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Spray characteristics of a pintle injector based on annular orifice area
Journal Pre-proof Spray characteristics of a pintle injector based on annular orifice area Suji Lee, Daehwan Kim, Jaye Koo, Youngbin Yoon PII:
S0094-5765(19)31385-2
DOI:
https://doi.org/10.1016/j.actaastro.2019.11.008
Reference:
AA 7753
To appear in:
Acta Astronautica
Received Date: 25 June 2019 Revised Date:
26 October 2019
Accepted Date: 2 November 2019
Please cite this article as: S. Lee, D. Kim, J. Koo, Y. Yoon, Spray characteristics of a pintle injector based on annular orifice area, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.11.008. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd on behalf of IAA.
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Spray characteristics of a pintle injector based on annular orifice area Suji Lee1, Daehwan Kim1, Jaye Koo2, and Youngbin Yoon3,* 1 Graduate Student, Department of Mechanical and Aerospace Engineering, Seoul National University, 1 Gwanakro, Gwanak-gu, Seoul, 08826, Republic of Korea 2 Professor, School of Aerospace and Mechanical Engineering, Korea Aerospace University, 76, Hanggongdaehakro, Deogyang-gu, Goyang-si, Gyeonggi-do, 10540, Republic of Korea 3 Professor, Department of Mechanical and Aerospace Engineering and the Institute of Advanced Aerospace Technology, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea * Address all correspondence to Youngbin Yoon, E-mail: [email protected].
13
14
As interest in low-cost reusable launch vehicles and extraterrestrial exploration has
15
increased in recent years, soft-landing techniques have become important. A pintle injector
16
can help realize this because it is capable of thrust control. However, research on this topic is
17
very limited, and general optimization design procedures have not been completely
18
established. In particular, no studies have examined orifice adjustment for annular flow,
19
which is important in thrust control. In this study, a new design concept for a pintle injector
20
is presented specifically to improve spray uniformity in a 400 N class engine; this maintains
21
the concentricity of the pintle rod associated with the radial flow’s orifice size. The primary
22
focus here was on spray tests that were conducted to obtain the control range of the orifice
23
area for annular flow. Spray characteristics such as spray angle, spray uniformity, and
24
droplet size were analyzed, from which empirical correlations were derived. Finally, the
25
optimum control range for the annular flow’s orifice area was estimated from the
26
perspective of atomization performance. This can be of reference to develop an enhanced
27
thrust control system.
28 29
Keywords: Throttleable liquid rocket engine, Pintle injector, Annular orifice area, Spray characteristics
30 31 32 33 34 35 36 37 38 39 40 41 42 43
Nomenclature
,
,
∗
Cylinder cross-sectional area Annular flow’s outlet area Radial flow’s outlet area Blockage factor Characteristic velocity Thrust coefficient Combustion chamber diameter Circumferential length of each hole Pintle diameter Rocket thrust Gap distance Outlet height Momentum flux ratio
44
Distance until annular flow first collides with radial flow
45
N
New dimensionless number
46
Number of total holes/slot
47
O/F
Oxygen to fuel mass flow rate ratio
48
P
New parameter
49
Combustion chamber pressure
50 51 52 53
!
Patternation index Relative flow intensity Cylinder inner radius Cylinder outer radius
54
"#
Sauter mean diameter
55
SUI
Spray uniformity index
56
TMR
Total momentum ratio
57
We
Weber number
58 59
1. Introduction
60
requirement for commercial launch services. Consequently, interest in developing reusable launch vehicles has
61
quickly increased in countries around the world. Planetary exploration for future energy sources has also attracted
62
attention. Soft landing technology is a key factor in reusable launchers and extrasolar planet exploration. A
63
throttleable rocket engine is an important technology that can help accomplish this mission, so extensive research is
64
required.
With the recent growth of the private space rocket market, price competitiveness has become an important
65
There are several ways to control thrust, including changing the propellant’s type or composition and adjusting
66
the area of the nozzle throat or nozzle exit. However, these approaches are difficult to control due to physical
67
limitations and high heat flux concentrated in the nozzle throat. In contrast, controlling the propellant flow rate is
68
regarded as the simplest method. The relationship between rocket thrust and propellant flow rate is defined by Eq.
69
(1):
70
$ %& ∙ ( ) ∙ * + ,
(1)
71
where , %&, ( , , , and are rocket thrust, propellant flow rate, nozzle exit velocity, exit area, exit pressure,
72
and free stream pressure, respectively. There are various ways to adjust flow rate, such as controlling differential
73
pressure or using a dual manifold, but the area control method is considered to be the most promising [1].
74 75
Fig. 1. Conceptual diagram of a pintle injector.
76 77
A pintle injector is a representative area control method and has the structure to control thrust. The propellant
78
flow rate is regulated by adjusting the injector orifice size using a specific moving device. Fig. 1 shows the basic
79
concept of the pintle injector, in which an area adjusting sleeve moves in the axial direction to control the propellant
80
orifice size. Fuel is injected in the axial direction of the combustion chamber in the form of annular flow along the
81
injector’s outer wall. The oxidizer flows into the pintle injector and forms a thin sheet in the radial direction through
82
the gap between the pintle and the sleeve. Propellants injected in the axial and radial directions collide with each
83
other at the end of the pintle, allowing mixing and atomization to proceed.
84
This pintle injector has several characteristics. First, it can control thrust and has consistent high performance
85
over a wide thrust range. Second, it is simple, allowing for cost and weight savings. For swirl or jet injectors
86
typically used in liquid rocket engines, multiple injectors are mounted on one plate. However, only one pintle
87
injector is required regardless of thrust, which can have a large range. Consequently, cost and weight can be reduced.
88
The third characteristic is combustion stability, as the pintle injector has recirculation zones around the injector.
89
Because the recirculation zone at the center of the combustion chamber acts as a deflector and mixer for unburned
90
droplets, it has a positive effect on combustion stability and performance [2, 3].
91
The pintle injector concept was first devised by TRW in the United Sates, and it was applied to the Apollo Lunar
92
Descent Engine (LMDE) in the 1960s. Since the early 2000s, pintle injector research has been carried out in industry
93
and academia. SpaceX applied the pintle injector used in the LMDE to the Merlin engine to develop a reusable
94
vehicle to reduce launch costs [4]. Northrop Grumman developed a TR202 prototype engine aimed at developing a
95
variable thrust rocket engine for future NASA take-offs and landings. The combustion characteristics were observed
96
through a 10:1 throttling level combustion test [5].
97
At Purdue University, a pintle injector for non-toxic bipropellants was developed and a combustion test was
98
performed. Several parameters related to the pintle injector design were chosen to investigate how they affect
99
combustion characteristics. In addition, as part of NASA’s Morpheus project, a pintle injector for the liquid
100
oxygen/liquid methane engine of a lunar lander was assembled and combustion tests were completed [6, 7]. At
101
Minas Gerais Federal University in Brazil, various combinations were used to determine injection patterns of radial
102
and annular flows, and the basic spray conditions of a prototype injector for a 1 kN engine [8]. In Germany, effects
103
of pintle injector geometry on combustion and heat load were investigated. Four different pintle injector
104
configurations were fabricated and evaluated for performance [9]. At the Indian Institute of Space Science and
105
Technology, instability growth rate and droplet size were observed when radial and annular flows collided at
106
different momentum ratios [10]. At the University of Tokyo, a combustion chamber applied a pintle injector, and the
107
flame structure and combustion characteristics based on momentum ratios were identified [11, 12]. At China’s
108
National University of Defense Technology, a numerical analysis was performed to investigate effects of pintle
109
injector geometry on the combustion chamber’s internal combustion field. Specifically, combustion characteristics
110
based on characteristic length, pintle opening distance, and pintle length were observed [13]. In Korea, at Chungnam
111
National University, spray patterns and combustion performance were observed for various canted slit type pintle
112
injectors [14-16]. Finally, at Korea Aerospace University, spray characteristics under various conditions were
113
analyzed. In addition, recirculation zone and spray breakup simulations were carried out using a Lagrangian
114
approach to numerical analysis [17-19].
115
Although some recent research has been conducted on pintle injectors many questions and limitations remain.
116
Compared to conventional injectors used in liquid rocket engines, general design procedures for pintle injectors have
117
not been completely assessed. More data on the characteristics of the pintle injector are required, especially in
118
academia. In particular, research on injection area control is needed, but no research related to the orifice area of the
119
annular flow has been completed. The orifice range is important to maintain performance across the entire thrust
120
range.
121
In this study, a pintle injector was designed for 400 N class liquid oxygen/gas methane to obtain optimal design
122
data. A new design was adopted to improve uniformity, and spray characteristics were observed using water and air
123
as simulants with several measurement techniques. Experiments were conducted to obtain the annular flow’s orifice
124
area control range based on atomization performance. Correlations were obtained for spray angle and mean droplet
125
diameter.
126
2. Pintle injector design
127
Table 1
128
Specifications of a 400 N engine. Chamber pressure (MPa) Vacuum thrust (N) O/F Chamber diameter (mm) Throttling level (%) Mass flow rate of liquid oxygen (g/s) Mass flow rate of methane (g/s)
1 400 3.44 54 20 to 100 83.4 24.24
129 130
The target engine of the pintle injector is a 400 N class small thruster that uses liquid oxygen and gaseous
131
methane; Table 1 shows the specifications. The oxygen to fuel mass flow rate ratio (O/F) was set to 3.44, which is
132
typical for a methane engine. Radial flow and annular flow were set as liquid oxygen and gaseous methane,
133
respectively. The chamber diameter was calculated using Eq. (2), related to engine performance factors: .
$ - ∙
134 135 136
/
0∙1 ∗ ∙12 ∙34
(2)
where , , ∗ , , and are combustion chamber diameter, relative flow intensity, characteristic velocity, thrust coefficient, and combustion chamber pressure, respectively. ∗ (associated with combustion efficiency) and
137
(associated with nozzle efficiency) were obtained using NASA CEA code [20]. The thrust control range was set
138
to 20–100%, to achieve 5:1 deep throttling.
