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A proposed design method for supersonic inlet to improve performance parameters
Aerospace Science and Technology 91 (2019) 583–592
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A proposed design method for supersonic inlet to improve performance parameters M. Farahani ∗ , M.M. Mahdavi Department of Aerospace Engineering, Sharif University of Technology, Azadi Street, P.O. Box 11365-11155, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 25 October 2018 Received in revised form 20 March 2019 Accepted 6 May 2019 Available online 9 May 2019 Keywords: Supersonic inlet design Pressure recovery Compression ramp
a b s t r a c t A new structure for the compression surfaces of a supersonic inlet is proposed which has improved the target performance parameter i.e. total pressure recovery ratio. This idea resulted in development of a new type of supersonic inlet, utilized four ramps and a cone simultaneously as the compression surfaces. A prototype of the proposed inlet has been designed for a free stream Mach number of 3 and its performance has been evaluated via numerical simulation for both design and off-design conditions. The performance of the newly designed inlet has been compared to the existing experimental data of two double-cone inlets. The acquired data are further compared with analytical calculations of maximum reachable TPR for some conventional supersonic inlet types. The results confirmed the effectiveness of the main idea of the proposed design methodology. The total pressure recovery ratio of the newly designed inlet at its design condition, M∞ = 3, is calculated to be 76.8%. © 2019 Elsevier Masson SAS. All rights reserved.
1. Introduction Air intakes are considered to be the most important parts of an air-breathing propulsion system of a supersonic flying vehicle. This importance has two clear aspects: first, from the pressure distribution analysis, air intakes usually partake the greatest share of thrust production; and second, as a result of both high velocity and shock structure effects, an improper design of the air intakes might have immense effects on the propulsion performance, when flying supersonically. Air inlets have to meet design objectives to provide a sufficient amount of air for the propulsion system, with highest reachable quality, and of course least cost. In addition, the inlet must be able to provide sufficient mass flow rate for all flight conditions of the inlet operation. The two major criteria of the inlet air quality are higher total pressure and lower distortion. Meanwhile, the cost of the entire inlet performance is described by its drag. This introduction suggests that these four quantities, mass flow rate, preserved total pressure, distortion, and drag are the most important objectives of an inlet that must be considered during its design process. The dimensionless forms of the mentioned parameters could be used as the main performance parameters of an air inlet.
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Corresponding author. E-mail addresses: [email protected] (M. Farahani), [email protected] (M.M. Mahdavi). https://doi.org/10.1016/j.ast.2019.05.014 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.
In addition to the above parameters – which are mostly related to the steady performance of an inlet. Stability margin (buzz limit) is another significant issue in the performance of a supersonic inlet. As this paper is focused on the steady performance, this parameter will not be considered here; however, distinct studies have been carried out by the present authors in order to identify the buzz phenomenon in the supersonic inlets [1–7]. The present study is an effort to develop a new type of air intake for the supersonic flight regime, with an improved performance criterion. Same as many other performance improvement and optimization studies, this study is not capable of meaningfully improve all performance parameters too. Thus, it is inevitable to draft a “target performance parameter”. The main target of this investigation is to increase the total pressure of the captured air, through lowering the total pressure drop in the inlet flow. Shock waves and boundary layers are two major loss mechanisms of the total pressure at the inlet. Consequently, there exist two different trends for minimizing the total pressure drop of an air inlet. The first trend is a set of studies and methods to control the boundary layer growth and to prevent separation. A few samples of these studies and methods could be found in refs. [8–12]. The second trend, consists of investigations which aimed to lower the total pressure loss through manipulating both the shock structure and the flow geometry in order to make the inlet more efficient or to increase its robustness when flying in off-design conditions.
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Nomenclature
α D M P X Re
Half Angle of Compression Surfaces Maximum body diameter Mach number Pressure Axial position Reynolds number, based on maximum body diameter
Abbreviations AIP MFR RC
Aerodynamics Interface Plane Mass Flow Rate Ratio Ramped Cone
Total Pressure Recovery Ratio
TPR
Subscripts 1st step 2nd step 3rd step A B C r
∞
First Compression Step (First Shock Wave) Second Compression Step (Second Shock Wave) Third Compression Step (Third Shock Wave) Zone A Zone B Zone C Ramp Free Stream
Fig. 1. Schematic of inlet with imaginary heat source, proposed by Soltani et al. [19].
