بهينه سازي شكل نازل تونل باد فراصوت با استفاده از روش معادلات الحاقي

چكيده انگليسي :

83 Design Optimization of Supersonic Wind Tunnel s Nozzle Using Adjoint Equations Mohammad Akhoondzade m akhoondzade@me iut ac ir Date of Submission 2015 05 18 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Ahmad Reza Pishevar apishe@cc iut ac irAbstract Supersonic nozzles are used in many applications such as propulsion systems turbines supersonicwind tunnels and mixing devices One of the important challenges in designing this kind of nozzles is theextreme sensitivity of outlet condition to variations in profile geometry The standard procedure to designsupersonic nozzles which produces uniform outlet ows is based on the method of characteristics MOC In this method the hyperbolic partial differential equations that govern the isentropic supersonic ow arereduced to ordinary differential equations along so called characteristic lines which emanate from a giveninitial line Moreover this method has limitations including disability in development for viscous flow impossibility of adding a constraint such as minimum length not designing the convergence part of nozzleand having assumption of perfect gas without phase changes Methods of optimization are used to eliminatethese limitations in design of supersonic nozzle One of these methods is adjoint equations This method hasbeen used for the external flow frequently and it has not been used for internal flow yet The purpose ofthis research is to use adjoint method to optimize the shape of supersonic nozzle to achieve maximumuniformity at the nozzle exit Firstly in order to obtain the accuracy of this method for different costfunctions and initial guesses an inverse design problem is solved It is shown that in this case the costfunction cannot be defined on the outlet boundary Also it is demonstrated that the velocity and densitycannot be used in defining the cost function Consequently cost function should be defined only withpressure and geometric parameters In addition changing the initial guess doesn t have an effect on the finalresults Examining the various cost functions on the solid wall and symmetry boundaries proper function isobtained This function is in the form of sum of minimum pressure gradient on the solid wall reaching 80percent of the nozzle length to outlet pressure on the symmetry boundary and fixing the height of the nozzlein the throat It is observed that this method is able to reduce the amount of non uniformity in the outlet ofthe nozzle The non uniformity obtained from the MOC is 2 2 percent and this value for adjoint method is0 17 In this design the length of the nozzle is 10 percent more than result of MOC If the length of thenozzle is considered equal to length of MOC the amount of non uniformity Increases to 0 28 percent whichis eight times less than the result of MOC Aside from the point that mentioned above this method is alsoused to reduce 10 percent of the length of the nozzle and the results are compared with the results of thegenetic algorithm It is observed that the adjoint method reduced the non uniformity from 1 percent ingenetic algorithm to 0 6 percent Runtime is 12 hours and the number of iterations required for convergenceis 4000 The problem is considered as inviscid steady state and two dimensional flow Furthermore theboundary conditions at the inlet is uniform and the gas is ideal Keywords Optimization Adjoint equation method Supersonic nozzle Internal flow

آخوندزاده، محمد

بهينه سازي شكل نازل تونل باد فراصوت با استفاده از روش معادلات الحاقي