139 140 141 142
Fig. 2. Combustor of the pintle injector [21]. Fig. 2 shows several parameters that can determine pintle injector geometry; there were three main design factors,
143
with the first being the ratio of chamber to pintle diameters ( / ). The diameter of the pintle injector was set at 11
144
mm, based on the recommended ratio of diameters 3 to 5 [21]. The second factor was skip distance, defined as the
145
ratio of distance (until the annular flow first collides with the radial flow) to pintle diameter ( / ); its
146
recommended value is one. Previous numerical results showed that combustion efficiency decreased when skip
147
distance was greater or less than one. When the skip distance equaled one, combustion efficiency was the highest
148
[13]. Therefore, skip distance was set to one, and was determined to be 11 mm to the pintle diameter. The third
149
parameter was the blockage factor (BF), defined as the ratio of the circumferential length of the holes or slot at the
150
end of the pintle to the pintle circumference. The BF is presented using Eq. (3), and the meaning of each parameter
151
is shown in Fig. 3 [21, 22].
152
$
67 ∙89 /8:
(3)
153
where and are number of total holes/slot and circumferential length of each hole, respectively. When BF
154
was less than one (i.e., the circumferential length of the holes is smaller than pintle circumference) there were
155
regions where annular and radial flow did not collide. To obtain a uniform spray pattern, a continuous slit type was
156
adopted. In this feature, the holes in Fig. 3 were in ring form and distributed in the pintle circumference direction
157
(Fig. 4). Ideally, the radial flow is uniformly sprayed on all pintle circumferences and forms a thin liquid sheet.
158
Because the BF equals one, all propellants participated in the mixing.
159
160 161
Fig. 3. Multi-hole type pintle geometry [22].
162
163 164
Fig. 4. New concept for maintaining concentricity of a pintle rod.
165 166
An important point in the design of a continuous slit-type injector is maintaining the concentricity of the pintle
167
rod. As shown in Fig. 4, the pintle rod is a moving part that moves axially in the combustion chamber and adjusts
168
the radial flow’s orifice area. If the pintle rod concentricity is not maintained, it will wobble inside the pintle and
169
eventually deteriorate the quality of the spray of the radial flow. This may be caused by the absence of a support for
170
concentricity of the pintle rod or the effect of the radial flow flowing into the pintle. Thus a new concept was applied
171
to maintain concentricity of the pintle rod. To support the concentricity of the pintle rod, a guide wall was enclosed
172
around the pintle rod, shown as red hatched lines in Fig. 4. This guide wall holds the pintle rod such that it does not
173
wobble inside the pintle. This guide wall also eliminates the effects of the flow inside the pintle by independently
174
separating the pintle rod from the inner passage of the radial flow.
175
The guide wall must be firmly fixed; this is achieved by placing several holes in the inlet area where the radial
176
flow enters the pintle, as shown in Section A-A in Fig. 4. In this area, the regions between the holes serve to connect
177
and support the guide wall with the outer wall. The radial flow is initially supplied into the multiple inlet holes, as
178
shown in Section A-A. It then passes through a cylinder region, as shown in Section B-B in Fig. 4, for mixing of the
179
fluids passing through each inlet hole. The cylinder region was placed before exiting the pintle outlet to form a
180
uniform distribution. After passing through the cylinder region, the radial flow through is distributed over the entire
181
circumference of the pintle as shown in Section C-C.
182
Fig. 5 (a) shows the final geometry of the pintle injector. It consisted of a pintle post (the core of the pintle
183
injector, with inner geometry as shown in Fig. 4), three manifolds to uniformly supply flows, pintle rod, and a
184
micrometer head (Mitutoyo MHN1-25MXN, resolution 0.001 mm) to adjust the radial flow’s orifice size. If the
185
geometry changed, each corresponding part could be independently replaced. Fig. 5 (b) shows the distribution plate
186
inserted between the middle and down manifold, which helped to uniformly distribute the annular flow. This plate
187
type was also used in a previous study to uniformly distribute propellant [8].
188 189 190 191 192 193 194 195
Fig. 5. Final geometry of the pintle injector; (a) whole view (b) section view.
196
3. Experimental setups and methods
197
3.1. Experimental conditions
198 199
Fig. 6. Control range with respect to throttling level.
200 201
Spray characteristics were observed at the minimum, mid-range, and maximum throttling levels of 20 60, and
202
100%, respectively. To achieve a deep throttling of 5:1, the differential pressure and the outlet height (H, related to
203
the outlet area of the radial flow) had to be adjusted simultaneously, a method widely used for thrust control. MIRA-
204
150A, a TRW binary propellant rocket engine, also used this mechanism. The injector’s moving part and the flow
205
control valve were mechanically linked to fulfill the desired throttling level [23]. Previous work showed that deep
206
throttling cannot be achieved under constant differential pressure. Therefore, it was necessary to consider
207
differential pressure control and area adjustable systems [24]. Fig. 6 shows the operating range of H according to
208
throttling levels as well as the corresponding mass flow rate and differential pressure. H was adjusted between 0.1
209
and 0.6 mm, a wide operation range that was accounted for when determining the minimum opening. The maximum
210
value of H was determined by considering the cylinder cross-sectional area ( ) inside the pintle injector and the
211
radial flow’s outlet area (, ). These areas are expressed by Eq. (4), and each is shown in Fig. 7. If ,
212
was larger than , the radial flow’s orifice size was fixed to even if H increased. In other words, the
213
variation of the H was meaningless in this range. Therefore, the maximum adjustment value of H was set to 0.6 mm,
214
to control H only for regions where , was less than .
215
$ ;* !! + ! , = , > @ > 0.6 %% , $ ; ∙
(4)
216
where and ! are cylinder inner radius and cylinder outer radius, respectively. H was linearly controlled based
217
on throttling levels. H values at thrust levels of 20, 60, and 100% were 0.1, 0.35, and 0.6 mm, respectively. The
218
mass flow rates corresponding to each H were 16.6, 49.68, and 83.58 g/s, respectively. The differential pressure to
219
satisfy the mass flow rate of each thrust level was also adjusted with H, as shown in Fig. 6.
220 221
Fig. 7. Schematic of a pintle tip.
222 223
The gap distance (G) of the annular flow was related to the orifice size control (Fig. 2). To determine the range
224
of G, spray characteristics were observed at each thrust level. G ranges used are shown in Table 2. The outlet area of
225
the annular flow (, ) is shown in Eq. (5), and the maximum area was set to 185.519 %%! : , $ ; ∙ C ) D
226
(5)
227
In Table 2, a specific G range was chosen for each throttling level to obtain accurate empirical correlations for spray
228
angle and droplet size. The down manifold was manufactured for each G (i.e., G was changed by replacing the down
229
manifold).
230
Table 2
231
Range of gap distance (G). , (%%! ) 185.519 148.252 111.087 73.991 46.414 37.128 26.706 18.177 8.258
232 233
Gap distance G (mm) 3.95 3.3 2.6 1.835 1.21 0.986 0.725 0.503 0.234
234
3.2. Spray imaging
235
Backlight photography was used to obtain the spray image, as shown in Fig. 8. A stroboscope (SUGAWARA
236
MS-230DA model) with a flash duration of 6 μs was used as the backlight. To acquire spray images, a digital
237
camera (Canon EOS 7D, 5184 x 3456 pixels, spatial resolution 47μm/pixel) and a lens (Canon EF 24-70mm) were
238
used. The frozen image was obtained by setting the camera exposure time and flash frequency of the stroboscope to
239
1/30 sec and 30 Hz, respectively. To obtain spray images with the proper depth of field and brightness, the camera
240
was set to f/11 and ISO 1000.
241
For the cold test, water and air were used as simulants for liquid oxygen and methane, respectively. For the
242
liquid, a needle valve was mounted on the feed line to regulate differential pressure. A mass flow meter
243
(KOMETER KTM-800, accuracy ±0.5%) was used to monitor the liquid flow rate, and the gas feed line was
244
equipped with a mass flow controller (MKP TSC-150, accuracy ±0.2%) for flow control between the gas supply
245
system and the manifold. The gas flow rate was adjusted such that O/F was always maintained at 3.44, regardless of
246
thrust.
247 248 249
Fig. 8. Spray imaging apparatus. 3.3. Spray pattern
250
To analyze the degree of uniformity, the spray pattern perpendicular to the spray direction was measured using
251
the optical patternator. This technique has a high spatial resolution and rapid characterization but can contain error
252
sources such as multiple scattering and signal attenuation [25]; error correction were therefore applied. To remove
253
multiple scattering, a two-phase structured laser illumination planar imaging (SLIPI) technique was used. This
254
method extracted a single scattering signal using a modulated laser sheet [26]. The experimental setup consisted of a
255
high-speed dual head laser (Photonics Industries DM20-527DH), SLIPI optics module (LaVision), and CMOS high-
256
speed camera (Photron FASTCAM SA5, 1024 x 1024 pixels) with a lens (AF MICRO NIKKOR 105 mm). The
257
camera was set to f/5.6 with an image rate of 3 kHz, and 300 images were obtained for each experiment condition.
258
The modulated laser sheet position was 7 mm from the end of the pintle rod in the axial direction, taking into
259
consideration the diameter of the small combustion chamber and field of view. An example of the spray pattern
260
obtained through the experimental setup is shown in Fig. 9, an averaged image at a throttling level of 20% and G of
261
0.986 mm.
262 263
Fig. 9. Spray pattern from the optical patternator with SLIPI.
264 265
To deal with signal attenuation, a compensation method proposed by Abu-Gharbieh et al. (2000) was used. This
266
method was based on the Beer-Lambert law and compensated for each pixel by applying a compensating algorithm
267
in a discrete way, as shown in Eq. (6): UV
" N $ " ∙ OPQRS ∙ ∑UWX "UN Y
268
(6)
269
where " N and " are compensated and observed pixel intensity, respectively, and is a balance value that
270
minimizes the difference between the right and left image averages. The detailed process to develop Eq. (6) was
271
presented in a previous study [27].
272 273 274
275
3.4. Droplet size
276
Droplet size is an important index of injector atomization characteristics and affects combustion efficiency [27].
