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A pressure-controllable bump based on the pressure-ridge concept
Accepted Manuscript A pressure-controllable bump based on the pressure-ridge concept
Zonghan Yu, Guoping Huang, Chen Xia, Joern Sesterhenn
PII: DOI: Reference:
S1270-9638(18)30354-7 https://doi.org/10.1016/j.ast.2019.02.015 AESCTE 5001
To appear in:
Aerospace Science and Technology
Received date: Revised date: Accepted date:
14 February 2018 11 February 2019 13 February 2019
Please cite this article in press as: Z. Yu et al., A pressure-controllable bump based on the pressure-ridge concept, Aerosp. Sci. Technol. (2019), https://doi.org/10.1016/j.ast.2019.02.015
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1
A pressure-controllable bump based on the pressure-ridge concept
2
Zonghan Yu1, Guoping Huang2, Chen Xia3
3
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing,
4
Jiangsu 210016, People’s Republic of China
5
Joern Sesterhenn4
6
Institute for Fluid Mechanics and Engineering Acoustics, Technical University of Berlin, Germany
7
2: Corresponding author, E-mail: [email protected]
8
Abstract: An innovative type of pressure distribution for the hypersonic aircraft forebody (bump) is
9
presented, and this design is based on the newly established known as pressure ridge (PR) flow
10
mechanism. Studies on the low-kinetic-energy fluid over the aircraft surface are summarized. Then, the
11
challenges of the inlet–airframe integration at high speeds are discussed. The flow structure around the
12
bump is analyzed in detail to eliminate the side-embedded shock (SES) effect at the inlet entrance. The
13
concept of PR is proposed to improve the overall aerodynamic characteristics of the bump, namely, the
14
boundary layer removal, the reduction of external drag, and the streamline direction at bump end-section.
15
On the basis of the developed inverse method to generate the bump surface by the prescribed pressure
16
distribution, the improved PR-derived bump is designed and numerically compared with the typical
17
pressure-controllable bump (PCB) while the identical leading edge profile is imposed. Results
18
demonstrate that the PR creates outward and inward pressure gradients. The removed amount of boundary
19
layer increases with the increase in outward pressure gradient. Meanwhile, the inward pressure gradient
1
1
determines the streamline pattern after the bump. The PR-derived bump is 29.2% lower in height than the
2
typical one by using a proper outward pressure gradient. The uniform area of the new bump is 30% wider
3
than that of the typical PCB. The near-wall streamlines of the new bump are adjusted from expanding to
4
the parallel, thereby relieving the side-compression. Changing the location, width, and peak value of the
5
PR can lead to great flexibility in the design and optimization of aircraft forebody subjected to hypersonic
6
flow.
7
Keywords: inverse design method, hypersonic boundary layer removal, external drag reduction,
8
propulsion–airframe integration
Nomenclature
9 10
PCB
=
pressure-controllable bump
11
SES
=
side-embedded shock
12
LKE
=
low-kinetic-energy
13
HKE
=
high-kinetic-energy
14
KKE
=
kinetic energy efficiency
15
H KE
=
thickness of kinetic energy efficiency loss
16
U
=
density
17
u
=
x-direction velocity
18
M
=
Mach number
19
J
=
specific heat ratio
20
p
=
static pressure 2
1
S
=
static pressure ratio
2
V
=
total pressure recovery coefficient
3
E
=
shock wave angle
4
W
=
half of the inlet width
5
D
=
start pressure gradient of central-line
6
M
=
spline ratio of the central-line
7
I
=
spline ratio of the end-section
8
S ,o u t
=
outward pressure gradient
9
S ,in
=
inward pressure gradient
G
=
deflection angle
10 11 12
Subscripts
13
f
=
freestream properties
14
*
=
stagnation properties
15
x
=
freestream direction
16
y
=
height direction
17
z
=
crosswise direction
18
peak
=
peak value
19
s
=
starting cross section of bump
20
e
=
ending cross section of bump
3
1
1.
Introduction
2
The inlet is the core element that provides efficient air compression to the propulsion system of
3
hypersonic air-breathing flight vehicles[1]. The performance of inlets depends mainly on two factors. One
4
is the inlet compression efficiency. An increase of 1% in the inlet compression efficiency leads to an
5
increase of approximately 4% in the specific impulse of the propulsion system[2]. Through applying
6
osculating theory to the inlet design, the 3D inward turning inlet configuration is designed on 2D basic
7
flow fields[3]. Thus, the aerodynamic characteristics of the inlets depend on the corresponding basic flow
8
fields. By designing the incident shock wave attached on the inlet lip and using isentropic compression,
9
osculating theory is validated to improve the inlet compression efficiency considerably. The other factor is
10
the flow quality at the inlet entrance position, which includes but is not limited to the mechanical energy,
11
the flow uniformity, and the mass capturing ratio. As illustrated in Figure 1, the boundary and entropy
12
layers develop rapidly along the airframe depending on the bluntness effect and the airframe length,
13
respectively[4], which are together defined as the low-kinetic-energy flow (LKE flow).
14 15
Figure 1 Schematic of the wave field in a hypersonic flow induced by freestream disturbance and surface
16
roughness[5]
4
1
In the past few decades, studies have widened the knowledge on LKE flow. Aero-optical distortions
2
caused by turbulent and laminar boundary layers are investigated to find a non-intrusive diagnostic tool
3
for quantifying the state and parameters of the boundary layer[6-8]. Particle image velocimetry
4
measurements are used as an advanced diagnostic technique to study flow structures at hypersonic
5
speeds[9, 10]. The high-speed schlieren system is developed to study growth and breakdown of boundary
6
layer by the air density difference[11, 12]. Apart from the techniques mentioned above, high-resolution
7
numerical simulation[13, 14] is also conducted to study the LKE flow, including the flow mechanism of
8
hypersonic boundary layer transition[15, 16], the effects of roughness to hypersonic boundary layer[17, 18], the
9
blunt leading edge effects on the flow structure[5], the shock wave/boundary layer interactions in
10
hypersonic flows[19, 20], and the prediction research of aerodynamic heating for hypersonic boundary
11
layer[21, 22]. A latest experimental study of Mach 10 shows that[23] the boundary layer thickness is measured
12
to be 23 mm at 1.83 m downstream the wind tunnel leading edge, where the momentum thickness
13
Reynolds number reaches 8000. Notably, the LKE flow in hypersonic speeds is a complex phenomenon
14
with a considerable influence on the original flow field and requires to be investigated.
15
In dealing with boundary layer in hypersonic speeds, the structure strength cannot be ignored. The
16
conventional inlets use diverters to remove the boundary layer, which will lead to high load on the
17
structure strength. By contrast, the inlet–airframe integration design can relieve the load of structure
18
strength using a convex-shaped forebody, which is named as bump, to remove boundary layer[24, 25]. The
19
concept of the bump is first introduced as a waverider geometry, which is based on conical flow theory to
20
increase the lift-to-drag ratio[26]. Through the airframe forebody compression and boundary layer removal,
21
the bump can remove boundary layer and be integrated with the forebody smoothly. Compared with other 5
1
technologies, the bump is evidently a better method to deal with the tradeoff between boundary layer
2
removal and external drag reduction.
