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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

Augmenting RANS Turbulence Models Guided by Field Inversion and Machine Learning

This report investigates the use of a data-driven approach, viz., Field Inversion and Machine Learning (FIML), to improve conventional RANS turbulence models like the Spalart-Allmaras model and the Menter SST k-ω model. One of the crucial aspects of using an ML-based approach with limited training data to produce corrections that are generalizable to a large range of flow configurations is to design appropriate “features” (inputs to the ML model). A model, based on guidance from the FIML methodology, is presented in analytical form. An additional list of potential features is provided. Although these were not used in the present correction, they were considered in the course of its development, and are included to fully document the complete process employed in the present work.

turbulence modeling↗
NASA NTRS2003

Testing of RANS Turbulence Models for Stratified Flows Based on DNS Data

In most geophysical flows, turbulence occurs at the smallest scales and one of the two most important additional physical phenomena to account for is strati cation (the other being rotation). In this paper, the main objective is to investigate proposed changes to RANS turbulence models which include the effects of stratifi- cation more explicitly. These proposed changes were developed using a DNS database on strati ed and sheared homogenous turbulence developed by Shih et al. (2000) and are described more fully in Ferziger et al. (2003). The data generated by Shih, et al. (2000) (hereinafter referred to as SKFR) are used to study the parameters in the k- model as a function of the turbulent Froude number, Frk. A modified version of the standard k- model based on the local turbulent Froude number is proposed. The proposed model is applied to a stratified open channel flow, a test case that differs significantly from the flows from which the modified parameters were derived. The turbulence modeling and results are discussed in the next two sections followed by suggestions for future work.

Venayagamoorthy, S. K.↗
NASA NTRS2015

LagRST Model Predictions of a Wingtip Vortex Floweld

The performance of the new LagRST models is compared with curvature corrected eddyviscosity RANS models. The Reynolds-stress models provide very good predictions of thisow without any additional curvature corrections. Along with comparison of predictionsof the vortex itself, some of the other measurements included in the oweld are comparedwith the predictions in the wake and over the wing. Dierences in predictions between thevarious RANS models in the wake region are small - not substantial, and all predictionsare in line with experimental measurements from 0.005c to 0.67c downstream of the trailingedge, at odds with what self-similar wake analysis would predict.

wing tip vortices↗
DOE OSTI2025

Simulations of Bypass Flow in Prismatic VHTRs

In prismatic Very-High Temperature Reactors (VHTRs), gaps occur between neighboring fuel assemblies referred to as bypass gaps. This work aims to measure the flow distribution between the bypass gaps between neighboring assemblies and the coolant channels within the assemblies. Computational fluid dynamics (CFD) was done using Reynolds-Averaged Navier Stokes (RANS) modeling in STAR-CCM+ to assess the ability of RANS models to accurately capture this phenomena. The RANS results were compared to experimental worked performed by Seoul National University (SNU) and Korea Atomic Energy Research Institute (KAERI) for validation. The CFD results showed good comparison with the experimental data available from SNU and flow split was characterized for multiple configurations, inlet mass flow rates, and bypass gap sizes.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. Finally, the presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

42 ENGINEERING↗
NASA NTRS2015

A Priori Analysis of a Compressible Flamelet Model using RANS Data for a Dual-Mode Scramjet Combustor

