# Multidisciplinary Optimization of Aircraft Aerodynamics for Distributed Propulsion Configurations
## 4 Multidisciplinary Analysis and Optimization in Aero-Propulsive Design
### Frameworks of Multidisciplinary Optimization  
The concept of MDO is to integrate the knowledge of various disciplines in the whole process of complex system design, to fully consider the interaction and coupling between disciplines for obtaining the overall optimal solution of the system [77]. Generally, the design constraints of MDO refer to the mission requirements of the subject, that is, the final target of an aircraft, such as total energy consumption, flight range, etc. The design variables refer to item values that could affect the development of the indicator results, such as the area of an aircraft or the number of propulsors [80; 81]. Figure 6 shows the different MDO frameworks in conventional and reform (regional/distributed) propulsion systems in TWB and BWB.  
In analytical aspects (reference collection from Table 1), a small number of sample cases completed the scheme configuration by experimental methods [82; 83]. Most of the cases are designed using the parametric model. After the propulsion-airframe scheme is established for these samples, the gradient-based optimization method is used to obtain the optimal model. In optimization (reference collection from Table 1), the models with more energy-saving and higher flight range have a MTOM between 400,000 and 440,000 kg. [PERSON] et al. arranged three propulsors in the PA position. The configuration scheme is designed by using a general parametric aircraft configuration scheme (design space exploration). The model-based agile framework is used as an MDO tool. The results show that the fuel/range ratio is 9.06 kg/km [68]. [PERSON] et al. installed four propulsorsat the UW position. The parametric model is used to create the initial configuration, and the multi-model generator module is applied to build the final model. Their best fuel/range ratio result is 11.09 kg/km [84]. [PERSON] applied eight propulsors at the BLI location. A parametric model with a few design parameters is drawn for the initial configurations. The MDO framework is built with a hierarchical strategy, and the final model is calculated through normal-boundary intersection. The optimal result of fuel/range ratio is 11.69 kg/km [8]. Most of these cases listed in Table 11 belong to multi-variate optimization. Its analysis algorithms are generally Reynolds-averaged Navier-Stokes equations, the vortex-lattice method, positive normal-boundary intersection, etc. These algorithms can obtain more significant optimization results. Comparatively, the demand for computing capacity is relatively big and requires a long computing time.  
Since many disciplines are involved in the multidisciplinary optimization of DP aircraft, its performance evaluation has considerable complexity. The integration of aerodynamics involves the coupling of aerodynamics, propulsion, structure, weight, stability, and control. These disciplines make multidisciplinary coupled analysis and collaborative optimization the core of DP aircraft design. Although research works on DP aircraft have been carried out, most of them are focused on configuration design. The exploration of the related energy-saving in integrated status and their outcomes, such as thrust distribution criterion, theoretical modeling, algorithms of large scale, and multi-level nesting MDO for DP aircraft configuration design, are still rare.