3
When integration concept is integrated into the design of propulsion systems, the incoming flow for
4
the inlet is non-uniform. Most design methods of inlets are based on the uniform incoming flow, which is
5
convenient to prescribe the aerodynamic parameters for inlet entrances. However, for the integration
6
design, the boundary layer along the airframe and forebody makes the incoming flow non-uniform, which
7
leads to the inapplicability of conventional design methods.
8
An improved bump-integrated 3D inward turning inlet design method is introduced in 2017[27],
9
which designs hypersonic inlets under non-uniform incoming flow condition. The corresponding design
10
method for bump is proposed to decrease the external drag of the propulsion system[28]. This method can
11
design bump by the prescribed pressure distribution. However, the side compression is large due to the
12
expanding flow surrounding bump and the compression flow of the inlet. Therefore, a side-embedded
13
shock (SES) occurs in the inlet (analyzed in Section 2.1 in detail), which complicates the shock system
14
and brings large energy loss. Meanwhile, the typical method has not built the relation between pressure
15
distribution aerodynamic characteristic clear enough.
16
This study proposes an innovative flow mechanism for bump design, which is called pressure ridge
17
(PR), to relieve the SES effect of inlet–bump integration. To realize this target, the flow field surrounding
18
bump and the possible reasons for the SES effect are analyzed (Section 2.2). Accordingly, the PR is
19
proposed to relieve the side compression of the inlet. According to the new pressure distribution, the
20
PR-derived bump is designed. Meanwhile, a typical pressure-controllable bump (PCB) with the identical
21
leading edge profile is generated for comparison to verify the improvement in the proposed PR flow 6
1
mechanism.
2
2.
Challenges in developing inlet–airframe integration at high speeds
3
The bump is used in the inlet–airframe integration to reduce external drag and the load of the
4
structure strength. In hypersonic speeds, the external drag and the flow pattern are two important factors
5
that should be improved. The external drag is in direct proportion to the x-direction projected area. Thus,
6
for bumps with identical leading edge, the bump height is critical for evaluating the external drag. The
7
other factor is the flow pattern over the bump surface. The flow pattern is expanded owing to the
8
crosswise pressure gradient. When the expanded streamlines are compressed in the inlet, a serious
9
crosswise compression effect called SES is induced, which is explained in the following subsection.
10
2.1.
Overlarge crosswise compression effect in the inlet: Side-embedded shock
11
Figure 2 illustrates the bump–inlet integration pattern and the numerical result in Mach 6 freestream
12
condition. At the bottom of the inlet, a strong crosswise compression is observed in the Mach contour.
13
The Mach number drops from 5 (colored in red) to 4.3 (colored in yellow) along the streamline. The
14
compression process can be equivalent to the oblique shock wave at the condition of M f
15
E = 1 2 .3 1q . The shock wave originates from the overlarge crosswise gradient. Thus, this effect is defined
16
as SES.
7
5,
1 2
Figure 2 SES effects at the bottom wall of a hypersonic bump inlet
3
The direct inducement of inlet compression is the flow deflection. Given the geometry change
4
between the airframe (the airframe is simplified as a flat plate in the current study) and the bump, a bump
5
shock wave originates at the leading edge position. The inlet should be located entirely after the bump
6
shock wave to minimize energy loss. Accordingly, the maximum height of inlet is restricted by the shape
7
of the bump shock wave, which indicates the contraction ratio at height direction is restricted. The
8
crosswise contraction ratio is large to ensure an excellent compression performance. Depending on the
9
expanded flow pattern over the bump surface and the demand of the crosswise contraction ratio
10
mentioned above, the overlarge crosswise compression of inflow occurs, which induces the SES effect.
11
Considering the overlarge crosswise compression, the SES will bring two negative effects to the inlet:
12
a) the overlarge compression creates a large adverse pressure gradient along flow direction, which leads
13
to the flow separation at the inlet corner area. As a result, the LKE flow accumulates at corners of the inlet
14
and develops along flow direction, which results in serious energy loss downstream. The total pressure
15
recovery ratio of the inlet decreases with the development of the separation bubble. b) The SES interacts
16
with the bump shock wave at the inlet lip position, which causes the shock wave distortion. Notably, the
17
pre-compressed airflow after the bump shock wave is spilled away with the enhancement in the shock 8
1
interaction, and this condition decreases the mass capturing performance of the inlet. The inlet is designed
2
on the basis of osculating theory (Figure 3). This theory simplifies the 3D inlet design into a series of
3
basic flow field design, which has been verified in [3]. However, the strong air compression in the
4
crosswise direction causes overlarge deflection angle of incoming flow. Consequently, the distorted flow
5
structure creates an “aerodynamic throat” (Figure 4), which results in the accumulation of flow at the
6
throat position and the decrease in critical Mach number. Ultimately, the structure becomes sensitive to
7
the inlet unstart.
8 9
Figure 3 Basic flow field for designing hypersonic inlets under non-uniform flow by osculating plane
10
theory
9
1 2
3
Figure 4 Aerodynamic throat depicted by the limiting streamlines of the bump inlet (Mach 6 freestream)
2.2.
Possible approaches to avoid SES effect
4
SES effect is mainly due to the overlarge deflection angle of the crosswise air compression at the
5
inlet entrance position. To eliminate SES effect, the inlet or the bump should be improved. One solution is
6
to decrease the crosswise contraction ratio of the inlet. This method directly reaches the target but will
7
evidently influence the crosswise compression ability. Therefore, the vertical contraction ratio should be
8
increased to ensure the compression ability of the inlet. Such increase can lead to the interaction of inlet
9
lip and the bump shock wave, which will bring additional shock drag to the inlet. The bump shock wave
10
is designed to cover all the inlet lip. When the lip area is large, the bump should be convex to create a
11
strong bump shock wave. This condition increases the overall size and external drag, which in turn results
12
in energy loss. This situation is opposite of the original intention of integration design. Thus, directly
13
decreasing crosswise contraction ratio of the inlet is not a preferred approach to avoid the SES.
14
The other approach is to change the flow pattern on the end-section of the bump, which is equivalent
15
to be depicted as the integration part between the bump and inlet. As mentioned in the introduction, the 10
1
performance of boundary layer removal is determined by the crosswise pressure gradient. The pressure
2
gradient also creates an expanded streamline pattern at the near-wall position of the bump. When the
3
streamline pattern of a certain inlet is expanded, the lip deflection angle is large. This condition can result
4
in the overlarge side compression. Therefore, the feasible approach to avoid SES is to arrange the
5
direction of streamlines from an expanding pattern to a parallel one. This method decreases the deflection
6
angle at the inlet entrance position and eliminates the inefficient compression of the inlet.
7
3.