In an effort to make large eddy simulation of hydrocarbon-fueled scramjet combustors more computationally accessible using realistic chemical reaction mechanisms, a compressible flamelet/progress variable (FPV) model was proposed that extends current FPV model formulations to high-speed, compressible flows. Development of this model relied on observations garnered from an a priori analysis of the Reynolds-Averaged Navier-Stokes (RANS) data obtained for the Hypersonic International Flight Research and Experimentation (HI-FiRE) dual-mode scramjet combustor. The RANS data were obtained using a reduced chemical mechanism for the combustion of a JP-7 surrogate and were validated using avail- able experimental data. These RANS data were then post-processed to obtain, in an a priori fashion, the scalar fields corresponding to an FPV-based modeling approach. In the current work, in addition to the proposed compressible flamelet model, a standard incompressible FPV model was also considered. Several candidate progress variables were investigated for their ability to recover static temperature and major and minor product species. The effects of pressure and temperature on the tabulated progress variable source term were characterized, and model coupling terms embedded in the Reynolds- averaged Navier-Stokes equations were studied. Finally, results for the novel compressible flamelet/progress variable model were presented to demonstrate the improvement attained by modeling the effects of pressure and flamelet boundary conditions on the combustion.

Quinlan, Jesse R.↗
NASA NTRS2003

Flow Control Analysis on the Hump Model with RANS Tools

A concerted effort is underway at NASA Langley Research Center to create a benchmark for Computational Fluid Dynamic (CFD) codes. both unstructured and structured, against a data set for the hump model with actuation. The hump model was tested in the NASA Langley 0.3-m Transonic Cryogenic Tunnel. The CFD codes used for the analyses are the FUN2D (Full Unstructured Navier-Stokes 2-Dimensional) code, the structured TLNS3D (Thin-Layer Navier-Stokes 3-Dimensional) code, and the structured CFL3D code, all developed at NASA Langley. The current investigation uses the time-accurate Reynolds-Averaged Navier-Stokes (RANS) approach to predict aerodynamic performance of the active flow control experimental database for the hump model. Two-dimensional computational results verified that steady blowing and suction and oscillatory suction/blowing can be used to significantly reduce the separated flow region on the model. Discrepancies do exist between the CFD results and experimental data in the region downstream of the slot with the largest differences in the oscillatory cases. Overall, the structured CFD codes exhibited similar behavior with each other for a wide range of control conditions, with the unstructured FUN2D code showing moderately different results in the separated flow region for the suction and oscillatory cases.

Viken, Sally A.↗
DOE OSTI2022

Development of Explainable Data-Driven Turbulence Models with Application to Liquid Fuel Nuclear Reactors

Liquid fuel nuclear reactors offer innovative possibilities in terms of nuclear reactor designs and passive safety systems. Molten Salts Reactors (MSRs) with a fast spectrum are a particular type of these reactors using liquid fuel. MSFRs often involve large open cavities in their core in which the liquid fuel circulates at a high speed to transport the heat generated by the nuclear reactions into the heat exchangers. This high-speed flow yields a turbulent field with large Reynolds numbers in the reactor core. Since the nuclear power, the neutron precursor’s transport and the thermal exchanges are strongly coupled in the MSFR’s core cavity, having accurate turbulent models for the liquid fuel flow is necessary to avoid introducing significant errors in the numerical simulations of these reactors. Nonetheless, high-accuracy simulations of the turbulent flow field in the reactor cavity of these reactors are usually prohibitively expensive in terms of computational resources, especially when performing multiphysics numerical calculations. Therefore, in this work, we propose a novel method using a modified genetic algorithm to optimize the calculation of the Reynolds Shear Stress Tensor (RST) used for turbulence modeling. The proposed optimization methodology is particularly suitable for advanced liquid fuel reactors such as the MSFRs since it allows the development of high-accuracy but still low-computational-cost turbulence models for the liquid fuel. We demonstrate the applicability of this approach by developing high accuracy Reynolds-Averaged Navier–Stokes (RANS) models (averaged flow error less than 5%) for a low and a large aspect ratio in a Backward-Facing Step (BFS) section particularly challenging for RANS models. The newly developed turbulence models better capture the flow field after the boundary layer tipping, over the extent of the recirculation bubble, and near the boundary layer reattachment region in both BFS configurations. The main reason for these improvements is that the developed models better capture the flow field turbulent anisotropy in the bulk region of the BFS. Then, we illustrate the interest in using this turbulence modeling approach for the case of an MSFR by quantifying the impact of the turbulence modeling on the reactor key parameters.

