D. Keith Walters

A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow

An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k- framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretransitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in comparison with commonly used models that exhibit no capability of predicting laminar-toturbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems. DOI: 10.1115/1.2979230

A New Model for Boundary Layer Transition Using a Single-Point RANS Approach

This paper presents the development and implementation of a new model for bypass and natural transition prediction using Reynolds-averaged Navier-Stokes computational fluid dynamics (CFD), based on modification of two-equation, linear eddy-viscosity turbulence models. The new model is developed herein based on considerations of the universal character of transitional boundary layers that have recently been documented in the open literature, and implemented into a popular commercial CFD code (FLUENT) in order to assess its performance. Two transitional test cases are presented: (1) a boundary layer developing on a flat heated wall, with free-stream turbulence intensity (Tu∞) ranging from 0.2 to 6%; and (2) flow over a turbine stator vane, with chord Reynolds number 2.3 × 10 5 , and Tu∞ from 0.6 to 20%. Results are presented in terms of Stanton number, and compared to experimental data for both cases. Results show good agreement with the test cases and suggest that the new approach has potential as a predictive tool.

Computational Fluid Dynamics Study of Wake-Induced Transition on a Compressor-Like Flat Plate

Recent experimental work has documented the importance of wake passing on the behavior of transitional boundary layers on the suction surface of axial compressor blades. This paper documents computational fluid dynamics (CFD) simulations using a commercially available general-purpose CFD solver, performed on a representative case with unsteady transitional behavior. The study implements an advanced version of a three-equation eddy-viscosity model previously developed and documented by the authors, which is capable of resolving boundary layer transition. It is applied to the test cases of steady and unsteady boundary layer transition on a two-dimensional flat plate geometry with a freestream velocity distribution representative of the suction side of a compressor airfoil. The CFD results are analyzed and compared to a similar experimental test case from the open literature. Results with the model show a dramatic improvement over more typical Reynolds-averaged Navier-Stokes (RANS)-based modeling approaches, and highlight the importance of resolving transition in both steady and unsteady compressor aerosimulations.

A Method for Three-Dimensional Navier–Stokes Simulations of Large-Scale Regions of the Human Lung Airway

A new methodology for CFD simulation of airflow in the human bronchopulmonary tree is presented. The new approach provides a means for detailed resolution of the flow features via three-dimensional Navier–Stokes CFD simulation without the need for full resolution of the entire flow geometry, which is well beyond the reach of available computing power now and in the foreseeable future. The method is based on a finite number of flow paths, each of which is fully resolved, to provide a detailed description of the entire complex small-scale flowfield. A stochastic coupling approach is used for the unresolved flow path boundary conditions, yielding a virtual flow geometry that allows accurate statistical resolution of the flow at all scales for any set of flow conditions. Results are presented for multigenerational lung models based on the Weibel morphology and the anatomical data of Hammersley and Olson (1992, “Physical Models of the Smaller Pulmonary Airways,” J. Appl. Physiol., 72(6), pp. 2402–2414). Validation simulations are performed for a portion of the bronchiole region (generations 4–12) using the flow path ensemble method, and compared with simulations that are geometrically fully resolved. Results are obtained for three inspiratory flowrates and compared in terms of pressure drop, flow distribution characteristics, and flow structure. Results show excellent agreement with the fully resolved geometry, while reducing the mesh size and computational cost by up to an order of magnitude.

A simple and robust linear eddy‐viscosity formulation for curved and rotating flows

Purpose – The purpose of this paper is to present a new eddy‐viscosity formulation designed to exhibit a correct response to streamline curvature and flow rotation. The formulation is implemented into a linear k‐ e turbulence model with a two‐layer near‐wall treatment in a commercial computational fluid dynamics (CFD) solver.Design/methodology/approach – A simple, robust formula is developed for the eddy‐viscosity that is curvature/rotation sensitive and also satisfies realizability and invariance principles. The new model is tested on several two‐ and three‐dimensional problems, including rotating channel flow, U‐bend flow and internally cooled turbine airfoil conjugate heat transfer. Predictions are compared to those with popular eddy‐viscosity models.Findings – Converged solutions to a variety of turbulent flow problems are obtained with no additional computational expense over existing two‐equation models. In all cases, results with the new model are superior to two other popular k‐ e model variants, ...