277
Especially for the pintle injector, it was necessary to maintain droplet size throughout the entire thrust range to
278
achieve a certain atomization efficiency. To observe droplet size, an experimental apparatus consisted of the high
279
speed camera used in the optical patternator, a long distance microscope (LaVision QM1) with a magnification lens
280
x2.0, and the stroboscope. The spatial resolution 4.59μm/pixel, and 200 images were taken per case. Droplet size
281
was measured at a point 20 mm from the pintle tip in the axial direction to the outline of the spray field.
282
283 284
Fig. 10. Image processing for droplet size measurement.
285 286
Fig. 10 shows the image processing procedure used to measure droplet size. The raw image taken by the camera
287
was recorded in grayscale, and the optimal threshold was calculated based on Otsu’s method. In the resulting binary
288
image, droplets were clearly visible apart from the background. The spray image contained background errors such
289
as dust on the detector. To eliminate these errors, a background image taken without spraying was also binarized and
290
then subtracted from the spray image. In the last step, droplets in the image boundary were excluded. Non-circular
291
droplets were removed based on the ratio of a minor axis length to a major axis length. This processing was
292
performed for each image and diameters were judged based on the ratio of the extracted from 200 images per
293
experimental case.
294
To analyze droplet size, the Sauter mean diameter (SMD) was used. The SMD, also called Z! , is expressed in
295
Eq. (7) as a ratio of volume to surface, and is a representative diameter that reflects evaporation rate and combustion
296
reaction [28]: ∑ 6[ ∙8[\
"# $ ∑
297
6[ ∙8[]
298
where and are the number of droplets and the middle diameter in size range ^, respectively.
299
4. Results and discussion
300
4.1. Spray structure
301 302 303
Fig. 11. Spray images with various throttling levels and gap distances.
(7)
304
Fig. 11 shows spray images for all experimental conditions. The breakup process was classified into two types: (i)
305
atomization immediately after collision of the radial and annular flows and (ii) droplets split from a liquid sheet after
306
collision. The second type was observed when the throttling level was 20% and the G was greater than 1.835 mm.
307
To set the criterion for dividing the two breakup mechanisms, momentum flux ratio (J) and Weber number (We) for
308
two-phase flow, defined as Eq. (8) and Eq. (9), respectively:. $
309 fO $
310
] _`[a ∙b`[a
] _cde ∙bcde
(8) ]
_cde ∙Cbcde Vb`[a D ∙ g`[a
(9)
311
where hi , h 0 , (i , ( 0 and j 0 are gas density, liquid density, gas velocity, liquid velocity, and liquid
312
surface tension, respectively. The characteristic length of the pintle injector was defined as H. Results confirmed that
313
the second breakup type occurred when J was greater than 6.4 and We was less than 4.13. In this region, there was a
314
specific breakup length and droplet size was relatively large. That is, atomization efficiency was relatively low, and
315
accounting for the small thruster, combustion efficiency can be adversely affected. This again illustrated that annular
316
flow orifice size control was important to optimum spray performance. To obtain optimum injector parameters,
317
spray characteristics were therefore analyzed except for this region.
318
For the first breakup type, the typical atomization process is shown in Fig. 12. After the thin liquid sheet in the
319
radial direction collided with the annular flow, a wave was generated by aerodynamic force, leading to the
320
disconnection of the liquid sheet. Furthermore, a liquid lump fell out of the end of the liquid sheet and then split into
321
smaller droplets.
322
323 324 325
Fig. 12. Atomization process.
326
To obtain the spray angle, 50 images were averaged for each case. The spray angle decreased with decreasing G
327
(Fig. 11), explained by total momentum ratio (TMR), which is closely related to the spray angle formation of the
328
pintle injector [21, 29]. TMR is defined in Eq. (10) and is expressed as the ratio of momentum of radial to annular
329
flows.
330
*m& ∙b,ndo[d`
k#l $ *m∙&b,
dppq`dn
(10)
331
At each throttling level, mass flow rates of the radial and annular flows were fixed. In addition, because H
332
associated with the radial flow orifice size was constant at each level, the radial flow momentum was fixed. As G
333
decreased, the annular flow’s orifice size also decreased while annular flow velocity increased. As a result, as G
334
decreased, annular flow momentum intensified and spray angle decreased.
335
336 337 338
Fig. 13. Relationship between spray angle and (a) total momentum ratio (rst) (b) the new dimensionless number, u = rst ∙ *v/w,.
339 340
Fig. 13 (a) shows that spray angle was proportional to TMR. When G was the same, the spray angles at all
341
throttling levels were nearly identical. From the perspective of TMR, it can be expressed as k#l ∝ y*V , under
342
conditions where G is the same in the entire throttling range. In other words, points with the same spray angle had
343
different TMRs. This is because H changes linearly with throttling level. Therefore, if the throttling level decreases
344
under the same G condition, TMR increases. For this characteristic, there was a gap (Fig. 13a) such that only the
345
correlation between the spray angle and TMR was expressed. Therefore, a new dimensionless number was defined to
346
represent spray angle tendency within the overall thrust range. Fig. 13 (b) shows spray angle tendency with a new
347
dimensionless number (N), defined by Eq. (11), which is the ratio of H to G in the TMR.
$ k#l ∙ */,
348
(11)
349
For N, it can be expressed as ∝ y*,. That is, if G is the same, the value of N is also constant
350
the throttling level. This allows the same spray angles to have one N and eliminates the gap that was observed
351
between the throttling levels in TMR and spray angle relationships. As a result, it can be expressed as one correlation
352
having a proportional relationship, such as the relationship between G and spray angle. The correlation between N
353
and spray angle (Fig. 13b) was defined as Eq. (12), with R2 = 0.98. This empirical equation will be used to predict
354
the spray angle in future spray conditions. "Q z{ z|}~O $ +177.83 ) 16007.17
355
356
irrespective of
(12)
4.2. Spray uniformity
357
Using the error correction methods discussed in Section 3.3, spray uniformity was analyzed. Experiments were
358
conducted for regions with G greater than 0.986 mm. When the throttling level was 20%, the second breakup type
359
was excluded, as mentioned in Section 4.1. To determine uniformity degree, a Patternation Index (PI) and Spray
360
Uniformity Index (SUI) were defined by Eq. (13) and Eq. (14), respectively:
362
e e
× 100
(13)
where | and are the number of sectors and intensity of the image per sector, respectively, and " $ ∑W *{ + {,!
363 364
e
*%, $ ∑W + ∑p
361
where { ≡ ∑p
e
e e /
and { ≡
/!
(14)
∑p e e
365
The PI and SUI represented spray symmetry, and circumferential uniformity and standard deviation of the spray
366
distribution [25, 30, 31]. Results of the spray uniformity analysis are shown in Fig. 14. PI, by definition, has a value
367
from zero to 200, and spray uniformity is higher with lower PI. PI and SUI averaged 20% and 0.26, respectively. In
368
addition, the standard deviations (σ) were 3.62% and 0.04 respectively. From the perspective of SUI, the standard
369
deviation appeared to be very small and this meant that the spray uniformity was almost constant irrespective of the
370
gap distance and the throttling level. When the spray uniformity associated with PI was expressed as a percentage,
371
and assuming that 100% was the ideal uniform distribution, the mean value of the spray uniformity from the PI data
372
was 90%. As an extension of this, the standard deviation of PI data was 1.81%. In this study, when the spray
373
uniformity was more than 90%, based on the average value of PI, and the standard deviation is within 5%, the
374
quality of the injector was considered suitable for experiments.
375 376
Fig. 14. Spray uniformity based on (a) Patternation Index (PI) and (b) Spray Uniformity Index (SUI).
377 378
4.3. Sauter mean diameter (SMD)
379
For the SMD analysis, J and We were selected. Fig. 15 shows SMD trend based on each dimensionless number,
380
and indicates that both were related to SMD. For the pintle injector, the first breakup was a vertical collision like a
381
jet in crossflow. At this time, liquid sheet breakup was caused by the transfer of gas momentum. In addition,
382
breakup was sustained by shear force due to the velocity difference between the radial and annular flows. Overall, it
383
seemed that complex mechanisms act on breakup.
384
385 386 387
Fig. 15. Relationship between SMD and: (a) momentum flux ratio () and (b) weber number ().
388
In Eq. (8), when G decreases, the velocity of gas (annular flow) increases, so that the momentum flux of the gas
389
corresponding to the denominator of J becomes relatively strong. Thus, J also decreases as G decreases. In other
390
words, it means that gas momentum transfer, which affects the liquid sheet, generally increased. Therefore, SMD
391
decreased proportionally as J decreased. For We, when G decreases at each throttling level, the velocity of gas
392
increases; thus, the force corresponding to the numerator of We becomes relatively strong from Eq. (9). Namely, it
393
indicates that relative velocity and the deforming force due to the shear force was intensified. Therefore, We and
394
SMD were inversely proportional to each other.
395
396
Fig. 16. Relationship between new parameter, = V. ∙ . and s.
397 398 399
To investigate which of the two dimensionless numbers had a greater impact on droplet formation, an empirical
400
correlation was derived. Fig. 16 shows the result, where Eq. (15) is the final correlation with R2 = 0.96. In Fig. 16,
401
the new parameter (P) on the x-axis is represented by VX.Z ∙ fO X.X in Eq. (15).
402
"# $ +111.45 ~|*VX.Z ∙ fO X.X , ) 490.12
403
Eq. (15) can also be expressed as Eq. (16), in which momentum transfer during the vertical collision of two flows
404
has a greater effect than the shear force in droplet formation. This was likely because the pintle injector created an
405
interaction between radial and annular flow. The correlation will be used to estimate the optimal G to obtain the
406
desired SMD.
407 408 409
"# $ 103.65 ~|*, + 5.57~| *fO, ) 490.12
(15)
(16)
410
4.4. Relationship between spray angle and SMD
411
412
Fig. 17. Relationship between spray angle and s.
