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It is critical in the Newton algorithm to find the optimum value of the objective function. The quasi Newton method modifies what was described above. The basic principle is that the direction of search is based off an n × n matrix which is similar to the inverse Hessian matrix. As iterations are performed, the n × n matrix becomes closer to the inverse Hessian matrix. One of the disadvantages of the Hessian matrix is that it requires partial second derivates which may not be possible for all functions. The quasi-Newton method avoids these problems by eliminating the need to evaluate second derivates. Chapter 4: System Description The system which an analysis is done is a regenerative organic Rankine cycle. In this system there is a boiler, expander, regenerator, condenser and pump. The regenerator transfers some of the useable heat exiting from the expander to the fluid stream before it enters the boiler. The reason this is necessary for the system is that when using an isentropic or dry fluid, the state of the fluid exiting the expander is always going to be superheated. Depending on the fluid and the pressure ratio of the expander, the temperature is much higher than the fluid stream after the pump. Therefore, there is a potential to return (or regenerate) some of that heat back into the system instead of dumpingittotheatmosphereinthecondenser. Thishelpsincreasecycleefficiency,since less heat input is needed to heat up the fluid to the expander input state. 31PDF Image | Exergoeconomic Analysis and Optimization of ORC
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