# Spillage-Adaptive Fixed-Geometry Bump Inlet of Wide Speed Range

^{*}

## Abstract

**:**

## 1. Introduction

_{throat}approaches 1.0. Xie [13,14] developed a three-layer model to predict the ICR limit at viscous conditions. The improvement of inlet start performance is carried out in two directions: one is to decrease the internal compression ratio and the other is to remove the boundary layer. Wang [15] developed an image detection method to quantitively analyze the correlation between shock oscillation and the dynamic wall pressure in hypersonic experiments. Yu [16] proposed a high external compression ratio basic flow field. The speed range is widened by approximately 3.5% in M 3.5 through decreasing the external/internal contraction ratio by 38%. Xiong [17] developed a new method to design the basic flow field, which can optimize the compression efficiency without meshing. The new basic flow field’s total pressure recovery (σ) increases by 7.65% than the original one. The σ of the newly designed inlet increases by 5.65%. Chen and Ding [18,19] proposed the external–internal basic flow field integration method based on the method of characteristics and the streamline tracing technique. This mechanism leads to more flexibility to reasonably arrange the external/internal flow. Similar methodologies are also developed by Qiao [20,21], and the starting speed range for M 7.0 inlet is widened to 4.5 (the self-starting Mach number is approximately 5.2). Zhou and Jin [22,23] developed a non-axisymmetric generalized internal conical basic flow field, which increases the design flexibility for the arbitrary inlet shapes and non-uniform inflow.

## 2. Analysis and the Candidate Solution for Inlet Start Issues

#### 2.1. SES Effects Caused by Overlarge Lateral Compression

_{∞}= 5, β = 12.31°, which forms a SES near the inlet bottom surface. The shock profile is clearly observed by the boundary between yellow and red colors. The SES effects will deteriorate the inlet performance in two aspects: (1) The internal shock system of the inlet distorts owing to the SES, which brings the additional energy loss; (2) the effective circulation area decreases, which forms an aerodynamic throat. Therefore, the flow capacity decreases and the inlet unstart can be easily induced.

#### 2.2. Modular Assessment Approach for the Spillage Pattern Analysis

_{1}and A

_{1}/B

_{1}). The spillage window then forms between the leading edge CD and the compression center (shown as the red-colored part in the figure). AOPC and BOPD are two unit-squares for simplicity. The detailed analysis is as follows: (1) the bottom line CD is identical for two patterns. This notion indicates that the areas of spillage windows are determined by the track length of compression centers L

_{cc}(e.g., curves OO

_{1}and AA

_{1}/BB

_{1}). (2) The hypotenuse of the spillage window (e.g., O

_{1}C and A

_{1}C) represents the streamwise span between the leading edge and the compression center. Specifically, the longer hypotenuse is led from a larger contraction ratio (i.e., a stronger incident shock). (3) In these two patterns with an identical inlet width space, the shock strength of central spillage pattern is larger than that of the side spillage pattern (O

_{1}C > A

_{1}C). The L

_{cc}of central spillage pattern is longer than that of the side spillage pattern, which leads to better spillage ability of the latter at the wide low speed range. As analyzed above, the side-spillage pattern holds larger potentials in flow spillage ability at low speed conditions.

#### 2.3. Novel Spillage-Adaptive Integration Pattern

## 3. Integrated Design of the Spillage-Adaptive Bump Inlet

_{shock}, the intercepting height H

_{intercept}, the bump width W

_{bump}, and the bump length L

_{bump}. The δ

_{shock}is determined by the freestream speed and the derived cone angle, which can be calculated by the axisymmetric conical shock equations. The leading edge is obtained by the intersection of the conical shock wave and intercept plane. In this study, the planes parallel to xoy are taken as the intercept plane. The H

_{intercept}is the height between the intercepting plane and the central line. The W

_{bump}and L

_{bump}are two related parameters. Herein, the bump leading edge is uniquely determined when δ

_{shock}, H

_{intercept}, and W

_{bump}(or L

_{bump}) are fixed.

