# Effects of Flow Spillage Strategies on the Aerodynamic Characteristics of Diverterless Hypersonic Inlets

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Flow Organization Strategies and Evaluation Methods for Non-Uniform Flow Fields

#### 2.1. Side-Spillage and Central-Spillage Flow Organization Strategies

_{x}= 3.85). The external/internal contraction ratio CR

_{x}is calculated as follows:

_{ex}is ratio of the free-flow tube to the throat tube (Figure 1: S

_{1}/S

_{2}). The internal contraction ratio CR

_{in}is the ratio of the throat tube to the outlet tube (Figure 1: S

_{2}/S

_{3}). It should be noted that there are apparent geometric differences between the two forms when using the same bump inlet design technique: (1) The height of Form 2 is 27.8% lower than that of Form 1. (2) The length of Form 2 is 28.3% shorter than that of Form 1. (3) S

_{zoy}represents the windward projection area of the whole bump inlet. The S

_{zoy}of Form 2 is 34.4% smaller than that of Form 1. The main reason for this difference in S

_{zoy}is the spillage strategy. Form 2 adopts side-spillage instead of central-spillage for the flow compression task. The longitudinal length of the inlet lip of Form 2 is shorter than that of Form 1. The total height of Form 2 is therefore lower than that of Form 1. For the purpose of integration, the bump of Form 1 has to be higher. The difference in height ultimately leads to the difference in S

_{zoy}. (4) The R

_{inlet}of Form 2 is 9.8% higher than that of Form 1, where the parameter R

_{inle}

_{t}is the usage of the inlet that is calculated by dividing the projection area of the inlet by that of the whole bump inlet, as follows:

_{wet}is calculated. This is the ratio of the wet surface to the volume, which indicates the impacts of the inlet on the downstream combustion chamber. The R

_{wet}of Form 2 is 23.5% higher than that of Form 1. This proves that there will be relatively less impact on friction and heat losses for Form 2. The geometric discrepancy indicates that Form 2 will suppress the external drag less than Form 1. To aerodynamically evaluate the performance of non-uniform bump inlet flow fields in detail, the evaluation methods for uniform flow fields need modification. This is discussed in the following section.

#### 2.2. Evaluation Methods for Non-Uniform Flow Fields of Bump Inlets

#### 2.2.1. Mass Capture Ratio

- Calculation of φ in uniform inflow conditions (Figure 2: left subplot):

- Calculation of φ in non-uniform inflow conditions (Figure 2: right subplot):

_{captured}is the ratio of S

_{abcd}to S

_{efgh}.

#### 2.2.2. Inlet Start Ability

_{in}/A

_{throat}) and total pressure recovery coefficient (σ

_{in-throat}= P

^{*}

_{throat}/P

^{*}

_{in}),

_{in}and CR are already determined; that is, the φ/(σ

_{in-throat}·q (M

_{throat})) is kept as a constant when the inlet starts. When φ/(σ

_{in-throat}·q (M

_{throat})) > 1, the captured mass flow exceeds the flow capacity to induce the inlet unstart. The flow spillage technique, along with the boundary-layer bleeding [33] and the variable-geometry technique [34], is an approach to improve the inlet start ability by enlarging the effective flow path. The method to determine the effective flow path of inlets is presented in Section 4.2.

#### 2.2.3. Compression Efficiency

_{KE}) [35] reflects useful internal energy, which is a more reasonable coefficient to evaluate non-uniform flow fields with thick boundary layers. The definition of η

_{KE}is as follows:

_{KE}-R

_{M}distribution to evaluate the inlet efficiency. An empirical relationship was determined on the basis of 2D inlet wind tunnel tests. The R

_{M}is the ratio of the freestream Mach number to the Mach number at exit. According to Van Wie’s definition, this ratio represents the flow deceleration degree of an inlet.