42 ENGINEERING↗
NASA NTRS2012

Performance of Reynolds Averaged Navier-Stokes Models in Predicting Separated Flows: Study of the Hump Flow Model Problem

Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump.

Cappelli, Daniele↗
DOE OSTI2021

Improved natural convection heat transfer correlations for reactor cavity cooling systems of high-temperature gas-cooled reactors: From computational fluid dynamics to Pronghorn

The Reactor Cavity Cooling System (RCCS) is a common reactor safety system in High Temperature Gas Cooled Reactors (HTGR) that removes heat from the Reactor Pressure Vessel (RPV) by radiation ($\sim 80\%$) and natural convection ($\sim 20\%$). For simulation of accident scenarios of HTGRs, intermediate fidelity and system codes models must be employed for limiting the models' execution time. While accurate quantification of the radiative heat transfer is available in these models, quantification of natural convection must rely on correlations of questionable accuracy for the Nusselt number. Commonly used correlations are based in experiments performed at low Rayleigh numbers and/or using isothermal walls in simplified geometries. Here, this work improves on the accuracy of natural convection heat transfer correlations in support for HTGR designs. These correlations include both local and average Nusselt numbers as a function of the global Rayleigh number, the local Rayleigh number, and the temperature profile at the hot wall of the RCCS. In the absence of dedicated experiments and the difficulty of performing high-fidelity simulations at realistic Rayleigh numbers, the data to fit the correlations are generated with Computational Fluid Dynamics (CFD) using Reynolds Averaged Navier-Stokes (RANS) models. First, a careful selection of the RANS turbulence model is performed by comparing the results obtained with different RANS turbulence models against high fidelity simulations of natural convection at $Ra \ 1 \times 10^{11}$ in a rectangular cavity. Next, the selected model is used to perform simulations of an HTGR cavity at different high Rayleigh numbers $\in [6.1 \times 10^{11},2.9 \times 10^{13}]$ to encompass several HTGR designs, assuming an isothermal RPV wall. The results obtained are used to fit a correlation for the average and space-varying Nusselt number as a function of the global and local Rayleigh numbers via a sparsity-promoting least-squares method. The selected RANS model is then used to perform simulations of a PBMR 400 HTGR cavity with the temperature profiles at the RPV wall obtained during a PLOFC transient. We use the results obtained to fit a temperature-dependent correction to the space-varying Nusselt number with the sparsity-promoting least-squares method. The results obtained in this work, enable system-level codes, such as Pronghorn, to perform higher-fidelity simulations of the heat exchange process in the RCCS while still maintaining a low computational cost.

42 ENGINEERING↗
NASA NTRS2012

Large Eddy/Reynolds-Averaged Navier-Stokes Simulations of CUBRC Base Heating Experiments

ven with great advances in computational techniques and computing power during recent decades, the modeling of unsteady separated flows, such as those encountered in the wake of a re-entry vehicle, continues to be one of the most challenging problems in CFD. Of most interest to the aerothermodynamics community is accurately predicting transient heating loads on the base of a blunt body, which would result in reduced uncertainties and safety margins when designing a re-entry vehicle. However, the prediction of heat transfer can vary widely depending on the turbulence model employed. Therefore, selecting a turbulence model which realistically captures as much of the flow physics as possible will result in improved results. Reynolds Averaged Navier Stokes (RANS) models have become increasingly popular due to their good performance with attached flows, and the relatively quick turnaround time to obtain results. However, RANS methods cannot accurately simulate unsteady separated wake flows, and running direct numerical simulation (DNS) on such complex flows is currently too computationally expensive. Large Eddy Simulation (LES) techniques allow for the computation of the large eddies, which contain most of the Reynolds stress, while modeling the smaller (subgrid) eddies. This results in models which are more computationally expensive than RANS methods, but not as prohibitive as DNS. By complimenting an LES approach with a RANS model, a hybrid LES/RANS method resolves the larger turbulent scales away from surfaces with LES, and switches to a RANS model inside boundary layers. As pointed out by Bertin et al., this type of hybrid approach has shown a lot of promise for predicting turbulent flows, but work is needed to verify that these models work well in hypersonic flows. The very limited amounts of flight and experimental data available presents an additional challenge for researchers. Recently, a joint study by NASA and CUBRC has focused on collecting heat transfer data on the backshell of a scaled model of the Orion Multi-Purpose Crew Vehicle (MPCV). Heat augmentation effects due to the presence of cavities and RCS jet firings were also investigated. The high quality data produced by this effort presents a new set of data which can be used to assess the performance of CFD methods. In this work, a hybrid LES/RANS model developed at North Carolina State University (NCSU) is used to simulate several runs from these experiments, and evaluate the performance of high fidelity methods as compared to more typical RANS models. .

