A new aerodynamic model for the prediction of vertical axis wind turbine performance is introduced. The model is fully three dimensional and is derived from consideration of both momentum and vortex theories. In the calculation process the turbine wake is modelled by a series of shed and trailing vortices. The overall shape of the wake, however, is determined from momentum theory. Comparison is made between the new model and a free vortex method. Although the accuracy levels of the two techniques are equivalent, the prescribed wake model is more than two orders of magnitude faster. The prescribed wake model is also shown to compare well with field data. Finally, the future development of the model is discussed.
Abstract. In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid, compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type schemes. Previously, this system was developed through computational studies by Mawlood [1]. However the new test cases for compressible flows, the shock tube problems namely the receding flow and shock waves were not investigated before by Mawlood [1]. Thus, the objective of this study is to develop a high-order compact (HOC) finite difference solver for onedimensional Euler equation. Before developing the solver, a detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. Spatial discretization of the Euler equation is based on flux-vector splitting. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. The AUSM scheme is based on the third-order compact scheme to the approximate finite difference equation was completely analyzed consequently. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with four test cases namely, unsteady shock tube, quasi-one-dimensional supersonic-subsonic nozzle flow, receding flow and shock waves in shock tubes. From these results, it was also carried out to ensure that the definition of Riemann problem can be identified. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement with the extension of the AUSM scheme from first-order to third-order accuracy in terms of shocks, contact discontinuities and rarefaction waves.
Computational fluid dynamics (CFD) is a well known tool to solve the fluid flow problems. In CFD analysis, the models use various types of Partial Differential Equation (PDE). The most common is hyperbolic equation. In order to solve the equation, high-order scheme is very reasonable to be applied due to the accuracy of result. So that, this study use modified Runge Kutta with Total Variation Diminishing (TVD) scheme and the model is half body airfoil (symmetrical airfoil NACA 0012). Firstly, parametric study over the size of suitable flow domain was carried out. If the length of airfoil chord is denoted by c, investigation effects on the size of flow domain is carried over the flow domain in x-direction which is 5c while in y-direction is 6c. Another two size flow domains had been used in this study are 5c×3c and 9c×3c respectively. The result shows a strong influence to the flow field solution occurred if the distance between airfoil surfaces to the outer boundary is relatively small. Through this parametric study, it had been suggested that the best way to solve the aerodynamics problem for the flow past through symmetrical airfoil by using the size of flow domain is 5c×6c. Using the same size of flow domain, it had been found that the developed computer code able to produce the result in a good agreement with ANSYS CFD-FLUENT software.
The continued research and development of high-order methods in Computational Fluid Dynamics (CFD) is primarily motivated by their potential to significantly reduce the computational cost and memory usage required to obtain a solution to a desired level of accuracy. The present work presents the developed computer code based on Finite Volume Methods (FVM) Cell-centred Finite Volume Method applied for the case of Quasi One dimensional Inviscid Compressible flow, namely the flow pass through a convergent divergent nozzle. In absence of the viscosity, the governing equation of fluid motion is well known as Euler equation. This equation can behave as Elliptic or as Hyperbolic partial differential equation depended on the local value of its flow Mach number. As result, along the flow domain, governed by two types of partial differential equation, in the region in which the local mach number is less than one, the governing equation is elliptic while the other part is hyperbolic due to the local Mach number is a higher than one. Such a mixed type of equation is difficult to be solved since the boundary between those two flow domains is not clear. However by treating as time dependent flow problems, in respect to time, the Euler equation becomes a hyperbolic partial differential equation over the whole flow domain. There are various Finite Volume Methods can be used for solving hyperbolic type of equation, such as Cell-centered scheme, Cusp Scheme Roe Upwind Scheme and TVD Scheme. The present work will concentrate on the case of one dimensional flow problem through five nozzle models. The results of implementation of Cell Centred Finite Volume method to these five flow nozzle problems are very encouraging. This approach able to capture the presence of shock wave with very good results.
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