Research Article
Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method
Muhammad Rafiq*,
Abdul Rehman,
Naveed Sheikh,
Muhammad Saleem,
Muhammad Umar Farooq
Issue:
Volume 7, Issue 2, December 2023
Pages:
27-36
Received:
13 October 2023
Accepted:
31 October 2023
Published:
11 November 2023
Abstract: The present study involves a numerical investigation of laminar boundary layer flow over a flat plate, controlled by the Prandtl equations. The flow is governed by a dimensionless third-order system of nonlinear ordinary differential equations. The finite difference method is employed to solve the system, which serves as an approximation technique. The study explores the properties of the finite difference method and discusses its efficacy in solving the boundary layer flow problem. Additionally, we discuss an inverse problem related to the Falkner-Skan equation, aiming to obtain precise values for the second derivative's initial value. This inverse problem is successfully resolved using an appropriate initial value procedure. The results obtained from the finite difference method and the inverse problem resolution is compared with those from cubic spline interpolation, proposed by Alavi and Aminikhan. By doing so, the reliability and accuracy of present approach is demonstrated. Overall, this study contributes to a better understanding of boundary layer flow and presents a viable numerical technique for tackling similar fluid dynamics problems. The findings shed light on the significance of choosing appropriate numerical methods for solving complex systems of equations in fluid mechanics.
Abstract: The present study involves a numerical investigation of laminar boundary layer flow over a flat plate, controlled by the Prandtl equations. The flow is governed by a dimensionless third-order system of nonlinear ordinary differential equations. The finite difference method is employed to solve the system, which serves as an approximation technique....
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Research Article
Development of a New Aerodynamic Method for the Mechanical Characterization of a Horizontal Axis Wind Turbine
Choupo Yuego*,
Maxwell Tientcheu Nsiewe,
Balbine Matuam Tamdem,
Nicolas Gnepie-Takam,
Alexis Kuitche
Issue:
Volume 7, Issue 2, December 2023
Pages:
37-46
Received:
14 October 2023
Accepted:
31 October 2023
Published:
11 November 2023
Abstract: The aim of this work is to propose a new method for calculating the aerodynamic forces of wind turbine blades and the power developed by them. To this end, the blade element momentum, prescribed wake and free wake methods were compared for speed ranges from 5 to 20m/s. The two-bladed NREL PHASE IV wind turbine with profile S 809 was used as the physical model, with the polars extrapolated to 90° using the Viterna method and then extended from -180 to 180° using flat theory. The largest error in power output was 47% at 5 m/s using PVM, the second largest was 16% at 10 m/s using BEM, and the third largest was 13% at 10 m/s using FVM. In or-der to reduce the percentage error of the PVM, the phenomen of vortex core growth has been in-tegrated into this method. The error at 5m/s was reduced from 47% to 8.29%, and the maximum error of the modified method was 9.19% observed at 18m/s. The new method was then compared to the Reynolds-averaged Navier-Stokes equation from the literature for the same velocity range. The maximum error observed was 8% at 10m/s for the RANS and 9.19% at 18 m/s for the new method.
Abstract: The aim of this work is to propose a new method for calculating the aerodynamic forces of wind turbine blades and the power developed by them. To this end, the blade element momentum, prescribed wake and free wake methods were compared for speed ranges from 5 to 20m/s. The two-bladed NREL PHASE IV wind turbine with profile S 809 was used as the phy...
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