Improvement in the pressure distribution to solve SES problem
8
As confirmed in the last section, the flow pattern of the bump is the main factor that can arrange the
9
near-wall flow pattern of the bump reasonably and eliminate the SES effect. The principle to improve the
10
bump performance is to create an appropriate pressure distribution for boundary layer removal and inlet
11
position presetting.
12
3.1.
Innovative type of pressure controlling mechanism: Pressure-ridge
13
The bump should be capable of removing boundary layer at high speeds. The pressure distribution of
14
the bump should also be reasonably arranged to make a less expanding pattern for preventing overlarge
15
side compression. In accordance with the description above, an innovative pressure distribution to control
16
pressure distribution of the bump is proposed, which is presented in Figure 5. It is a U-shape area, which
17
is presented in red color. This area has a higher pressure than the adjacent areas. This area uses high
18
pressure to create the pressure gradient with adjacent areas. Thus, low-kinetic boundary layer passing
19
through is avoided. Therefore, the mechanism is called PR.
11
1
Figure 5 Schematic of the innovative PR flow mechanism
2 3
The detail flow mechanism of PR can be described by the pressure gradient between PR and the
4
adjacent areas, which includes the pressure gradient at the outward and inward directions. S ,o u t is the
5
outward pressure gradient between PR and the bump leading edge. Depending on the S ,out gradient,
6
the boundary layer is diverted to two sides of the bump (streamline S2 in Figure 5). To fill the empty area
7
where the boundary layer has been removed, the high-kinetic fluid from the main flow (white
8
semitransparent layer in Figure 5) travels down toward the bump. S ,in is the inward pressure gradient
9
between PR and the rear-central part of the bump. Depending on S ,in , the previously expanding flow
10
will return to less expanding or even parallel, which decreases the deflection angle of the near-wall flow
11
and is helpful in eliminating the SES effect.
12
3.2.
Ideal pressure distribution of the bump depending on pressure ridge
13
The design parameters of PCB include the shock wave strength, the leading edge profile, the pressure
14
distribution on the central-line, the crosswise pressure distribution, and its transition pattern along the
15
flow direction. In this study, the PR mechanism is studied to improve bump design. Thus, the shock wave
16
strength and the leading edge profile are kept identical for every case. The approach to improve the bump 12
1
design is to design an ideal pressure distribution with the following features. On the one hand, the design
2
should remove the boundary layer efficiently with a small height. On the other hand, the design should
3
avoid inducing detached shock with a narrow PR width. The pressure distribution of key positions is
4
shown in Table 1 and Figure 6. The main differences between the new pressure distribution and the
5
typical one are described as below. For the aspect of the central-line pressure distribution, ߨǡ௫
6
increases by 3%, and its location moves 7% upward. Moreover, ߨௗǡ௫ decreases by 40%. This
7
distribution can be simply described as O -type pressure distribution. For the aspect of the crosswise
8
pressure distribution, ߨǡ௭ decreases by 5.8%, and its location moves 7% toward the leading edge.
9
This distribution can be simply described as M-type pressure distribution. The new type of pressure
10
distribution is to arrange PR close to the leading edge, which uses the front part of the bump to remove
11
boundary layer and the rear part of the bump to adjust the flow pattern.
12
Table 1 Design parameters of the new PR-derived bump and the typical PCB Type
Central-line ߨ௦ -ߨ -ɔ-Ƚ
End-section ߨ௦ --Ԅ-ߨǡ௭
Bump height/mm
Typical PCB New bump
2.4-1.7-8-0.38 2.4-1.0-8-0.30
3-600-0.8-2.5 3-600-0.8-2.5
95.0 67.3
13
14 13
1
Figure 6 Pressure distribution of the bump on two key positions: central-line (left) and end-section (right)
2
4.
3
4.1.
Comparison between the new and typical bumps
Preparations for the numerical simulation
4
A blunt leading edge with 3 mm radius is set approximately 0.7 m upstream the bump to produce
5
boundary layer. The mesh and boundary condition are set, as shown in Figure 7. The former is a C-shaped
6
mesh along the bump leading edge (the right side subplot), whereas the latter is a C-shaped mesh to
7
surround the bump leading edge (the middle subplot). The total meshes in the domain are approximately
8
0.7 million. To obtain the requested standard k–İ turbulence model, the minimum mesh height of
9
near-wall grid is 0.15 mm, and the grids in the y-direction are stretched with the increasing ratio of 1.2
10
refined with geometric proportion rule. The entire wall is adopted as no slip and adiabatic wall conditions.
11
Meanwhile, the freestream atmosphere condition is at 25 km altitude and Mach 6.
12 13
Figure 7 Structured mesh of the bump in the flow field with a blunt leading edge (3 mm blunted radius)
14
All results are calculated using CFX commercial software based on high-resolution numeric
15
turbulence and advection scheme. The numerical methods in this study have already been effectively
16
validated by You and Liang[29] using wind tunnel experiments, which showed that these methods can 14
1
calculate reasonable and reliable results. The numerical methods have also been validated in [28] through
2
the comparison with experimental study of bump, which is shown in Figure 8. The results show that the
3
relative error between numerical and experimental results is less than 7.4%, which indicates that the
4
numerical methods can effectively calculate the true flow field.
5
Figure 8 Experimental and numerical results: pressure distribution of the bump end-section in [28]
6
7
4.2.
Aerodynamic characteristics comparison between the new and typical bumps
8
On the basis of the PR mechanism established in this study, the new bump is designed. Figure 9
9
shows the new bump and the typical PCB. The aerodynamic characteristics of the two bumps are
10
compared numerically. The two bumps are based on the identical leading edge profile for comparison.
11
The amounts of the boundary layer removal and the energy loss caused by the bump shock wave
12
should be considered. Depending on the crosswise pressure gradient, the bump surface can effectively
13
remove the boundary layer. However, the curved shock also compresses the flow and causes energy loss.
14
Although the total pressure is positively correlated with the mechanical energy, a part of internal energy
15
can still be heated and used to generate thrust downstream. Notably, the total pressure cannot
16
comprehensively reflect the shock wave effects. In addition, the three boundary layer thicknesses
17
(nominal, momentum, and energy thicknesses) focus on the energy loss inside the boundary layer but do 15
1
not include the energy loss between the bump shock and the boundary layer. Similar to the definition of
2
momentum thickness, this study proposes a new parameter H KE , which converts the kinetic energy loss
3
(viscous condition) to an equivalent thickness (inviscid condition). The definition can be expressed as
4
follows:
5 6 7
H KE
³
f
0
U u 1 K KE dy U f uf
,
(1)
where K KE is the kinetic energy efficiency and is defined as follows: K KE
§ T * · § J 1 2 1 Mf V ¨1 ¨ J 1 2 © Tf* ¸¹ ¨© 2 Mf 2
1J
J
· ¸¸ . ¹
(2)
8
H KE distribution at the end-section of the bump is shown in Figure 10. In the range of z < 0.3 m (i.e.,
9
the bump central area), H KE of both bumps is kept in a low level (smaller than 0.0003), which indicates
10
that most of the LKE fluid has been diverted. In the range of 0.3< z <0.4 m (i.e., the adjacent area of the
11
bump leading edge), H KE of both bumps is approximately 3-4.5*10-4, but H KE of the new bump is
12
slightly less. The amount of the diverted LKE fluid accumulates in this region. In the range of z> 0.4 m
13
(i.e., the freestream), H KE of the new bump is greater than that of the typical one. For the new bump, the
14
removed boundary layer mainly locates at the freestream beside the bump leading edge. By contrast, the
15
removed boundary layer for the typical PCB mainly accumulates at the bump leading edge.
