Title: Mathematical Modelling, Design and Optimization of Airfoils and Aircrafts operating at specific Reynolds Number
Abstract: Airfoil design and optimization have become vital aspects of aircraft design in recent years. It still attracts growing interest in the aeronautics community in the search for the most optimum airfoil design of high lift and low drag for a specific operating condition (Reynolds number).
Elizarov et al. [1] presented the theory to design an airfoil with Clmax ≥ 1.5 with a high aerodynamic ratio (K) ≈ 150, under airfoil thickness constraint of 0.17 ≤ t ≤ 0.19. The airfoil design process was done by defining the class of velocity distributions and solving them through the inverse method. Separation free high lift airfoil was designed for viscous compressible flow using an iterative method to account for compressibility and viscous distribution. Computational codes coupled with mathematical optimization techniques constitute a powerful tool for developing new airfoil designs for specific requirements. The viscous theory is used for low-speed calculations as well as for sophisticated transonic flow until separation occurs. Navier stokes equations are used in airfoil shape optimization for very low Reynolds number (Re) and laminar flow separation [2]. Potential flow theory and Euler equations are also utilized for airfoil design purposes. In recent times, the viscous inviscid method is also proven remarkable CFD method for airfoil design [3]. The parameterization method provides completeness and controllability to produce a broader variety of airfoil shapes. Various parametric methods have been developed like Bezier (Bernstein polynomial) or parametric curve, PARSEC, Hicks-Henne, Nash equilibrium genetic algorithm and Basis-spline curve method [3]. Genetic algorithm is utilized to find more precise, optimum and considerable solutions for aerodynamic optimization design problems. This design technique is specifically concerned with the wing of aircraft. The gradient-based method is mostly preferred for high-speed applications whereas heuristic algorithms are suitable for low-speed applications. In the CFD method, the Re plays an important role. For high Re, where viscous effects are negligible, compressible Euler equations are used. Otherwise, compressible and incompressible RANS equations are used for airfoil design and optimization. Two equation models, eddy viscosity and Spalart–Allmaras single and multi-equation turbulence model are commonly used for these purposes. CFD based on the laminar to turbulent conversion model is used for computing stream variables [3]. For airfoil design and optimization, two basic approaches are considered. They are inverse design method based on gradient optimization and direct search algorithm based on numerical optimization. The inverse design method is used when the design is concerned with fluid dynamics parameters such as pressure distribution whereas direct numerical optimization is adopted if geometry having an aerodynamic shape depends on various constraints [2]. In recent years, automated designs methods are used to produce airfoil shapes with definite features but it first requires the consideration of pressure distribution. It necessitates an inner-outer iteration system [3]. Through Joukowsky transformation investigations on airfoils, it is known that the airfoil profile can be expressed through conformal mapping and analytical function of finite series of Fourier expansions. This integrated design method is proven to be more accurate than the traditional inverse design method. XFOIL is based on solving viscous integral boundary layer equation and inviscid Euler equation for airfoil flow predictions [4].
In this research, the use of both physical and mathematical modelling along with optimization algorithms to generate new optimum airfoil designs for high lift and low drag for specific operational conditions will be performed. The experimental analysis will also be done by implementing these new airfoils on 3D printed small-scale aircraft models and testing them in the subsonic wind tunnel to correlate with numerical results. This research will focus on addressing several important research questions such as:
How can novel mathematical modelling techniques be used for designing new airfoils?
What parameters (camber, thickness etc.) affect the design of an airfoil for various Re conditions?
Can currently available numerical codes (i.e. commercial/open source) be used to obtain high-fidelity results in aircraft design at the initial design stages?
Can one improve the level of fidelity of results obtained from the conceptual design stage itself through the implementation of advanced design techniques in aircraft design?
This research has the following objectives:
Develop a new design framework in airfoil and aircraft design
Testing of new airfoils generated though computational methodology in XFOIL and CFD for different Re
Include the new airfoils in opensource conceptual aircraft design code called CEASIOM and test them on wing and other control surfaces in order to find better performance aircraft designs
Generate new aircraft designs designed with novel airfoils generated in Step 1.
Implement new airfoils on 3D printed small-scale aircraft models and testing in IIAEM's subsonic wind-tunnel to correlate with numerical results.
In this research, the problem of finding the optimum design for high lift and low drag for the specific operational condition will be performed based on initial mathematical modelling and subsequent physics-based analysis. The use of modern technology like CFD and high-fidelity modelling and analysis will be used to achieve the goals.
Publication Year: 2021
Publication Date: 2021-09-24
Language: en
Type: article
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