_{out}. The flow direction is adjusted from expanded to parallel by the inward pressure gradient ▽

_{in}. The π

_{peak}is the peak value of PR, and the W

_{peak}is the width of PR.

_{out}and the flow uniformity depends on▽

_{in}. Variables ▽

_{out}and ▽

_{in}are designed for the corresponding boundary layer thickness and the flow expansion ratio. The schematic of the inlet presetting location is shown in Figure 5 with the translucent red part. The upper boundary is the bump shock, the lower boundary is the bump surface, and the left/right boundaries are the HKE flow regions that are within the PR. The inlet lip (i.e., the inlet entrance) should be set in this region and capture the certain amount of mass flow for the engine. The area of inlet exit is calculated by the streamwise projected area of inlet lip and the contraction ratio. While the shape of inlet exit is assigned by the combustion chamber.

_{LKE}to evaluate the low kinetic energy (LKE) flow ratio of the reference inlet entrance is proposed in this study. This factor is the equivalent LKE flow area divided by the area between shock and bump, that indicates the usage of the inlet presetting region. The definition is as follows:

_{shock}(z) is the y-coordinate of shock position at a specific z-coordinate, y

_{bump}(z) is the y-coordinate of bump surface at a specific z-coordinate, H

_{KE}is the equivalent thickness of the kinetic energy loss, which converts the kinetic energy loss to an equivalent thickness in the inviscid condition. This factor is defined as:

_{∞}, u

_{∞}are the parameters of freestream. The η

_{KE}is the kinetic energy efficiency and is defined as:

^{*}is the temperature, σ is the total pressure recovery. R

_{LKE}distribution at the inlet presetting region is shown in Figure 6. The abscissa is the half width of the inlet. The bump width is 0.698 m. The R

_{LKE}is lower than 0.0113 when W < 0.2 m, which indicates that the boundary layer is well diverted, and the HKE occupies most of the region. The R

_{LKE}is larger than 0.0113 when W > 0.2 m, which indicates that the boundary layer diversion ratio is small. The distribution of R

_{LKE}is flat when W < 0.2 m, but it rapidly increases when W > 0.2 m. The inlet width is finally determined as 0.4 m.

## 4. Aerodynamic Characteristics of the New Bump Inlet

#### 4.1. Preparation of Numerical Simulation

**U**is the conservative vector,

**F**

_{c}is the convective flux vector,

**F**

_{v}is the viscous flux vector,

**n**= n

_{x}

**i**+ n

_{y}

**j**+ n

_{z}

**k**is the unit normal vector, t is the time, Ω is the control volume, and S is the control volume surface. The vectors

**U**,

**F**

_{c}, and

**F**

_{v}are defined as:

_{x}~Π

_{z}are given by:

^{−5}.

_{BL}) is 2.0 m. Thereby, it can create inflow conditions with various nominal boundary layer thicknesses as 9.00, 21.05, 32.37, 41.72 mm at M 6.0, which are successively 5.1%, 11.8%, 18.2%, 23.4% of the inlet entrance height. To obtain the requested standard k–ε turbulence model, the minimum mesh height of near-wall grid is 0.15 mm, and the grids in the y-direction are stretched with the increasing ratio of 1.2 refined with geometric proportion rule. The y+ is kept as 20~110 to meet the standard k–ε turbulence model. A C-grid is set to surround the bump, which accurately fits the bump leading edge. An O-grid is set in the internal flow field of inlet, which accurately fits the inlet wall. A grid independence study is conducted for the bump inlet configuration. The mesh ranging between 3.5 and 6.0 million is generated. The results are shown in Table 1. The σ is the total pressure recovery, the π is the static pressure ratio, which is calculated by the exit pressure divided by the freestream pressure. The φ is the mass capturing ratio. All the aerodynamic characteristics in the current work are obtained by mass-averaged method on corresponding position (e.g., the freestream, the throat, the inlet exit, etc.,). Due to the aerodynamic characteristics discrepancy between different meshes, the reasonable mesh in the domain is approximately 4.3 million.

