# Data reduction in viscoelastic turbulent channel flows

Monday, October 12, 2009 - 11:00am - 11:40am

EE/CS 3-180

Antony Beris (University of Delaware)

Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flows

typically generate a tremendous volume of information (terabytes per run.

Data reduction is therefore essential in order to allow for an efficient

processing of the data, let alone its preservation for future studies.

However, previous attempts, using a projection of the velocity to the top

Karhunen-Loeve (K-L) modes, failed to produce velocity fields that could

generate the DNS conformation field adequately. In an effort to rectify

this deficiency we investigate here three different approaches that attempt

to introduce small scale information. First, we extended the K-L analysis

that allowed us to use a hybrid measure, based on a weight of the

pseudodissipation and the fluctuating kinetic energy, as a new objective

function. Second, we used a K-L decomposition of the vorticity field using

the enstrophy (average of the square of vorticity fluctuations) as our new

objective function. As a third attempt, we used again the standard velocity

K-L approach, but in the reconstruction stage of the conformation tensor we

compensated by suitably rescaling the Weissenberg number. It is shown here

that, whereas the first two methods fail to give any improvement over the

classical K-L approach, we were able to reconstruct fairly accurately the

conformation field using the third approach, even with a relatively small

set of 1714 K-L modes. The rescaling factor in that method was calculated

objectively, based on the ratio of DNS vs. K-L-reconstructed based estimates

of the extensional deformation rate in the buffer layer. Given that fact,

we hope that this approach can also provide the starting point for future

investigations into low-dimensional modeling of viscoelastic turbulence as

well as other multiscale applications.

typically generate a tremendous volume of information (terabytes per run.

Data reduction is therefore essential in order to allow for an efficient

processing of the data, let alone its preservation for future studies.

However, previous attempts, using a projection of the velocity to the top

Karhunen-Loeve (K-L) modes, failed to produce velocity fields that could

generate the DNS conformation field adequately. In an effort to rectify

this deficiency we investigate here three different approaches that attempt

to introduce small scale information. First, we extended the K-L analysis

that allowed us to use a hybrid measure, based on a weight of the

pseudodissipation and the fluctuating kinetic energy, as a new objective

function. Second, we used a K-L decomposition of the vorticity field using

the enstrophy (average of the square of vorticity fluctuations) as our new

objective function. As a third attempt, we used again the standard velocity

K-L approach, but in the reconstruction stage of the conformation tensor we

compensated by suitably rescaling the Weissenberg number. It is shown here

that, whereas the first two methods fail to give any improvement over the

classical K-L approach, we were able to reconstruct fairly accurately the

conformation field using the third approach, even with a relatively small

set of 1714 K-L modes. The rescaling factor in that method was calculated

objectively, based on the ratio of DNS vs. K-L-reconstructed based estimates

of the extensional deformation rate in the buffer layer. Given that fact,

we hope that this approach can also provide the starting point for future

investigations into low-dimensional modeling of viscoelastic turbulence as

well as other multiscale applications.

MSC Code:

76A10

Keywords: