1 Introduction

The conditions of start and unstart are common problems in hypersonic inlets. There are many reasons that led to unstart of hypersonic inlets such as high back pressure, big attack angle, and low Mach number. The unstart inlet often caused the pressure load of compressing surface increased sharply, the coefficient of resistance increased, and the heat load changed [1,2,3]. All these changes could make damage of the component structure and the stable fly condition of the vehicles. Also the decreased captured mass flow for unstart inlet could not supply the enough oxidant into the combustor; thus, the engine could not work effectively. Thus the unstart characteristics of hypersonic inlets have been widely focused, and many scholars have made studies in this area.

The flow field oscillation and unstable characteristics of the unstart inlet caused by anti-pressure were experimentally studied by Tan [4, 5]. The results showed that the flow field could oscillate when the anti-pressure was strong enough. Also the characteristics of flow field were measured by PIV (particle image velocimetry) by Wagner [6, 7]. Results showed that the shock chain was moved forward in isolator, and there were some flow vibration at a frequency of 124 Hz. The instantaneous velocity of shock wave was measured by Rodi [8] and Weiting [1]. The study conducted by Hawkins [9] indicated that the vibration of pressure could increase, and the vibration frequency could be more than 100 Hz when the inlet was under unstart. McDaniel [10] pointed out that the separation of boundary layer which induced by ignition of fuel on the sidewall of combustor could lead to unstart of inlet. The characteristics of unstart/restart of hypersonic inlets caused by variations of attack angle of freestream were numerically studied by Chang [11].

In the above, a lot of work about the unstable characteristics of hypersonic inlets were mainly focused on the influence of anti-pressure. Few studies were emphasized on the critical starting Mach number or low Mach number without anti-pressure. We are still confused with the reason and mechanism of flow oscillation in hypersonic inlets under low Mach number without anti-pressure. In order to explore this reason and mechanism of flow oscillation, the characteristics of flow field and the shockwave during the period of flow oscillation under the critical starting Mach number were discussed in detail.

2 Numerical Model

Physical model of the hypersonic inlet as shown in Fig. 1 was used to study the characteristics of flow field and the shockwave under the critical starting Mach number (Ma3.8) while the designed mach number was 6.

Fig. 1
figure 1

Model of hypersonic inlet

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Numerical simulations were conducted using the Reynolds-averaged Navier-Stokes (RANS) equation. The structured mesh of quadrilateral cells was generated around the physical models with a grid size of 400(x-direction) by 400(y-direction) cells. Mesh refinement tests have been carried out on a finer mesh of 500 by 500 cells, and grid independence has been found. Grid stretching is applied to near-center body surface to increase the resolution of the boundary layer.

The initial far-field flow condition was shown in Table 1. An adiabatic wall condition was assumed. The pressure of outlet was set to zero.

Table 1 Flow conditions at the entrance
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3 Results and Analysis

3.1 Total Characteristics of Flow Field

The total mass flow rate between inflow and outlet and the mass average Mach number of outlet showed in Figs. 2 and 3 indicate that flow field of hypersonic inlet was under periodic oscillation at the critical starting Mach number.

Fig. 2
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Total mass flow rate between inflow and outlet

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Fig. 3
figure 3

Mass-weighted average Mach number of outlet

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As shown in Fig. 4a, there was a small “separation bubble” near the shut in the flow field which is defined as the initial condition of one period under the critical Mach number(Ma3.8) while the designed Mach number was 6. According to the capture mass flux and the flow field, the hypersonic inlet was started under this initial condition. Also we could see that the separation shockwave interacted with the lip shockwave, and the end point of separation shockwave was in the internal compressing channel. As the compute step moved on, when the flow field was under one fourth period as shown in Fig. 4b, the “separation bubble” was so large that only few mass flows into the internal channel were captured. The separation shockwave could not interact with the lip shockwave anymore, but interact with the external compression shockwave and then form a strong shockwave which is apart from the lip. As the compute step kept moving on, when the flow field was under two fourth period as shown in Fig. 4c, the “separation bubble” became smaller than that in Fig. 4b. It was showed that the captured mass flows increased under this condition. The separation shockwave still interacted with the external compression shockwave and then form a strong shockwave. However, the strong shockwave was moving toward the lip. Just as the compute step is going on, when the flow field was under one period as shown in Fig. 4d, the “separation bubble” and the flow field became same as that in Fig. 4a. It suggested that the flow field and shockwave have completed one oscillation period.