16
Figure 10 Thickness of kinetic energy loss Figure 9 Configurations of the new and typical PCBs distribution at the end-section of the bump 1
The ı contours at the end-section of bumps are demonstrated in Figure 11. It is evident that the
2
thickness of LKE flow are similar between two bumps. The boundary layer removal performance of two
3
bumps is similar to each other, but with only a small difference in the removed boundary layer’s location
4
(the new bump’s removed flow locates farther from the bump central-line than that of the typical one).
5
Nevertheless, the new bump is 29.2% lower in height than the typical PCB. It indicates that the central
6
part of the typical PCB is unnecessary high, which will induce additional energy loss and external drag. In
7
summary, the new bump can obtain similar boundary layer removal ability with less height.
8 9
Figure 11 ı contours at the end-section of bumps
10
Figure 12 demonstrates the pressure contour of the bump to depict the boundary layer removal
11
mechanism in detail. Notably, the pressure of the typical PCB is greater than that of the new bump, but
12
the new bump holds greater S ,in and S ,out than the typical PCB. The S ,out improves the
13
boundary layer removal performance of the new bump. Meanwhile, the kinetic efficiency contour is
14
obtained at different sections along the flow direction. The limiting streamlines are generated from the
15
same rake upstream the bump. Notably, the new bump has a clearer PR area than the typical one. When 17
1
the new bump is subjected to the incoming flow, a large S ,out leads to a large diverted amount of the
2
boundary layer.
3 4
Figure 12 Pressure and kinetic efficiency on the crosswise direction: typical (left) and new bump (right)
5
Figure 13 shows a 3D view of the pressure (the black solid line) and K K E (the red solid line), and
6
this figure uses y-direction heights to present their values. The pressure and the K K E value are extracted
7
from the bump surface every 225 mm along x-direction. Depending on different values of K K E , the
8
pressure distribution on the bump is segmented into three areas. The green area is occupied by the
9
high-kinetic-energy fluid (HKE fluid), where the boundary layer has been removed and the HKE fluid in
10
the higher layer comes down and fills up. The red area is PR area, where the pressure is higher than that in
11
the adjacent areas. The yellow area is occupied by the removed LKE fluid. By presenting pressure values
12
by height, tiny differences are found between the two pressure distributions. The two bumps have similar
13
S ,o u t , but the peak pressure of the typical PCB is unnecessarily high, which results in a convex bump
14
configuration. Meanwhile, the PR of the typical PCB is unnecessarily wide, which brings two
15
disadvantages. On the one hand, the high pressure distribution leads to a high bump configuration, which
16
imposes large external drag. On the other hand, the PR occupies additional space against the bump central
17
area, which expands the streamline pattern. The deflection angle of an inlet with a certain contraction
18
ratio increases with the increase in the expanding degree of the streamline pattern. Therefore, the 18
1
over-expanding streamline pattern will cause overlarge side compression, which may ultimately induce
2
SES.
3 4
Figure 13 3D view of surface pressure of bumps: typical (left) and new bump (right)
5
Figure 14 is the comparison of limiting streamlines on the two bumps. In the figure, the black solid
6
line represents the streamlines of the typical PCB, whereas the red solid line represents the streamlines of
7
the new bump. The black and red streamlines are generated from the same rake at the height position of
8
0.48 mm. The new bump has two features. At the front part of the bump, the S ,o u t of the new bump is
9
greater than that of the typical one. Therefore, the streamlines of the new bump have a larger deflection
10
angle and are thus farther to the central-line than those of the typical one. At the rear part of the bump, the
11
streamlines of the new bump are nearly parallel to the x-direction.
12 13
Figure 14 Limiting streamlines over bumps 19
1
As mentioned in Section 2.1, the main cause of SES effects is the crosswise flow deflection. The
2
flow direction needs to be adjusted to parallel for integration design. In this study, Ɂ is calculated to
3
present the crosswise flow deflection at the end-section of bumps. It is defined as follows: GZ
4
arctan
VZ . VX
(3)
5
Figure 15 shows the Ɂ contours of bumps. The Ɂ of the typical PCB is larger than that of the
6
new bump. For bump-inlet integration, the central-part of bump is the important area to control crosswise
7
flow deflection. Meanwhile, it is also the area to preset inlets. Due to S ,in , the crosswise flow
8
deflection at central-part has been decreased significantly. For the new bump, the area where z < 0.15 m is
9
relatively uniform (Ɂ < 1.5) to preset inlets. It is 30% wider than the typical PCB. It reveals that the new
10
bump is more suitable for the integration design with a hypersonic inlet than the typical PCB.
11 Figure 15 Ɂ contours at the end-section of bumps
12
13
5.
Conclusion
14
This study proposes an innovative mechanism called PR to prescribe bump pressure distribution. The
15
target is to relieve side compression effects in bump-inlet integration. PR is defined as a relative high
16
pressure area on the bump surface and parallel to the edge. The four design parameters for bump pressure 20
1
distribution are the peak value, the position, the inward pressure gradient of PR S ,in and the outward
2
pressure gradient S ,out .
3
Accordingly, the new bump based on PR mechanism is designed. Under the identical leading edge
4
profile, the new bump is numerically compared with the typical PCB. The results show that the new
5
PR-derived bump is 29.2% lower in height than the typical PCB. The S ,out is the key factor for
6
boundary layer removal. It proves PR can increase the efficiency of boundary layer removal considerably.
7
The streamlines at the end-section of bump (i.e., the presetting position of inlet) have been re-adjusted
8
by PR. Owing to lateral components of S ,in , the streamlines after PR change from expanding to parallel.
9
The uniform area of the new bump is 30% wider than that of the typical PCB. Thus, it can relieve the side
10
compression effects, which is evidently helpful for bump–inlet integration.
11
The innovative PR mechanism is proposed. It builds the relation between pressure distribution and
12
aerodynamic characteristics, thus improving the design efficiency. This mechanism can improve boundary
13
layer removal ability of bump by arranging pressure distribution reasonably. Compared with typical
14
approach to prescribe pressure distribution, PR makes a good balance of boundary layer removal, external
15
drag control and integration capability.
16
Acknowledgments: This study is supported by the Funding of Jiangsu Innovation Program for Graduate
17
Education (KYLX15_0259). The colleagues from the Institute for Fluid Mechanics and Engineering
18
Acoustics in Technical University of Berlin are gratefully acknowledged for their cooperation.