One of the first known innovations in this context was through the use of compression surfaces to increase the compression stages. This Idea has been proposed by Ferry and Nucci in 1946 [13] and increased the reachable total pressure, in comparison to the un-started internal compression. It should be mentioned that Ferry and Nucci actually proposed their method, for the conventional 2D and/or for conical supersonic inlets. A few other studies used optimization loops to reach an optimum performance in the so-called conventional inlet structures. These optimization codes aimed at various target parameters and have used various optimization variables. For example, Rodriguez [14] used 13 geometrical optimization variables to design an optimized inlet for four distinct sets of target functions and geometrical constraints, by using the simplex algorithm. In another example, Zha et al. [15] used the genetic algorithm with 6 geometrical constraints and 8 optimization variables to design an inlet with an optimized TPR. In addition to the above studies, other researchers have studied consequences of several unconventional conversions on the inlet geometry. Chernyavsky et al. [16] studied the effect of sweep angle in the ramp leading edge and were succeeded to increase the total pressure recovery. Their study was carried out for a range of Mach numbers M∞ = 3 − 8. It should be mentioned that their TPR for a free stream Mach number of 3 was the same as the TPR for the design point of the present study, 64 percent [16]. In another effort, Kim and Song [17] studied the effect of bump addition to the ramp surface of a 2D inlet. Their result showed a 3 percent improvement in the total pressure recovery ratio of the sample inlet for the design Mach number of M∞ = 2. Bump inlets are of interest both as an alternative compression surface and as a boundary layer diverter. Yu et al. [18] have provided an effective, inverse design method for the bump inlets. In another effort, Soltani et al. [19] placed an imaginary heat source in front of the cowl lip of an axisymmetric conical intake and studied its effects on the shock structure and on the inlet performance. They succeeded to decrease the intake drag coefficient by 18 percent. Fig. 1 shows a 3D Schematic of the proposed Idea of using an imaginary heat source. Utilization of a bypass duct in an intake is another Idea which has been proposed by Kim et al. [20]. The proposed inlet of their study intentionally captured a surplus amount of flow rate. This superfluity of the captured flow enables the inlet to bypass the
Fig. 2. TPR of core, bypass and net captured flow of air inlet of [20].
excess mass flow rate with lower TPR losses. This idea is more effective to remove the bow shock effects from the core flow through spillage. Fig. 2 shows the resulting total pressure recovery for various mass flow rates. As it is evident, the core flow seems to have a more efficient and a more robust performance in preserving the total pressure ratio, in comparison to the net captured air of the core plus bypass flow. Similar to the Kim et al. [20] proposal several other studies, have focused on ideas to make inlets more robust in the case of the off-design flight conditions. The throat area and the cowling position angle are the two usual parameters for controlling the off-design spillage which results in deterioration of both TPR and MFR. For conical inlets, these parameters, TPR and MFR, are varied by the axial position of the spike. Maru et al. [21] proposed a new spike design through employing several rows of cone frustums. Their technique ensured that the throat area and cowling position did not have significant effects on the TPR or MFR. In another study, Weir et al. [22] suggested a canaled center-body which provided an alternate mechanism to control the throat area, instead of varying the spike position. 2. The proposed inlet A supersonic inlet could yield more TPR as its number of shock wave compression stages are increased. This fact has motivated designers to implement several ideas to improve the shock structure of supersonic inlets. The present study, however, proposes a new idea and its implementation will result in a new inlet type. The main idea is to study whether appendation of two transverse oblique shocks with increase the TPR of a conical shock structure formed instead of a conventional axisymmetric external-compression inlet. The aforementioned oblique shocks will increase compression stages on the inlet flow and a resultant increase in the final TPR value is expected. For convenience, this new type of inlet is called “RC inlet” in the present paper (the term
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Fig. 3. A generic geometry, simulating RC-inlet for zero-dimensional analysis. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
“RC inlet” has been adopted as an abbreviation of “a ramped-cone inlet”). The study started with a generic geometry, composed of two transverse ramps and a chasing cone. Fig. 3 depicts this schematic geometry with arbitrary lengths and angles. The backward boundary of the domain of this figure is a pressure contour on an assumed cross plate, where the conical shock trace (red zone) is completely inscribed inside the oblique shocks intersection (turquoise zone). A hypothetical axisymmetric cowl behind the cone in the above geometry has been assumed in order to create a hypothetical normal shock. Accounting to this normal shock, the shock structure on the above geometry – in its zero-dimensional form, would be approximately similar to that of the generic RC inlet. However, the above geometry, with its infinite ramp span, is not a realistic design for the compression surfaces of an inlet. It is, therefore, beneficial to run the zero-dimensional analysis for the corresponding RC inlet. This zero-dimensional analysis is based on the shock-expansion theory. The so called “conical-shock on lip” assumption for a hypothetical cowl lip means that the cowl lip is of a circular type on which the conical shock lies. In this shock structure, it is assumed that almost all of the captured mass flow will pass through the four distinct shock waves. The first confronting shock wave is an oblique shock rooted from the closest ramp. This shock turns the horizontal upstream flow through a turning angle of “αr ”, upward of the first ramp which is equal to the half angle of the ramp. This turning angle, assigns the flow direction in the affected zone of the first shock, called “zone A” in this paper. Moreover, this angle determines values of both Mach number and total pressure in this zone, zone A. It should be mentioned that the above shock structure has two distinct zones, shown as “zone A” in Fig. 3, owing that the codename of zone A, is defined on the basis of the “closest ramp” where the free stream particles first encounter. These two zones will intersect with each other, turquoise zone of Fig. 3, and create other zone called “zone B”. The flow in this zone, zone B, has been influenced by both ramps i.e. zone B is the region behind both oblique shocks. After confronting the second oblique shock wave, the flow direction of zone A turns in a manner to satisfy the second ramp tangency condition. The corresponding turning angle of the second shock could be determined from a simple geometrical analysis as:
α2nd = arctg sin (αr )
(1)
in which the term αr denotes the half angle of the ramps. The above turning angle, as well as the flow Mach number in zone A, define the flow characteristics in zone B.