#### 4.2. Aerodynamic Characteristics of the Spillage-adaptive Integration at the Design Condition

_{1}is 0.4% higher than φ

_{2}. The M

_{exit,1}is 3.6% lower than M

_{exit,2}. The total pressure recovery σ

_{1}is 2.0% higher than σ

_{2}. The exit static pressure π

_{1}is 7.1% lower than π

_{2}. The R

_{M}is the ratio of the deceleration, which is M

_{exit}divided by M

_{∞}. The kinetic energy efficiency η

_{KE,1}is almost the same with η

_{KE,2}. The two integration patterns maintain similar performance in the design condition.

_{out}and accumulates at the corner between the bump and the flat plate. (2) The inlets are located after the bump shock; thus, no interaction exists between the bump shock and the incident shock at design condition. Meanwhile, the LKE flow affects the two shocks. The bump shock and the incident shock distort by the influence of the LKE flow. The bump shock has not attached well to the leading edge. The incident shock distorts upstream, which decreases the mass capturing ratio. (3) The PR mechanism and the side spillage pattern demonstrate that the streamlines at the inlet bottom wall are uniform. No concentrating trend can be observed for the streamlines. This notion indicates that the flow field of inlet is uniform to avoid overlarge side compression. Specifically, the SES effects (Section 2.1) are avoided in the new bump inlet.

#### 4.3. Start-Ability of the New Spillage-Adaptive Bump Inlet

_{exit}decreases. At low speeds, the actual capture area of the inlet decreases with the increase in spillage. The actual contraction ratio of the inlet decreases which results in reduction in π

_{exit}. The shock system is affected by the flow spillage, and variables σ and η

_{KE}decrease.

_{spillage}is used in this work to better analyze the influence of flow spillage on the inlet start-ability. This concept is defined as the spilled mass flow of the low speed condition (${\dot{m}}_{\mathrm{design}\hspace{0.33em}\mathrm{condition}}-{\dot{m}}_{\mathrm{low}\hspace{0.17em}\mathrm{Mach}\hspace{0.17em}\hspace{0.17em}\mathrm{condition}}$) divided by that of the design condition (${\dot{m}}_{\mathrm{design}\hspace{0.33em}\mathrm{condition}}$). The equation is given by:

_{spillage}-M

_{∞}distribution is shown in Figure 14. The analysis is as follows: (1) the relationship between two parameters is quasi-parabolic. (2) The φ

_{spillage}decreases by 9.5% when the M

_{∞}decreases from 6.0 to 5.0. This value decreases by 17.3% when the M

_{∞}decreases from 5.0 to 4.0. The σ

_{throat}at M

_{∞}= 4.0 is 15.0% lower than that at M

_{∞}= 6.0. The σ

_{exit}at M

_{∞}= 4.0 is 8.1% lower than that at M

_{∞}= 6.0. The results reveal that the main energy loss by the flow spillage is caused at the inlet compression section. The incident shock and the spillage are the main cause of the energy loss for the low speed conditions. (3) The φ

_{spillage}increases by 11.8% between M

_{∞}= 4.0 and 3.0. This factor increases by 16.0% between M

_{∞}= 3.0 and 2.5. The flow spillage is high at M

_{∞}> 4.0 and M

_{∞}< 3.0, while it is relatively lower between M

_{∞}= 3.0 and 4.0, which shows less sensitivity of incident shock distortion at this speed range.

_{∞}= 2.0–5.0) are demonstrated in Figure 15, which shows the interaction between the incident shock and the thick boundary layer (L

_{BL}= 3.5 m). The detailed analysis is as follows: 1) the shock system of M

_{∞}= 5.0 is similar to that of M

_{∞}= 6.0 (shown in Figure 13). Flow spillage (9.5%) occurs at the upper part of the inlet lip. 2) When M

_{∞}decreases to 4.0, the spillage increases by 26.8% than the design condition. The incident shock distorts the upstream to make a spillage window at the compression center and the side wall of the inlet. The LKE fluid accumulates around the side wall. This phenomenon restricts the flow capacity by forming an aerodynamic throat that is smaller in area than the geometry. 3) The decrease in M

_{∞}leads to the main flow spilling from the adjacent region of the compression center. Two impact patterns of spillage to the flow field can be observed. In the speed range of M 3.0 to 5.0, the spillage ratio is lower than 40%. The spilled flow has not encountered bump shock. In the speed range of M 2.0 to 3.0, the spillage ratio is over 40%. The interaction between the inlet incident shock and the bump shock leads to the change in the external flow field, which can be observed on the middle section (colored in red).