_{KE}-R

_{M}relationship based on the experiment of a typical side-compression inlet:

## 3. Methodology of Numerical Simulation

#### 3.1. Numerical Method for the External–Internal Flow Fields

**U**,

**F**,

_{c}**F**,

_{v}**n**,

**t**, Ω, and

**S**are the conservative vector, convective flux vector, viscous flux vector, unit normal vector, time, control volume, and control volume surface, respectively. The definitions of the vectors

**U**,

**F**, and

_{c}**F**are given as follows:

_{v}_{x}~Π

_{z}are defined as follows:

#### 3.2. Three-Dimensional-Structured Mesh for Bump Inlet Flow Fields

#### 3.3. Setup for Numerical Simulation

^{−6}. The simulation for the mixed external–internal flow field is a special case in the determination of the turbulence model. Zhang et al. [39] investigated the influence of different turbulence models on the numerical results. Both k–ε and k-ω turbulence models matched well with the wind tunnel data of a mixed-compression supersonic inlet. The authors also validated the k–ε turbulence model in an experimental study [24] of a typical central-spillage bump inlet. The detailed verification process is demonstrated in Appendix A. Based on the above results and analysis, the k–ε turbulence model was adopted for numerical simulation in this study. A grid independence test has been verified in previous studies [40]. The inflow conditions for the numerical simulation are shown in Table 2, where H is the cruise altitude, M

_{∞}is the inflow Mach number, V is the inflow speed, P

_{∞}is the freestream static pressure, and P

_{d}is the freestream dynamic pressure.

## 4. Results and Discussion

#### 4.1. Aerodynamic Characteristics under the Cruise Conditions

_{b}was set to 1 (π

_{b}= P

_{b}/P

_{∞}, P

_{b}: backpressure; P

_{∞}: freestream static pressure). Then, based on the initial flow field, π

_{b}was gradually increased in small increments until the inlet unstarted.

#### 4.1.1. Compression Efficiency

_{b}boundary conditions are reported in Table 3. As the π

_{b}increases, the terminal shock train [41,42] occurs near the exit and then moves forward. When the terminal shock train passes the throat and interacts with the incident shock, the inlet unstart is induced. As a result, the mass capture ratio will deteriorate substantially, along with other aerodynamic characteristics. It should be noted that Form 1 can suppress 99.6 P

_{∞}backpressure, while Form 2 can suppress 104.1 P

_{∞}backpressure. The maximum anti-backpressure ability of Form 2 is approximately 4.52% higher than that of Form 1 based on identical CR

_{x}. The small difference in CR

_{x}is caused by differences in the amount of the boundary layer captured. As demonstrated in Figure 1, a part of the inlet lip is integrated with the bump surface. For the purpose of comparison, the foremost point of the inlet lip was situated at the same longitudinal position (x = 700 mm from the bump’s leading edge) for both forms. For Form 1, all of the boundary layer within the inlet-captured area is swallowed downstream, while for Form 2, the boundary layer is continuously diverted away until the flow passes by the rearmost point of the inlet lip on the bump surface. Hence, the boundary layer in Form 2 is thinner than that in Form 1. This leads to a slightly larger available range of backpressures for Form 2.

_{KE}(1) relation, while the red dashed line is the η

_{KE}(2) relation. The definition of η

_{KE}is given in Section 2.2.3. The R

_{M}is the Mach number ratio of the freestream position to the target position (i.e., throat and exit in this paper). According to the relation between η

_{KE}and R

_{M}, the upper-right region of these two curves represents higher efficiency, and vice versa. The analysis is as follows:

- Comparison of bump inlets with η
_{KE}(1) and η_{KE}(2) curves:

_{KE}(1) and η

_{KE}(2) curves were obtained from the cases with uniform inflow conditions, while the results of the present study are based on non-uniform and thick boundary layer (i.e., 23.4% of inlet height) inflow conditions. Hence, the η

_{KE}of the two curves will be lower when faced with more severe inflow conditions.

- η
_{KE}at the throat and exit positions:

_{KE}to decrease. The η

_{KE}discrepancy of the throat position between two forms (labels beyond the η

_{KE}(2) curve in Figure 4) is approximately 0.51%, while that of the exit position (labels between the η

_{KE}(1) and η

_{KE}(2) curves) is 0.10%. The η

_{KE}of Form 2 decreases by 0.62% at the isolator part. The decrease ratio for Form 1 is 1.0%. It should be noted that there is only a small discrepancy between the two forms, which indicates that the useful compressed flow of the two forms is of equivalent magnitude.

#### 4.1.2. Anti-Backpressure Capability

_{b}= 18.5, the backpressure does not affect the internal shock system, as shown in Figure 5a.