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Huang, G., Zuo, F., Qiao, W., and Xia, C. "Design Method of Internal Waverider Inlet with Bump Compression Surface," Aiaa/sae/asee Joint Propulsion Conference. 2017.
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22
23
Zonghan Yu, Guoping Huang, Chen Xia, Joern Sesterhenn
PII: DOI: Reference:
S1270-9638(18)30354-7 https://doi.org/10.1016/j.ast.2019.02.015 AESCTE 5001
To appear in:
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Received date: Revised date: Accepted date:
14 February 2018 11 February 2019 13 February 2019
Please cite this article in press as: Z. Yu et al., A pressure-controllable bump based on the pressure-ridge concept, Aerosp. Sci. Technol. (2019), https://doi.org/10.1016/j.ast.2019.02.015
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1
A pressure-controllable bump based on the pressure-ridge concept
2
Zonghan Yu1, Guoping Huang2, Chen Xia3
3
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing,
4
Jiangsu 210016, People’s Republic of China
5
Joern Sesterhenn4
6
Institute for Fluid Mechanics and Engineering Acoustics, Technical University of Berlin, Germany
7
2: Corresponding author, E-mail: [email protected]
8
Abstract: An innovative type of pressure distribution for the hypersonic aircraft forebody (bump) is
9
presented, and this design is based on the newly established known as pressure ridge (PR) flow
10
mechanism. Studies on the low-kinetic-energy fluid over the aircraft surface are summarized. Then, the
11
challenges of the inlet–airframe integration at high speeds are discussed. The flow structure around the
12
bump is analyzed in detail to eliminate the side-embedded shock (SES) effect at the inlet entrance. The
13
concept of PR is proposed to improve the overall aerodynamic characteristics of the bump, namely, the
14
boundary layer removal, the reduction of external drag, and the streamline direction at bump end-section.
15
On the basis of the developed inverse method to generate the bump surface by the prescribed pressure
16
distribution, the improved PR-derived bump is designed and numerically compared with the typical
17
pressure-controllable bump (PCB) while the identical leading edge profile is imposed. Results
18
demonstrate that the PR creates outward and inward pressure gradients. The removed amount of boundary
19
layer increases with the increase in outward pressure gradient. Meanwhile, the inward pressure gradient
1
1
determines the streamline pattern after the bump. The PR-derived bump is 29.2% lower in height than the
2
typical one by using a proper outward pressure gradient. The uniform area of the new bump is 30% wider
3
than that of the typical PCB. The near-wall streamlines of the new bump are adjusted from expanding to
4
the parallel, thereby relieving the side-compression. Changing the location, width, and peak value of the
5
PR can lead to great flexibility in the design and optimization of aircraft forebody subjected to hypersonic
6
flow.
7
Keywords: inverse design method, hypersonic boundary layer removal, external drag reduction,
8
propulsion–airframe integration
Nomenclature
9 10
PCB
=
pressure-controllable bump
11
SES
=
side-embedded shock
12
LKE
=
low-kinetic-energy
13
HKE
=
high-kinetic-energy
14
KKE
=
kinetic energy efficiency
15
H KE
=
thickness of kinetic energy efficiency loss
16
U
=
density
17
u
=
x-direction velocity
18
M
=
Mach number
19
J
=
specific heat ratio
20
p
=
static pressure 2
1
S
=
static pressure ratio
2
V
=
total pressure recovery coefficient
3
E
=
shock wave angle
4
W
=
half of the inlet width
5
D
=
start pressure gradient of central-line
6
M
=
spline ratio of the central-line
7
I
=
spline ratio of the end-section
8
S ,o u t
=
outward pressure gradient
9
S ,in
=
inward pressure gradient
G
=
deflection angle
10 11 12
Subscripts
13
f
=
freestream properties
14
*
=
stagnation properties
15
x
=
freestream direction
16
y
=
height direction
17
z
=
crosswise direction
18
peak
=
peak value
19
s
=
starting cross section of bump
20
e
=
ending cross section of bump
3
1
1.
Introduction
2
The inlet is the core element that provides efficient air compression to the propulsion system of
3
hypersonic air-breathing flight vehicles[1]. The performance of inlets depends mainly on two factors. One
4
is the inlet compression efficiency. An increase of 1% in the inlet compression efficiency leads to an
5
increase of approximately 4% in the specific impulse of the propulsion system[2]. Through applying
6
osculating theory to the inlet design, the 3D inward turning inlet configuration is designed on 2D basic
7
flow fields[3]. Thus, the aerodynamic characteristics of the inlets depend on the corresponding basic flow
8
fields. By designing the incident shock wave attached on the inlet lip and using isentropic compression,
9
osculating theory is validated to improve the inlet compression efficiency considerably. The other factor is
10
the flow quality at the inlet entrance position, which includes but is not limited to the mechanical energy,
11
the flow uniformity, and the mass capturing ratio. As illustrated in Figure 1, the boundary and entropy
12
layers develop rapidly along the airframe depending on the bluntness effect and the airframe length,
13
respectively[4], which are together defined as the low-kinetic-energy flow (LKE flow).
14 15
Figure 1 Schematic of the wave field in a hypersonic flow induced by freestream disturbance and surface
16
roughness[5]
4
1
In the past few decades, studies have widened the knowledge on LKE flow. Aero-optical distortions
2
caused by turbulent and laminar boundary layers are investigated to find a non-intrusive diagnostic tool
3
for quantifying the state and parameters of the boundary layer[6-8]. Particle image velocimetry
4
measurements are used as an advanced diagnostic technique to study flow structures at hypersonic
5
speeds[9, 10]. The high-speed schlieren system is developed to study growth and breakdown of boundary
6
layer by the air density difference[11, 12]. Apart from the techniques mentioned above, high-resolution
7
numerical simulation[13, 14] is also conducted to study the LKE flow, including the flow mechanism of
8
hypersonic boundary layer transition[15, 16], the effects of roughness to hypersonic boundary layer[17, 18], the
9
blunt leading edge effects on the flow structure[5], the shock wave/boundary layer interactions in
10
hypersonic flows[19, 20], and the prediction research of aerodynamic heating for hypersonic boundary
11
layer[21, 22]. A latest experimental study of Mach 10 shows that[23] the boundary layer thickness is measured
12
to be 23 mm at 1.83 m downstream the wind tunnel leading edge, where the momentum thickness
13
Reynolds number reaches 8000. Notably, the LKE flow in hypersonic speeds is a complex phenomenon
14
with a considerable influence on the original flow field and requires to be investigated.
15
In dealing with boundary layer in hypersonic speeds, the structure strength cannot be ignored. The
16
conventional inlets use diverters to remove the boundary layer, which will lead to high load on the
17
structure strength. By contrast, the inlet–airframe integration design can relieve the load of structure
18
strength using a convex-shaped forebody, which is named as bump, to remove boundary layer[24, 25]. The
19
concept of the bump is first introduced as a waverider geometry, which is based on conical flow theory to
20
increase the lift-to-drag ratio[26]. Through the airframe forebody compression and boundary layer removal,
21
the bump can remove boundary layer and be integrated with the forebody smoothly. Compared with other 5
1
technologies, the bump is evidently a better method to deal with the tradeoff between boundary layer
2
removal and external drag reduction.
