James G. Coder

Computational Fluid Dynamics Compatible Transition Modeling Using an Amplification Factor Transport Equation

A new laminar–turbulent transition model for low-turbulence external aerodynamic applications is presented that incorporates linear stability theory in a manner compatible with modern computational fluid dynamics solvers. The model uses a new transport equation that describes the growth of the maximum Tollmien–Schlichting instability amplitude in the presence of a boundary layer. To avoid the need for integration paths and nonlocal operations, a locally defined nondimensional pressure-gradient parameter is used that serves as an estimator of the integral boundary-layer properties. The model has been implemented into the OVERFLOW 2.2f solver. Comparisons of predictions using the new model with high-quality wind-tunnel measurements of airfoil section characteristics confirm the predictive qualities of the model, as well as its improvement over the current state of the art in computational fluid dynamics transition modeling at approximately half the computational expense.

Experimental Investigation into the Effect of Gurney Flaps on Various Airfoils

The aerodynamic effects of the application of Gurney flaps of different heights and chordwise locations to five airfoils have been investigated in the Pennsylvania State University low-speed, low-turbulence wind tunnel. The effectiveness of each Gurney flap/airfoil combination is measured by the change in the maximum lift coefficient of the airfoil. When grouped by flap height and plotted against chordwise location, there is considerable scatter in the data, indicating that the effectiveness of the Gurney flap is strongly influenced by airfoil shape. Two anomalous cases are considered in detail. In the first case, the increase in cl,max is considerably different for two airfoils with the addition of a Gurney flap having the same height and mounted at the same chordwise location. The second case is one in which a Gurney flap of a specific height and mounting location is found to increase cl,max on one airfoil and decrease it on another. For these cases, pressure distributions, lift curves, and drag polars ...

DPW-5 Analysis of the CRM in a Wing-Body Configuration Using Structured and Unstructured Meshes

*† ‡ § ** †† ‡‡ Two general purpose Reynolds Averaged Navier-Stokes (RANS) flow solvers, OVERFLOW and BCFD, are used to analyze the NASA Common Research Model (CRM) in a wing-body configuration. The codes are run on structured and unstructured common grid families built specifically for the 5 th AIAA CFD Drag Prediction Workshop (DPW-5) allowing for meaningful comparison of data. There are six grid sizes in the family ranging from a 0.6 million cell “Tiny” mesh up to a 138 million cell “Super-Fine” mesh. Results from a grid convergence study are evaluated for each solver and grid type with focus on isolating individual effects of turbulence model and differencing scheme on computed forces, moments and wing pressures. A “Medium” mesh consisting of 5.1 million cells is used to run the wing-body configuration through an angle-of-attack sweep as part of a buffet onset study. The solutions are used to better understand variations in high speed wing separation prediction driven by the strengthening shock and by corner flow physics at the wing-body juncture. Numerical simulation of side-of-body separation continues to be a challenge for RANS methods where solutions are sensitive to grid density and turbulence model, amongst other variables. However, a newly developed quadratic constitutive relation (QCR) is employed with favorable results. Two additional studies are conducted to: a) investigate how well common grid solutions compare with those on a grid built using best practices for a given flow solver, and b) quantify the effects of transition and wing twist to provide additional corrections needed for comparisons of CFD results with experimental data.

Analysis of the Common Research Model Using Structured and Unstructured Meshes

Two general-purpose Reynolds-averaged Navier–Stokes flow solvers, OVERFLOW and BCFD, are used to analyze the NASA Common Research Model in a wing–body configuration. The codes are run on structured and unstructured common-grid families built specifically for the Fifth AIAA CFD Drag Prediction Workshop, allowing for a meaningful comparison of data. The results from a grid-convergence study are evaluated for each solver and grid type with focus on isolating individual effects of turbulence model and differencing scheme on computed forces, moments, and wing pressures. A medium mesh consisting of 5.1 million cells is used for a buffet-onset study to better understand variations in high-speed wing-separation prediction driven by the strengthening shock and by corner-flow physics at the wing–body juncture. Numerical simulation of side-of-body separation continues to be a challenge for Reynolds-averaged Navier–Stokes methods, in which solutions are sensitive to grid density and turbulence model, among other vari...

A CFD-Compatible Transition Model Using an Amplification Factor Transport Equation

A new laminar-turbulent transition model for low-turbulence external aerodynamic applications is developed that incorporates linear stability theory in a manner compatible with modern CFD solvers. The model utilizes a new transport equation that describes the growth of the maximum instability amplitude in the presence of a boundary layer. To avoid the need for integration paths and non-local operations, a locally-defined non-dimensional pressure gradient parameter is utilized that serves as an estimator of the integral boundarylayer properties. The model has been implemented into the OVERFLOW 2.2e solver. Comparisons of predictions using the new model with high-quality, wind-tunnel measurements of airfoil section characteristics confirm the predictive qualities of the model, as well as its improvement over the current state of the art in CFD transition modeling.