Salazar, Giovanni↗
DOE OSTI2022

Simulation and Reynolds-averaged Navier-Stokes modeling of a three-component Rayleigh-Taylor mixing problem with thermonuclear burn

Rayleigh-Taylor mixing in the presence of a third component with intermediate density is investigated through three-dimensional large-eddy simulation (LES) with a high-order compact finite-difference code. Two configurations are considered: (1) a symmetric configuration in which the Atwood number between the heavy and intermediate components matches the Atwood number between the intermediate and light components and (2) an asymmetric configuration in which the Atwood number between the heavy and intermediate components is an order of magnitude greater than the Atwood number between the intermediate and light components. Mass fraction covariances are extracted, and proposed Reynolds-averaged Navier-Stokes (RANS) closures for density-specific-volume and density-mass-fraction covariances are evaluated in an a priori fashion. Additionally, a multicomponent extension of the k - Φ - L - a - V RANS model [Morgan, Phys. Rev. E 104, 015107 (2021)] is presented which includes model equations for the upper-triangular elements of the mass fraction covariance matrix. This model, referred to as the k - Φ - L - a - C model, is compared against results from LES and against other RANS models. Profiles of average mass fraction, mass-fraction covariance, and density-specific-volume covariance obtained with the k - Φ - L - a - C model are found to agree well with LES data. Finally, the impact of three-component turbulent mixing on average reaction rate is investigated in both premixed and nonpremixed cases by heating the mixing layer and allowing it to undergo thermonuclear (TN) burn. A closure model for average reaction rate is proposed for use with the k - Φ - L - a - C model, and when this model is applied, improved agreement is obtained between LES and RANS in total TN neutron production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRSDate not supplied

Computational Analysis of a Boundary-Layer Ingesting Tailcone Thruster Configuration Within the National Transonic Facility Using the LAVA Solver

Boundary-layer ingesting (BLI) propulsion systems are one of the many technologies currently under investigation within the aerospace community to meet NASA’s Advanced Air Transport Technology project goal of a sustainable future in aviation. To that end, an experimental campaign was conducted in the National Transonic Facility (NTF) to study the propulsion-airframe integration effects of the Boundary-Layer Ingesting Tailcone System installed in the aft portion of a 2.7% scale design of the NASA Common Research Model (CRM). This test was accompanied by a numerical simulation effort using the Launch, Ascent, and Vehicle Aerodynamics (LAVA) solver, to validate the applicability of current best-practice Reynolds-averaged Navier Stokes (RANS) models in accurately predicting the relevant flow-physics in free-air. A total of 205 steady RANS simulations were performed using LAVA, covering the range of conditions present in the NTF test matrix. Flow conditions ranged from 5- to 15-million Reynolds number, Mach numbers of 0.75, 0.80 and 0.85, and angles-of-attack between –3° and 4°. Four different mass-flow plugs were also tested to assess propulsor operating condition effects. Sensitivity to these flow conditions are analyzed in detail, especially in terms of the nacelle flow distortion which was the main subject of the study. Aerodynamic load coefficients, aftbody boundary-layer measurements and fuselage pressure tap results are also discussed, providing a wide range of validation results from this experimental campaign. This validation effort shows that current best-practices using RANS models within the LAVA solver flow solver are well suited for predicting the inlet flow distortion characteristics of novel aircraft configurations employing BLI at the aft end of the fuselage.