_{b}was analyzed in detail: (1) When π

_{b}= 37.9, a high-pressure region (HPR) occurs at the lower part upstream of the exit (x = 3.2 m). This region is located completely after the last reflection shock, which apparently does not affect the shock system. (2) When π

_{b}= 61.8, this region moves forward to the tail of the isolator (x = 3.05 m), where the flow is compressed from M 2.3 to M 1.6. The shock strength is equivalent to an oblique shock with M

_{∞}= 2.3, β = 43°. (3) When π

_{b}= 83.3, the end shock moves forward to x = 2.67 m. There is a relatively large pressure gap between the HPR (π ≈ 100) at the upper side and the lower side of the exit, which leads to the flow deflection. (4) When π

_{b}= 89.3, the end shock moves forward to x = 2.60 m. The tail region of the isolator is occupied by the high-pressure flow. The pressure decreases in the expansion section. Thus, the pressure upstream is larger than the pressure downstream. This results in reduced sensitivity to the backpressure fluctuation. (5) When π

_{b}= 99.6, the end shock moves forward to x = 2.52 m. The HPR with π ≈ 100 occupies the rear part of the isolator. The end shock is observed near the throat, which leads to high sensitivity to the backpressure and causes the inlet to unstart.

_{b}= 15.6~76.4 was analyzed in detail (see Figure 6): (1) When π

_{b}= 15.6, it is effectively in the through-flow condition, where the internal shock system has not been affected by the backpressure. In contrast with Form 1, Form 2 splits the inflow into two paths. The area of the isolator changes correspondingly to half that of Form 1, and the length of the isolator is also shorter. This leads to changes in the frequency of the reflection shocks. There are three reflection shocks for Form 2 and four reflection shocks for Form 1. (2) When π

_{b}= 32.7, the HPR occurs at the exit, while the discrepancy in the aerodynamic characteristics between π

_{b}= 32.7 and π

_{b}= 15.6 is small. (3) When π

_{b}= 57.0, the HPR moves forward to x = 2.130 m. Due to the interaction between the backpressure and the reflected shock, the position of the last reflection point moves slightly downstream compared to the through-flow condition. (4) When π

_{b}= 76.4, the HPR moves forward to x = 2.107 m. The flow experiences deceleration and compression at x > 2.107 m.

_{b}= 85.6~110.0 was analyzed in detail (see Figure 7): (1) When π

_{b}= 85.6, the HPR moves to x = 2.072 m. The end shock is pushed upstream to the middle of the isolator at π

_{b}≈ 85.0 for both forms. (2) When π

_{b}= 100.6, the HPR is pushed to x = 1.889 m. The ring-like region can be clearly observed at the rear part of the isolator, as shown in red. A relatively high-pressure gap occurs at the upper wall adjacent to the exit, which leads to the non-uniformity of the local flow. (3) When π

_{b}= 104.1, the high-pressure area is pushed to x = 1.875 m. Compared with π

_{b}= 100.6, the area of the HPR further increases at π

_{b}= 104.1. The pressure gap between the reflected shock and the middle of the cross-section restricts the effective flow path, which leads to a decrease in the φ. (4) When π

_{b}increases from 104.1 to 110.0, the first reflection shock is not strong enough to withstand the backpressure. The end shock moves from x = 1.875 m to x = 1.402 m. A bow shock is clearly observed in front of the inlet lip. The inlet unstarts at π

_{b}= 110.0.

_{b}. The rear part of the isolator is affected by the backpressure, and the M distribution becomes relatively uniform. This reveals that the flow distortion varies under different π

_{b}conditions. Under the through-flow condition, the distortion is caused by the reflection shock system, whereas under the condition with the backpressure effects, the uniformity of the outflow increases correspondingly. (3) The shape of the reflected shock is determined by the cross-section shape as well as the inflow condition. Form 2 adopts an equal-cross-section circular isolator. Therefore, when the incident shock reflects at the V-shaped compression center and hits the upper wall of the isolator, the shock is split into two reflection shocks. This phenomenon can also be observed from the longitudinal M distribution, where the number of M isolines increases from one to two after the first reflection shock.

#### 4.2. Aerodynamic Characteristics under a Wide Range of Inflow Speed Conditions

_{spillage}is the ratio of the spilled mass flow to the captured mass flow under cruise conditions. The incident shock detaches from the inlet lip when the inflow speed decelerates. Thus, the φ

_{spillage}increases with the decrease in M

_{∞}. When the spilled mass flow is larger than the decrease in inlet flow capacity, the inlet will start. When the spilled mass flow is not enough to cover the decrease in inlet flow capacity, the inlet will unstart due to the flow congestion. For Form 2, the φ

_{spillage}–M

_{∞}relation can be described as a quadratic function:

_{∞}is the freestream Mach number.

