## Open Resources

## On-going Projects

## 1. Fourth-order RANS-based turbulence closure

High-order statistical closures based on the Reynolds-averaged Navier-Stokes (RANS) equations have been proposed for turbulence modeling in the 40s, but have not received proper attention even though this is the only approach, where the amount of physics contained in the equations solved is explicitly linked to the number of these equations. Indeed, a solution of the complete set of RANS equations is infinitely close to the accurate solution of the Navier-Stokes equations. Thus, by increasing the closure order, the epistemic uncertainty in a turbulence model, which is due to the lack of the flow physics knowledge, is reduced and the accuracy of model predictions can be improved.

This project advances the development of a fourth-order statistical closure (FORANS closure) capable of accurate description of wall-bounded turbulent flows in a wide range of flow parameters without artificial wall functions and other corrections of the transport equations and without varying values of model coefficients. Reduced-order closures can be developed from the FORASN closure for industrial applications on physics-based grounds.

As in other RANS models, the modeling of terms associated with turbulent diffusion, interaction of turbulent velocity and pressure fields, and dissipation are required to close the FORANS equations. What makes a FORANS closure more attractive than all other RANS models is a possibility to model the turbulent diffusion terms using truncated Gram-Charlier series expansions (GCSE). These models are simple algebraic expressions obtained rigorously with no unknown coefficient involved. They include only velocity moments of the orders lower than the 4th and are applicable in non-Gaussian turbulent flows.

S. V. Poroseva, B. E. Kaiser, J. A. Sillero, S. M. Murman, “Validation of a Closing Procedure for Fourth-Order RANS
Turbulence Models with DNS Data in an Incompressible Zero-Pressure-Gradient Turbulent Boundary Layer,”
* Int. J. Heat Fluid Flow*, 2015.

S. V. Poroseva, S. M. Murman, “ Sensitivity of a New Velocity/Pressure-Gradient Model to Reynolds Number,”
*Proc. TSHP-10*, Chicago, IL, July 6-July 9, 2017.

AIAA2015-3067

S. V. Poroseva, S. M. Murman, “ Reynolds-Stress Simulations of Wall-Bounded Flows Using a New Velocity/Pressure-Gradient Model,”
*Proc. TSHP-9*, Melbourne, Australia, June 30-July 3, 2015.

S. V. Poroseva, S. M. Murman, “
On Modelling Velocity/Pressure-Gradient Correlations in Higher-Order RANS Statistical Closures,”
*Proc. the 19th Australasian Fluid Mechanics Conference*, Melbourne, Australia, December 8-11, 2014.

AIAA2014-2207

## 2. DNS of a spatially developing incompressible mixing layer

Flow conditions used in DNS are close to those from the experiments by Bell & Mehta (1990), where untripped boundary layers co-flowing on both sides of a splitter plate mix downstream the plate. No artificial perturbations are used in simulations to trigger the flow transition to turbulence. DNS are conducted using the spectral-element code Nek5000.

AIAA2017-3641

AIAA2018-3226.

Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. Flow visualization using FieldView software was possible thanks to Intelligent Light who provided an academic license.

## 3. RANS-DNS simulations for uncertainty quantification in DNS data

S. V. Poroseva, J. D. Colmenares F., S. M. Murman, “"On the accuracy
of RANS simulations with DNS data," * Physics of Fluids *, 2016, 28(11). DOI: 10.1063/1.4966639
manuscript.

## 4. Laminar-turbulent transition: modeling, simulation, experiment.

(in progress)

## Open Resources

## OpenFOAM source files

for two benchmark cases:
a 2D ZPG boundary layer over a flat plate and a 2D bump-in-channel flow (see description at TMBWG),
with the standard formulations of Spalart-Allmaras, Wilcox’s 2006 version
of k-ω, and SST 1994 turbulence models (also as described at the TMBWG website) can be downloaded
here as a single zip file. Changes to the original OpenFOAM files are
documented here . ** Important note:** the
source files are for the OpenFOAM version 2.3.0 only. Any later version of OpenFOAM will, unfortunately, require additional "cleaning"
to get simulation results comparable to those of the NASA codes. If you use our files, please refer to our
paper AIAA2014-2087, where the results obtained with these files
were initially presented. This will be highly appreciated.

## DNS data for 3rd, 4th, and 5th-order velocity moments in a zero-pressure gradient boundary layer over a flat plate at Re_{θ }= 4100 and 5200.

The data are described in
*
S.V. Poroseva, B.E. Kaiser, J.A. Sillero, S.M. Murman, “Validation of a Closing Procedure for Fourth-Order
RANS Turbulence Models with DNS Data in an Incompressible Zero-Pressure-Gradient Turbulent Boundary Layer,”
Int. J. Heat and Fluid Flow, 2015, http://dx.doi.org/10.1016/j.ijheatfluidflow.2015.06.010. *
They can be downloaded here as a single zip-file.
The zip-file contains 6 data files that can be open with any text editor.

## Experimental data for stationary and rotating cylindrical pipe flow

The data were first published in
*
Zaets, P. G., Kurbatskii, A. F., Onufriev, A. T., Poroseva S. V., Safarov, N. A., Safarov, R. A.,
Yakovenko S. N. “Experimental study and mathematical simulation of the characteristics of
a turbulent flow in a straight circular pipe rotating about its longitudinal axis.”
J. Appl. Mech. and Tech. Physics, 1998, 39(2), pp. 249-260. * (See also * A. F. Kurbatskii and S. V. Poroseva, “Modelling turbulent diffusion in a rotating cylindrical pipe flow.”
Int. J. Heat and Fluid Flow, 1999, 20(3), pp. 341-348. *)
The data can be downloaded here as a single xlsx-file.