AATT↗
NASA NTRSDate not supplied

Computational Analysis of a Boundary Layer Ingesting Tailcone Thruster Configuration Using the LAVA Curvilinear Solver

Boundary layer ingesting (BLI) propulsion systems are one of the many technologies currently under investigation within the aerospace community to meet NASA's Advanced Air Transport Technology project goal of a sustainable future in aviation. To that end, an experimental campaign was conducted in the National Transonic Facility (NTF) wind tunnel to study the propulsion-airframe integration effects of the Boundary Layer Ingesting Tailcone System installed in the aft portion of a 2.7% scale design of the NASA Common Research Model (CRM). This test was accompanied by a numerical simulation effort using the Launch, Ascent, and Vehicle Aerodynamics (LAVA) curvilinear solver to validate the applicability of current best-practice Reynolds-Averaged Navier-Stokes (RANS) models in accurately predicting the relevant flow physics in free-air. A total of 205 steady RANS simulations were performed using LAVA, covering the range of conditions present in the NTF test matrix. Flow conditions ranged from 5- to 15-million Reynolds number, Mach numbers of 0.75, 0.80 and 0.85, and angles of attack between -3 and 4 degrees. Four different mass-flow plugs were also tested to assess propulsor operating condition effects. Sensitivity to these flow conditions is analyzed in detail, especially in terms of the nacelle flow distortion which was the main subject of the study. Aerodynamic load coefficients, aft body boundary layer measurements and fuselage pressure tap results are also discussed, providing a wide range of validation results from this experimental campaign. This validation effort shows that current best-practices using RANS models within the LAVA curvilinear solver flow solver are well suited for predicting the inlet flow distortion characteristics of novel aircraft configurations employing BLI at the aft end of the fuselage. This talk will cover the combined experimental and numerical efforts that resulted from this BLI-focused investigation.

ARMD↗
DOE OSTI2021

Effects of turbulence-radiation coupling in pressurized oxy-combustion

Concerns over climate change have led to numerous efforts in developing low-carbon energy technologies. Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emission in power generation. Due to the strong impact of pressure on thermal radiation, heat transfer in POC differs significantly from the situation of conventional atmospheric pressure combustion. Thus thermal radiation in POC needs to be investigated to aid new combustor development. The present computational work is a step in this direction, initiating a systematic analysis of thermal radiation and heat transfer in a pilot-scale POC combustor, which has been developed at Washington University in St. Louis (WUSTL). In a POC process, pulverized coal is burned under elevated pressure and O2-CO2 environment. While most previous computational works on flame radiation focused on atmospheric pressure condition, this work considered a pressurized flame. Specifically, a 15-bar POC combustor of power 50 kW is modeled employing the Ansys FLUENT commercial platform, using both Reynolds-averaged Navier-Stokes (RANS) modeling and large-eddy simulation (LES). A recently published and validated global radiation model is used to predict the radiative property of the flue gas. The discrete ordinates (DO) radiation model is chosen to solve the radiative transport equation. Incident radiation on the walls of the combustor is identified and investigated. It is revealed that for this pilot-scale, pressurized combustor, thermal radiation exhibits similar patterns in the RANS and LES models. However, the magnitudes of radiation are different in both models, presumably because interactions between radiation and turbulence are embedded in the LES model but not in the RANS model. This difference thereby underlines the major goal of this research: investigating the impact of such turbulence-to-radiation coupling on thermal radiation in a pilot-scale POC setting. Most previous studies on turbulence-to-radiation interactions focused on bench-scale, atmospheric pressure flames. This work is the first effort to extend this study to a pilot-scale, pressurized flame.