413 414 415
Fig. 17 shows the relationship between spray angle and SMD for G at each throttling level. Spray angle and SMD
416
had a linear relationship at each throttling level. When G was fixed, the spray angle was almost constant in the
417
whole thrust range. This is because, as described in Section 4.1, the spray angle changed according to G irrespective
418
of the throttling level. In addition, since G and the spray angle were proportional, the spray angle tended to increase
419
when G increased. On the other hand, SMD was different at each throttling level when G was fixed. For example,
420
when G was fixed at 0.986 mm, SMD at the 100, 60, and 20% throttling levels were 114.17, 227.12, and 493.20 μm,
421
respectively. This is because SMD was related not only to G but also to several factors associated with the throttling
422
level as shown in Eq. (16). When the throttling level was lowered under the fixed condition of G, SMD increased
423
with J increased and We decreased. This study focused on atomization performance, so the control range of G to
424
maintain constant SMD at all thrust levels was estimated and discussed in Section 4.5.
425
4.5. Variations in G and spray angle with SMD
426
The control range of G with constant SMD was obtained from an empirical equation (Section 4.3). In addition,
427
spray angle variation at the same time was estimated by Eq. (12). To analyze the resulting variations, three cases
428
(SMD = 100, 150, and 200 μm) were selected as examples based on ranges typically used in a liquid rocket engine
429
[32].
430
Fig. 18. Variation ranges (constant s) of (a) gap distance and (b) spray angle.
431 432 433
Fig. 18 (a) shows the control range of G required to maintain the corresponding SMD. When SMD was constant,
434
the throttling level and G were linearly related. This indicated that the annular flow orifice area could be linearly
435
controlled based on throttling level. For radial flow, mass flow rate and H also had a linear relationship that
436
controlled outlet area. Therefore, the orifice sizes of radial and annular flows could be adjusted linearly for thrust
437
control. In addition, as the target SMD became smaller, the overall control range scale decreased. This is because G
438
must be further reduced in order to produce smaller droplets because the gas momentum flux and deforming force
439
must be stronger through increasing the gas velocity.
440
Fig. 18 (b) shows the variation range of the spray angle when G in the corresponding SMD was controlled (Fig.
441
18a). Spray angle also changed linearly with throttling level, and when the target SMD decreased, the change range
442
decreased. This is associated with the results in Fig. 18 (a), because the gas momentum was enhanced when G
443
became smaller as SMD decreased. Results of this study can help predict the G control range to maintain SMD and
444
spray angle variation. Furthermore, these data will be used to develop a control system for the radial and the annular
445
flows.
446
5. Conclusions
447
In this study, a pintle injector for a 400 N small liquid rocket engine was designed and research was conducted to
448
derive optimal design parameters. The developed pintle injector adopted the continuous slit type to achieve a
449
uniform spray pattern. In addition, the new design concept maintained the concentricity of the pintle rod. The
450
primary focus was the control range of the annular flow’s orifice area. For this, gap distance related to the annular
451
flow’s orifice area was selected as a representative parameter, various down manifolds were fabricated, and spray
452
characteristics were observed by replacing the down manifold at each thrust level. Spray angle was linearly related
453
to the total momentum ratio. As gap distance decreased under a fixed flow rate condition, the annular flow
454
momentum intensified due to the increased annular flow velocity, which in turn decreased the total momentum ratio
455
and narrowed spray angle. A new dimensionless number, which had a high correlation with spray angle throughout
456
the thrust range, was defined by introducing the ratio of outlet height associated with the radial flow’s outlet area to
457
gap distance in the total momentum ratio, and a correlation equation was subsequently developed. The Sauter mean
458
diameter was related to both momentum flux ratio and Weber number. It was also confirmed that momentum flux
459
ratio associated with momentum transfer had a greater effect on droplet formation. From the spray characteristics
460
results, the gap distance control range to maintain a constant Sauter mean diameter over the entire thrust range was
461
calculated based on atomization efficiency. Furthermore, the gap distance was linearly controlled by throttling level.
462
In the future, when spray characteristics are set for a target engine, these results will be of reference to estimate
463
the control range for the annular flow’s orifice size. The procedures and results of this study can be applied to a
464
linear control system for simultaneous control of the orifice sizes for radial and annular flows. Thus, an optimal
465
throttleable pintle injector with high atomization efficiency can be realized.
466
Acknowledgments
467
This work was supported by Advanced Research Center Program (NRF-2013R1A5A1073861) through the
468
National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) contracted through
469
Advanced Space Propulsion Research Center at Seoul National University and by the National Research Foundation
470
of Korea(NRF) grant funded by the Korea government(MSIP) (2019M1A3A1A02076963).
471
References
472
[1] M. J. Casiano, J. R. Hulka, V. Yang, Liquid-propellant rocket engine throttling: a comprehensive review, J. Propul. Power,
473 474 475
26 (5) (2010) 897-923. [2] G. A., Dressler, J. M. Bauer, TRW pintle engine heritage and performance characteristics, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Huntsville, AL, 2000.
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[3] D. T. Harrje, Liquid propellant rocket combustion instability, NASA, NASA-SP-194, 1972.
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[4] E. Seedhouse, SpaceX - making commercial spaceflight a reality, Springer, New York, 2013.
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[5] J. M. Gromski, A. N. Majamaki, S. G. Chianese, V. D. Weinstock, T. S. Kim, Northrop Grumman TR202 LOX/LH2 deep
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throttling engine technology project status," 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Nas
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hville, TN, 2010.
481 482 483 484 485 486 487 488 489 490
[6] B. L. Austin, S. D. Heister, W. E. Anderson, Characterization of pintle engine performance for nontoxic hypergolic biprope llants, J. Propul. Power, 21 (4) (2005) 627-635. [7] M. J. Bedard, T. W. Feldman, A. Rettenmaier, W. Anderson, Student design/build/test of a throttleable LOX-LCH4 thrust chamber, 48th AIAA/SAE/ASEE Joint Propulsion Conference & Exhibit, Atlanta, Ga., 2012. [8] R. N. Rezende, A. Pimenta, V. C. Perez, Experiments with pintle injector design and development," 51th AIAA/SAE/ASE E Joint Propulsion Conference, Orlando, FL, 2015. [9] B. B. Vasques, O. J. Haidn, “Effect of pintle injector element geometry on combustion in a liquid oxygen/liquid methane rocket engine, 7th European Conference for Aeronautics and Aerospace Sciences, Milan, Italy, 2017. [10] S. Ninish, A. Vaidyanathan, K. Nandakumar, Spray characteristics of liquid-liquid pintle injector, Exp. Therm. Fluid Sci., 97 (2018) 324-340.
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[11] K. Sakaki, H. Kakudo, S. Nakaya, M. Tsue, H. Isochi, K. Suzuki, K. Makino, T. Hiraiwa, Optical measurements of ethanol/li
492
quid oxygen rocket engine combustor with planar pintle injector, 51th AIAA/SAE/ASEE Joint Propulsion Conference,
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Orlando, FL, 2015.
494 495 496 497 498 499 500 501
[12] K. Sakaki, T. Funahashi, S. Nakaya, M. Tsue, R. Kanai, K. Suzuki, T. Inagawa, T. Hiraiwa, Longitudinal combustion instabi lity of a pintle injector for a liquid rocket engine combustor, Combust. Flame, 194 (2018) 115-127. [13] X. Fang, C. Shen, Study on atomization and combustion characteristics of LOX/methane pintle injectors, Acta Astronaut. 136 (2017) 369-379. [14] H. Ryu, I. Yu, T. Kim, Y. Ko, S. Kim, H. Kim, Combustion performance of the canted slit type pintle injector rocket engine by blockage factor, Proceedings of the Korean Society of Propulsion Engineers Conference, Jeju, Korea, 2016. [15] I. Yu, S. Kim, Y. Ko, S. Kim, J. Lee, H. Kim, Combustion performance of a pintle injector rocket engine with canted slit shape by characteristic length and total momentum ratio, J. Korean Soc. Propuls. Eng., 21 (1) (2017) 36-43.
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[16] S. Kim, W. Kim, T. Kim, Y. Ko, S. Kim, H. Kim, Analysis on combustion phenomena by spray pattern of
503
canted slit type pintle injector, Proceedings of the Korean Society of Propulsion Engineers Conference, Jeju,
504
Korea, 2016.
505 506 507 508 509 510 511 512 513
[17] M. Son, K. Yu, J. Koo, O. C. Kwon, J. S. Kim, Injection condition effects of a pintle injector for liquid rocket engines on atomization performances, J. ILASS-Korea, 20 (2) (2015) 114-120. [18] M. Son, K. Radhakrishnan, Y. Yoon, J. Koo, Numerical study on the combustion characteristics of a fuel-centered pintle i njector for methane rocket engines, Acta Astronaut. 135 (2017) 139-149. [19] K. Radhakrishnan, M. Son, K. Lee, J. Koo, Lagrangian approach to axisymmetric spray simulation of pintle injector for li quid rocket engines,” Atomization Spray., 28 (5) (2018) 443-458. [20] S. Gordon, B. J. McBride, Computer program for calculation of complex chemical equilibrium compositions and applications Ⅱ. users manual and program description, NASA Reference Publication 1311, E-8017-1, 1996. [21] N. Ashgriz, Handbook of Atomization and Sprays, Springer, New York, 2011.
514 515 516 517 518 519 520 521 522 523 524 525
[22] S. Lee, J. Koo, Y. Yoon, Technology and developing trends of pintle injector for throttleable engine, J. Korean Soc. Propuls. Eng., 21 (4) (2017) 107-118. [23] R. J. Johnson, B. R. Boyd, T. H. Smith, Application of the Mira 150A variable-thrust engine to manned lunar flying systems, J. Spacecraft Rockets, 5 (7) (1968) 849-851. [24] S. Park, J. Nam, K. Lee, J. Koo, Y. Hwang, Prediction on throttling performance of a movable sleeve injector for deep throttling, J. Korean Society for Aeronautical and Space Sciences, 46 (6) (2018) 487-495. [25] Y. Yoon, H. Koh, D. Kim, T. Khil, Spray visualization using laser diagnostics, J. Korean Society of Visualization, 3 (2) (2005) 3-13. [26] M. Storch, Y. N. Mishra, M. Koegl, E. Kristensson, S. Will, L. Zigan, E. Berrocal, Two-phase SLIPI for instantaneous LIF and Mie imaging of transient fuel sprays, Opt. Lett., 41 (23) (2016) 5422-5425. [27] R. Abu-Gharbieh, J. L. Persson, M. Försth, A. Rosén, A. Karlström, T. Gustavsson, Compensation method for attenuated planar laser images of optically dense sprays, Appl. Optics, 39 (8) (2000) 1260-1267.
