طراحي بهينه‌ي مبدل‌هاي پوسته و لوله‌يي با استفاده از نظريه‌ي ساختاري

HEAT EXCHANGER DESIGN BASED ON CONSTRUCTAL THEORY

در اين نوشتار طراحي مبدل پوسته و لوله‌يي با استفاده از روش جديد و كارآمدِ نظريه‌ي ساختاري ــ روش نوين طراحي بهينه در زمينه‌هاي فني و مهندسي ــ مورد بررسي قرار گرفته است. هدفِ اين بررسي بهينه‌سازي مبدل پوسته و لوله‌يي با ديدگاه كاهش هزينه‌ي كلي مبدل با استفاده از نظريه‌ي ساختاري است. هزينه‌ي كلي مبدل ناشي از هزينه‌ي سرمايه‌گذاري اوليه و هزينه‌ي عملياتي است. به‌كارگيري نظريه‌ي ساختاري موجب افزايش ضريب انتقال كلي مبدل پوسته و لوله‌يي و درنتيجه كاهش هزينه‌ي سرمايه‌گذاري براي ساخت سطح انتقالِ حرارت مي‌شود. همچنين هزينه‌ي عملياتي ناشي از هزينه‌ي انرژي پمپاژ براي غلبه بر افت فشار ناشي از اصطكاك در اين روش كمينه‌سازي مي‌شود. در نهايت از الگوريتم ژنتيك براي بهينه‌سازي تابع هدف كه يك مدل رياضي براي هزينه‌ي مبدل پوسته و لوله‌يي طراحي‌شده بر مبناي نظريه‌ي ساختاري است، استفاده مي‌كنيم. نتايج حاصل از اين تحقيق بيش از 50% كاهش در هزينه‌هاي كلي مبدل را نشان مي‌دهد.

Because of the extensive application of heat exchangers in industrial processes, designers take their cost optimization as an important objective. In this paper, a procedure is introduced for economic optimization of the shell and tube heat exchangers by using constructal theory. The constructal law was stated by Adrian Bejan in 1996, as follows: “for a finite system to persist in time, it must evolve in such a way that it provides access to the currents that flow through it” (Bejan, 2000). In this theory, flow configuration is optimized to provide the easiest possible access to the flow current that causes the construction of fractal, dental or tree shaped structures. We rely on the constructal law of maximization of flow access, in order to distribute the volume of tube side fluid flow optimally through the shell side flowing volume, so that heat transfer is maximized. The optimization of flow geometry leads to a tree-shaped structure, in which the ratio between the total tube contact area and the body size is optimized. The optimization is subjected to fixed total heat duty. The optimized configuration and shape of the heat exchanger (diameter, length, baffle spacing and number of tubes) are the result of a genetic algorithm based optimal trade-off between pumping cost investment cost. A Genetic algorithm optimizes the tree-shaped constructal exchanger and gives optimum tube diameter, tube length, baffle spacing, ratio between successive tube diameters and ratio between successive tube lengths, to the branching positions of the tree-flow structure. The effectiveness of the explained method was evaluated by analyzing case studies taken from the literature. Comparison between traditionally designed exchangers and new exchanger designs, based on constructal theory, exhibits that significant cost minimization is possible. Above all, in the case studies, a reduction of total costs up to 52% was observed. The optimization results of the case study verify the ability of this new method to cost optimize S&T heat exchangers.