Effects of streamwise vortex breakdown on supersonic combustion

This paper presents a numerical simulation study of the combustion structure of streamwise vortex breakdown at Mach number 2.48. Hydrogen fuel is injected into a combustor at sonic speed from the rear of a hypermixer strut that can generate streamwise vortices. The results show that the burning behavior is enhanced at the points of the shock waves that are incident on the vortex and therefore the vortex breakdown in the subsonic region occurs due to combustion. The breakdown domain in the mainstream is found to form a flame-holding region suited to combustion and to lead to a stable combustion field with detached flames. In this way, streamwise vortex breakdown has an essential role in combustion enhancement and the formation of flames that hold under supersonic inflow conditions. Finally, the combustion property defined here is shown to coincide with the produced-water mass flow. This property shows that the amount of combustion is saturated at equivalence ratios over $0.4$, although there is a slight increase beyond 1.

Figure 1

Schematic diagram of a hypermixer strut.

Figure 2

Contours of the flame index in planes perpendicular to flow behind a hypermixer strut for $\varphi =0.4$ and $\theta ={36}^{\circ }$.

Figure 3

Configuration of the computational domain from (a) the lateral view and (b) the rear view; red-filled parts are jet orifices in the trailing edge of the strut injector and the red square denotes the calculated region.

Figure 4

Water products ${\dot{m}}_{{\mathrm{H}}_2\mathrm{O}}$ integrated in a plane vertical to flow as a function of $X$.

Figure 5

Mixing efficiency ${\eta }_m$ and combustion efficiency ${\eta }_c$ for $\varphi =0.2$ at $\theta ={22}^{\circ }$ and ${36}^{\circ }$.

Figure 6

Contours of (a) ${\mathrm{H}}_2\mathrm{O}$ products ${\rho }_{{\mathrm{H}}_2\mathrm{O}}$ and (b) subsonic region rendered in red for $\varphi =0.4$ and $\theta ={36}^{\circ }$ at $Z=0$ mm.

Figure 7

Isosurface of the second invariant of the velocity gradient tensor $Q$ at $\theta ={36}^{\circ }$ (a) without fuel injection and (b) with fuel injection $\varphi =0.4$. Positive and negative streamwise vorticities are rendered in red and blue, respectively.

Figure 8

Schlieren images from a side view at $Z=-5.5$ mm for $\varphi =0.4$ and $\theta ={36}^{\circ }$ (a) without fuel injection and (b) with fuel injection $\varphi =0.4$.

Figure 9

Spatial development of the enstrophy minus its streamwise vorticity component.

Figure 10

Schematic of streamwise vortex breakdowns.

Figure 11

Streamwise variations in circulations for various equivalence ratios at (a) $\theta ={22}^{\circ }$ and (b) $\theta ={36}^{\circ }$.

Figure 12

Contours of (a) streamwise vorticities ${\omega }_x$, (b) hydrogen densities ${\rho }_{{\mathrm{H}}_2}$, and (c) heat releases $Q_{\text{HR}}$ in various planes vertical to the mainstream flow at $\theta ={22}^{\circ }$ and $\varphi =0.4$.

Figure 13

Contours of (a) $\mathrm{OH}$ products ${\rho }_{\mathrm{OH}}$ and (b) static temperature $T$ for $\varphi =0.4$ and $\theta ={22}^{\circ }$ at $Z=0$ mm.

Figure 14

Contours of (a) mixedness $Z_{FO}$ and (b) flame index $G_{FO}$ in various planes vertical to the mainstream flow at $\theta ={22}^{\circ }$ and $\varphi =0.8$.

Figure 15

Contours of flame index for $\varphi =0.8$ at $Z=0$ mm and (a) $\theta ={22}^{\circ }$ and (b) $\theta ={36}^{\circ }$.

Figure 16

Schematic of the entrainment process of ${\mathrm{H}}_2$ due to a streamwise vortex.

Figure 17

Streamwise variations in combustion properties ${\mathcal{Q}}_{\varphi }$ and produced-water mass flows ${\dot{m}}_{{\mathrm{H}}_2\mathrm{O}}$ for various equivalence ratios at (a) $\theta ={22}^{\circ }$ and (b) $\theta ={36}^{\circ }$.

Figure 18

Combustion property ${\mathcal{Q}}_{\varphi }$ vs equivalence ratio $\varphi$.

Figure 19

Specific impulse $I_{\mathrm{sp}}$ as a function of the flight Mach number for hydrogen-fueled engines.

Figure 20

Terms $I\text{–}III$ in the vorticity equation (A1) integrated over the cross-sectional area perpendicular to the $X$ direction (a) without fuel injection and (b) with fuel injection $\varphi =0.4$ at $\theta ={36}^{\circ }$.

Figure 21

Streamwise velocity component $u_1$ at the vortex center $(Y,Z)=(0,0)$ without fuel injection and with fuel injection $\varphi =0.4$ at $\theta ={36}^{\circ }$.

Figure 22

Streamwise variations in circulations without fuel injection, with reacting and nonreacting flows $\left(\varphi =0.2\right)$ at (a) $\theta ={22}^{\circ }$ and (b) $\theta ={36}^{\circ }$.