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Two lax, but acceptable assumptions has been made in this procedure. The first one neglects particles that exist in the proximity of the bisector plane of the inter-ramps space. The previous two-stages model of the transverse oblique shocks is valid only for particles which are adequately away from the bisector plane. Particles that are in the vicinity of the bisector plane sense the presence of both ramps simultaneously, which means that these particles would be transferred to zone B via a single oblique shock wave, third oblique shock. This oblique shock is stronger than the previous two oblique shocks. This clearly indicate that the third oblique shock, causes a higher total pressure loss and the corresponding Mach number of the flow in this region would be low. However, zone B covers only a thin frontal area and the losses of total pressure and Mach number in this region do not cause significant effect on the average Mach number and on the total pressure of the final captured flow. Based on this argument, it is assumed that the third oblique shock can be neglected and the entire influence of ramps on the shock structure, could be modeled by a two-stage oblique shocks model. The second so-called lax assumption is the uniformity of the flow in zone B. The third oblique shock has significant effect on this assumption, but as state into previous section, this shock wave could be neglected in the first assumption. Thus the uniformity of flow in zone B is a fair assumption. By justifying these two assumptions, the two-stage shock model is capable of determining all flow variables in zone B, Mach number, total pressure, and velocity direction. The remaining two shock waves, a conical shock and a hypothetical normal shock, might be treated in a similar manner as the first oblique shock was handled. The conical shock wave is propagating only in zone B hence its affected zone called “zone C”, red zone in Fig. 3, could be determined from the Taylor-Maccoll method [23]. The following hypothetical normal shock wave, which lies in zone C, could be treated by the normal shock relations. An alternative way to model these two shocks is to consider them as waves that would be generated in a complete conical external compression intake. Connors and Meyer [24] published a paper which applies similar assumption, hence their result could be utilized to model the previous two shock waves simultaneously. Their paper analytically determines the maximum reachable TPR for each Mach number and the corresponding cone angle for a generic conical intake. Table 1 presents the steps of the zero-dimensional analysis of the shock structure, used in this investigation. In each step of the procedure shown in Table 1, the fraction of the total pressure loss is calculated. Three steps mentioned in the above table results in some percentages of total pressure drop. The final total pressure recovery ratio of the shock structure is then determined from the following equation:
TPRfinal
= TPR1st step (M∞ , αr ) ∗ TPR2nd step (MA , αr ) ∗ TPR3rd step (MB ) (2) where
MA = f1 (M∞ , αr )
(3)
MB = f2 (MA , αr )
(4)
The above equation suggests that by utilizing this procedure, the maximum reachable TPR of the final shock structure for any given free stream Mach number, could be determined as a function of ramp angle. Fig. 4a shows the TPR results as a function of ramp angle obtained from equation (2) for various free stream Mach numbers.
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Table 1 Summary of three steps of compression by shock waves in zero-dimensional analysis. Step
1 2 3
Step definition
First oblique shock Second oblique shock Conical + normal shock
Neighboring zones Upstream
Downstream
Free stream Zone A Zone B
Zone A Zone B Hypothetical subsonic diffuser
Ramp/cone effective angle
Determination procedure
αr
Oblique shock relations Oblique shock relations See ref. [24]
Arctg(sin (αr )) Optimized cone angle for Mach number of zone B
Fig. 4. Results of effectiveness investigation of appending the ramps. TPR of zero-dimensional RC-inlet as function of ramp angle, in various Mach numbers. a) In raw form. b) In normalized form.