Li, Lei↗
NASA NTRSDate not supplied

Simulation and Modeling of Hypersonic Turbulent Boundary Layers Subject to Favorable Pressure Gradients due to Streamline Curvature

Direct numerical simulations (DNS) of favorable-pressure-gradient turbulent boundary layers are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models. The favorable pressure gradient is induced by the streamwise curvature of the two-dimensional, planar, convex measurement surface used during experiments at the Texas A&M University. The DNS data shows good comparison with the measured velocity profiles, strain rates, and some, but not all, of the Reynolds-stress components. The discrepancies between the predicted and the measured wall-normal as well as shear stress components are primarily attributed to the lower than actual values inferred from typical PIV measurements of turbulent boundary layers. The DNS data shows a zero or slightly negative Reynolds shear stress in the outer part of the boundary-layer, which is indicative of the decaying turbulent motion under a strong favorable pressure gradient. The DNS data is also compared with the results of RANS computations based on commonly used zero, one, and two equation eddy-viscosity models. The RANS models yield reasonable comparisons with the DNS-based skin friction under zero and weak pressure gradients, but significant discrepancies under a strong pressure gradient. The k-w SST model provided the best overall predictions of skin friction, except in the region where the flow transitions from a favorable to an adverse pressure gradient. While the RANS models examined herein also give good predictions of the Reynolds shear stress under a sufficiently weak pressure gradient, none of those models are able to appropriately capture the reduction in the Reynolds stresses when the flow was subjected to a strong pressure gradient. An a priori assessment of the turbulent heat-flux prediction based on the assumption of a constant turbulent Prandtl number with the DNS data shows that while the constant turbulent Prandtl number model is effective in predicting the wall-normal component of turbulent heat flux, it does not capture the turbulent heat transfer in the streamwise direction for all the pressure gradient cases. The failure of the constant turbulent Prandtl number model highlights a requirement for more advanced models of the turbulent heat flux.

turbulent boundary layers↗
NASA NTRS2019

Turbulent Axial Odometer Model

A Galilean-invariant field equation is proposed and tested on standard turbulence model test cases. The field equation provides an additional non-dimensional outer scale which allows the turbulence models to reproduce the axial normal stress increase with Re seen in high Reynolds numbers experiments. The field equation provides a Reynolds number for every point based on the length of turbulent flow upstream of that point in the domain. This outer scale equation can be considered an odometer that gives a length scale conjectured to be related to the large streamwise structures that are seen in turbulent flow and that require run length to develop. A new RANS model using this additional scale is able to match the Reynolds number variation of the normal stresses seen at high Reynolds number. Furthermore, the good attached flow prediction capabilities of current RANS models appears to be attained. Using this scale equation, the entire Reynolds-stress state appears to be predicted correctly, over a large run length Reynolds number range such as experienced in aircraft design.

Olsen, Michael E.↗
NASA NTRS2019

Turbulent Axial Odometer Model

A Galilean-invariant field equation is proposed and tested on standard turbulence model test cases. The field equation provides an additional non-dimensional outer scale which allows the turbulence models to reproduce the axial normal stress increase with Re seen in high Reynolds numbers experiments. The field equation provides a Reynolds number for every point based on the length of turbulent flow upstream of that point in the domain. This outer scale equation can be considered an odometer that gives a length scale conjectured to be related to the large stream wise structures that are seen in turbulent flow and that require run length to develop. A new RANS model using this additional scale is able to match the Reynolds number variation of the normal stresses seen at high Reynolds number. Furthermore, the good attached flow prediction capabilities of current RANS models appears to be attained. Using this scale equation, the entire Reynolds-stress state appears to be predicted correctly, over a large run length Reynolds number range such as experienced in aircraft design.

Olsen, Michael E.↗