A CFD Study of Wake-Induced Transition on a Compressor-Like Flat Plate

Recent experimental work has documented the importance of wake passing on the behavior of transitional boundary layers on the suction surface of axial compressor blades. This paper documents computational fluid dynamics (CFD) simulations using a commercially-available general-purpose CFD solver, performed on a representative case with unsteady transitional behavior. The study implements a new, advanced version of a three-equation eddy-viscosity model previously developed and documented by the authors, which is capable of resolving boundary-layer transition. It is applied to the test cases of steady and unsteady boundary-layer transition on a 2-D flat plate geometry with a freestream velocity distribution representative of the suction side of a compressor airfoil. The CFD results are analyzed and compared to a similar experimental test case from the open literature. Results with the new model show a dramatic improvement over more typical RANS-based modeling approaches, and highlight the importance of resolving transition in both steady and unsteady compressor aero simulations.Copyright

A New Model for Boundary-Layer Transition Using a Single-Point RANS Approach

This paper presents the development and implementation of a new model for bypass and natural transition prediction using Reynolds-Averaged Navier-Stokes (RANS) CFD, based on modification of two-equation, linear eddy-viscosity turbulence models. The new model is developed herein based on considerations of the universal character of transitional boundary layers that have recently been documented in the open literature, and implemented into a popular commercial CFD code (Fluent) in order to assess its performance. Two transitional test cases are presented: (1) a boundary layer developing on a flat heated wall, with free-stream turbulence intensity (Tu∞ ) ranging from 0.2 to 6%; and (2) flow over a turbine stator vane, with chord Reynolds number 2.3×105 , and Tu∞ from 0.6 to 20%. Results are presented in terms of Stanton number, and compared to experimental data for both cases. Results show good agreement with the test cases and suggest that the new approach has potential as a predictive tool.Copyright

Computational Study of Jet-in-Crossflow and Film Cooling Using a New Unsteady-Based Turbulence Model

This paper documents a computational investigation of the unsteady behavior of jet-in-crossflow applications. Improved prediction of fundamental physics is achieved by implementing a new unsteady, RANS-based turbulence model developed by the authors. Two test cases are examined that match experimental efforts previously documented in the open literature. One is the well-documented normal jet-in-crossflow, and the other is film cooling on the pressure side of a turbine blade. All simulations are three-dimensional, fully converged, and grid-independent. High-quality and high-density grids are constructed using multiple topologies and an unstructured, super-block approach to ensure that numerical viscosity is minimized. Computational domains include the passage, film hole, and coolant supply plenum. Results for the normal jet-in-crossflow are for a density ratio of 1 and velocity ratio of 0.5 and include streamwise velocity profiles and injected flow or “coolant” distribution. The Reynolds number based on the average jet exit velocity and jet diameter is 20,500. This represents a good test case since normal injection is known to exaggerate the key flow mechanisms seen in film-cooling applications. Results for the pressure side film-cooling case include coolant distribution and adiabatic effectiveness for a density and blowing ratio of 2. In addition to the in-house model that incorporates new unsteady physics, CFD simulations utilize standard, RANS-based turbulence models, such as the “realizable” k-e model. The present study demonstrates the importance of unsteady physics in the prediction of jet-in-crossflow interactions and for film cooling flows that exhibit jet liftoff.Copyright

Numerical study of gas-cyclone airflow: an investigation of turbulence modelling approaches

A numerical study of unsteady single-phase vortical flow inside a cyclone is presented. Two different geometric configurations have been considered, with the goal of assessing several different turbulence modelling approaches for this class of problem. The models investigated include three Reynolds-averaged Navier–Stokes models: a commonly used two-equation eddy-viscosity model, a differential Reynolds stress model (DRSM) and an eddy-viscosity model sensitised to rotational and curvature (RC) effects which was recently developed and implemented into a commercial CFD (computational fluid dynamics) code by the authors. Results were also obtained using large eddy simulation (LES). The computational results are analysed and compared with available experimental data. The RC-sensitised eddy-viscosity model shows significant improvement over the standard eddy-viscosity model. The RC-sensitised model, DRSM and LES model predictions of the mean flowfield are in good agreement with the experimental data. The results suggest that curvature- and rotation-sensitive eddy-viscosity models may provide a practical alternative to more computationally intensive approaches.

Simulations of Cyclic Breathing in the Conducting Zone of the Human Lung

Computational fluid dynamics (CFD) simulations were performed to predict the air flow in the human lung during cyclic breathing. The study employed a morphologically complex computational geometry generated using a combination of patient-specific CT-scan data for the extrathoracic and upper airway regions and a representative branching geometry for the lower airways that is available in the open literature. The geometry extended throughout the entire conducting zone and includes 16 partially resolved airway generations. For each generation beyond the third, only a fraction of the airway branches were retained, resulting in truncated flow outlets (for inspiratory flow) in generations 414. The inhalation and exhalation air flow boundary conditions were prescribed based on a physiologically realistic ventilation pattern, which was obtained using a whole-body model of human physiology. The flow was driven by specifying time-varying volumetric flowrates applied at each of the distal boundaries, while the oral boundary was maintained at constant (atmospheric) pressure. The study investigated the effectiveness of three different mass flow distribution schemes to drive the air flow. It was found that prescribed mass flow distribution fractions based on the square of the airway cross-sectional area produced the best results in terms of a uniform distal pressure distribution, while all methods produced reasonable results in terms of mass flow distribution throughout the lung airway geometry.Copyright