The paper presents a method for the design and optimization of a multi-element airfoil-based inertial particle separator. To facilitate design in an interactive manner, a MATLAB graphical user interface was developed with the following capabilities: 1) design of individual airfoil elements; 2) orientation and arrangement of the airfoils to form a multi-element airfoil-based inertial particle separator system by employing translational, scaling, and rotational functions; 3) analysis of the inertial particle separator system; and 4) optimum design of the inertial particle separator system using an evolutionary algorithm-based direct-search optimization technique. The design of individual airfoils was achieved through the use of the PROFOIL code, a state-of-the-art multipoint inverse airfoil design program. Multiple airfoils were arranged to form a multi-element airfoil-based inertial particle separator system subject to geometric constraints. A two-dimensional analysis tool for the multi-element airfoil was linked to the synthesis component of the graphical user interface to carry out flow and particle trajectory analysis component of the program. For the optimization component of the program, a computational objective function was implemented and coupled with a pattern search optimizer of the Direct Search Toolbox in MATLAB. Design and optimization was achieved using multivariable optimization. The paper presents two design examples to demonstrate the design method. Nomenclature C d = particle drag coefficient c = airfoil chord length D eq = equivolumetric or mean volumetric diameter F a = aerodynamic force F g = gravitational force g = gravitational acceleration constant i, k = unit direction vectors in the wind reference frame i p , k p = unit direction vectors in the body reference frame m p = particle mass, p V p n = surface normal vector p = ambient pressure Re = Reynolds number based on particle diameter, a D eq U= a r p = particle position S = particle surface projection on the U perpendicular plane S p = particle surface area t = time U = magnitude of particle relative velocity in the body reference frame, jUj U = particle relative velocity in the body reference frame, V a V p V a = freestream velocity in the body reference frame, u a i w a k V p = particle volume V p = particle velocity in the body reference frame, dr p =dt x, z = axes in the wind reference frame x p , z p = axes in the body reference frame z = pressure head = angle between the z p axis and z axis a = ambient air viscosity a = ambient air density p = particle mass density = shear stress
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