526
[28] H. L. Arthur, Atomization and sprays, Hemisphere Publishing Corporation, New York, 1989.
527
[29] S. Lee, J. Koo, Y. Yoon, Technology and developing trends of pintle injector for throttleable engine, J. Korean
528
Soc. Propuls. Eng., 21 (4) (2017) 107-118.
529
[30] R. W. Tate, Spray patternation, J. Ind. Eng. Chem., 52 (10) (1960) 49A-58A.
530
[31] Y. Cao, The image analysis for optical Spray patternation, M.S. Thesis, Queen’s University, 2000.
531
[32] Х. В. Кесаев,Расчёт форсунок двигателя В.Д.Курпатенков, Publishing House MAI, Moscow, 1987.
Table 1 Specifications of a 400 N engine. Chamber pressure (MPa) Vacuum thrust (N) O/F Chamber diameter (mm) Throttling level (%) Mass flow rate of liquid oxygen (g/s) Mass flow rate of methane (g/s)
1 400 3.44 54 20 to 100 83.4 24.24
Table 2 Range of gap distance (G). ܣ,௨ (݉݉ଶ ) 185.519 148.252 111.087 73.991 46.414 37.128 26.706 18.177 8.258
Gap distance G (mm) 3.95 3.3 2.6 1.835 1.21 0.986 0.725 0.503 0.234
Fig. 1. Conceptual diagram of a pintle injector.
Fig. 10. Image processing for droplet size measurement.
Fig. 11. Spray images with various throttling levels and gap distances.
Fig. 12. Atomization process.
Fig. 13. Relationship between spray angle and (a) total momentum ratio () (b) the new dimensionless number, = ∙ / .
Fig. 14. Spray uniformity based on (a) Patternation Index (PI) and (b) Spray Uniformity Index (SUI).
Fig. 15. Relationship between SMD and: (a) momentum flux ratio (ࡶ) and (b) weber number (ࢃࢋ).
Fig. 16. Relationship between new parameter, = . ∙ . and .
Fig. 17. Relationship between spray angle and ࡿࡹࡰ.
Fig. 18. Variation ranges (constant ࡿࡹࡰ) of (a) gap distance and (b) spray angle.
Fig. 2. Combustor of the pintle injector [21].
Fig. 3. Multi-hole type pintle geometry [22].
Fig. 4. New concept for maintaining concentricity of a pintle rod.
Fig. 5. Final geometry of the pintle injector; (a) whole view (b) section view.
Fig. 6. Control range with respect to throttling level.
Fig. 7. Schematic of a pintle tip.
Fig. 8. Spray imaging apparatus.
Fig. 9. Spray pattern from the optical patternator with SLIPI.
Highlights • • • • •
New design concept for a pintle injector was introduced to improve uniformity in a 400 N class liquid rocket engine Spray tests helped find the control range of the annular flow’s orifice area An appropriate correlation equation was developed for the parameters The control range was estimated using empirical correlations with respect to the degree of atomization A database for linear control system design was established
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0094-5765(19)31385-2
DOI:
https://doi.org/10.1016/j.actaastro.2019.11.008
Reference:
AA 7753
To appear in:
Acta Astronautica
Received Date: 25 June 2019 Revised Date:
26 October 2019
Accepted Date: 2 November 2019
Please cite this article as: S. Lee, D. Kim, J. Koo, Y. Yoon, Spray characteristics of a pintle injector based on annular orifice area, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.11.008. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd on behalf of IAA.
1 2
3 4 5 6 7 8 9 10 11 12
Spray characteristics of a pintle injector based on annular orifice area Suji Lee1, Daehwan Kim1, Jaye Koo2, and Youngbin Yoon3,* 1 Graduate Student, Department of Mechanical and Aerospace Engineering, Seoul National University, 1 Gwanakro, Gwanak-gu, Seoul, 08826, Republic of Korea 2 Professor, School of Aerospace and Mechanical Engineering, Korea Aerospace University, 76, Hanggongdaehakro, Deogyang-gu, Goyang-si, Gyeonggi-do, 10540, Republic of Korea 3 Professor, Department of Mechanical and Aerospace Engineering and the Institute of Advanced Aerospace Technology, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea * Address all correspondence to Youngbin Yoon, E-mail: [email protected].
13
14
As interest in low-cost reusable launch vehicles and extraterrestrial exploration has
15
increased in recent years, soft-landing techniques have become important. A pintle injector
16
can help realize this because it is capable of thrust control. However, research on this topic is
17
very limited, and general optimization design procedures have not been completely
18
established. In particular, no studies have examined orifice adjustment for annular flow,
19
which is important in thrust control. In this study, a new design concept for a pintle injector
20
is presented specifically to improve spray uniformity in a 400 N class engine; this maintains
21
the concentricity of the pintle rod associated with the radial flow’s orifice size. The primary
22
focus here was on spray tests that were conducted to obtain the control range of the orifice
23
area for annular flow. Spray characteristics such as spray angle, spray uniformity, and
24
droplet size were analyzed, from which empirical correlations were derived. Finally, the
25
optimum control range for the annular flow’s orifice area was estimated from the
26
perspective of atomization performance. This can be of reference to develop an enhanced
27
thrust control system.
28 29
Keywords: Throttleable liquid rocket engine, Pintle injector, Annular orifice area, Spray characteristics
30 31 32 33 34 35 36 37 38 39 40 41 42 43
Nomenclature
,
,
∗
Cylinder cross-sectional area Annular flow’s outlet area Radial flow’s outlet area Blockage factor Characteristic velocity Thrust coefficient Combustion chamber diameter Circumferential length of each hole Pintle diameter Rocket thrust Gap distance Outlet height Momentum flux ratio
44
Distance until annular flow first collides with radial flow
45
N
New dimensionless number
46
Number of total holes/slot
47
O/F
Oxygen to fuel mass flow rate ratio
48
P
New parameter
49
Combustion chamber pressure
50 51 52 53
!
Patternation index Relative flow intensity Cylinder inner radius Cylinder outer radius
54
"#
Sauter mean diameter
55
SUI
Spray uniformity index
56
TMR
Total momentum ratio
57
We
Weber number
58 59
1. Introduction
60
requirement for commercial launch services. Consequently, interest in developing reusable launch vehicles has
61
quickly increased in countries around the world. Planetary exploration for future energy sources has also attracted
62
attention. Soft landing technology is a key factor in reusable launchers and extrasolar planet exploration. A
63
throttleable rocket engine is an important technology that can help accomplish this mission, so extensive research is
64
required.
With the recent growth of the private space rocket market, price competitiveness has become an important
65
There are several ways to control thrust, including changing the propellant’s type or composition and adjusting
66
the area of the nozzle throat or nozzle exit. However, these approaches are difficult to control due to physical
67
limitations and high heat flux concentrated in the nozzle throat. In contrast, controlling the propellant flow rate is
68
regarded as the simplest method. The relationship between rocket thrust and propellant flow rate is defined by Eq.
69
(1):
70
$ %& ∙ ( ) ∙ * + ,
(1)
71
where , %&, ( , , , and are rocket thrust, propellant flow rate, nozzle exit velocity, exit area, exit pressure,
72
and free stream pressure, respectively. There are various ways to adjust flow rate, such as controlling differential
73
pressure or using a dual manifold, but the area control method is considered to be the most promising [1].
74 75
Fig. 1. Conceptual diagram of a pintle injector.
76 77
A pintle injector is a representative area control method and has the structure to control thrust. The propellant
78
flow rate is regulated by adjusting the injector orifice size using a specific moving device. Fig. 1 shows the basic
79
concept of the pintle injector, in which an area adjusting sleeve moves in the axial direction to control the propellant
80
orifice size. Fuel is injected in the axial direction of the combustion chamber in the form of annular flow along the
81
injector’s outer wall. The oxidizer flows into the pintle injector and forms a thin sheet in the radial direction through
82
the gap between the pintle and the sleeve. Propellants injected in the axial and radial directions collide with each
83
other at the end of the pintle, allowing mixing and atomization to proceed.
84
This pintle injector has several characteristics. First, it can control thrust and has consistent high performance
85
over a wide thrust range. Second, it is simple, allowing for cost and weight savings. For swirl or jet injectors
86
typically used in liquid rocket engines, multiple injectors are mounted on one plate. However, only one pintle
87
injector is required regardless of thrust, which can have a large range. Consequently, cost and weight can be reduced.
88
The third characteristic is combustion stability, as the pintle injector has recirculation zones around the injector.
89
Because the recirculation zone at the center of the combustion chamber acts as a deflector and mixer for unburned
90
droplets, it has a positive effect on combustion stability and performance [2, 3].
91
The pintle injector concept was first devised by TRW in the United Sates, and it was applied to the Apollo Lunar
92
Descent Engine (LMDE) in the 1960s. Since the early 2000s, pintle injector research has been carried out in industry
93
and academia. SpaceX applied the pintle injector used in the LMDE to the Merlin engine to develop a reusable
94
vehicle to reduce launch costs [4]. Northrop Grumman developed a TR202 prototype engine aimed at developing a
95
variable thrust rocket engine for future NASA take-offs and landings. The combustion characteristics were observed
96
through a 10:1 throttling level combustion test [5].