#### 4.4. Effects of Boundary Layer Thickness to Aerodynamic Characteristics

_{BL}is the length for boundary layer development. When the L

_{BL}decreases from 3.5 to 1.0 m, the LKE ratio of the captured inflow decreases. Accordingly, the M

_{exit}and σ increase, and the gradient of these two parameters decrease with the L

_{BL}. This phenomenon can be explained on the basis of the boundary layer thickness. The nominal boundary layer thickness δ (i.e., the height where 99% of mainstream speed locates) is positively correlated to the development length of boundary layer, which is shown as,

_{BL}in this study, and δ denotes the boundary layer thickness. Considering 0 < δ < 1, the decrease in x will lead to the decrease in δ. When L

_{BL}decreases with the identical ∆x, the σ will increase, but the ∆σ will decrease. This condition explains the trend in Figure 16b. The Mach number will increase with the decrease in L

_{BL}, but ∆M will decrease, which can explain the trend in Figure 16a.

_{KE}increase to a certain extent. When L

_{BL}decreases from 3.5 to 2.0 m, the mass capturing ratio φ only increases by 2.6%, while it increases by 13.7% when L

_{BL}decreases from 2.0 to 1.0 m. This notion indicates that the incident shock is distorted by the disturbance of the boundary layer at L

_{BL}> 2.0 m. Meanwhile, the disturbance at L

_{BL}< 2.0 m is not strong enough to induce shock distortion. The η

_{KE}is positively related to the L

_{BL}. According to the definition of η

_{KE}(Equation (3)), a highly nonlinear relationship exists between η

_{KE}and L

_{BL}. A clear trend in the η

_{KE}-L

_{BL}distribution is difficult to obtain. The η

_{KE}-R

_{M}distribution is presented in the following analysis to evaluate the overall compressing efficiency of inlet. The inlet efficiency is shown in Figure 17. The hypersonic inlet expert Van Wie [38] proposed to use the kinetic efficiency η

_{KE}for the inlet performance evaluation. The definition of η

_{KE}is shown in Equation (3). This expression includes the kinetic energy of the inlet exit and the transferred internal energy caused by the flow expansion. The η

_{KE}-R

_{M}distribution is used to show the inlet efficiency. Van wie [38,39,40,41] proposed the η

_{KE}-R

_{M}relation below, which is based on 2D inlet experiments.

_{KE}-R

_{M}relation, which is based on side-compression inlet experiments. The relation is shown as follows:

_{KE}(1) relation, and the red dashed line indicates the η

_{KE}(2) relation. The higher inlet efficiency locates at the upper-right side of the figure. The lower inlet efficiency locates at the lower-left side of the figure. When the L

_{BL}decreases from 3.5 to 2.0 m, the η

_{KE}-R

_{M}distribution is almost parallel to the η

_{KE}(1) and η

_{KE}(2) curves, which indicates that the inlet efficiency remains steady in this L

_{BL}range. When the L

_{BL}decreases from 2.0 to 1.0 m, the η

_{KE}-R

_{M}distribution approaches the η

_{KE}(2) curve. This notion indicates that the inlet efficiency starts to increase in this L

_{BL}range.

## 5. Conclusions

_{BL}> 2.0 m, the σ is rapidly increased with the decrease in L

_{BL}while at L

_{BL}< 2.0 m, the φ is rapidly increased with the decrease in L

_{BL.}The analysis on the inlet efficiency indicated that the performance of the new spillage-adaptive bump inlet (results with thick boundary layer) is close to that of the side compression inlet (results without LKE inflow).

