Abstract. This paper examines various first order approximation methods commonly used in structural optimization. It considers several attempts at improving the approximation by using previous analytical results and introduces an adaptation of a first order approximation method using an exponent adjusted to better fit the constraints and reduce the overall number of iterations needed to attain the optimum.
This paper describes a formal optimization procedure for helicopter rotor blade designs which minimizes hover horsepower while assuring satisfactory forward flight performance. flight analysis programs with a general purpose optimization procedure.resulting optimization system provides a systematic evaluation of the rotor blade design variables and their interaction, thus reducing the time and cost of designing advanced rotor blades. The paper discusses the basis for and details of the overall procedure, describes the generation of advanced blade designs for representative Army helicopters, and compares designs and design effort with those from the conventional approach which is based on parametric studies and extensive cross-plots.The approach is to couple hover and forward
A computational fluid dynamics (CFD) model of an electric arc furnace (EAF) has been developed and validated against measurements at the EAF combustion gap. Modeled processes include fluid flow, combustion reactions, radiative heat transfer, turbulence, and NOx formation. This model is used to identify the NOx formation mechanisms and to analyse potential NOx control strategies.The model successfully predicts the NOx emission trends. NOx formation is primarily due to N 2 from air ingress through the slag door or roof ring gap, flowing into the high temperature regions near the burners. N 2 in the oxygen supply is also important. NOx levels correlate with N 2 and O 2 levels in the furnace. Reducing N 2 and excess O 2 in the furnace is recommended for NOx abatement. Unlike many combustion devices, controlling temperature is not recommended for reducing NOx emissions. Large reductions in NOx emissions are predicted by (in order of importance, from highest to lowest): controlling exhaust flows to limit air ingress, closing the slag door and increasing the purity of the oxygen supply.KEY WORDS: NOx; CFD; modeling; EAF; pollution control. mechanism.There are four ways of controlling Thermal NOx formation: reduce the temperature, the nitrogen concentration, the oxygen concentration and the dwell time of the gases at the peak temperatures. Thermal NOx formation is very temperature sensitive and therefore many combustion devices control NOx formation by reducing the peak temperatures by adding more mass per unit heat release. These strategies include exhaust gas recirculation (common in cars and boilers), high excess air and steam injection (common in gas turbines). Temperature control is not recommended for EAFs as high gas temperatures are needed to melt the steel.Most combustion devices consume large amounts of air; hence there is an ample supply of nitrogen. However, EAFs do not purposely inject air; therefore reducing the air ingress into the furnace is an attractive strategy. This requires sealing the furnace as much as possible and operating at slightly positive pressure. Air and other sources of nitrogen should be kept out of the hot spots including the arc and the oxy-fuel burners.A third potential NOx control strategy is to reduce the oxygen concentration. NOx formation is greatly reduced in a reducing environment. This is implemented in many combustion devices by staging the air injection. The fuel is initially burnt fuel rich. Then some energy may be extracted to reduce the temperature. Then air is rapidly injected to fully oxidize the fuel and to rapidly lower the temperature. This process is called "staged combustion" and is common in large coal boilers. The EAF already uses staged combustion. Any NOx formed in the lower half of the furnace will be reduced if the upper half of the furnace has a reducing environment. Combustible gases can then be burnt off at the combustion gap. Available information suggests that the combustion gap is not a significant source of NOx.The above mentioned knowledge of NOx form...
The purpose of this study is to develop exact analytic solutions for the pressure response of a finite conductivity fracture. This model should be able to verify the existence of various flow regimes found in earlier studies. It is hoped that this solution could be modified to give simplified expressions for well pressures for all times and all fracture conductivity ranges. The present work poses and solves the problem of a vertical finite conductivity fracture of elliptical cross-section. The flow within the fracture is assumed to be incompressible and the reservoir is assumed to be infinite. The elliptical fracture geometry was chosen to facilitate the expression of fracture and reservoir pressures as eigenfunction expansions. The solution is obtained by expressing the reservoir pressure as a series of Mathieu functions, and the fracture pressure as a series of cosines. The coefficients in these series satisfy an infinite set of linear relations, termed Fredholm sum equations. Exact solutions to these sum equations are obtained in forms which resemble continued fractions of summations, or equivalently, which require iteration of rational forms. A great deal of effort has been expended to speed the calculation of the solutions, however, only partial success has been achieved. The solutions become increasingly difficult to compute as time decreases. So, approximate solutions for well pressures are given for extremely low values of time. These solutions indicate that behavior of an elliptical fracture is essentially the same as that of a rectangular fracture. Indeed, the well pressures calculated in this work are quite close to those for a rectangular fracture. Generally applicable simplified well solutions have not been found.
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