We present preliminary development of an approach for simulating high Reynolds number steady compressible flow in two space dimensions using a Cartesian cut-cell finite volume method. We consider both laminar and turbulent flow with both low and high cell Reynolds numbers near the wall. The approach solves the full Navier-Stokes equations in all cells, and uses a wall model to address the resolution requirements near boundaries and to mitigate mesh irregularities in cut cells. We present a quadratic wall model for low cell Reynolds numbers. At high cell Reynolds numbers, the quadratic is replaced with a newly developed analytic wall model stemming from solution of a limiting form of the Spalart-Allmaras turbulence model which features a forward evaluation for flow velocity and exactly matches characteristics of the SA turbulence model in the field. We develop multigrid operators which attain convergence rates similar to inviscid multigrid. Investigations focus on preliminary verification and validation of the method. Flows over flat plates and compressible airfoils show good agreement with both theoretical results and experimental data. Mesh convergence studies on sub- and transonic airfoil flows show convergence of surface pressures with wall spacings as large as approx.0.1% chord. With the current analytic wall model, one or two additional refinements near the wall are required to obtain mesh converged values of skin friction.

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Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

A comprehensive review of aerofoil shape parameterization methods that can be used for aerodynamic shape optimization is presented. Seven parameterization methods are considered for a range of desi...

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A Geometric Comparison of Aerofoil Shape Parameterisation Methods

A synergistic glance at the prospects of distributed propulsion technology and the electric aircraft concept for future unmanned air vehicles and commercial/military aviation

In this paper, an explicit wall model based on a power-law velocity profile is proposed for the simulation of the incompressible flow around airfoils at high Reynolds numbers. This wall model is particularly suited for the wall treatment involved in Cartesian grids. Moreover, it does not require an iterative procedure for the friction velocity determination. The validation of this power-law wall model is assessed for Reynolds-averaged Navier-Stokes simulations of the flow around a two-dimensional airfoil using the lattice Boltzmann approach along with the Spalart-Allmaras turbulence model. Good results are obtained for the prediction of the aerodynamic coefficients and the pressure profiles at two Reynolds numbers and several angles of attack. The explicit power-law is thus well suited for a simplified near-wall treatment at high Reynolds numbers using Cartesian grids.

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An explicit power-law-based wall model for lattice Boltzmann method–Reynolds-averaged numerical simulations of the flow around airfoils

Supercritical natural laminar flow airfoil optimization for regional aircraft wing design

An inverse airfoil design process is presented that makes use of the CST parameterization method. The CST method is very powerful in that it can easily represent any airfoil shape within the entire design space of smooth airfoils. This makes it an ideal modeling technique for an inverse design process because accurate airfoil geometry treatment is required. The downfall of some inverse design processes is that they do not accurately handle the leading edge region due to large ow gradients and high curvature distributions. One way to account for this is by representing airfoils with smooth analytic functions, such as the CST method. The inverse airfoil design process presented is based on the relation between pressure residuals and the required airfoil shape change. The pressure residuals give the sign of the normal vector with which to modify the airfoil shape. The CST method is then used as the smoothing algorithm. The inverse design method is simple, accurate, and ecient. It is shown to accurately determine the airfoil geometry in both subsonic and transonic ows. Since this method simply examines pressure distributions to modify the airfoil shape, the ow solver can be kept separate from the inverse design process, allowing any delity ow solver to be used.

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Inverse Airfoil Design Utilizing CST Parameterization

