Modelling of Vortex Generators within the Integral Boundary-Layer Theory

Abstract

One of the most commonly used flow control techniques to trim the aerodynamic performance of wind turbine blades are vortex generators. This passive device, which does not require any active energy, is gaining an increasing interest in this sector especially due to the trend of increasing wind turbine size. Vortex generators are a flow control technique used to prevent or at least lessen the severity of flow separation. The streamwise vortices shed at the free tips of the vortex generators increase the mixing between the high-energy flow in the outer part of the boundary-layer with the low energy regions near the walls. The shed vortices are defined by the strength of the vortices just downstream of the device, the streamwise decay of the vortex strength and the vortex trajectory. In order to assess and optimise the use of vortex generators, there is a need to accurately model the effect of this device in a cost and time efficient way. This could be achieved by modelling vortex generators using integral boundary-layer codes. XFOIL and RFOIL are two well-known integral boundary-layer codes. These two codes rely on Prandtl’s theory stating that a flow field around an object can be divided into two areas: the inviscid outer flow and the viscid inner flow. The inviscid part of the flow is solved using a streamfunction panel method while the viscid boundary-layer solution is prescribed by the boundary-layer equations and additional closure relations. Both solutions are strongly interconnected to each other. A suitable methodology to model the effect of vortex generators into integral boundary-layer codes is the source term approach. This approach was already initiated by Kerho and Kramer1 but is revised carefully in this thesis. The introduction of the streamwise vortices results in an increase in dissipation. To simulate this, the shear-lag equation is modified by introducing an additional source term to the equilibrium shear stress coefficient. The strength of this additional source term is varied over the chord to mimic the downstream decay of the shed vortex circulation. Implementing the source term into XFOIL and RFOIL allows to capture the expected effect of vortex generators on the boundary-layer properties. The source term shape function is prescribed by three parameters: the source term strength, the decay rate and the location of the vortex generators. Because the source term depends on the vortex generator geometry and the local flow properties, its value is calibrated for different airfoil/vortex generator configurations using reference data. Afterwards, these calibrated source terms are related back to the vortex generator parameters and local boundary-layer properties to establish an empirical relation for the source term integral. To do so, a multiple variable linear regression is applied in which the independent variables are the vortex generator height, vortex generator length, inflow angle, local boundary-layer momentum thickness and edge velocity. The source term empirical relation is implemented in XFOIL and RFOIL. Implementing the source term empirical relation led to the development of the foundations of the design tools XFOILVG and RFOILVG. These two codes are extensively validated to evaluate the performance and identify code limitations. Validating the source term empirical relation and its implementation, is realised by comparing the codes’ predictions with reference data from the data base that was already used to set up the source term relation. To further validate the robustness and generality of the code with respect to airfoil selection and Reynolds number, external data sets adopted from literature are used. Based on the validation results, it is believed that the source term approach to model vortex generators within the integral boundary-layer theory is very promising. To further elaborate on this method, recommendations for further work are made. These recommendations concern the data base used to set up the source term empirical relation, the effect of vortex generators on the friction coefficient and the role and value of adding a transition model.