This figure shows the maximum reachable TPR for any ramp angle for each free stream Mach number. It is clearly seen that appending the ramps has improved TPR value. In addition, an optimal ramp angle can be deduced for each free stream Mach number from the maximum value of the corresponding TPR. Fig. 4a shows that, for a free stream Mach number of 3, the shock structure for the hypothetical intake which has compression surfaces similar to that of Fig. 3, and a ramp angle of 11 degrees, can reach a total pressure recovery ratio of 0.84. In addition, the cone angle for this optimized design would be 28 degrees which has been determined in accordance with Connors and Meyers procedure [24]. Fig. 4b illustrates similar data normalized to the zero ramp angle case. From this figure it is seen that by means of appending the ramps, the corresponding values of TPR of a conical external compression inlet has been increased about 42 percent for M∞ = 3, 68% for M∞ = 3.5 and finally 95% for M∞ = 4. This result suggests that these ramps become more effective as the upstream Mach number is increased. The above results display the level of effectiveness of the ramps and the optimum ramp angle; however, this zero-dimensional analytical simulation of the RC-intake performance, does not show any details involved in the geometrical optimization of each component i.e. ramp sweep angle, the distance between the cone and the ramp’s apex, and the optimized shape of the cowl lip. This insufficiency would be eliminated by means of a three-dimensional design optimization loop in which a full 3D geometry of the final RC-type inlet could be extracted. Fig. 5 shows the corresponding final intake geometry. 3. Numerical simulation As the final step of this study, the performance of the final geometry of the resulting optimized RC-inlet has been numerically simulated in order to verify the effectiveness of the proposed method. These sets of simulations are used to calculate the total pressure recovery of the present RC-inlet operating at its design point. In addition, variation of mass flow rate ratio, Mach number and angle of attack on the performance of the inlet are investigated. The final results are compared with the corresponding TPR outputs of multi-cone inlets which had been experimentally stud-
Fig. 5. 3D view of the final RC-inlet geometry (cut through a symmetric plane).
ied by Connors and Wise [25]. In addition, analytical computations of Connors and Meyers [24] have been used to compare performance of the present RC-inlet for its designed condition with a maximum reachable TPR with a few other 2D and axisymmetric inlets. 3.1. Simulation setup The simulations of flow field around the RC-inlet, has been performed from the well-known Ansys Fluent CFD code. The solutions are focused on the steady-state behavior of the inlet. The Flow equations have been solved in density-based form by using the implicit Roe-FDS formulation. According to the 4-plane-symmetrical nature of the RC-inlet and in order to reduce the computational costs, an octant slice of the full scale inlet geometry has been used to run the simulations which is an appropriate condition for the zero degrees angle of attack condition. The numerical domain of each octant of the inlet has been discretized by 250,000 cells. In this case, the rest of the inlet has been modeled by the symmetry planes which are the side boundaries of the numerical domain. The upstream flow is modeled by the “pressure far-field” boundary condition and the AIP at the end of the inlet duct has been modeled by the “pressure outlet” boundary condition. Fig. 6a depicts a cut view of the structured mesh on a symmetry plane of the present RC-inlet.
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Fig. 7. Effect of Reynolds number on the TPR for a sample inlet geometry.
Fig. 8. The supersonic inlet used for validation.
Fig. 9. Location of pressure ports on the validation inlet.
Fig. 6. Generated numerical mesh. a) On a symmetric plane. b) On a symmetric plane and half geometry walls.
For the case of the flow simulations used to investigate the intake performance for non-zero angles of attack, a half slice of the full geometry must be used. This half geometry consists of four similar octants and is shown in Fig. 6b. This figure provides an insight into to the full structure of the generated numerical grid. It should be mentioned that the present simulations are based on the inviscid assumption. This assumption would clearly result in an over-estimation of the total pressure recovery, but it has been assessed to be helpful to eliminate the size effects on the TPR. Note that the size effects should be eliminated in the present simulations because this study is focused on a maximum reachable TPR for the new inlet type, not for a certain inlet with a specific size. To compensate for the effects of the over-estimation of TPR in the present RC-inlet performance, its total pressure recovery output at the design-point has been compared to the inviscid analytical calculations of Connors and Meyers. [24] The other benchmark which has been used in this study for comparison is the experimental performance data of two axisymmetric inlets, provided by Connors and Wise [25], however, these performance data count for the viscous losses in TPR. However, it is noted that TPR output of these inlets based on the viscous losses are sufficiently close to that inviscid values. This viscous independency is mainly due to the correlation of TPR and Reynolds number of the inlet which as depicted in Fig. 7.
