A Numerical Method For Unsteady Low Reynolds Number Flows And Application To Micro Air Vehicles

Micro air vehicles (MAVs) have many advantages which make them suitable for abroad military and civilian applications. Since MAV was defined in 1990's, active study in scientific and aerospace engineering community, motivated by interest in MAVs, has been increasing rapidly. However, there are significant technical challenges that are hindering the efficient utilization of MAV's technology, and low Reynolds number aerodynamics is one of the most important problems. The primary focus of this paper is the low Reynolds number aerodynamics associated with fixed and flapping wing MAVs, including numerical simulation method for unsteady low Reynolds number flows, dynamic mesh generation and low Reynolds number flowfield mechanisms of fixed/flapping wings.Tranditional compressible flow algorithms tend to fare poorly for low speed flowfields, not only in terms of convergence and stability, but also in terms of accuracy. Therefore, a preconditioning technology is expanded into solving the unsteady compressible Navier-Stokes equations, and an effective numerical method for simulating 3-dimensional unsteady low speed flowfields with moving boundaries is developed in this paper. This method is based on a dual time-stepping scheme, combined with low Mach number preconditioning and an implicit matrix-free LU-SGS iteration on unstructured dynamic meshes. Because preconditioning modifies the governing equations, that induces the change of system's eigenvalues and eigenvectors, characteristic boundary conditions are also modified to suit with the preconditioned characteristic system. Compared with experimental results whenever possible, the computed results indicate that this algorithm shows satisfactory improvement of solution efficiency and accuracy for low speed flow problems.Dynamic mesh generation is an important task for performing simulations of unsteady flow with moving boundaries. Dynamic mesh deformation method based on Delaunay graph mapping is non-iterative and is therefore efficient for unsteady flow solutions. However, intersections occur occasionally between the background graph elements for complex geometries with large relative movements. It not only consumes more time but also deteriorates mesh quality to regenerate the graph and to relocate grid points. Therefore, a dynamic mesh generation method based on double Delaunay graph mapping is proposed in this paper. A virtual and a real background graph in conjunction with a virtual and a real mapping are generated by appending some assistant points in the initial graph. The assistant points and grid points move according to the virtual graph and virtual mapping, the real graph and real mapping respectively. The results of test cases indicate that the double graph mapping method absolutely avoids the problems caused by the intersections of graph elements and shows dramatic improvement of mesh quality, efficiency and robustness for complex problems with moving boundariesAs solution of unsteady flows due to flexible flapping-wings is not possible by mesh deformation and overset grids alone unless grid regeneration is employed, an effective strategy which combines mesh deformation based on Delaunay graph mapping and unstructured overset grids is proposed in this paper. A Delaunay graph is generated for each body-fitted grid cluster which overlaps or is embedded within an off-body background grid cluster. At each time step, the graph moves according to the wing's motion and deformation, and the grids move to new positions according to a one-to-one mapping between the graph and the grid. Then, intergrid-boundary definition is implemented automatically for computation. In order to efficiently implement overset grid procedure, the idea of hierarchical grid organization is adopted, and an efficient data search algorithm is developed. Also intergrid boundary redefinition algorithm is designed for both cell-centered and vertex-centered schemes in order to achieve higher spatial accuracy.The low Reynolds number flows around a micro air vehicle with low aspect ratio fixed-wing are numerically simulated in this paper. The lift/drag performance, flow structure, and the influence of tip vortices and winglet on the aerodynamics are studied as well as the unsteady phenomena at high angle of attack. The results of numerical study indicate that the 3D flow structure around low aspect ratio wing at low Reynolds number is much complex. The tip vortices affect not only the flow structure but also lift and drag generation. The shedding and interacting of vortices cause unsteadiness in aerodynamic performance at high angle of attack.The unsteady low Reynolds number flows due to a bird-like flexible flapping-wing model are simulated according to the condition of that the computed mean lift equals its weight and the mean thrust equals the body drag. The flow structure, lift and thrust generation mechanisms, aerodynamic power requirement are studied. The thrust performance at different Strouhal number and the vortex street of a 2D flexible flapping airfoil are analyzed. The results show that the initial torsion shape, the flexibility of the flapping wing and the match of them are very important for successful flapping wing MAVs. The leading edge vortex which is generated and adheres to upper surface during downstroke is a primary mechanism for lift generation. The unsteady viscous flow fields of dual flapping airfoils in tandem configurations are also simulated in this paper. The variations of aerodynamic forces and thrust efficiency as functions of different parameters, such as phase difference, horizontal distance, frequency, etc, are numerical studied as well as the aerodynamic interactions between the fore and hind airfoils.Dragonflies have the ability to control aerodynamic forces for flight by modulating the phase relationship between forewings and hindwings. In this paper, unsteady flows of a dragonfly model in hovering (advance ratio J=0) and in forward flight with medium-speed (J=0.3) are simulated on dynamic overset unstructured grids. At each J, thirteen phases from 0o to 360o with interval of 30o are considered. The aerodynamic force and power varying with the phase as well as the aerodynamic interaction are studied. Also the flow structure and aerodynamic force generation mechanism are discussed. It is found that the period average vertical force and power are presented in"U"shape as a function of the phase. The vertical force generated by the model is enough to balance the weight, and the aerodynamic power also agrees with the statistical data of real dragonflies. In the wide phase region of [90o, 270o], the aerodynamic interaction is relatively strong and quite stable. The vertical force and power is relatively small and stay roughly constant. All these results may be useful for explaining the unusual phase relationships used by dragonflies.For phenomenological analysis of the unsteady flow due to a flapping-wing MAV, a smoke flow visualization experiment is carried out in a low speed wind tunnel by using a high-speed camera. This experiment helps us better understand the unsteady vortex dynamics and the flow structures caused by a flapping wing.