3,938 research outputs found
Turbulence modeling
The performance of existing two-equation eddy viscosity models was examined. An effort was made to develop better models for near-wall turbulence using direct numerical simulations of plane channel and boundary layer flows. The asymptotic near-wall behavior of turbulence was used to examine the problems of current second order closure models and develop new models with the correct near-wall behavior. Rapid Distortion Theory was used to analytically study the effects of mean deformation on turbulence, obtain analytical solutions for the spectrum tensor, Reynolds stress tensor, anisotropy tensor and its invariants, which can be used in the turbulence model development. The potential of the renormalization group theory in turbulence modeling was studied, as well as compressible turbulent flows, and modeling of bypass transition
Turbulence modeling
In recent years codes that use the Navier-Stokes equations to compute aerodynamic flows have evolved from computing two-dimensional flows around simple airfoils to computing flows around full scale aircraft configurations. Most flows of engineering interest are turbulent and turbulence models are needed for their prediction. Yet, it is known that present turbulence models are adequate only for simple flows and do poorly in complicated flows such as three-dimensional separation, or large-scale unsteadiness. The same progress that allowed the development of these aerodynamic codes, namely the introduction of supercomputers, has allowed us to compute directly turbulent flows, albeit only for simple flows at moderate Reynolds numbers. These direct turbulence simulations provide us with detailed data that experimentalists were not able to measure. This work is motivated by the fact that data exists for developing better turbulence models and by the need for better models to compute flows of engineering interest. The objective is to develop turbulence models for engineering applications. The model categories that show promise for immediate use are on the two-equation level and the Reynolds-stress level
Modeling of turbulence and transition
The first objective is to evaluate current two-equation and second order closure turbulence models using available direct numerical simulations and experiments, and to identify the models which represent the state of the art in turbulence modeling. The second objective is to study the near-wall behavior of turbulence, and to develop reliable models for an engineering calculation of turbulence and transition. The third objective is to develop a two-scale model for compressible turbulence
Long's Vortex Revisited
The conical self-similar vortex solution of Long (1961) is reconsidered, with
a view toward understanding what, if any, relationship exists between Long's
solution and the more-recent similarity solutions of Mayer and Powell (1992),
which are a rotational-flow analogue of the Falkner-Skan boundary-layer flows,
describing a self-similar axisymmetric vortex embedded in an external stream
whose axial velocity varies as a power law in the axial (z) coordinate, with
phi=r/z^n being the radial similarity coordinate and n the core growth rate
parameter. We show that, when certain ostensible differences in the
formulations and radial scalings are properly accounted for, the Long and
Mayer-Powell flows in fact satisfy the same system of coupled ordinary
differential equations, subject to different kinds of outer-boundary
conditions, and with Long's equations a special case corresponding to conical
vortex core growth, n=1 with outer axial velocity field decelerating in a 1/z
fashion, which implies a severe adverse pressure gradient. For pressure
gradients this adverse Mayer and Powell were unable to find any
leading-edge-type vortex flow solutions which satisfy a basic physicality
criterion based on monotonicity of the total-pressure profile of the flow, and
it is shown that Long's solutions also violate this criterion, in an extreme
fashion. Despite their apparent nonphysicality, the fact that Long's solutions
fit into a more general similarity framework means that nonconical analogues of
these flows should exist. The far-field asymptotics of these generalized
solutions are derived and used as the basis for a hybrid spectral-numerical
solution of the generalized similarity equations, which reveal the existence of
solutions for more modestly adverse pressure gradients than those in Long's
case, and which do satisfy the above physicality criterion.Comment: 30 pages, including 16 figure
-theory for fractional gradient PDE with VMO coefficients
In this paper, we prove estimates for the fractional derivatives of
solutions to elliptic fractional partial differential equations whose
coefficients are . In particular, our work extends the optimal regularity
known in the second order elliptic setting to a spectrum of fractional order
elliptic equations.Comment: 10 page
Critical assessment of Reynolds stress turbulence models using homogeneous flows
In modeling the rapid part of the pressure correlation term in the Reynolds stress transport equations, extensive use has been made of its exact properties which were first suggested by Rotta. These, for example, have been employed in obtaining the widely used Launder, Reece and Rodi (LRR) model. Some recent proposals have dropped one of these properties to obtain new models. We demonstrate, by computing some simple homogeneous flows, that doing so does not lead to any significant improvements over the LRR model and it is not the right direction in improving the performance of existing models. The reason for this, in our opinion, is that violation of one of the exact properties can not bring in any new physics into the model. We compute thirteen homogeneous flows using LRR (with a recalibrated rapid term constant), IP and SSG models. The flows computed include the flow through axisymmetric contraction; axisymmetric expansion; distortion by plane strain; and homogeneous shear flows with and without rotation. Results show that for most general representation for a model linear in the anisotropic tensor, performs either better or as good as the other two models of the same level
- …