8540

7921

كارشناسي ارشد

تبديل انرژي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده مكانيك

1392

ده،85ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

ابراهيم شيراني

محمدرضا سليم پور

27/11/92

احمدرضا پيشه ور، محمدرضا توكلي

مهندسي مكانيك

ID7921

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Optimal Design of Vascular Systems Using Biologically Inspired Design Mohammad Sayed Razavi Rizi m sayedrazavi@gmail com Dec 29th 2013 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 8311 Iran Degree M Sc Language FarsiSupervisor Prof Ebrahim Shirani eshirani@ictp itABSTRACTIn the present study a general method for obtaining the optimal geometry of vascular systems is developed Forthis purpose a Y shaped configuration that consists of the mother branch and two daughter branches is used The total energy loss which is the sum of the viscous dissipation and metabolic loss is minimized Minimizingthe total energy loss results in the optimal distribution of WSS Using optimal distribution of WSS and thecontinuity equation at the junction of bifurcation a relationship between diameters of mother and daughtervessels is obtained Also the optimal distribution of WSS leads to viscous loss that is proportional to the volumeof conduit Therefore minimization of the volume of bifurcation results in the optimal bifurcation angle Moreover it is shown that the optimal WSS provides minimal flow resistance The optimal relationship betweendiameters of the mother and daughter vessels is obtained for both Newtonian and non Newtonian fluids Also turbulent flows are considered using the non dimensional friction factor as a function of Reynolds number It isshown that for both Newtonian and non Newtonian fluids the optimal relationship between the mother anddaughter branches are the same as Murray s law However for turbulent flows the relationship betweendiameters of the mother and daughter branches are a function of the tube roughness Moreover it is shown thatthe optimal WSS is obtained a constant for laminar flows However the optimal WSS in turbulent flows is afunction of tube roughness and diameters Based on the arbitrary distribution of WSS a general formulation for optimal bifurcation angle is proposed Forthe derivation of the optimal bifurcation angle the power law model is used It is observed that increasing theWSS of daughter branches compared to the value of mother branch leads to smaller bifurcation angle In order to investigate the effect of the Reynolds number on the analytical results numerical simulations havebeen performed Using non Newtonian power law and Carreau models analytical results have been tested Forthe simulation a Y shaped configuration with a mother branch and two daughter branches has been chosen Theflow resistance has been computed for different ratios of the diameter of the mother branch to the diameter ofthe daughter branches The results show that by increasing Re the optimal diameters ratio changes form 0 8 angles rather than 75 which is predicted analytically In other words when the inertia effect becomes dominant predicted by analytical formulations to one Also the increase of Re leads to the smaller optimal bifurcationsmaller bifurcation angles leads to smaller energy dissipation in the bifurcation Key words Vascular System Murray s law Flow Resistance Constructal Theory

ابراهيم شيراني

محمدرضا سليم پور

احمدرضا پيشه ور، محمدرضا توكلي