#### LESSONS OF EASTER ISLAND

March 17th, 2016

The aerodynamically coupled flap-pitch equations of motion of a single blade have been derived in a rotating frame as function of the azimuth angle W, When W = Wt, the equations represent the motion of the tth blade. To derive the equations of motion of all the blades as a single unit, the coefficients in the equations may be expressed in terms of the so-called multiblade coordinates. This is done by

expanding all trigonometric functions such as products of sine and cosine functions as the sums of relevant sine and cosine terms. Groups of terms containing factors 1, cos(W), sin(W), … may be identified and individually set equal to zero to give N equations of motion for an N-bladed rotor for the fixed frame harmonics of each blade...

The dynamics of compressor stall has been re-parameterized in a form that would facilitate the construction of a non-linear control law for the active non-linear control of compressor stall. The regions of stable performance in parameter space

Root Locus Fig. 5.11 Root locus plot illustrating the effect of the negative feedback of D/c |

(y = Jn, H > 0, J = Js = 0), unstable performance (y = yn or H < 0, J = 0) were identified. This has led to the belief that a control law that maintains both y = yn, H > 0 and J = Js = 0 would actively stabilize the compressor. One observes that by merely setting the throttle at its optimum equilibrium position does not maintain, J = Js = 0. An additional control input must aim to manipulate the transient and control pressure dynamics defined by Eq...

Read MoreThe capacity, Q, of a cell is the approximate amount of charge that can be stored in the cell when it is fully charged. Thus, the capacity is the amount of electric charge that a battery can store, which is stated in units of ampere-hour (A-h). The state of charge (SOC) is defined as the percentage of the capacity (Qavaiiabie) available at any time with respect to the maximum available capacity (Q = Qmax) of a battery. The SOC of an ideal cell can be expressed in terms of the initial state of charge, the capacity, and the charging current as,

In terms of the discharging current it is,

For finite values of the SOC, the above equation is expressed as,

where g(s) is the charge-transfer efficiency which is equal to unity for low values of the SOC.

The state of charge is an extremely important ...

Read MoreProblems of structural dynamics and aeroelasticity of wind turbine rotors are relatively well understood. Major progress in the field of wind turbine rotor dynamics was achieved during last three decades of the twentieth century thanks to improvements in performance of modern computers and application of nonlinear elastic model-based analysis to both helicopter and wind turbine rotors. An extensive summary of the current status of rotorcraft aeroelasticity is given by Friedmann (2003) and Friedmann and Hodges (2003). Friedmann and Hodges (2003) show that many different analytical methods have been developed in the field of helicopter rotor blade dynamics which are also applicable to wind turbines...

Read MoreElectronic controllers for jet engines were developed in the 1980s. Currently, the jet engine controllers use highly customized computers to synthesize the control laws with a number of sensor inputs and actuator outputs. Such electronic controllers result in higher engine operating efficiencies by allowing for precise engine control through the use of multiple control loops and improved control laws to reduce transient overshoot or undershoot. It also allows implementation of control algorithms which would be difficult to implement using traditional wired circuitry. Current engine control systems are generally implemented digitally and cannot be overruled by the pilot and for this reason are referred to as full-authority digital engine controllers (FADEC)...

Read MoreA solar cell is a device that converts light from the sun directly into electricity. They are also called photovoltaic devices. There are a wide variety of solar cells available in the market, and they are all differentiated by their different materials and structures. All of these have one target which is to produce maximum amount of energy while leaving minimum installation and production cost at a low. More than half of the solar cells available in the market are made of silicon as they are very cheap due to their huge availability in the earth’s crust. As it is very easily accessible, silicon is the most researched, developed, and used element to date in terms of solar cells.

Read More4.1 Introduction

Wind power has evolved rapidly in the last two decades with regard to both power rating and size of wind turbines that are currently being installed. In the past few years, several developments have taken place. There has not only been a continuous increase in the rated power of wind turbines being installed, but also in the development of reliable wind turbines rated around 2-10 MW which are grid safety code compliant and suitable for different installation environments— onshore and offshore, as it can be seen in the commercial products currently in the market.

Broadly, wind turbines (Manwell et al...

Read MoreCompressor surge and rotating stall vibrations place fundamental limitations on aircraft engine performance and remain persistent problems in the development of axial compressor and fan stages. Compressor surge and rotating stall are purely

fluid mechanic instabilities, while blade flutter, stall flutter, and surge flutter and their variants are aeroelastic instabilities involving both blade vibrations and fluid motion. Although both rotating stall flutter and rotating stall tend to occur when the blades of a compressor or fan are operating at high incidence angles and/or speed, and unsteady viscous flow separation plays a key roll in both of these phenomena, the various fluttering phenomenon are precursors to compressor surge.

Surge is characterized by large amplitude fluctuations of the p...

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