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.

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

A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. In addition, the viscous procedure used in the ALESEP techniques has been modified to allow for wall suction. A series of two-dimensional calculations is presented as a verification of the prediction capability of the interaction techniques with the Roberts' transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. Wall suction has been applied to a similar interaction calculation to demonstrate its effect on the separation bubble. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.

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Analysis of transitional separation bubbles on infinite swept wings

A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. In order to improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction were investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low speed and high speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart-Allmaras-type models to state-of-the-art seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall.

Improved Two-Dimensional Dynamic Stall Prediction with Structured and Hybrid Numerical Methods

Implicit Implementation of the Full e^n Transition Criterion

The computation of boundary-layer properties and laminar-to-turbulent transition location is a complex problem generally not undertaken in the context of aircraft design. Yet this is just what must be done if an aircraft designer is to exploit the advantages of laminar flow while making the proper trade-offs between inviscid drag, structural weight and skin friction. To facilitate this process, a new tool is developed. This thesis presents a designoriented method for the aerodynamic analysis of supersonic wings including approximate means for estimating transition and total drag. The method consists of a boundary-layer solver combined with a fast and robust transition scheme based on the well-known en criterion. The boundary-layer analyses employed are computationally inexpensive but sufficiently accurate to provide guidance for advanced design studies and to be incorporated in multidisciplinary design optimization. The boundary-layer solver is based on an enhanced quasi-3D sweep/taper theory which is shown to agree well with three-dimensional Navier-Stokes results. The transition calculation scheme is implemented within the boundary-layer solver and automatically triggers a turbulence model at the predicted transition front. The laminar instability amplification values used in the en criterion are based on algebraic fits to linear stability results for streamwise and crossflow modes. This parametric transition prediction method compares favorably with exact linear theory on relevant geometries and successfully computes transition for a supersonic flight test. Integration of the present design method with numerical optimization is discussed, and airfoil section and wing/body shape optimizations are performed. Wing/body drag minimization studies suggest that low-sweep supersonic aircraft with extensive laminar flow may have a significant drag advantage over conventional designs.

An aerodynamic design method for supersonic natural laminar flow aircraft

The positive pressure gradient, downstream of the suction peak at the leading edge of an airfoil at incidence, may, under some conditions, induce large perturbations on the general pattern of the flow.

J. L. Bonnet

Papers

A Calculation Method of Leading-Edge Separation Bubbles