This figure shows that the total pressure recovery ratio of any inlet approaches its inviscid limit for large scales, high Reynolds number. Furthermore, TPR approaches its creeping limit for very low Reynolds number. Note that the inlets of Connors and Wise have been tested at a Reynolds number of 2.5 × 106 , hence, their output TPR could be assumed to be close to its inviscid value. 3.2. Validation The simulation setup has been validated, using experimental performance data of an axisymmetric, single-cone inlet. This inlet has been designed for a free stream Mach number of M∞ = 2. Experimental performance study of this inlet has been performed by the authors and further detail of the experimental data and setup has been presented in ref. [26]. Fig. 8 shows the wind tunnel model of this inlet. The static pressure distribution over both the spike and the outer cowl surfaces has been measured for this intake. The pressure distribution on these two surfaces is used to validate the simulation setup on the same geometry. Fig. 9 shows the location of static pressure ports on the spike and on the outer cowl surfaces of this intake. There are 16 pressure taps on the outer cowl surface and 27 ports on the spike surface of the model. Moreover, three total pressure rakes has been embedded in this intake; however, the output of these rakes are not used in this validation procedure. The inaccuracy of the experimental measurements for the inlet shown in Fig. 8, has been investigated and reported in ref. [26] and are presented in Table 2. Moreover, all measurements were
Table 2 Measurement inaccuracies at the validation experimental test.
P0∞ /P0∞
P0 /P0
P/P
(P/P∞ )/(P/P∞ )
M/M
T0∞ /T0∞
T/T
0.01%
0.73%
0.74%
1.04%
0.8%
0.03%
1%
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Fig. 10. Comparison of the numerical prediction of the pressure on the spike surface, with experimental data.
Fig. 12. Comparison of the numerical prediction of the pressure on the external cowl surface, with experimental data.
Fig. 11. Center-body of the validation inlet.
repeated several times to ensure the repeatability of the measurements. The result shows that the maximum differences in successive measurements of a sample parameter (P/P∞ ) is about 1.04%. Fig. 10 shows both the measured and predicted static pressure distribution on the spike surface. The numerical simulations were performed at the same conditions of the numerical case, i.e. both the free stream condition and inlet back pressure were exactly the same for the two cases. As it is shown in Fig. 10, the conical shock wave increases the static pressure up to 2.65 times that of the free stream pressure. Then the first normal shock increases the static pressure to nearly 5 times larger than the free stream pressure. After that, nearly linear decrease in the static pressure occurs which continues until X = 1.5 and just a local pressure increase near the throat ( DX ∼ 1) D disrupts it. This pressure jump had been formed by the viscosity dominance in the throat region where the inviscid numerical solution has failed to simulate it. Moreover, the experimental model used four struts to hold the spike which the present simulation scheme did not model then. However, this model inaccuracy resulted in a 25 percent error in the calculation of the static pressure at the throat, which could be acceptable, since it had a negligible effect on the total performance of the intake. Fig. 11 shows an image of the center-body of this inlet, the mentioned struts are reviled in this figure. The second notable error in the numerical result of Fig. 10 is related to the downstream value of the pressure at the second norX mal shock ( D = 1.5). The numerical solution has over-estimated the static pressure downstream of this shock wave by about 15 percent. In the same manner, Fig. 12 shows the static pressure distribution on the external cowl surface. According to this figure, the main trend of the numerical result and the experimental data are similar.
Fig. 13. A sample Mach number contour on the ramp surface and the symmetry planes of the RC-inlet.
4. Results 4.1. Flow structure around an RC-inlet as seen the new RC-inlet has a significantly unconventional geometry, therefore, would be convenient to make a perception to its flow structure before proceeding the performance-study. Fig. 13 depicts a cross view of the present inlet and its Mach number contour. The Mach number contour is illustrated for a free stream Mach number of 3, zero degrees angle of attack and in the presence of some flow spillage. For legibility of this figure, both the spike and the cowl surfaces are colored in solid gray and the Mach number contour has been shown on the both ramp surfaces and the symmetry planes. Orange color on the ramps shows a reduction in the Mach number over ramp surfaces as a result of the presence of oblique shocks which are rooted from the ramp leading edges. The green region surrounded the spike represents Mach number reduction due to the conical shock wave rooted from the spike apex. At last, the blue region represents the subsonic zone following the spillage bow shock. As it is clearly shown in Fig. 13, the spillage bow shock is located behind the cowl lip protrusion. This suggests that some parts of the cowl lip are submerged in the spilled subsonic zone, while other parts of the cowl lip are exposed to the supersonic flow. This result unveils the characteristic procedure of spillage in the RC-inlets. In the case of low spillage rates in RC-inlets, the spilled flow is limited to a small region at the intersection of the cowl lip and the ramp surface. As the spillage rate is increased, this small region grows and the subsonic zone covers a larger area on the cowl lip. Finally, just for the extreme spillage conditions, the cowl lip would be submerged in the subsonic region completely.
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Fig. 15. Comparison of TPR of present RC-inlet in design point, with maximum reachable TPR of 4 axisymmetric inlet types (curves from Connors and Meyers [24]).
Fig. 16. TPR of the present inlet and axisymmetric inlets of Connors and Wise [25], as function of MFR.
Fig. 14. Mach number contours of several cross plane around the present RC-inlet.
In order to make a perspective insight, Fig. 14 shows the Mach number contour of the present RC-inlet on an identically spaced cross planes. These contours are extracted for the same flight conditions of Fig. 13 and the Mach number range is the same too. Fig. 14a shows the Mach number contour on a cross plane, located 0.3D behind the apex point of the ramps. As seen from this figure, every pair of the neighboring ramps, form a complicated shock wave with the triangular cross-section on this plane. The first cross plane, Fig. 14a, is located ahead of the spike surface, thus it does not encompass the influence zone of the spike. In return, propagation of the conical shock (rooted from the spike apex) is shown in Fig. 14b as small green regions. Fig. 14c shows a crossplane which crosses the cowl lip of the inlet. This figure shows the subsonic captured flow as well as the spillage regions in the corners of the cowl section. In summary, Fig. 14d and Fig. 14e show the shock structure on the rest of the inlet and transition of the complicated shock structure to a nearly conical sonic boom. 4.2. RC-intake performance in design point One of the first touchstones to umpire the performance of the new RC-inlet is to compare its TPR at design point with the maximum reachable TPR of other inlet at the same free stream condi-
tion. Fig. 15 shows the results of this comparison. The TPR output of the present RC-inlet has been predicted from the CFD simulation and is equal to 76. The zero-dimensional analysis, had previously predicted the same parameter to reach 84 percent, the difference in the values is obviously due to the different levels of the fidelity between the 3D flow simulation and the zero dimensional analysis. These values are compared to the analytical calculation of the maximum reachable TPR of a few inlets [24] in Fig. 15. It should be noted that the fidelity of the analytical curves is the same as that of the zero dimensional calculation of the TPR of the present inlet. As seen from Fig. 15, data compares very well with each other. However, Fig. 15 shows that the present inlet yields more TPR in comparison to other inlet types at the same free stream Mach number of M∞ = 3. 4.3. Mass flow rate dependency It is known that in off design operation mass flow rate has significant effect on the TPR and any reduction of the mass flow rate leads to the subcritical operation of the inlet and results in a spillage. This spillage usually dictates a bow shock wave which deteriorates the shock structure design and decreases the total pressure recovery ratio significantly. Fig. 16 shows the effect of TPR on the mass flow rate ratio, for the present inlet and for two other inlets which were experimentally studied by Connors and Wise [24]. According to Fig. 16, the present intake has a reasonable correlation between TPR and MFR, further it has higher total pressure recovery ratio for all MFRs considered here when compared to two other inlets. Fig. 17 shows the Mach number contours for several values of the spillage flow. The first contours, Fig. 17a represents the supercritical condition of the RC-inlet and the following three contours, represent the subcritical conditions with approximately 5 percent
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Fig. 18. Drag coefficient of the present inlet, versus normalized MFR.
Fig. 19. TPR of the present inlet and axisymmetric inlets of Connors and Wise [25], as function of MFR.
MFR Fig. 17. Mach number contour for four values of MFR . a) 1, b) 0.95, c) 0.85, d) max 0.76. (Left: contour on the ramp-side symmetry plane and corresponding ramp. Right: contour on the ramp-far symmetry plane.)
(Fig. 17b), 15 percent (Fig. 17c) and 26 percent (Fig. 17d) of flow spillage in their captured flow. The spilled amount of the inlet flow is characterized by the percentage of the drop in MFR, compared to the corresponding supercritical MFR case (MFRmax ). In addition to the above data, dependency of the drag coefficient of the present inlet to mass flow rate ratio might be of interest. Fig. 18 shows the pressure drag coefficient of the present inlet as a function of normalized MFR. This curve has not been compared to experimental inlets, because the net pressure drag in the experimental data of Connors and Wise [24] are not exact. However, to make a comparative sense, it should be noted that the approximation of the pressure drag coefficient in the first experimental inlet is a linear interpolation between CD = 0.4 at a normalized MFR of 0.7 and CD = 0.165 at a normalized MFR of 1. 4.4. Mach number dependency The effect of variation of the free stream Mach number on TPR is another important criterion in the off-design analysis. Similar to the previous section, this dependency on the present RC-inlet has been studied and the results are compared with the experimental data of the inlets of Connors and Wise [24]. Fig. 19 depicts the total pressure recovery ratio of these inlets for various Mach numbers.
Fig. 20. Normalized supercritical MFR of the mentioned inlets, as function of Mach number.
Inlet mass flow rate (MFR) is another performance parameter which varies with variation of the free stream Mach number. Fig. 20 shows the corresponding variations for the supercritical operation of the present inlet and the data is compared with the experimental inlets of Connors and Wise. Note that the curves in this figure have been normalized with the supercritical MFR for the design Mach number (M∞ = 3). Fig. 20 shows that the supercritical MFR of the present inlet has more coherence with the free stream Mach number than the other two inlets of ref. [25]. This severe sensitivity to the Mach number variation is rooted in small throat area which had been obtained by the TPR optimization and causes intense spillage in below-design Mach numbers. Further studies incorporating a multidisciplinary optimization of RC-inlet is expected to alleviate this problem. As a supplement to the Mach number dependency of the present inlet, the off-design performance at a subsonic Mach number of 0.7 had been simulated. The results showed that the present
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Fig. 21. Supercritical MFR of RC-inlet as a function of angle of attack, normalized by its value in zero angle of attack.
inlet yields 0.99 percent TPR, while the normalized MFR in this Mach number drops down to 0.35 percent 4.5. Angle of attack dependency The other off-design condition to be studied on the new inlet type is its operation at non-zero angle of attack. The main parameter studied in accordance to angle of attack variations, is the robustness of the captured mass flow rate ratio. Fig. 21 shows the supercritical MFR of the present inlet in various angles of attack, alongside of the aforementioned inlets of Connors and Wise. All three curves in this figure, have been normalized by the critical MFR at zero degrees angle of attack (i.e. MFRmax ) in order to demonstrate the percentage of MFR drop of each inlet geometry, at each angle of attack. According to this figure, the MFR drop trend in RC-inlet is almost similar to the second intake of Connors and Wise [25]. Fig. 22 shows the flow structure on the RC-inlet, exposed to a ten degrees angle of attack. Note that the back pressure has been set to zero, in order to measure the supercritical MFR; thus the termination shock has been completely swallowed.
Fig. 22. Mach number contour on a) symmetry plane and b) its perpendicular plane.
Declaration of Competing Interest There is no competing interest for authors in this paper. References
5. Conclusions A new configuration for a supersonic air inlet has been proposed. The novel idea of this new configuration was through the simultaneous use of a cone and four ramps as compression surfaces. This new configuration suggests a new type of supersonic inlet. A sample version of this new inlet type has been designed for a free stream Mach number of 3 and its performance has been studied by a numerical simulation for both design-point and offdesign operations. The design-point performance has been compared with the analytical predictions of Connors and Meyers [24] for the maximum reachable TPR of a few conventional conical inlet types. In addition, the off-design performance has been compared to the experimental results of two conical inlets, published by Connors and Wise [25]. Both design-point and off-design results, show an acceptable performance with a higher reachable TPR when compared with similar inlets and with a few conical inlet types. The results suggest that the simultaneous utilization of cone and ramps as compression surfaces would lead to a notable increase in the reachable total pressure recovery of the air inlet. Introduction of the new RC-inlet type is the main conclusion of the present paper. Further studies on this proposed inlet type, include to design of a new optimized sample of this inlet type and study its unsteady behavior and instability characteristics at various conditions.
[1] M. Farahani, A. Jaberi, Study of buzz phenomenon using visualization of external shock structure, Proc. Inst. Mech. Eng. G, J. Aerosp. Eng. (2018), https:// doi.org/10.1177/0954410018785261. [2] A. Daliri, M. Farahani, J. Sepahi-Younsi, Novel method for supersonic inlet buzz measurement in wind tunnel, J. Propuls. Power 34 (1) (2017) 273–280. [3] M.R. Soltani, et al., Effects of bleed position on the stability of a supersonic inlet, J. Propuls. Power (2016) 1153–1166. [4] M.R. Soltani, J. Sepahi-Younsi, Buzz cycle description in an axisymmetric mixed-compression air intake, AIAA J. 54 (3) (2015) 1040–1053. [5] M.R. Soltani, M. Farahani, Effects of angle of attack on inlet buzz, J. Propuls. Power 28 (4) (2012) 747–757. [6] M. Soltani, M. Farahani, Experimental investigation of effects of Mach number on the flow instability in a supersonic inlet, Exp. Tech. 37 (3) (2013) 46–54. [7] M. Soltani, M. Farahani, M.A. Kaji, An experimental study of buzz instability in an axisymmetric supersonic inlet, Sci. Iran. 18 (2) (2011) 241–249. [8] C.E. Wittliff, R.W. Byrne, Preliminary Investigation of a Supersonic Scoop Inlet Derived from a Conical-Spike Nose Inlet, NACA Research Memorandum L51G11, 1951. [9] M.R. Soltani, J.S. Younsi, M. Farahani, Effects of boundary-layer bleed parameters on supersonic intake performance, J. Propuls. Power 31 (3) (2015) 826–836. [10] A. Sóbester, Tradeoffs in jet inlet design: a historical perspective, J. Aircr. 44 (3) (2007) 705, https://doi.org/10.2514/1.26830. [11] H.-J. Tan, R.-W. Guo, Design and wind tunnel study of a top-mounted diverterless inlet, Chin. J. Aeronaut. 17 (2) (2004) 72–78. [12] B.H. Anderson, J. Tinapple, L. Surber, Optimal Control of Shock Wave Turbulent Boundary Layer Interactions Using Micro-Array Actuation, AIAA paper 2006-3197, 2006. [13] A. Ferri, L.M. Nucci, Preliminary Investigation of a New Type of Supersonic Inlet, NACA Technical Report 1104, 1952. [14] D.L. Rodriguez, Multidisciplinary Optimization of a Supersonic Inlet Using a Cartesian CFD Method, AIAA paper 2004-4492, 2004.
