**3.4 Nozzles**

A supersonic nozzle design is a significant work for hypersonic vehicles, which devotes to produce most of the thrust force and helps to improve the vehicle's internal/external integral level. Two-dimensional (2D) and axisymmetric minimum length nozzles (MLNs) with constant and variable specific heat were designed using the method of characteristics (MOCs) [20, 21], as can be seen in

**Figure 18.** *Isograms of flow field Mach number in different nozzles.*

**Figure 19.**

*Diagram of nonlinearly compressed nozzle process.*

**Figure 18**, where Case 1 is for constant specific heat, 2-D and conservation of mass; Case 2 for constant specific heat, 2-D and eliminating wave theory; Case 3 for constant specific heat, axisymmetrical and conservation of mass; Case 4 for constant specific heat, axisymmetrical and eliminating wave theory; Case 5 for varying specific heat, 2-D and conservation of mass; Case 6 for varying specific heat, 2-D and eliminating wave theory; Case 7 for varying specific heat, axisymmetrical and conservation of mass; and finally, Case 8 for varying specific heat, axisymmetrical and eliminating wave theory. MOC is a numerical technique which has great advantages in accuracy and efficiency for solving hyperbolic partial differential equations.

After the two-dimensional supersonic nozzle design is finished, the flow field is simultaneously obtained with the MOC solution. Concerning the three-dimensional nozzle design, using the streamline tracing technique, the present work designed a three-dimensional asymmetric nozzle with a pre-determined offset circular entrance. However, the nozzles designed by MOC may have excellent thrust performance, but the length goes beyond the geometry constraints of the scramjet engine and does not meet the trim and lift-to-drag ratio requirements. As shown in **Figure 19**, a nonlinear compression technique can be used to truncate the streamline of the perfect nozzle, by preserving the initial major expansion parts of nozzle

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**Figure 21.**

and making the remaining nonlinear compressed. **Figure 20** shows three kinds of typical generated three-dimensional asymmetric nozzle. Numerical studies were performed to investigate the design parameters, such as the pre-determined offset size, the nonlinear truncation parameters, and so on. **Figure 21** shows the simu-

*Contour of Mach number under different truncation parameters. (a) 0.10–0.50 (b) 0.10–0.60 (c) 0.10–0.70 (d) 0.20–0.50 (e) 0.20–0.60 (f) 0.20–0.70 (g) 0.30–0.50 (h) 0.30–0.60 (i) 0.30–0.70 (j) 0.40–0.50 (k) 0.40–0.60 (l)* 

*Three-dimensional nonlinear truncated streamline traced nozzle: (a) circular, (b) rectangle, and (c) circular* 

lated Mach number contours with different truncation parameters.

*0.40–0.70 (First parameter is* A *= x* B *' /x* B *and second one is* B *= x* A*/x* B*).*

*Airframe-Propulsion Integration Design and Optimization*

*DOI: http://dx.doi.org/10.5772/intechopen.85187*

**Figure 20.**

*to rectangle.*

*Airframe-Propulsion Integration Design and Optimization DOI: http://dx.doi.org/10.5772/intechopen.85187*

**Figure 20.**

*Hypersonic Vehicles - Past, Present and Future Developments*

*Isograms of flow field Mach number in different nozzles.*

*Diagram of nonlinearly compressed nozzle process.*

**Figure 18**, where Case 1 is for constant specific heat, 2-D and conservation of mass; Case 2 for constant specific heat, 2-D and eliminating wave theory; Case 3 for constant specific heat, axisymmetrical and conservation of mass; Case 4 for constant specific heat, axisymmetrical and eliminating wave theory; Case 5 for varying specific heat, 2-D and conservation of mass; Case 6 for varying specific heat, 2-D and eliminating wave theory; Case 7 for varying specific heat, axisymmetrical and conservation of mass; and finally, Case 8 for varying specific heat, axisymmetrical and eliminating wave theory. MOC is a numerical technique which has great advantages in accuracy and efficiency for solving hyperbolic

After the two-dimensional supersonic nozzle design is finished, the flow field is simultaneously obtained with the MOC solution. Concerning the three-dimensional nozzle design, using the streamline tracing technique, the present work designed a three-dimensional asymmetric nozzle with a pre-determined offset circular entrance. However, the nozzles designed by MOC may have excellent thrust performance, but the length goes beyond the geometry constraints of the scramjet engine and does not meet the trim and lift-to-drag ratio requirements. As shown in **Figure 19**, a nonlinear compression technique can be used to truncate the streamline of the perfect nozzle, by preserving the initial major expansion parts of nozzle

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**Figure 18.**

**Figure 19.**

partial differential equations.