97
At Purdue University, a pintle injector for non-toxic bipropellants was developed and a combustion test was
98
performed. Several parameters related to the pintle injector design were chosen to investigate how they affect
99
combustion characteristics. In addition, as part of NASA’s Morpheus project, a pintle injector for the liquid
100
oxygen/liquid methane engine of a lunar lander was assembled and combustion tests were completed [6, 7]. At
101
Minas Gerais Federal University in Brazil, various combinations were used to determine injection patterns of radial
102
and annular flows, and the basic spray conditions of a prototype injector for a 1 kN engine [8]. In Germany, effects
103
of pintle injector geometry on combustion and heat load were investigated. Four different pintle injector
104
configurations were fabricated and evaluated for performance [9]. At the Indian Institute of Space Science and
105
Technology, instability growth rate and droplet size were observed when radial and annular flows collided at
106
different momentum ratios [10]. At the University of Tokyo, a combustion chamber applied a pintle injector, and the
107
flame structure and combustion characteristics based on momentum ratios were identified [11, 12]. At China’s
108
National University of Defense Technology, a numerical analysis was performed to investigate effects of pintle
109
injector geometry on the combustion chamber’s internal combustion field. Specifically, combustion characteristics
110
based on characteristic length, pintle opening distance, and pintle length were observed [13]. In Korea, at Chungnam
111
National University, spray patterns and combustion performance were observed for various canted slit type pintle
112
injectors [14-16]. Finally, at Korea Aerospace University, spray characteristics under various conditions were
113
analyzed. In addition, recirculation zone and spray breakup simulations were carried out using a Lagrangian
114
approach to numerical analysis [17-19].
115
Although some recent research has been conducted on pintle injectors many questions and limitations remain.
116
Compared to conventional injectors used in liquid rocket engines, general design procedures for pintle injectors have
117
not been completely assessed. More data on the characteristics of the pintle injector are required, especially in
118
academia. In particular, research on injection area control is needed, but no research related to the orifice area of the
119
annular flow has been completed. The orifice range is important to maintain performance across the entire thrust
120
range.
121
In this study, a pintle injector was designed for 400 N class liquid oxygen/gas methane to obtain optimal design
122
data. A new design was adopted to improve uniformity, and spray characteristics were observed using water and air
123
as simulants with several measurement techniques. Experiments were conducted to obtain the annular flow’s orifice
124
area control range based on atomization performance. Correlations were obtained for spray angle and mean droplet
125
diameter.
126
2. Pintle injector design
127
Table 1
128
Specifications of a 400 N engine. Chamber pressure (MPa) Vacuum thrust (N) O/F Chamber diameter (mm) Throttling level (%) Mass flow rate of liquid oxygen (g/s) Mass flow rate of methane (g/s)
1 400 3.44 54 20 to 100 83.4 24.24
129 130
The target engine of the pintle injector is a 400 N class small thruster that uses liquid oxygen and gaseous
131
methane; Table 1 shows the specifications. The oxygen to fuel mass flow rate ratio (O/F) was set to 3.44, which is
132
typical for a methane engine. Radial flow and annular flow were set as liquid oxygen and gaseous methane,
133
respectively. The chamber diameter was calculated using Eq. (2), related to engine performance factors: .
$ - ∙
134 135 136
/
0∙1 ∗ ∙12 ∙34
(2)
where , , ∗ , , and are combustion chamber diameter, relative flow intensity, characteristic velocity, thrust coefficient, and combustion chamber pressure, respectively. ∗ (associated with combustion efficiency) and
137
(associated with nozzle efficiency) were obtained using NASA CEA code [20]. The thrust control range was set
138
to 20–100%, to achieve 5:1 deep throttling.
139 140 141 142
Fig. 2. Combustor of the pintle injector [21]. Fig. 2 shows several parameters that can determine pintle injector geometry; there were three main design factors,
143
with the first being the ratio of chamber to pintle diameters ( / ). The diameter of the pintle injector was set at 11
144
mm, based on the recommended ratio of diameters 3 to 5 [21]. The second factor was skip distance, defined as the
145
ratio of distance (until the annular flow first collides with the radial flow) to pintle diameter ( / ); its
146
recommended value is one. Previous numerical results showed that combustion efficiency decreased when skip
147
distance was greater or less than one. When the skip distance equaled one, combustion efficiency was the highest
148
[13]. Therefore, skip distance was set to one, and was determined to be 11 mm to the pintle diameter. The third
149
parameter was the blockage factor (BF), defined as the ratio of the circumferential length of the holes or slot at the
150
end of the pintle to the pintle circumference. The BF is presented using Eq. (3), and the meaning of each parameter
151
is shown in Fig. 3 [21, 22].
152
$
67 ∙89 /8:
(3)
153
where and are number of total holes/slot and circumferential length of each hole, respectively. When BF
154
was less than one (i.e., the circumferential length of the holes is smaller than pintle circumference) there were
155
regions where annular and radial flow did not collide. To obtain a uniform spray pattern, a continuous slit type was
156
adopted. In this feature, the holes in Fig. 3 were in ring form and distributed in the pintle circumference direction
157
(Fig. 4). Ideally, the radial flow is uniformly sprayed on all pintle circumferences and forms a thin liquid sheet.
158
Because the BF equals one, all propellants participated in the mixing.
159
160 161
Fig. 3. Multi-hole type pintle geometry [22].
162
163 164
Fig. 4. New concept for maintaining concentricity of a pintle rod.
165 166
An important point in the design of a continuous slit-type injector is maintaining the concentricity of the pintle
167
rod. As shown in Fig. 4, the pintle rod is a moving part that moves axially in the combustion chamber and adjusts
168
the radial flow’s orifice area. If the pintle rod concentricity is not maintained, it will wobble inside the pintle and
169
eventually deteriorate the quality of the spray of the radial flow. This may be caused by the absence of a support for
170
concentricity of the pintle rod or the effect of the radial flow flowing into the pintle. Thus a new concept was applied
171
to maintain concentricity of the pintle rod. To support the concentricity of the pintle rod, a guide wall was enclosed
172
around the pintle rod, shown as red hatched lines in Fig. 4. This guide wall holds the pintle rod such that it does not
173
wobble inside the pintle. This guide wall also eliminates the effects of the flow inside the pintle by independently
174
separating the pintle rod from the inner passage of the radial flow.
175
The guide wall must be firmly fixed; this is achieved by placing several holes in the inlet area where the radial
176
flow enters the pintle, as shown in Section A-A in Fig. 4. In this area, the regions between the holes serve to connect
177
and support the guide wall with the outer wall. The radial flow is initially supplied into the multiple inlet holes, as
178
shown in Section A-A. It then passes through a cylinder region, as shown in Section B-B in Fig. 4, for mixing of the
179
fluids passing through each inlet hole. The cylinder region was placed before exiting the pintle outlet to form a
180
uniform distribution. After passing through the cylinder region, the radial flow through is distributed over the entire
181
circumference of the pintle as shown in Section C-C.
182
Fig. 5 (a) shows the final geometry of the pintle injector. It consisted of a pintle post (the core of the pintle
183
injector, with inner geometry as shown in Fig. 4), three manifolds to uniformly supply flows, pintle rod, and a
184
micrometer head (Mitutoyo MHN1-25MXN, resolution 0.001 mm) to adjust the radial flow’s orifice size. If the
185
geometry changed, each corresponding part could be independently replaced. Fig. 5 (b) shows the distribution plate
186
inserted between the middle and down manifold, which helped to uniformly distribute the annular flow. This plate
187
type was also used in a previous study to uniformly distribute propellant [8].
188 189 190 191 192 193 194 195
Fig. 5. Final geometry of the pintle injector; (a) whole view (b) section view.
196
3. Experimental setups and methods
197
3.1. Experimental conditions
198 199
Fig. 6. Control range with respect to throttling level.
200 201
Spray characteristics were observed at the minimum, mid-range, and maximum throttling levels of 20 60, and
202
100%, respectively. To achieve a deep throttling of 5:1, the differential pressure and the outlet height (H, related to
203
the outlet area of the radial flow) had to be adjusted simultaneously, a method widely used for thrust control. MIRA-
204
150A, a TRW binary propellant rocket engine, also used this mechanism. The injector’s moving part and the flow
205
control valve were mechanically linked to fulfill the desired throttling level [23]. Previous work showed that deep
206
throttling cannot be achieved under constant differential pressure. Therefore, it was necessary to consider
207
differential pressure control and area adjustable systems [24]. Fig. 6 shows the operating range of H according to
208
throttling levels as well as the corresponding mass flow rate and differential pressure. H was adjusted between 0.1
209
and 0.6 mm, a wide operation range that was accounted for when determining the minimum opening. The maximum
210
value of H was determined by considering the cylinder cross-sectional area ( ) inside the pintle injector and the
211
radial flow’s outlet area (, ). These areas are expressed by Eq. (4), and each is shown in Fig. 7. If ,
212
was larger than , the radial flow’s orifice size was fixed to even if H increased. In other words, the
213
variation of the H was meaningless in this range. Therefore, the maximum adjustment value of H was set to 0.6 mm,
214
to control H only for regions where , was less than .
215
$ ;* !! + ! , = , > @ > 0.6 %% , $ ; ∙
(4)
216
where and ! are cylinder inner radius and cylinder outer radius, respectively. H was linearly controlled based
217
on throttling levels. H values at thrust levels of 20, 60, and 100% were 0.1, 0.35, and 0.6 mm, respectively. The
218
mass flow rates corresponding to each H were 16.6, 49.68, and 83.58 g/s, respectively. The differential pressure to
219
satisfy the mass flow rate of each thrust level was also adjusted with H, as shown in Fig. 6.
220 221
Fig. 7. Schematic of a pintle tip.
222 223
The gap distance (G) of the annular flow was related to the orifice size control (Fig. 2). To determine the range
224
of G, spray characteristics were observed at each thrust level. G ranges used are shown in Table 2. The outlet area of
225
the annular flow (, ) is shown in Eq. (5), and the maximum area was set to 185.519 %%! : , $ ; ∙ C ) D
226
(5)
227
In Table 2, a specific G range was chosen for each throttling level to obtain accurate empirical correlations for spray
228
angle and droplet size. The down manifold was manufactured for each G (i.e., G was changed by replacing the down
229
manifold).
