Optimization Of The Aft-Body Geometry Of An Axi-Symmetric Slender Body To Minimize Wave Drag
Abstract
Extensive work on slender axi-symmetric bodies in transonic and supersonic flow has been carried out and well documented in the 1970’s. With the progress of CFD that has taken place in the following decades, codes are available to look into the detailed flow characteristics and the resulting wave drag, in particular due to the geometry of the aft-body. However, to the authors’ knowledge, the optimum drag of axi-symmetric bodies need further elaboration. Therefore it is the objective of present work look carefully into the drag mechanism due to geometry of the aft-body, in particular and more significantly, to find a way to optimize the total drag. The objective of this work is to investigate an axi-symmetric slender body geometry which has a minimum drag, particularly in the transonic and supersonic flow regime.    This research is started by conducting numerical computation studies of the previous existing axi-symmetric slender bodies to gain physical understanding of the effect of aft-body geometry to the overall wave drag. This CFD approach is conducted by using a commercially available flow solver called Fluents/Rampant. This code solves the basic equation of fluid flow for inviscid flow.    From this study, physical understanding of the phenomena, such as correlation between wave drag and wave distribution at the aft-body geometry, can be gained. The result of the study shows, for the body with pointed end, appearance of expansion wave at the aft-body and followed by a shock wave somewhere on the aft body. On the other hand, for the body with base area, an expansion fan appears at the corner connecting the aft body to the base. The expansion fan deflects the flow behind the body toward the centerline and flows comming from the upper and lower surface meet. The collision of the two streams results in the generation of shock waves somewhere downstream the base area. Based on the physical understanding gained above, a practical method of reducing the wave drag of a given body is developed for both cases, body with pointed end and body with base area. In this method, a shock wave generator is placed at a particular location on the aft body. By trial and error, a particular location of the shock wave generator placement is found which result in lowering the wave drag of the original body Finally, another effort to minimize the wave drag of an axiymmetric cylindrical body is conducted by utilizing an optimization routine. A Modified Feasible Direction (MFD) based optimization program is developed. In this method, objective function uses the simple drag equation formulated by Von Karman and Moore. The MFD optimization program developed is intended to solve the two cases mentioned before; axi-symmtric slender body with pointed end and axi-symmetric slender body with base area.   After validating the MFD optimization program by evaluating the existing axi-symmetric slender bodies, the program is used to search for optimum aft body geometries which minimize the wave drag.   The results show that the MFD optimization program can be utilized in an aerodynamic optimization problem which has not been done before.References
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