Optimization of Heating Element Profile of Ljungstrom Using Discrete Orthogonal Functions and Adjoint Method

In this paper, optimization of CU element profile of Ljungstrom in power plant has been investigated in order to increase its performance, reduce pressure drop and reach minimum price. First, a three-dimensional model was developed and then the desired model is simulated. To optimize the proplem, geometry parameters rewrite in form of unknown coefficient vectors by using orthogonal functions and then by using adjoint method, optimal value of geometric coefficients, plates angle and flow velocity are obtained. Objective function is defined based on the maximum Nusselt number, minimum pressure drop coefficient and minimum price and according to them, the design parameters are determined. So, with angles between 20 and 70 degrees for different Reynolds numbers, the optimal coefficients of the profile are determined and variations of the coefficients with ratio of the heat transfer to the pressure drop are investigated. Results show that when pressure drop is more important, small Reynolds number and angle are more efficient, and when heat transfer is important, large Reynolds number and angle are effective. For angles about 70 degrees and Reynolds number about 8000, maximum of function is obtained. At angles greater than 70 and at Reynolds numbers greater than 8000, although the heat transfer coefficient increases, the flow experiences high pressure drop, which reduces objective function.