Determination of a RANS Model Form for Incompressible Wall-bounded Turbulent Flows using the Macroscopic Forcing Method and Validation on a Prolate Sphere
Abstract
The main goal of this project is to reveal, verify, and validate accurate model forms forturbulent momentum closures in flows involving turbulent boundary layer separationover curved surfaces. A longstanding challenge in turbulence modeling is a lack ofdirection in determining differential equations that govern the mean field of underlyingturbulent flows. While the mean fields themselves are measurable, there has not yet beena systematic approach that can directly measure the differential equations governing themean fields. As a result, the quest for universal and truly predictive turbulence modelshas long remained unfulfilled.We have developed a physics-based statistical technique, called the Macroscopic ForcingMethod (MFM), for revealing the differential operators acting on the mean fields ofquantities transported by underlying fluctuating flows. Specifically, MFM can preciselydetermine the turbulence closure operators (model form) for scalar and momentumtransport. MFM acts similar to the way that molecular dynamics simulations revealtransport coefficients for a continuum model, except that in MFM both inputs and outputsare in continuum space and MFM does not make any simplifying assumption such asseparation of scales between turbulence and mean features. Most importantly, MFM canquantify key model characteristics including non-locality and anisotropy of theturbulence closure operator. Understanding of these characteristics provides anunprecedented advancement in the development of universal turbulence models.In this project we apply MFM to canonical flows that involve challenging features ofinterest, i.e., turbulent boundary layer separation over smooth surfaces. In its mostcomprehensive form, MFM would determine a full non-local and tensorial eddydiffusivity kernel describing the dependency of all Reynolds stress components at a givenlocation to mean velocity gradient at all other locations. In our research however, we willavoid this expensive path. Instead, through a novel utilization of MFM, we will probecrucial subset information that determines spatiotemporal moments of the eddydiffusivity kernel at each location. Our preliminary study indicates that for any given setof kernel moments one can construct closure models in the form of differential equationswhose solution kernels match the given moments leading to substantial improvement inpredictive capability via matching only few leading moments. Using MFM we willdetermine leading moments associated with the eddy diffusivity operator in a tensorialform. Examining the impact of each moment on model prediction, allows a systematicand quantitative identification of key missing pieces in current RANS models. Onceimproved model forms are obtained through canonical studies, their universality will betested through a validation campaign in collaboration with experimental studiessupported by ONR. Specifically, we will test our models against data obtained from flowover a prolate sphere over a range of angles of attack and under steady and maneuveringconditions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 20, 2020
- Source ID
- N000142012718
Entities
People
- Ali Mani
Organizations
- Office of Naval Research
- Stanford University
- United States Navy