Inviscid Circulatory-Pressure Field Derived from the Incompressible Navier-Stokes Equations

The static-pressure field in the steady and incompressible Navier–Stokes momentum equation is decomposed into circulatory (inviscid) and dissipative (viscous) partial-pressure fields. It is shown analytically that the circulatory-pressure integral over the surface of a lifting body of thickness recovers the lift generating Kutta–Joukowski theorem in the far field, and results in Maskell’s formula for the vortex-induced drag plus an additional pressure-loss term that tends to zero for an infinitely thin wake. A Poisson equation for the circulatory-pressure field is implemented as a transport equation into the FLUENT 13 solver. Numerical examples include a circular cylinder at Re=8.5×105, the S809 airfoil at Re=2×106, and the ONERA M6 wing at Re=1×106. It is shown that the circulatory-pressure field does indeed behave as an inviscid pressure field of a fully viscous solution, and provides insight into the nature of pressure drag and its contributions to local form and vortex-induced drag.

Application of the Amplification Factor Transport Transition Model to the Shear Stress Transport Model

A method is described for applying the linear-stability-based amplification factor transport (AFT) transition model to the popular, two-equation shear stress transport (SST) eddy-viscosity model, yielding the SST-AFT framework. The turbulent kinetic-energyequation is modified by introducing a new source term that improves its ability to maintain laminar flow without affecting its near-wall behavior in fully turbulent regions. This source term includes a turbulence suppression function that maintains laminar flow until the critical amplification factor is reached. Test cases using the SST-AFT model are presented for a zeropressure-gradient flat plate and several airfoils, including a multi-element one. Predictions with SST-AFT compare favorably with experiment, confirming the potential capabilities of the new transition/turbulence framework.

OVERFLOW Analysis of the DLR-F11 High-Lift Configuration Including Transition Modeling

The OVERFLOW Reynolds-averaged Navier–Stokes solver has been used to predict the aerodynamic characteristics of the DLR-F11 high-lift configuration for the conditions prescribed for the second AIAA Computational Fluid Dynamics High-Lift Prediction Workshop. A grid-convergence study is performed for the geometry with the slat and flap brackets excluded. The influence of including the brackets in the computational geometry is considered, and the effects of varying Reynolds number are analyzed for the brackets-on configuration. An optional case for the workshop, but a focus of this paper, is the inclusion of laminar–turbulent transition in the solutions. Two computational-fluid-dynamics-compatible transition models are used for the analysis, and their behaviors are discussed. A turbulence-model-verification study, which was also an optional case for the workshop, is included.

Contributions to HiLiftPW-3 Using Structured, Overset Grid Methods

The High-Lift Common Research Model (HL-CRM) and the JAXA Standard Model (JSM) were analyzed computationally using both the OVERFLOW and LAVA codes for the third AIAA High-Lift Prediction Workshop. Geometry descriptions and the test cases simulated are described. With the HL-CRM, the effects of surface smoothness during grid projection and the effect of partially sealing a flap gap were studied. Grid refinement studies were performed at two angles of attack using both codes. For the JSM, simulations were performed with and without the nacelle/pylon. Without the nacelle/pylon, evidence of multiple solutions was observed when a quadratic constitutive relation is used in the turbulence modeling; however, using time-accurate simulation seemed to alleviate this issue. With the nacelle/pylon, no evidence of multiple solutions was observed. Laminar-turbulent transition modeling was applied to both JSM configuration, and had an overall favorable impact on the lift predictions.

One-Equation Transition Closure for Eddy-Viscosity Turbulence Models in CFD

A method is presented to reduce the order of the Langtry-Menter transition model by replacing the transport equation containing the transition criterion with a locally-defined algebraic correlation. The new method has the same applicability and generality as the original form of the model, and test cases run in OVERFLOW for the S809 and E387 airfoils show that comparable accuracy is achieved. The primary validation cases use the twoequation SST model as the underlying turbulence model, as this was used in the original model. A method is presented for using the Spalart-Allmaras turbulence model with the transition closure models, but the results were found to be very dependent on free-stream conditions. The overall applicability of the transition models to one-equation turbulence models is discussed, and goals for future development are listed. Nomenclature a1 = SST modeling constant Cp = pressure coefficient cd = section profile-drag coefficient cl