_{π}and ε

_{M}in Table 4 are the compression and deceleration ratios for the decrease in the unit area, respectively. Their definitions are as follows:

_{π}and ε

_{M}is demonstrated in Figure 10. As the M

_{∞}decreases, the ε

_{π}increases and the ε

_{M}decreases correspondingly. As M

_{∞}decelerates from 6.0 to 5.0, the ε

_{π}of both forms increases to the same degree, while the ε

_{π}of Form 2 decreases to a greater extent than that of Form 1. This indicates that the flow spillage is beneficial to the inlet start ability, but the φ

_{spillage}should be carefully designed to avoid a decrease in the inlet’s compression ability.

_{A}is proposed. This represents the relative error between the equivalent exit area A

_{equ}and the real exit area A

_{exit}. The definition is as follows:

_{equ}is the equivalent area of the inlet’s exit; it is calculated by the following mass equation:

_{A}is finally determined by the following equation:

_{A}can reflect the magnitude of the flow distortion. A larger ε

_{A}means that more of the boundary layer accumulates in the inlet. Except for the friction loss induced by the inlet wall, the flow distortion is the main cause of the accumulation of the boundary layer. Figure 11 demonstrates the impacts of inflow speeds on inlet distortion and flow spillage. The ε

_{A}decreases with the M

_{∞}due to the boundary layer accumulation. The decrease in the ratio of ε

_{A}is high at M 3.0–5.0 and relatively low in other speed ranges. The φ

_{spillage}increases rapidly with the decrease in M

_{∞}. The detailed analysis is as follows:

- Spillage ability of two forms at M ∈ [3.0,6.0]:

_{A}(∆ε

_{A}/∆M) is largest at M 3.0–5.0 for Form 1, which reaches approximately 6.18 × 10

^{−2}. This value is similar to the ∆ε

_{A}/∆M of Form 1 at M 5.0–6.0 (6.00 × 10

^{−2}), which indicates that the spillage ability of Form 2 at M 3.0–5.0 is similar to that of Form 1 at M 5.0–6.0. For the Mach range of 5.0–6.0, the ∆ε

_{A}/∆M of Form 2 is 41% lower than that of Form 1. This shows that Form 1 can maintain a better incident shock shape than Form 2.

- Explanation for the ε
_{A}discrepancy:

_{A}discrepancy of the two forms at different speeds results from the incident shock system and the spillage pattern. When the inlet flow capacity is large enough to handle the captured inflow, the incident shock system will remain steady at the design point (i.e., M 6.0). For Form 1, there is an evident increase in the corner boundary layer due to the strong side compression, which clearly decreases the actual flow area. Hence, the incident shock distorts from the inlet lip to the mainstream, and the flow is spilled away from the central part of the inlet lip. For Form 2, the incident shock system remains relatively steady at M 5.0–6.0. There is a bow-shaped boundary layer region that occurs around M 4.0. This region becomes larger when the M

_{∞}decreases. The flow in the inlet consists of the near-wall boundary layer and the unspilled mainstream. For Form 2, the φ

_{spillage}/∆M at M 2.5–3.0 is more than twice that at M 3.0–5.0. This indicates that the mainstream is spilled away under low-Mach conditions, exceeding the flow capacity. Thereby, the ∆ε

_{A}/∆M decreases at M 2.5–3.0, which shows less change in the actual flow area than that at M 3.0–5.0.

- Self-adaptive flow spillage feature of the side-spillage form:

_{spillage}of Form 2 continuously increases with the M

_{∞}, imparting a self-adaptive feature to the inflow speeds. The amount of captured inflow is then reduced to match the decreased inlet flow capacity, making the inlet start ability better under low-Mach conditions when using a fixed inlet configuration.

#### 4.3. Impacts of Inflow Conditions on the Compression Efficiency

_{KE}-R

_{M}-π

_{b}distribution and the right subplot is the η

_{KE}-R

_{M}-M

_{∞}distribution. The inflow condition remains steady when π

_{b}increases. Thereby, the η

_{KE}of both forms increases with π

_{b}. Meanwhile, the trend for the right subplot is not monotonic. The η

_{KE}decreases at M 3.5–6.0 and increases at M 2.5–3.5 for Form 2. The impacts of the inflow conditions are mainly determined based on two aspects: the incident shock system and the boundary layer thickness. As the M

_{∞}decreases, the incident shock detaches from the inlet lip and moves forward, which leads to a decrease in the η

_{KE}. As the M

_{∞}decreases, the boundary layer thickness decreases, which leads to an increase in the η

_{KE}. The results reveal that at M 3.5–6.0, the distortion of incident shock is the main reason for the decrease in η

_{KE}. At M 2.5–3.5, the decrease in the boundary layer’s thickness is the main reason for the increase in η

_{KE}.