*Three-dimensional nonlinear truncated streamline traced nozzle: (a) circular, (b) rectangle, and (c) circular to rectangle.*

#### **Figure 21.**

*Contour of Mach number under different truncation parameters. (a) 0.10–0.50 (b) 0.10–0.60 (c) 0.10–0.70 (d) 0.20–0.50 (e) 0.20–0.60 (f) 0.20–0.70 (g) 0.30–0.50 (h) 0.30–0.60 (i) 0.30–0.70 (j) 0.40–0.50 (k) 0.40–0.60 (l) 0.40–0.70 (First parameter is* A *= x* B *' /x* B *and second one is* B *= x* A*/x* B*).*

and making the remaining nonlinear compressed. **Figure 20** shows three kinds of typical generated three-dimensional asymmetric nozzle. Numerical studies were performed to investigate the design parameters, such as the pre-determined offset size, the nonlinear truncation parameters, and so on. **Figure 21** shows the simulated Mach number contours with different truncation parameters.

**Figure 22.**

*Three-dimensional asymmetric nozzle design process.*

**Figure 23.** *Pareto front with six selected cases.*

**Figure 24.** *Inlet and outlet shapes of six selected optimization: (a) inlet shape and (b) outlet shape.*

**Figure 22** shows the whole design process. Thereafter, a multiobjective design optimization has been performed, using orthogonal design, Kriging surrogate model with objective functions of thrust and lift force. Numerical simulations were conducted to validate the accuracy of surrogate models and to provide details of flow fields. The optimization results were examined to investigate the key factors and underlying flow physics that influenced the nozzle performance and to offer a preliminary guide to design a better nozzle with a suitable length. Six cases were selected from the Pareto front as illustrated in **Figures 23** and **24**. The design variables of these cases are used to obtain new design results. New numerical simulations were performed to verify the reliability of surrogate models and to provide a deeper insight of nozzle performance, as can be seen in **Figure 25**.

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**Figure 26.**

*Airframe-Propulsion Integration Design and Optimization*

*DOI: http://dx.doi.org/10.5772/intechopen.85187*

**4. Airframe-propulsion integration**

*Mach number contour of six Pareto front cases.*

**Figure 25.**

Busemann inlet is then truncated.

the scramjet can be seen in **Figure 27**.

*Integration of cone-derived waverider and truncated Busemann inlet.*

The integration method for the cone-derived waverider and scramjet is introduced as the following. The basic Busemann flow field is decided according to the area ratio between inlet and outlet surfaces of the inward-turning inlet, which can be calculated using the stream thrust analysis. As a result, the Busemann inlet can be obtained. The length of the Busemann inlet is too large, and its upper surface of inlet is horizontal which is not appropriate for integration with the waverider. The

The angle of the truncation cone should not be too large and is chosen between 3 degree and 5 degree in the present studies. Meanwhile, the semiapex angle of the truncation cone should be smaller than that of the waverider. Accordingly, iterations are necessary to find out the appropriate basic Busemann flow field. The basic flow field of the cone-derived waverider is decided with the design parameters, for example, the inflow Mach number and an appropriate compression angle. The shock angle and the semiapex angle can be calculated. As mentioned before, the semiapex angle must be larger than that of the truncated Busemann inlet. **Figure 26** shows the integration of the inlet and the waverider compression surface. An integration example of the cone-derived waverider and

**Figure 28** compares the contour of Mach number of original cone-derived waverider and integrated vehicle. It can be observed that shock waves attach the bottom leading edges of surfaces of both vehicles. **Figure 29** shows simulation

*Airframe-Propulsion Integration Design and Optimization DOI: http://dx.doi.org/10.5772/intechopen.85187*

*Hypersonic Vehicles - Past, Present and Future Developments*

*Three-dimensional asymmetric nozzle design process.*

**Figure 22.**

**Figure 23.**

**Figure 24.**

*Pareto front with six selected cases.*

**Figure 22** shows the whole design process. Thereafter, a multiobjective design optimization has been performed, using orthogonal design, Kriging surrogate model with objective functions of thrust and lift force. Numerical simulations were conducted to validate the accuracy of surrogate models and to provide details of flow fields. The optimization results were examined to investigate the key factors and underlying flow physics that influenced the nozzle performance and to offer a preliminary guide to design a better nozzle with a suitable length. Six cases were selected from the Pareto front as illustrated in **Figures 23** and **24**. The design variables of these cases are used to obtain new design results. New numerical simulations were performed to verify the reliability of surrogate models and to provide a deeper insight of nozzle performance,

*Inlet and outlet shapes of six selected optimization: (a) inlet shape and (b) outlet shape.*

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as can be seen in **Figure 25**.

**Figure 25.** *Mach number contour of six Pareto front cases.*