For aerodynamic modeling and optimization, it is desirable to limit the number of design variables to reduce model complexity and the requirements of the applied optimization scheme. The Class/Shape Transformation (CST) surface parameterization method presented by Kulfan has proven to be particularly useful for this while maintaining a wide range of applications. These include everything from smooth airfoils to 3D axi-symmetric bodies and wings. However, the CST method is confined to smooth geometries. This limits the CST method in applications incorporating discontinuous surfaces such as high lift aerodynamics with circulation control (CC) slots and flaps. The trailing edge slot on a circulation control wing (CCW) airfoil is not well modeled by the CST method. A parameterization of a CCW airfoil will result in the trailing edge slot being smoothed over. Therefore, a modified CST method must be utilized. For the case of parameterizing a known CCW airfoil, this is accomplished by detecting drastic changes in curvature and beginning a new parameterization in a "multi-surface parameterization" method. For creating a new CCW airfoil, this is achieved by modifying the 2D CST equations to incorporate a slot thickness term that also includes the horizontal location. These two methods can then be extended into 3D to model a circulation control wing (CCW) or even a blended wing body (BWB) aircraft incorporating CCW. The multi-surface parameterization modification can also be used to model other complex geometries to further enhance the robust nature of the CST method, thus creating a valuable design tool.

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A Surface Parameterization Method for Airfoil Optimization and High Lift 2D Geometries Utilizing the CST Methodology

The design of circulation control (CC) dual radius flap systems were investigated to characterize the parameters that make up the flap surface to offer further knowledge into the CC field of study. Multiple dual radius flap geometries, along with variants, were developed by varying specific flap parameters from a baseline configuration that had previously developed. The aerodynamics of the different flap geometries were analyzed using two-dimensional CFD. This research will explore the design of CC pneumatic flap systems to improve the performance of existing CC flap configurations, and provide insight into the characteristics of the CC flap geometry.

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Design and Performance of Circulation Control Flap Systems

This paper provides an overview of the Circulation Control modeling research that has been performed, and is still ongoing, at Cal Poly, San Luis Obispo. This work started in 2005 with the interest of applying Circulation Control technologies to advanced aircraft designs. After the initial investigations into this, it was apparent that there was a long history of experimental work in this area to build on, but a number of deciencies existed in the modeling capabilities. For Circulation Control enabled aircraft, these included: few available tools to accurately model the takeo and landing performance, the limitations in the standard regulations with respect to takeo and landing requirements, the inconsistent published results in modeling the aerodynamics of these problems, and the lacking of tools necessary to model the coupling of the propulsion system and the aerodynamics. These were some of the problems that Cal Poly researchers, both students and faculty, identied as avenues of exploration, and these are the areas that have received the majority of the focus since the beginning of this work. This is the work that will be summarized in this paper.

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Overview of Recent Circulation Control Modeling Activities at Cal Poly

Circulation Control is a high-lift method discovered in 1935 when Henry Coanda accidentally stumbled upon the technology. Research was conducted in the 1970’s and 1980’s to develop this technique, but the idea fell out of vogue until recently. Energy is introduced into the flow field by means of a jet ejected tangentially from a slot located near the trailing edge of the airfoil; thus changing the effective chamber of the airfoil and increasing lift. Extreme Short Take-Off and Landing (ESTOL) vehicles can use this technology to alleviate today’s congested airports by reutilizing the small runways that are currently unexploited due to the recent trend of bigger aircraft. By examining the angle-of-attack, flap deflection angle, and jet blowing coefficient, a design space was analyzed for lift and drag revealing three-dimensional lift coefficients up to 3.5. After collecting the data, balanced field length and landing distances were calculated. These results revealed that the shortest balanced field length of 2,400 feet would be for a flap deflection angle of thirty degrees and a blowing coefficient equal to 0.35. Similarly, the shortest landing distance was calculated to be 2,000 feet for a flap deflection angle of ninety degrees and a blowing coefficient of 0.34. Both of these values fall within the NASA defined mission requirements 46 for an ESTOL aircraft to have a balanced field length and landing distance between 2,000 to 3,000 feet, proving Circulation Control to be an extremely viable resource for ESTOL technology.

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David D. Marshall

Papers

Inverse Airfoil Design Utilizing CST Parameterization

A Surface Parameterization Method for Airfoil Optimization and High Lift 2D Geometries Utilizing the CST Methodology

Design and Performance of Circulation Control Flap Systems

Overview of Recent Circulation Control Modeling Activities at Cal Poly

Circulation Control and Its Application to Extreme Short Take-Off and Landing Vehicles