Fig. 4
figure 4

Mach number contour in one oscillation period. (a) t = 0, (b) t = 1/4 T, (c) t = 1/2 T, (d) t = T

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From the simulation results above, many unsteady characteristics could also be obtained by steady method. Thus the steady numerical method at some certain extent could be used to obtain some unsteady characteristics of the oscillation flow of hypersonic inlet from the numerical stratagem. Yu [12] has also proved that many of the shockwave oscillation features with anti-pressure of hypersonic inlet could be realized by steady numerical method.

3.2 Detailed Analysis of the Periodic Oscillation of Flow Field

In order to fully understand the oscillation process and find the oscillation mechanism, we have made more detailed analysis about the change of flow field, the shockwave, the mass flow of throat and outlet, and the “separation bubble” under every compute step of one oscillation period.

As shown in Fig. 5, the captured mass flux in the throat and outlet also showed the periodic oscillation of the flow field. The max and minimum captured mass flux of throat were 0.55 and 0.18. The inlet experienced start, unstart, and restart periodic processes. However, it showed that the max and minimum captured mass flux of outlet were 0.5 and 0.24.

Fig. 5
figure 5

Coefficient of mass captured at the throat and outlet

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From Fig. 5, the change of captured mass flux at the throat and outlet was not same with each other. The change of captured mass flux at the outlet was later than that at the throat. At some certain time step, both conditions arrived at the same point. However, this condition could not be maintained. The mass flow would be blocked at the area of the throat when the captured mass flux at the entrance of the inlet was large than the max captured mass flux at the throat. At this time, the “separation bubble” would be increased gradually by this “blocking” factor, and the separation shockwave would be splitted out from the lip. Thus the spillage of flow out from the internal channel is realized and the captured mass flow is decreased. Though the mass flux flow through the outlet was increased, the max flux released was always less than the max captured at the entrance. So the effect of “blocking” could not be solved.

From Fig. 6, the “separation bubble” became larger and larger due to the mass flow that is captured from the entrance at initial condition that could not all pass through the throat. The captured flow would spill some out from the entrance of the inner channel to meet the passing of the mass flux that accumulated at the throat through the outlet. The separation shockwave became far away from the position of the lip. The captured mass flow could all pass through the outlet when the “separation bubble” was large enough; the “separation bubble” and separation shockwave would not move forward anymore. However, the instantaneous capability of the inlet became very strong.

Fig. 6
figure 6

“Separation bubble” became larger at the first half period

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From Fig. 7, the “separation bubble” became smaller and smaller due to the strong capability of the mass captured in the internal channel at the second period. The captured mass flow became max at the throat again when the flow field of inlet experienced one period. The “separation bubble” became smallest again. The separation shockwave again moved in the internal channel. The flow field and shockwave experienced one oscillation period.

Fig. 7
figure 7

“Separation bubble” became smaller at the second period

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4 Conclusion

  1. (a)

    If there was a periodic oscillation of the flow field under the critical starting Mach number of hypersonic inlet, the inlet would experience start-unstart-restart process.

  2. (b)

    The blocking of captured mass flow at the throat and the unmatched mass flux in internal channel were the main factors that lead to the periodic oscillation of flow field and shockwave.

  3. (c)

    The steady numerical method at some extent could be used to obtain some important unsteady characteristics of the oscillation flow of hypersonic inlet from the numerical stratagem.