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 10.**Results based on the fixed/variable specific heat ratio: (

**a**) Total temperature T

^{*}distribution; (

**b**) Total pressure P

^{*}distribution.

**Figure 12.**Validation of the numerical methods for the bump inlet integration ((

**a**) M6 scaled wind tunnel test; (

**b**) longitude pressure distribution of the experimental and numerical results).

**Figure 15.**Incident shock system at low speed conditions (L

_{BL}= 3.5 m). (

**a**) M

_{∞}= 5.0; (

**b**) M

_{∞}= 4.0; (

**c**) M

_{∞}= 3.5; (

**d**) M

_{∞}= 3.0; (

**e**) M

_{∞}= 2.5; (

**f**) M

_{∞}= 2.0.

**Figure 16.**Aerodynamic characteristics of inlet exit under different boundary layer thicknesses (unit of L

_{BL}: m). (

**a**) σ-M

_{exit}distribution; (

**b**) σ-L

_{BL}distribution; (

**c**) η

_{KE}-L

_{BL}distribution; (

**d**) φ-L

_{BL}distribution.

Type | Mesh Number | σ_{exit} | π_{exit} | M_{exit} | φ_{throat} |
---|---|---|---|---|---|

Coarse grid | 3.5 million | 0.487 | 17.812 | 3.014 | 0.747 |

Medium grid | 4.3 million | 0.489 | 18.371 | 3.018 | 0.748 |

Fine grid | 6.0 million | 0.489 | 18.374 | 3.018 | 0.748 |

Spillage Position | M_{∞} | φ_{throat} | M_{exit} | σ_{exit} | π_{exit} | R_{M} | η_{KE} |
---|---|---|---|---|---|---|---|

1. Side spillage | 6.0 | 0.748 | 3.02 | 0.49 | 18.4 | 0.499 | 0.969 |

2. Central spillage | 6.0 | 0.745 | 2.94 | 0.48 | 17.1 | 0.487 | 0.968 |

M_{∞} | φ_{throat} | φ_{spillage} | M_{exit} | σ_{exit} | π_{exit} | R_{M} | η_{KE} |
---|---|---|---|---|---|---|---|

6.0 | 0.748 | 0 | 3.02 | 0.49 | 18.4 | 0.499 | 0.969 |

5.0 | 0.676 | 9.5% | 2.49 | 0.53 | 13.0 | 0.497 | 0.961 |

4.0 | 0.547 | 26.8% | 1.78 | 0.45 | 11.1 | 0.445 | 0.921 |

3.5 | 0.508 | 32.1% | 1.53 | 0.53 | 9.9 | 0.437 | 0.920 |

3.0 | 0.459 | 38.6% | 1.22 | 0.64 | 9.2 | 0.405 | 0.927 |

2.5 | 0.339 | 54.6% | 0.81 | 0.75 | 8.2 | 0.324 | 0.933 |

2.0 | 0.253 | 66.1% | 0.95 | 0.83 | 3.6 | 0.475 | 0.931 |

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**MDPI and ACS Style**

Yu, Z.; Huang, G.; Wang, R.; Musa, O.
Spillage-Adaptive Fixed-Geometry Bump Inlet of Wide Speed Range. *Aerospace* **2021**, *8*, 340.
https://doi.org/10.3390/aerospace8110340

**AMA Style**

Yu Z, Huang G, Wang R, Musa O.
Spillage-Adaptive Fixed-Geometry Bump Inlet of Wide Speed Range. *Aerospace*. 2021; 8(11):340.
https://doi.org/10.3390/aerospace8110340

**Chicago/Turabian Style**

Yu, Zonghan, Guoping Huang, Ruilin Wang, and Omer Musa.
2021. "Spillage-Adaptive Fixed-Geometry Bump Inlet of Wide Speed Range" *Aerospace* 8, no. 11: 340.
https://doi.org/10.3390/aerospace8110340