentioned above all imply the logarithmic (power) law of the wall for the mean
velocity, which is not valid in many complex flows. To incorporate more physics into the model, wall stress models based on
boundary layer approximations have been proposed in recent years. In this method, turbulent boundary-layer equations are solved
numerically on an embedded near-wall mesh to compute the wall stress. These equations are forced at the outer boundary by the
tangential velocities from LES, while no-slip conditions are applied at the wall. The turbulent eddy viscosity is modeled by a
RANS type model, such as the mixing-length model with wall damping. Reasonable success has been achieved in predicting
attached flows and flows with fixed separation points, such as the backward facing step flow. Cabot and Moin found that, in the
case of the backward facing step, improved solutions were obtained when the mixing-length eddy viscosity was lowered from
the standard RANS value. A dynamic procedure was suggested to determine the suitable model coefficient.
Author
Reynolds Averaging; Turbulent Flow; Wall Flow; Large Eddy Simulation; Dynamic Models
20010022653 Stanford Univ., Center for Turbulence Research, Stanford, CA USA
Flow in an Impellar Stirred Tank Using an Immersed Boundary Method
Verzicco, R., Stanford Univ., USA; Annual Research Briefs - 2000: Center for Turbulence Research; December 2000, pp.
251-261; In English; See also 20010022631; No Copyright; Avail: CASI; A03, Hardcopy; A03, Microfiche
The present study is concerned with the flow induced by an impeller in a cylindrical tank. Although this is a model problem,
it is relevant to many chemical and food-industry technological processes. In the last decade significant effort has been devoted
to simulate and predict such flows since full-scale testing is very expensive and considerable savings could be achieved if reliable
numerical models could predict the performance of prototypes. Despite the relatively simple geometries and the low Reynolds
numbers involved, the simulation of these turbulent flows is considerably challenging. Some of the difficulties encountered are
the strongly inhomogeneous nature of the turbulence, the small surface of the impeller blades, and the large disparity in time and
length of flow scales. In particular, given the short blade lengths, the boundary layers developing on their surfaces will not be fully
developed; therefore, all turbulence models based on wall functions would give inaccurate results. In addition, RANS models,
even when implemented in the unsteady form, are unlikely to capture all of the time scales ranging from that of the vortex shedding
at the blade tips to the large scale meridional circulation induced in the tank. DNS and LES approaches, in contrast, do not suffer
from the above-mentioned problems although they are more computationally expensive, especially when applied to complex
geometry flows. However, in a recent paper by Verzicco et al., it has been shown that the combination of the ’immersed boundary’
(IB) procedure with DNS and LES simulations can efficiently be used for the accurate prediction and analysis of many technologi-
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