3
When integration concept is integrated into the design of propulsion systems, the incoming flow for
4
the inlet is non-uniform. Most design methods of inlets are based on the uniform incoming flow, which is
5
convenient to prescribe the aerodynamic parameters for inlet entrances. However, for the integration
6
design, the boundary layer along the airframe and forebody makes the incoming flow non-uniform, which
7
leads to the inapplicability of conventional design methods.
8
An improved bump-integrated 3D inward turning inlet design method is introduced in 2017[27],
9
which designs hypersonic inlets under non-uniform incoming flow condition. The corresponding design
10
method for bump is proposed to decrease the external drag of the propulsion system[28]. This method can
11
design bump by the prescribed pressure distribution. However, the side compression is large due to the
12
expanding flow surrounding bump and the compression flow of the inlet. Therefore, a side-embedded
13
shock (SES) occurs in the inlet (analyzed in Section 2.1 in detail), which complicates the shock system
14
and brings large energy loss. Meanwhile, the typical method has not built the relation between pressure
15
distribution aerodynamic characteristic clear enough.
16
This study proposes an innovative flow mechanism for bump design, which is called pressure ridge
17
(PR), to relieve the SES effect of inlet–bump integration. To realize this target, the flow field surrounding
18
bump and the possible reasons for the SES effect are analyzed (Section 2.2). Accordingly, the PR is
19
proposed to relieve the side compression of the inlet. According to the new pressure distribution, the
20
PR-derived bump is designed. Meanwhile, a typical pressure-controllable bump (PCB) with the identical
21
leading edge profile is generated for comparison to verify the improvement in the proposed PR flow 6
1
mechanism.
2
2.
Challenges in developing inlet–airframe integration at high speeds
3
The bump is used in the inlet–airframe integration to reduce external drag and the load of the
4
structure strength. In hypersonic speeds, the external drag and the flow pattern are two important factors
5
that should be improved. The external drag is in direct proportion to the x-direction projected area. Thus,
6
for bumps with identical leading edge, the bump height is critical for evaluating the external drag. The
7
other factor is the flow pattern over the bump surface. The flow pattern is expanded owing to the
8
crosswise pressure gradient. When the expanded streamlines are compressed in the inlet, a serious
9
crosswise compression effect called SES is induced, which is explained in the following subsection.
10
2.1.
Overlarge crosswise compression effect in the inlet: Side-embedded shock
11
Figure 2 illustrates the bump–inlet integration pattern and the numerical result in Mach 6 freestream
12
condition. At the bottom of the inlet, a strong crosswise compression is observed in the Mach contour.
13
The Mach number drops from 5 (colored in red) to 4.3 (colored in yellow) along the streamline. The
14
compression process can be equivalent to the oblique shock wave at the condition of M f
15
E = 1 2 .3 1q . The shock wave originates from the overlarge crosswise gradient. Thus, this effect is defined
16
as SES.
7
5,
1 2
Figure 2 SES effects at the bottom wall of a hypersonic bump inlet
3
The direct inducement of inlet compression is the flow deflection. Given the geometry change
4
between the airframe (the airframe is simplified as a flat plate in the current study) and the bump, a bump
5
shock wave originates at the leading edge position. The inlet should be located entirely after the bump
6
shock wave to minimize energy loss. Accordingly, the maximum height of inlet is restricted by the shape
7
of the bump shock wave, which indicates the contraction ratio at height direction is restricted. The
8
crosswise contraction ratio is large to ensure an excellent compression performance. Depending on the
9
expanded flow pattern over the bump surface and the demand of the crosswise contraction ratio
10
mentioned above, the overlarge crosswise compression of inflow occurs, which induces the SES effect.
11
Considering the overlarge crosswise compression, the SES will bring two negative effects to the inlet:
12
a) the overlarge compression creates a large adverse pressure gradient along flow direction, which leads
13
to the flow separation at the inlet corner area. As a result, the LKE flow accumulates at corners of the inlet
14
and develops along flow direction, which results in serious energy loss downstream. The total pressure
15
recovery ratio of the inlet decreases with the development of the separation bubble. b) The SES interacts
16
with the bump shock wave at the inlet lip position, which causes the shock wave distortion. Notably, the
17
pre-compressed airflow after the bump shock wave is spilled away with the enhancement in the shock 8
1
interaction, and this condition decreases the mass capturing performance of the inlet. The inlet is designed
2
on the basis of osculating theory (Figure 3). This theory simplifies the 3D inlet design into a series of
3
basic flow field design, which has been verified in [3]. However, the strong air compression in the
4
crosswise direction causes overlarge deflection angle of incoming flow. Consequently, the distorted flow
5
structure creates an “aerodynamic throat” (Figure 4), which results in the accumulation of flow at the
6
throat position and the decrease in critical Mach number. Ultimately, the structure becomes sensitive to
7
the inlet unstart.
8 9
Figure 3 Basic flow field for designing hypersonic inlets under non-uniform flow by osculating plane
10
theory
9
1 2
3
Figure 4 Aerodynamic throat depicted by the limiting streamlines of the bump inlet (Mach 6 freestream)
2.2.
Possible approaches to avoid SES effect
4
SES effect is mainly due to the overlarge deflection angle of the crosswise air compression at the
5
inlet entrance position. To eliminate SES effect, the inlet or the bump should be improved. One solution is
6
to decrease the crosswise contraction ratio of the inlet. This method directly reaches the target but will
7
evidently influence the crosswise compression ability. Therefore, the vertical contraction ratio should be
8
increased to ensure the compression ability of the inlet. Such increase can lead to the interaction of inlet
9
lip and the bump shock wave, which will bring additional shock drag to the inlet. The bump shock wave
10
is designed to cover all the inlet lip. When the lip area is large, the bump should be convex to create a
11
strong bump shock wave. This condition increases the overall size and external drag, which in turn results
12
in energy loss. This situation is opposite of the original intention of integration design. Thus, directly
13
decreasing crosswise contraction ratio of the inlet is not a preferred approach to avoid the SES.
14
The other approach is to change the flow pattern on the end-section of the bump, which is equivalent
15
to be depicted as the integration part between the bump and inlet. As mentioned in the introduction, the 10
1
performance of boundary layer removal is determined by the crosswise pressure gradient. The pressure
2
gradient also creates an expanded streamline pattern at the near-wall position of the bump. When the
3
streamline pattern of a certain inlet is expanded, the lip deflection angle is large. This condition can result
4
in the overlarge side compression. Therefore, the feasible approach to avoid SES is to arrange the
5
direction of streamlines from an expanding pattern to a parallel one. This method decreases the deflection
6
angle at the inlet entrance position and eliminates the inefficient compression of the inlet.
7
3.