## 5. Conclusions

- A more compact configuration: Form 2 is 27.8% lower in height and 28.3% shorter in length. The windward projection area of Form 2 is 34.4% smaller than that of Form 1. The usage of the inlet for Form 2 is 9.8% higher than for Form 1.
- A steadier performance: The maximum backpressure of Form 2 is 4.52% higher than that of Form 1. The aerodynamic characteristics of the two forms are similar under the cruise conditions, while Form 2 shows more steady performance under off-design conditions, e.g., the decreased effective flow path of Form 2 is 41% lower than that of Form 1 at M 5.0–6.0.
- A better start ability: Through establishing a self-adaptive flow spillage feature, Form 2 extends the effective operational Mach range by approximately 250% without any boundary-layer bleeding or variable-geometry techniques.
- A reduced impact on the propulsion system: The wet specific surface area R
_{wet}of Form 2 is 23.5% higher than that of Form 1. As a result, there will be relatively fewer impacts on friction and heat losses for Form 2.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Verification of the k–ε Turbulence Model

**Figure A1.**Schematic (

**left**) and installation view (

**right**) of a central-spillage diverterless hypersonic inlet.

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**Figure 1.**Configurations of two bump inlets (

**upper side**: side-spillage inlet, Form 2;

**lower side**: central-spillage inlet, Form 1).

**Figure 2.**Schematic of obtaining the inlet’s mass capture ratio:

**left**, uniform inflow condition;

**right**, non-uniform inflow condition.

**Figure 5.**Pressure contours of the central-spillage integrated form under different backpressures (Form 1). (

**a**) π

_{b}= 18.5, (

**b**) π

_{b}= 37.9, (

**c**) π

_{b}= 61.8, (

**d**) π

_{b}= 83.3, (

**e**) π

_{b}= 89.3, (

**f**) π

_{b}= 99.6.

**Figure 8.**Streamlines and M isolines of the new side-spillage integrated form (Form 2). (

**a**) π

_{b}= 15.6, (

**b**) π

_{b}= 32.7, (

**c**) π

_{b}= 57.0, (

**d**) π

_{b}= 76.4, (

**e**) π

_{b}= 85.6, (

**f**) π

_{b}= 100.6, (

**g**) π

_{b}= 104.1, (

**h**) π

_{b}= 110.0.

**Table 1.**Geometric parameters of two diverterless hypersonic inlets (unit of length: m; unit of area: m

^{2}).

Form | L_{total} | W_{bump} | W_{inlet} | CR_{x} | H_{total} | S_{zoy} | R_{inlet} | R_{wet} |
---|---|---|---|---|---|---|---|---|

1 | 3.307 | 1.166 | 0.2 | 0.385 | 0.367 | 0.224 | 0.37 | 0.026 |

2 | 2.371 | 1.166 | 0.2 | 0.385 | 0.265 | 0.147 | 0.41 | 0.034 |

H (km) | M_{∞} | V (m/s) | P_{∞} (Pa) | P_{d} (Pa) |
---|---|---|---|---|

24.0 | 6.0 | 1786.71 | 2930.67 | 73,852.9 |

22.9 | 5.5 | 1633.65 | 3487.13 | 73,840.0 |

21.7 | 5.0 | 1481.01 | 4218.43 | 73,822.6 |

20.3 | 4.5 | 1328.79 | 5205.96 | 73,852.5 |

18.8 | 4.0 | 1180.29 | 6594.92 | 73,862.7 |

17.1 | 3.5 | 1032.75 | 8615.61 | 73,862.2 |

15.2 | 3.0 | 887.93 | 11,652.8 | 73,863.5 |

12.9 | 2.5 | 737.68 | 16,882.2 | 73,849.5 |

10.0 | 2.0 | 598.79 | 26,372.6 | 73,843.0 |

Form | π_{b} | M_{∞} | Status | φ | M_{exit} | σ | R_{M} | η_{KE} |
---|---|---|---|---|---|---|---|---|