230
Table 2
231
Range of gap distance (G). , (%%! ) 185.519 148.252 111.087 73.991 46.414 37.128 26.706 18.177 8.258
232 233
Gap distance G (mm) 3.95 3.3 2.6 1.835 1.21 0.986 0.725 0.503 0.234
234
3.2. Spray imaging
235
Backlight photography was used to obtain the spray image, as shown in Fig. 8. A stroboscope (SUGAWARA
236
MS-230DA model) with a flash duration of 6 μs was used as the backlight. To acquire spray images, a digital
237
camera (Canon EOS 7D, 5184 x 3456 pixels, spatial resolution 47μm/pixel) and a lens (Canon EF 24-70mm) were
238
used. The frozen image was obtained by setting the camera exposure time and flash frequency of the stroboscope to
239
1/30 sec and 30 Hz, respectively. To obtain spray images with the proper depth of field and brightness, the camera
240
was set to f/11 and ISO 1000.
241
For the cold test, water and air were used as simulants for liquid oxygen and methane, respectively. For the
242
liquid, a needle valve was mounted on the feed line to regulate differential pressure. A mass flow meter
243
(KOMETER KTM-800, accuracy ±0.5%) was used to monitor the liquid flow rate, and the gas feed line was
244
equipped with a mass flow controller (MKP TSC-150, accuracy ±0.2%) for flow control between the gas supply
245
system and the manifold. The gas flow rate was adjusted such that O/F was always maintained at 3.44, regardless of
246
thrust.
247 248 249
Fig. 8. Spray imaging apparatus. 3.3. Spray pattern
250
To analyze the degree of uniformity, the spray pattern perpendicular to the spray direction was measured using
251
the optical patternator. This technique has a high spatial resolution and rapid characterization but can contain error
252
sources such as multiple scattering and signal attenuation [25]; error correction were therefore applied. To remove
253
multiple scattering, a two-phase structured laser illumination planar imaging (SLIPI) technique was used. This
254
method extracted a single scattering signal using a modulated laser sheet [26]. The experimental setup consisted of a
255
high-speed dual head laser (Photonics Industries DM20-527DH), SLIPI optics module (LaVision), and CMOS high-
256
speed camera (Photron FASTCAM SA5, 1024 x 1024 pixels) with a lens (AF MICRO NIKKOR 105 mm). The
257
camera was set to f/5.6 with an image rate of 3 kHz, and 300 images were obtained for each experiment condition.
258
The modulated laser sheet position was 7 mm from the end of the pintle rod in the axial direction, taking into
259
consideration the diameter of the small combustion chamber and field of view. An example of the spray pattern
260
obtained through the experimental setup is shown in Fig. 9, an averaged image at a throttling level of 20% and G of
261
0.986 mm.
262 263
Fig. 9. Spray pattern from the optical patternator with SLIPI.
264 265
To deal with signal attenuation, a compensation method proposed by Abu-Gharbieh et al. (2000) was used. This
266
method was based on the Beer-Lambert law and compensated for each pixel by applying a compensating algorithm
267
in a discrete way, as shown in Eq. (6): UV
" N $ " ∙ OPQRS ∙ ∑UWX "UN Y
268
(6)
269
where " N and " are compensated and observed pixel intensity, respectively, and is a balance value that
270
minimizes the difference between the right and left image averages. The detailed process to develop Eq. (6) was
271
presented in a previous study [27].
272 273 274
275
3.4. Droplet size
276
Droplet size is an important index of injector atomization characteristics and affects combustion efficiency [27].
277
Especially for the pintle injector, it was necessary to maintain droplet size throughout the entire thrust range to
278
achieve a certain atomization efficiency. To observe droplet size, an experimental apparatus consisted of the high
279
speed camera used in the optical patternator, a long distance microscope (LaVision QM1) with a magnification lens
280
x2.0, and the stroboscope. The spatial resolution 4.59μm/pixel, and 200 images were taken per case. Droplet size
281
was measured at a point 20 mm from the pintle tip in the axial direction to the outline of the spray field.
282
283 284
Fig. 10. Image processing for droplet size measurement.
285 286
Fig. 10 shows the image processing procedure used to measure droplet size. The raw image taken by the camera
287
was recorded in grayscale, and the optimal threshold was calculated based on Otsu’s method. In the resulting binary
288
image, droplets were clearly visible apart from the background. The spray image contained background errors such
289
as dust on the detector. To eliminate these errors, a background image taken without spraying was also binarized and
290
then subtracted from the spray image. In the last step, droplets in the image boundary were excluded. Non-circular
291
droplets were removed based on the ratio of a minor axis length to a major axis length. This processing was
292
performed for each image and diameters were judged based on the ratio of the extracted from 200 images per
293
experimental case.
294
To analyze droplet size, the Sauter mean diameter (SMD) was used. The SMD, also called Z! , is expressed in
295
Eq. (7) as a ratio of volume to surface, and is a representative diameter that reflects evaporation rate and combustion
296
reaction [28]: ∑ 6[ ∙8[\
"# $ ∑
297
6[ ∙8[]
298
where and are the number of droplets and the middle diameter in size range ^, respectively.
299
4. Results and discussion
300
4.1. Spray structure
301 302 303
Fig. 11. Spray images with various throttling levels and gap distances.
(7)
304
Fig. 11 shows spray images for all experimental conditions. The breakup process was classified into two types: (i)
305
atomization immediately after collision of the radial and annular flows and (ii) droplets split from a liquid sheet after
306
collision. The second type was observed when the throttling level was 20% and the G was greater than 1.835 mm.
307
To set the criterion for dividing the two breakup mechanisms, momentum flux ratio (J) and Weber number (We) for
308
two-phase flow, defined as Eq. (8) and Eq. (9), respectively:. $
309 fO $
310
] _`[a ∙b`[a
] _cde ∙bcde
(8) ]
_cde ∙Cbcde Vb`[a D ∙ g`[a
(9)
311
where hi , h 0 , (i , ( 0 and j 0 are gas density, liquid density, gas velocity, liquid velocity, and liquid
312
surface tension, respectively. The characteristic length of the pintle injector was defined as H. Results confirmed that
313
the second breakup type occurred when J was greater than 6.4 and We was less than 4.13. In this region, there was a
314
specific breakup length and droplet size was relatively large. That is, atomization efficiency was relatively low, and
315
accounting for the small thruster, combustion efficiency can be adversely affected. This again illustrated that annular
316
flow orifice size control was important to optimum spray performance. To obtain optimum injector parameters,
317
spray characteristics were therefore analyzed except for this region.
318
For the first breakup type, the typical atomization process is shown in Fig. 12. After the thin liquid sheet in the
319
radial direction collided with the annular flow, a wave was generated by aerodynamic force, leading to the
320
disconnection of the liquid sheet. Furthermore, a liquid lump fell out of the end of the liquid sheet and then split into
321
smaller droplets.
322
323 324 325
Fig. 12. Atomization process.
326
To obtain the spray angle, 50 images were averaged for each case. The spray angle decreased with decreasing G
327
(Fig. 11), explained by total momentum ratio (TMR), which is closely related to the spray angle formation of the
328
pintle injector [21, 29]. TMR is defined in Eq. (10) and is expressed as the ratio of momentum of radial to annular
329
flows.
330
*m& ∙b,ndo[d`
k#l $ *m∙&b,
dppq`dn
(10)
331
At each throttling level, mass flow rates of the radial and annular flows were fixed. In addition, because H
332
associated with the radial flow orifice size was constant at each level, the radial flow momentum was fixed. As G
333
decreased, the annular flow’s orifice size also decreased while annular flow velocity increased. As a result, as G
334
decreased, annular flow momentum intensified and spray angle decreased.
335
336 337 338
Fig. 13. Relationship between spray angle and (a) total momentum ratio (rst) (b) the new dimensionless number, u = rst ∙ *v/w,.
339 340
Fig. 13 (a) shows that spray angle was proportional to TMR. When G was the same, the spray angles at all
341
throttling levels were nearly identical. From the perspective of TMR, it can be expressed as k#l ∝ y*V , under
342
conditions where G is the same in the entire throttling range. In other words, points with the same spray angle had
343
different TMRs. This is because H changes linearly with throttling level. Therefore, if the throttling level decreases
344
under the same G condition, TMR increases. For this characteristic, there was a gap (Fig. 13a) such that only the
345
correlation between the spray angle and TMR was expressed. Therefore, a new dimensionless number was defined to
346
represent spray angle tendency within the overall thrust range. Fig. 13 (b) shows spray angle tendency with a new
347
dimensionless number (N), defined by Eq. (11), which is the ratio of H to G in the TMR.
$ k#l ∙ */,
348
(11)
349
For N, it can be expressed as ∝ y*,. That is, if G is the same, the value of N is also constant
350
the throttling level. This allows the same spray angles to have one N and eliminates the gap that was observed
351
between the throttling levels in TMR and spray angle relationships. As a result, it can be expressed as one correlation
352
having a proportional relationship, such as the relationship between G and spray angle. The correlation between N
353
and spray angle (Fig. 13b) was defined as Eq. (12), with R2 = 0.98. This empirical equation will be used to predict
354
the spray angle in future spray conditions. "Q z{ z|}~O $ +177.83 ) 16007.17
355
356
irrespective of
(12)
4.2. Spray uniformity
357
Using the error correction methods discussed in Section 3.3, spray uniformity was analyzed. Experiments were
358
conducted for regions with G greater than 0.986 mm. When the throttling level was 20%, the second breakup type
359
was excluded, as mentioned in Section 4.1. To determine uniformity degree, a Patternation Index (PI) and Spray
360
Uniformity Index (SUI) were defined by Eq. (13) and Eq. (14), respectively:
362
e e
× 100
(13)
where | and are the number of sectors and intensity of the image per sector, respectively, and " $ ∑W *{ + {,!
363 364
e
*%, $ ∑W + ∑p
361
where { ≡ ∑p
e
e e /
and { ≡
/!