Improvement in the pressure distribution to solve SES problem
8
As confirmed in the last section, the flow pattern of the bump is the main factor that can arrange the
9
near-wall flow pattern of the bump reasonably and eliminate the SES effect. The principle to improve the
10
bump performance is to create an appropriate pressure distribution for boundary layer removal and inlet
11
position presetting.
12
3.1.
Innovative type of pressure controlling mechanism: Pressure-ridge
13
The bump should be capable of removing boundary layer at high speeds. The pressure distribution of
14
the bump should also be reasonably arranged to make a less expanding pattern for preventing overlarge
15
side compression. In accordance with the description above, an innovative pressure distribution to control
16
pressure distribution of the bump is proposed, which is presented in Figure 5. It is a U-shape area, which
17
is presented in red color. This area has a higher pressure than the adjacent areas. This area uses high
18
pressure to create the pressure gradient with adjacent areas. Thus, low-kinetic boundary layer passing
19
through is avoided. Therefore, the mechanism is called PR.
11
1
Figure 5 Schematic of the innovative PR flow mechanism
2 3
The detail flow mechanism of PR can be described by the pressure gradient between PR and the
4
adjacent areas, which includes the pressure gradient at the outward and inward directions. S ,o u t is the
5
outward pressure gradient between PR and the bump leading edge. Depending on the S ,out gradient,
6
the boundary layer is diverted to two sides of the bump (streamline S2 in Figure 5). To fill the empty area
7
where the boundary layer has been removed, the high-kinetic fluid from the main flow (white
8
semitransparent layer in Figure 5) travels down toward the bump. S ,in is the inward pressure gradient
9
between PR and the rear-central part of the bump. Depending on S ,in , the previously expanding flow
10
will return to less expanding or even parallel, which decreases the deflection angle of the near-wall flow
11
and is helpful in eliminating the SES effect.
12
3.2.
Ideal pressure distribution of the bump depending on pressure ridge
13
The design parameters of PCB include the shock wave strength, the leading edge profile, the pressure
14
distribution on the central-line, the crosswise pressure distribution, and its transition pattern along the
15
flow direction. In this study, the PR mechanism is studied to improve bump design. Thus, the shock wave
16
strength and the leading edge profile are kept identical for every case. The approach to improve the bump 12
1
design is to design an ideal pressure distribution with the following features. On the one hand, the design
2
should remove the boundary layer efficiently with a small height. On the other hand, the design should
3
avoid inducing detached shock with a narrow PR width. The pressure distribution of key positions is
4
shown in Table 1 and Figure 6. The main differences between the new pressure distribution and the
5
typical one are described as below. For the aspect of the central-line pressure distribution, ߨǡ௫
6
increases by 3%, and its location moves 7% upward. Moreover, ߨௗǡ௫ decreases by 40%. This
7
distribution can be simply described as O -type pressure distribution. For the aspect of the crosswise
8
pressure distribution, ߨǡ௭ decreases by 5.8%, and its location moves 7% toward the leading edge.
9
This distribution can be simply described as M-type pressure distribution. The new type of pressure
10
distribution is to arrange PR close to the leading edge, which uses the front part of the bump to remove
11
boundary layer and the rear part of the bump to adjust the flow pattern.
12
Table 1 Design parameters of the new PR-derived bump and the typical PCB Type
Central-line ߨ௦ -ߨ -ɔ-Ƚ
End-section ߨ௦ --Ԅ-ߨǡ௭
Bump height/mm
Typical PCB New bump
2.4-1.7-8-0.38 2.4-1.0-8-0.30
3-600-0.8-2.5 3-600-0.8-2.5
95.0 67.3
13
14 13
1
Figure 6 Pressure distribution of the bump on two key positions: central-line (left) and end-section (right)
2
4.
3
4.1.
Comparison between the new and typical bumps
Preparations for the numerical simulation
4
A blunt leading edge with 3 mm radius is set approximately 0.7 m upstream the bump to produce
5
boundary layer. The mesh and boundary condition are set, as shown in Figure 7. The former is a C-shaped
6
mesh along the bump leading edge (the right side subplot), whereas the latter is a C-shaped mesh to
7
surround the bump leading edge (the middle subplot). The total meshes in the domain are approximately
8
0.7 million. To obtain the requested standard k–İ turbulence model, the minimum mesh height of
9
near-wall grid is 0.15 mm, and the grids in the y-direction are stretched with the increasing ratio of 1.2
10
refined with geometric proportion rule. The entire wall is adopted as no slip and adiabatic wall conditions.
11
Meanwhile, the freestream atmosphere condition is at 25 km altitude and Mach 6.
12 13
Figure 7 Structured mesh of the bump in the flow field with a blunt leading edge (3 mm blunted radius)
14
All results are calculated using CFX commercial software based on high-resolution numeric
15
turbulence and advection scheme. The numerical methods in this study have already been effectively
16
validated by You and Liang[29] using wind tunnel experiments, which showed that these methods can 14
1
calculate reasonable and reliable results. The numerical methods have also been validated in [28] through
2
the comparison with experimental study of bump, which is shown in Figure 8. The results show that the
3
relative error between numerical and experimental results is less than 7.4%, which indicates that the
4
numerical methods can effectively calculate the true flow field.
5
Figure 8 Experimental and numerical results: pressure distribution of the bump end-section in [28]
6
7
4.2.
Aerodynamic characteristics comparison between the new and typical bumps
8
On the basis of the PR mechanism established in this study, the new bump is designed. Figure 9
9
shows the new bump and the typical PCB. The aerodynamic characteristics of the two bumps are
10
compared numerically. The two bumps are based on the identical leading edge profile for comparison.
11
The amounts of the boundary layer removal and the energy loss caused by the bump shock wave
12
should be considered. Depending on the crosswise pressure gradient, the bump surface can effectively
13
remove the boundary layer. However, the curved shock also compresses the flow and causes energy loss.
14
Although the total pressure is positively correlated with the mechanical energy, a part of internal energy
15
can still be heated and used to generate thrust downstream. Notably, the total pressure cannot
16
comprehensively reflect the shock wave effects. In addition, the three boundary layer thicknesses
17
(nominal, momentum, and energy thicknesses) focus on the energy loss inside the boundary layer but do 15
1
not include the energy loss between the bump shock and the boundary layer. Similar to the definition of
2
momentum thickness, this study proposes a new parameter H KE , which converts the kinetic energy loss
3
(viscous condition) to an equivalent thickness (inviscid condition). The definition can be expressed as
4
follows:
5 6 7
H KE
³
f
0
U u 1 K KE dy U f uf
,
(1)
where K KE is the kinetic energy efficiency and is defined as follows: K KE
§ T * · § J 1 2 1 Mf V ¨1 ¨ J 1 2 © Tf* ¸¹ ¨© 2 Mf 2
1J
J
· ¸¸ . ¹
(2)
8
H KE distribution at the end-section of the bump is shown in Figure 10. In the range of z < 0.3 m (i.e.,
9
the bump central area), H KE of both bumps is kept in a low level (smaller than 0.0003), which indicates
10
that most of the LKE fluid has been diverted. In the range of 0.3< z <0.4 m (i.e., the adjacent area of the
11
bump leading edge), H KE of both bumps is approximately 3-4.5*10-4, but H KE of the new bump is
12
slightly less. The amount of the diverted LKE fluid accumulates in this region. In the range of z> 0.4 m
13
(i.e., the freestream), H KE of the new bump is greater than that of the typical one. For the new bump, the
14
removed boundary layer mainly locates at the freestream beside the bump leading edge. By contrast, the
15
removed boundary layer for the typical PCB mainly accumulates at the bump leading edge.
