Modification of the Standard k-epsilon Turbulence Model for Multi-Element Airfoil Application Using Optimization Technique

Abstract

The use of multi-element airfoils has been known as a major approach to boost up the lift of wing without dramatic increase in its drag. In fact, the conguration helps to reduce the chance of o w separation over the airfoil. However, the use of a complicated geometry such as multi-element airfoil would normally cause complexity in o w behavior. The experience has shown that the o w eld complexities cannot be properly modeled using standard two-equation k-epsilon turbulence model. Therefore, it is important to improve the accuracy of general turbulence models in specic applications and complex computational domains. In this work, we extend a suitable objective function based on evaluating the empirical constants of the turbulence model. The essence of dened objective function is to quantify the inaccuracy between the numerical solution and the measurement. The inaccuracy measured by the dened objective function is suitably reduced using a suitable minimization technique. Eventually, the developed optimization algorithm results in new empirical constants dieren t than the classical ones, which are routinely used in the standard model. The modied turbulence model is then utilized to solve a multi-element airfoil conguration consisted of NACA 0012 airfoil section with a Krueger and a trailing ap. This conguration is chosen to verify the modied turbulence model because the experimental pressure coecien t data is available for this case at three dieren t Mach numbers. The current investigation shows that the results of the current modied turbulence model are considerably better than the classical turbulence model.