1 | 1.0 | 6.0 | Start | 0.745 | 2.94 | 0.48 | 0.487 | 0.968 |

1 | 18.5 | 6.0 | Start | 0.745 | 2.86 | 0.45 | 0.473 | 0.966 |

1 | 37.9 | 6.0 | Start | 0.745 | 2.30 | 0.36 | 0.380 | 0.954 |

1 | 61.8 | 6.0 | Start | 0.737 | 1.71 | 0.23 | 0.283 | 0.930 |

1 | 64.9 | 6.0 | Start | 0.746 | 1.65 | 0.25 | 0.273 | 0.934 |

1 | 83.3 | 6.0 | Start | 0.734 | 1.48 | 0.25 | 0.245 | 0.933 |

1 | 89.3 | 6.0 | Start | 0.740 | 1.32 | 0.20 | 0.218 | 0.920 |

1 | 99.6 | 6.0 | Start | 0.763 | 1.11 | 0.16 | 0.183 | 0.907 |

1 | 105.0 | 6.0 | Unstart | 0.031 | - | - | - | - |

2 | 1.0 | 6.0 | Start | 0.748 | 3.02 | 0.49 | 0.499 | 0.969 |

2 | 15.6 | 6.0 | Start | 0.748 | 2.90 | 0.44 | 0.479 | 0.964 |

2 | 32.7 | 6.0 | Start | 0.748 | 2.90 | 0.44 | 0.479 | 0.964 |

2 | 57.0 | 6.0 | Start | 0.746 | 1.97 | 0.35 | 0.326 | 0.952 |

2 | 76.4 | 6.0 | Start | 0.748 | 1.97 | 0.29 | 0.326 | 0.942 |

2 | 85.6 | 6.0 | Start | 0.748 | 1.73 | 0.25 | 0.286 | 0.933 |

2 | 100.6 | 6.0 | Start | 0.748 | 1.24 | 0.15 | 0.205 | 0.904 |

2 | 104.1 | 6.0 | Start | 0.747 | 1.12 | 0.14 | 0.185 | 0.899 |

2 | 110.0 | 6.0 | Unstart | 0.023 | - | - | - | - |

Form | M_{∞} | Status | σ | φ_{spillage} | ε_{A} | ε_{M} | ε_{π} | η_{KE} |
---|---|---|---|---|---|---|---|---|

1 | 6.0 | Start | 0.48 | 0 | 53.7% | 0.514 | 4.307 | 0.968 |

1 | 5.0 | Start | 0.51 | 8.80% | 47.7% | 0.518 | 3.678 | 0.958 |

1 | 4.0 | Unstart | - | - | - | - | - | - |

2 | 6.0 | Start | 0.49 | 0 | 53.4% | 0.528 | 4.894 | 0.969 |

2 | 5.0 | Start | 0.53 | 9.50% | 49.9% | 0.534 | 3.457 | 0.961 |

2 | 4.0 | Start | 0.45 | 26.80% | 39.6% | 0.598 | 2.952 | 0.921 |

2 | 3.5 | Start | 0.53 | 32.10% | 36.5% | 0.608 | 2.633 | 0.920 |

2 | 3.0 | Start | 0.64 | 38.60% | 34.0% | 0.654 | 2.447 | 0.927 |

2 | 2.5 | Start | 0.75 | 54.60% | 33.3% | 0.821 | 2.181 | 0.933 |

2 | 2.0 | Unstart | - | - | - | - | - | - |

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## Share and Cite

**MDPI and ACS Style**

Yu, Z.; Huang, H.; Wang, R.; Lei, Y.; Yan, X.; Jin, Z.; Musa, O.; Huang, G.
Effects of Flow Spillage Strategies on the Aerodynamic Characteristics of Diverterless Hypersonic Inlets. *Aerospace* **2022**, *9*, 771.
https://doi.org/10.3390/aerospace9120771

**AMA Style**

Yu Z, Huang H, Wang R, Lei Y, Yan X, Jin Z, Musa O, Huang G.
Effects of Flow Spillage Strategies on the Aerodynamic Characteristics of Diverterless Hypersonic Inlets. *Aerospace*. 2022; 9(12):771.
https://doi.org/10.3390/aerospace9120771

**Chicago/Turabian Style**

Yu, Zonghan, Huihui Huang, Ruilin Wang, Yuedi Lei, Xueyang Yan, Zikang Jin, Omer Musa, and Guoping Huang.
2022. "Effects of Flow Spillage Strategies on the Aerodynamic Characteristics of Diverterless Hypersonic Inlets" *Aerospace* 9, no. 12: 771.
https://doi.org/10.3390/aerospace9120771