16
Figure 10 Thickness of kinetic energy loss Figure 9 Configurations of the new and typical PCBs distribution at the end-section of the bump 1
The ı contours at the end-section of bumps are demonstrated in Figure 11. It is evident that the
2
thickness of LKE flow are similar between two bumps. The boundary layer removal performance of two
3
bumps is similar to each other, but with only a small difference in the removed boundary layer’s location
4
(the new bump’s removed flow locates farther from the bump central-line than that of the typical one).
5
Nevertheless, the new bump is 29.2% lower in height than the typical PCB. It indicates that the central
6
part of the typical PCB is unnecessary high, which will induce additional energy loss and external drag. In
7
summary, the new bump can obtain similar boundary layer removal ability with less height.
8 9
Figure 11 ı contours at the end-section of bumps
10
Figure 12 demonstrates the pressure contour of the bump to depict the boundary layer removal
11
mechanism in detail. Notably, the pressure of the typical PCB is greater than that of the new bump, but
12
the new bump holds greater S ,in and S ,out than the typical PCB. The S ,out improves the
13
boundary layer removal performance of the new bump. Meanwhile, the kinetic efficiency contour is
14
obtained at different sections along the flow direction. The limiting streamlines are generated from the
15
same rake upstream the bump. Notably, the new bump has a clearer PR area than the typical one. When 17
1
the new bump is subjected to the incoming flow, a large S ,out leads to a large diverted amount of the
2
boundary layer.
3 4
Figure 12 Pressure and kinetic efficiency on the crosswise direction: typical (left) and new bump (right)
5
Figure 13 shows a 3D view of the pressure (the black solid line) and K K E (the red solid line), and
6
this figure uses y-direction heights to present their values. The pressure and the K K E value are extracted
7
from the bump surface every 225 mm along x-direction. Depending on different values of K K E , the
8
pressure distribution on the bump is segmented into three areas. The green area is occupied by the
9
high-kinetic-energy fluid (HKE fluid), where the boundary layer has been removed and the HKE fluid in
10
the higher layer comes down and fills up. The red area is PR area, where the pressure is higher than that in
11
the adjacent areas. The yellow area is occupied by the removed LKE fluid. By presenting pressure values
12
by height, tiny differences are found between the two pressure distributions. The two bumps have similar
13
S ,o u t , but the peak pressure of the typical PCB is unnecessarily high, which results in a convex bump
14
configuration. Meanwhile, the PR of the typical PCB is unnecessarily wide, which brings two
15
disadvantages. On the one hand, the high pressure distribution leads to a high bump configuration, which
16
imposes large external drag. On the other hand, the PR occupies additional space against the bump central
17
area, which expands the streamline pattern. The deflection angle of an inlet with a certain contraction
18
ratio increases with the increase in the expanding degree of the streamline pattern. Therefore, the 18
1
over-expanding streamline pattern will cause overlarge side compression, which may ultimately induce
2
SES.
3 4
Figure 13 3D view of surface pressure of bumps: typical (left) and new bump (right)
5
Figure 14 is the comparison of limiting streamlines on the two bumps. In the figure, the black solid
6
line represents the streamlines of the typical PCB, whereas the red solid line represents the streamlines of
7
the new bump. The black and red streamlines are generated from the same rake at the height position of
8
0.48 mm. The new bump has two features. At the front part of the bump, the S ,o u t of the new bump is
9
greater than that of the typical one. Therefore, the streamlines of the new bump have a larger deflection
10
angle and are thus farther to the central-line than those of the typical one. At the rear part of the bump, the
11
streamlines of the new bump are nearly parallel to the x-direction.
12 13
Figure 14 Limiting streamlines over bumps 19
1
As mentioned in Section 2.1, the main cause of SES effects is the crosswise flow deflection. The
2
flow direction needs to be adjusted to parallel for integration design. In this study, Ɂ is calculated to
3
present the crosswise flow deflection at the end-section of bumps. It is defined as follows: GZ
4
arctan
VZ . VX
(3)
5
Figure 15 shows the Ɂ contours of bumps. The Ɂ of the typical PCB is larger than that of the
6
new bump. For bump-inlet integration, the central-part of bump is the important area to control crosswise
7
flow deflection. Meanwhile, it is also the area to preset inlets. Due to S ,in , the crosswise flow
8
deflection at central-part has been decreased significantly. For the new bump, the area where z < 0.15 m is
9
relatively uniform (Ɂ < 1.5) to preset inlets. It is 30% wider than the typical PCB. It reveals that the new
10
bump is more suitable for the integration design with a hypersonic inlet than the typical PCB.
11 Figure 15 Ɂ contours at the end-section of bumps
12
13
5.
Conclusion
14
This study proposes an innovative mechanism called PR to prescribe bump pressure distribution. The
15
target is to relieve side compression effects in bump-inlet integration. PR is defined as a relative high
16
pressure area on the bump surface and parallel to the edge. The four design parameters for bump pressure 20
1
distribution are the peak value, the position, the inward pressure gradient of PR S ,in and the outward
2
pressure gradient S ,out .
3
Accordingly, the new bump based on PR mechanism is designed. Under the identical leading edge
4
profile, the new bump is numerically compared with the typical PCB. The results show that the new
5
PR-derived bump is 29.2% lower in height than the typical PCB. The S ,out is the key factor for
6
boundary layer removal. It proves PR can increase the efficiency of boundary layer removal considerably.
7
The streamlines at the end-section of bump (i.e., the presetting position of inlet) have been re-adjusted
8
by PR. Owing to lateral components of S ,in , the streamlines after PR change from expanding to parallel.
9
The uniform area of the new bump is 30% wider than that of the typical PCB. Thus, it can relieve the side
10
compression effects, which is evidently helpful for bump–inlet integration.
11
The innovative PR mechanism is proposed. It builds the relation between pressure distribution and
12
aerodynamic characteristics, thus improving the design efficiency. This mechanism can improve boundary
13
layer removal ability of bump by arranging pressure distribution reasonably. Compared with typical
14
approach to prescribe pressure distribution, PR makes a good balance of boundary layer removal, external
15
drag control and integration capability.
16
Acknowledgments: This study is supported by the Funding of Jiangsu Innovation Program for Graduate
17
Education (KYLX15_0259). The colleagues from the Institute for Fluid Mechanics and Engineering
18
Acoustics in Technical University of Berlin are gratefully acknowledged for their cooperation.
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