(14)
∑p e e
365
The PI and SUI represented spray symmetry, and circumferential uniformity and standard deviation of the spray
366
distribution [25, 30, 31]. Results of the spray uniformity analysis are shown in Fig. 14. PI, by definition, has a value
367
from zero to 200, and spray uniformity is higher with lower PI. PI and SUI averaged 20% and 0.26, respectively. In
368
addition, the standard deviations (σ) were 3.62% and 0.04 respectively. From the perspective of SUI, the standard
369
deviation appeared to be very small and this meant that the spray uniformity was almost constant irrespective of the
370
gap distance and the throttling level. When the spray uniformity associated with PI was expressed as a percentage,
371
and assuming that 100% was the ideal uniform distribution, the mean value of the spray uniformity from the PI data
372
was 90%. As an extension of this, the standard deviation of PI data was 1.81%. In this study, when the spray
373
uniformity was more than 90%, based on the average value of PI, and the standard deviation is within 5%, the
374
quality of the injector was considered suitable for experiments.
375 376
Fig. 14. Spray uniformity based on (a) Patternation Index (PI) and (b) Spray Uniformity Index (SUI).
377 378
4.3. Sauter mean diameter (SMD)
379
For the SMD analysis, J and We were selected. Fig. 15 shows SMD trend based on each dimensionless number,
380
and indicates that both were related to SMD. For the pintle injector, the first breakup was a vertical collision like a
381
jet in crossflow. At this time, liquid sheet breakup was caused by the transfer of gas momentum. In addition,
382
breakup was sustained by shear force due to the velocity difference between the radial and annular flows. Overall, it
383
seemed that complex mechanisms act on breakup.
384
385 386 387
Fig. 15. Relationship between SMD and: (a) momentum flux ratio () and (b) weber number ().
388
In Eq. (8), when G decreases, the velocity of gas (annular flow) increases, so that the momentum flux of the gas
389
corresponding to the denominator of J becomes relatively strong. Thus, J also decreases as G decreases. In other
390
words, it means that gas momentum transfer, which affects the liquid sheet, generally increased. Therefore, SMD
391
decreased proportionally as J decreased. For We, when G decreases at each throttling level, the velocity of gas
392
increases; thus, the force corresponding to the numerator of We becomes relatively strong from Eq. (9). Namely, it
393
indicates that relative velocity and the deforming force due to the shear force was intensified. Therefore, We and
394
SMD were inversely proportional to each other.
395
396
Fig. 16. Relationship between new parameter, = V. ∙ . and s.
397 398 399
To investigate which of the two dimensionless numbers had a greater impact on droplet formation, an empirical
400
correlation was derived. Fig. 16 shows the result, where Eq. (15) is the final correlation with R2 = 0.96. In Fig. 16,
401
the new parameter (P) on the x-axis is represented by VX.Z ∙ fO X.X in Eq. (15).
402
"# $ +111.45 ~|*VX.Z ∙ fO X.X , ) 490.12
403
Eq. (15) can also be expressed as Eq. (16), in which momentum transfer during the vertical collision of two flows
404
has a greater effect than the shear force in droplet formation. This was likely because the pintle injector created an
405
interaction between radial and annular flow. The correlation will be used to estimate the optimal G to obtain the
406
desired SMD.
407 408 409
"# $ 103.65 ~|*, + 5.57~| *fO, ) 490.12
(15)
(16)
410
4.4. Relationship between spray angle and SMD
411
412
Fig. 17. Relationship between spray angle and s.
413 414 415
Fig. 17 shows the relationship between spray angle and SMD for G at each throttling level. Spray angle and SMD
416
had a linear relationship at each throttling level. When G was fixed, the spray angle was almost constant in the
417
whole thrust range. This is because, as described in Section 4.1, the spray angle changed according to G irrespective
418
of the throttling level. In addition, since G and the spray angle were proportional, the spray angle tended to increase
419
when G increased. On the other hand, SMD was different at each throttling level when G was fixed. For example,
420
when G was fixed at 0.986 mm, SMD at the 100, 60, and 20% throttling levels were 114.17, 227.12, and 493.20 μm,
421
respectively. This is because SMD was related not only to G but also to several factors associated with the throttling
422
level as shown in Eq. (16). When the throttling level was lowered under the fixed condition of G, SMD increased
423
with J increased and We decreased. This study focused on atomization performance, so the control range of G to
424
maintain constant SMD at all thrust levels was estimated and discussed in Section 4.5.
425
4.5. Variations in G and spray angle with SMD
426
The control range of G with constant SMD was obtained from an empirical equation (Section 4.3). In addition,
427
spray angle variation at the same time was estimated by Eq. (12). To analyze the resulting variations, three cases
428
(SMD = 100, 150, and 200 μm) were selected as examples based on ranges typically used in a liquid rocket engine
429
[32].
430
Fig. 18. Variation ranges (constant s) of (a) gap distance and (b) spray angle.
431 432 433
Fig. 18 (a) shows the control range of G required to maintain the corresponding SMD. When SMD was constant,
434
the throttling level and G were linearly related. This indicated that the annular flow orifice area could be linearly
435
controlled based on throttling level. For radial flow, mass flow rate and H also had a linear relationship that
436
controlled outlet area. Therefore, the orifice sizes of radial and annular flows could be adjusted linearly for thrust
437
control. In addition, as the target SMD became smaller, the overall control range scale decreased. This is because G
438
must be further reduced in order to produce smaller droplets because the gas momentum flux and deforming force
439
must be stronger through increasing the gas velocity.
440
Fig. 18 (b) shows the variation range of the spray angle when G in the corresponding SMD was controlled (Fig.
441
18a). Spray angle also changed linearly with throttling level, and when the target SMD decreased, the change range
442
decreased. This is associated with the results in Fig. 18 (a), because the gas momentum was enhanced when G
443
became smaller as SMD decreased. Results of this study can help predict the G control range to maintain SMD and
444
spray angle variation. Furthermore, these data will be used to develop a control system for the radial and the annular
445
flows.
446
5. Conclusions
447
In this study, a pintle injector for a 400 N small liquid rocket engine was designed and research was conducted to
448
derive optimal design parameters. The developed pintle injector adopted the continuous slit type to achieve a
449
uniform spray pattern. In addition, the new design concept maintained the concentricity of the pintle rod. The
450
primary focus was the control range of the annular flow’s orifice area. For this, gap distance related to the annular
451
flow’s orifice area was selected as a representative parameter, various down manifolds were fabricated, and spray
452
characteristics were observed by replacing the down manifold at each thrust level. Spray angle was linearly related
453
to the total momentum ratio. As gap distance decreased under a fixed flow rate condition, the annular flow
454
momentum intensified due to the increased annular flow velocity, which in turn decreased the total momentum ratio
455
and narrowed spray angle. A new dimensionless number, which had a high correlation with spray angle throughout
456
the thrust range, was defined by introducing the ratio of outlet height associated with the radial flow’s outlet area to
457
gap distance in the total momentum ratio, and a correlation equation was subsequently developed. The Sauter mean
458
diameter was related to both momentum flux ratio and Weber number. It was also confirmed that momentum flux
459
ratio associated with momentum transfer had a greater effect on droplet formation. From the spray characteristics
460
results, the gap distance control range to maintain a constant Sauter mean diameter over the entire thrust range was
461
calculated based on atomization efficiency. Furthermore, the gap distance was linearly controlled by throttling level.
462
In the future, when spray characteristics are set for a target engine, these results will be of reference to estimate
463
the control range for the annular flow’s orifice size. The procedures and results of this study can be applied to a
464
linear control system for simultaneous control of the orifice sizes for radial and annular flows. Thus, an optimal
465
throttleable pintle injector with high atomization efficiency can be realized.
466
Acknowledgments
467
This work was supported by Advanced Research Center Program (NRF-2013R1A5A1073861) through the
468
National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) contracted through
469
Advanced Space Propulsion Research Center at Seoul National University and by the National Research Foundation
470
of Korea(NRF) grant funded by the Korea government(MSIP) (2019M1A3A1A02076963).
471
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472
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473 474 475
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Table 1 Specifications of a 400 N engine. Chamber pressure (MPa) Vacuum thrust (N) O/F Chamber diameter (mm) Throttling level (%) Mass flow rate of liquid oxygen (g/s) Mass flow rate of methane (g/s)
1 400 3.44 54 20 to 100 83.4 24.24
Table 2 Range of gap distance (G). ܣ,௨ (݉݉ଶ ) 185.519 148.252 111.087 73.991 46.414 37.128 26.706 18.177 8.258
Gap distance G (mm) 3.95 3.3 2.6 1.835 1.21 0.986 0.725 0.503 0.234
Fig. 1. Conceptual diagram of a pintle injector.
Fig. 10. Image processing for droplet size measurement.
Fig. 11. Spray images with various throttling levels and gap distances.
Fig. 12. Atomization process.
Fig. 13. Relationship between spray angle and (a) total momentum ratio () (b) the new dimensionless number, = ∙ / .
Fig. 14. Spray uniformity based on (a) Patternation Index (PI) and (b) Spray Uniformity Index (SUI).
Fig. 15. Relationship between SMD and: (a) momentum flux ratio (ࡶ) and (b) weber number (ࢃࢋ).
Fig. 16. Relationship between new parameter, = . ∙ . and .
Fig. 17. Relationship between spray angle and ࡿࡹࡰ.
Fig. 18. Variation ranges (constant ࡿࡹࡰ) of (a) gap distance and (b) spray angle.
Fig. 2. Combustor of the pintle injector [21].
Fig. 3. Multi-hole type pintle geometry [22].
Fig. 4. New concept for maintaining concentricity of a pintle rod.
Fig. 5. Final geometry of the pintle injector; (a) whole view (b) section view.
Fig. 6. Control range with respect to throttling level.
Fig. 7. Schematic of a pintle tip.
Fig. 8. Spray imaging apparatus.
Fig. 9. Spray pattern from the optical patternator with SLIPI.
Highlights • • • • •
New design concept for a pintle injector was introduced to improve uniformity in a 400 N class liquid rocket engine Spray tests helped find the control range of the annular flow’s orifice area An appropriate correlation equation was developed for the parameters The control range was estimated using empirical correlations with respect to the degree of atomization A database for linear control system design was established
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: