A procedure for computing the optimal variation of the blades' pitch angle of an H-Darrieus wind turbine that maximizes its torque at given operational conditions is proposed and presented along with the results obtained on a 7 kW prototype. The CARDAAV code, based on the “Double-Multiple Streamtube” model developed by the first author, is used to determine the performances of the straight-bladed vertical axis wind turbine. This was coupled with a genetic algorithm optimizer. The azimuthal variation of the blades' pitch angle is modeled with an analytical function whose coefficients are used as variables in the optimization process. Two types of variations were considered for the pitch angle: a simple sinusoidal one and one which is more general, relating closely the blades' pitch to the local flow conditions along their circular path. A gain of almost 30% in the annual energy production was obtained with the polynomial optimal pitch control.

The paper presents three modifications for an improved performance in terms of increased power output of a straight-bladed VAWT by varying its pitch. Modification I examines the performance of a VAWT when the local angle of attack is kept just below the stall value throughout its rotation cycle. Although this modification results in a very significant increase in the power output for higher wind speeds, it requires abrupt changes in the local angle of attack making it physically and mechanically impossible to realize. Modification II improves upon the first by replacing the local angle of attack by the blade static-stall angle only when the former exceeds the latter. This step eliminates the two jumps in the local effective angle of attack curve but at the cost of a slight decrease in the power output. Moreover, it requires a discontinuous angle of attack correction function which may still be practically difficult to implement and also result in an early fatigue. Modification III overcomes the limitation of the second by ensuring a continuous variation in the local angle of attack correction during the rotation cycle through the use of a sinusoidal function. Although the power output obtained by using this modification is less than the two preceding ones, it has the inherent advantage of being practically feasible.

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This paper describes an analysis method for an inertial particle separator system modeled as a multi-element airfoil configuration. The analysis method is implemented in a numerical tool that is able to perform impingement analysis using spherical, nonspherical particles as well as water droplets for a range of Reynolds number (10 4 Re 5 10 5 ). A limitations of the analysis tool is that it lacks an appropriate particle rebound model for the treatment of particle-wall collisions. The usefulness of the analysis tool is its use in conjunction with a multipoint inverse design tool for the design of a multi-element airfoil based inertial particle separator system model in an inverse fashion as opposed to the direct design methods being employed currently for this task. With such a design and analysis tool at hand, the design space can be explored as well as tradeoff studies can be performed that can aid in the development of a more efficient design methodology for multi-element airfoil based inertial particle separator systems.= Runge-Kutta coefficients used to integrate the momentum equation l 0 ; n 0 = trajectory direction vector l 1 ; n 1 = airfoil panel plane direction vector 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 r p;i x p;i ; z p;i = particle current position during trajectory integration r p;i1 x p;i1 ; z p;i1 = particle new position during trajectory integration S = particle surface projection on the U * perpendicular plane S p = particle surface area s = airfoil panel surface arc length,= trajectory parametric equation parameter t 1 , t 2 = airfoil panel parametric equation parameters U = magnitude of particle relative velocity in body reference frame, jUj U = particle relative velocity in body reference frame, V a V p U 0 = initial particle relative velocity in body reference frame V a = freestream velocity in body reference frame, u a i w a k V i u i ; w i = current particle velocity during the trajectory integration V i1 u i1 ; w i1 = new particle velocity during the trajectory integration V p = particle volume V p = particle velocity in body reference frame, dr p =dt V 1 = unperturbed freestream velocity in wind reference frame, u 1 i w 1 k V 0 a = initial freestream velocity in body reference frame V 0 p = initial particle velocity in body reference frame u= axes in wind reference frame x p ; z p = axes in body reference frame x 0 ; z 0 = initial particle location in wind reference frame x 1 ; z 1 , x 2 ; z 2 = airfoil panel coordinates z = pressure head = geometric angle of attack with respect to airfoil chord line = impingement efficiency, dz 0 =ds x = step along the x axis z = step along the z axis = angle between the z p axis and z axis a = ambient air viscosity a = ambient air density p = particle mass density = time step in Runge-Kutta integration = shear stress = shape factor

A design procedure for subscale airfoils with full-scale leading edges that exhibit full-scale water droplet impingement characteristics in an incompressible, inviscid ow is presented. The design procedure uses validated airfoil design, ow analysis, and water droplet impingement simulation codes to accomplish the task. To identify and isolate important design variables in the design, numerous trade studies were performed. This paper presents the results of the trade studies and brie y discusses the role of important design variables in the subscale airfoil design. The effect of these design variables on circulation, velocity distribution, and impingement characteristics is discussed along with the accompanying implications and compromises in the design. A strategy to incorporate viscous effects into the design is also presented. This article also presents the design of a half-scale airfoil model with a 5% upper and 20% lower full-scale surface of the Learjet 305 airfoil leading edge and compares its aerodynamic as well as the droplet impingement characteristics with that of the Learjet 305 airfoil. NomenclatureC l = airfoil lift coef cient c = airfoil chord length c m0 = airfoil zero-lift pitching moment coef cient at c/4 F r = Froude number, V`/ cg Ï K = droplet inertia parameter, rwd 2 V`/18cm K S = trailing-edge thickness parameter M = freestream Mach number Re = freestream Reynolds number, rV`c/m R U = droplet freestream Reynolds number, rdV`/m S = airfoil surface arc length measured from the leading edge where S = 0 T = freestream static temperature V = surface velocity V`= freestream velocity x, y = airfoil coordinates x m , x m = upper and lower surface match locations x r, x r = upper and lower surface pressure recovery locations x 0, y 0 = initial horizontal and vertical displacement of the droplet v 1 = design velocity level for segment 1 a = angle of attack relative to the chord line ae = effective angle of attack relative to the nose section chord line, a 2 g a*, ā * = upper and lower surface multipoint design angle-of-attack distribution b = local impingement ef ciency G = circulation strength normalized by V`c fs G = circulation strength, m 2 /s Presented as Paper 96-0635 at g = nose droop angle d = droplet diameter h = normalized subscale airfoil chord length, c ss /c fs m = air viscosity r = air density rw = water density t = nite trailing-edge angle fle = leading-edge arc limit Subscripts fs = full-scale airfoil i = inviscid l = lower surface ss = subscale airfoil u = upper surface v = viscous