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[15] G.-C. Zha, et al., High-performance supersonic missile inlet design using automated optimization, J. Aircr. 34 (6) (1997) 697–705. [16] B. Chernyavsky, et al., 3-D Hypersonic Inlet Optimization Using a Genetic Algorithm, AIAA paper 98-3582, 1998. [17] S.D. Kim, D.J. Song, Numerical study on performance of supersonic inlets with various three-dimensional bumps, J. Mech. Sci. Technol. 22 (8) (2008) 1640–1647. [18] Z. Yu, G. Huang, C. Xia, Inverse design and Mach 6 experimental investigation of a pressure controllable bump, Aerosp. Sci. Technol. 81 (2018) 204–212, https://doi.org/10.1016/j.ast.2018.08.006. [19] M. Soltani, M. Farahani, J.S. Younsi, Performance study of a supersonic inlet in the presence of a heat source, Sci. Iran. 18 (3) (2011) 375–382. [20] H. Kim, et al., Flow simulation of supersonic inlet with bypass annular duct, J. Propuls. Power 27 (1) (2011) 29, https://doi.org/10.2514/1.49028.
[21] Y. Maru, et al., Multi-row disk arrangement concept for spike of axisymmetric air inlet, in: 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2004. [22] L.J. Weir, B.W. Sanders, J. Vachon, A New Design Concept for Supersonic Axisymmetric Inlets, AIAA paper 2002-3775, 2002. [23] J.D. Anderson, Modern Compressible Flow: With Historical Perspective, vol. 12, McGraw-Hill, New York, 1990. [24] J.F. Connors, R.C. Meyers, Design Criteria for Axisymmetric and TwoDimensional Supersonic Inlets and Exits, NACA Technical Note 3589, 1956. [25] J.F. Connors, G.A. Wise, J.C. Lovell, Investigation of Translating-Double-Cone Axisymmetric Inlets with Cowl Projected Areas 40 and 20 Percent of Maximum at Mach Numbers from 3.0 to 2.0, NACA Research Memorandum E57C06, 1957. [26] M.R. Soltani, M. Farahani, Performance study of an inlet in supersonic flow, Proc. Inst. Mech. Eng. G, J. Aerosp. Eng. 227 (1) (2013) 159–174.
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Aerospace Science and Technology www.elsevier.com/locate/aescte
A proposed design method for supersonic inlet to improve performance parameters M. Farahani ∗ , M.M. Mahdavi Department of Aerospace Engineering, Sharif University of Technology, Azadi Street, P.O. Box 11365-11155, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 25 October 2018 Received in revised form 20 March 2019 Accepted 6 May 2019 Available online 9 May 2019 Keywords: Supersonic inlet design Pressure recovery Compression ramp
a b s t r a c t A new structure for the compression surfaces of a supersonic inlet is proposed which has improved the target performance parameter i.e. total pressure recovery ratio. This idea resulted in development of a new type of supersonic inlet, utilized four ramps and a cone simultaneously as the compression surfaces. A prototype of the proposed inlet has been designed for a free stream Mach number of 3 and its performance has been evaluated via numerical simulation for both design and off-design conditions. The performance of the newly designed inlet has been compared to the existing experimental data of two double-cone inlets. The acquired data are further compared with analytical calculations of maximum reachable TPR for some conventional supersonic inlet types. The results confirmed the effectiveness of the main idea of the proposed design methodology. The total pressure recovery ratio of the newly designed inlet at its design condition, M∞ = 3, is calculated to be 76.8%. © 2019 Elsevier Masson SAS. All rights reserved.
1. Introduction Air intakes are considered to be the most important parts of an air-breathing propulsion system of a supersonic flying vehicle. This importance has two clear aspects: first, from the pressure distribution analysis, air intakes usually partake the greatest share of thrust production; and second, as a result of both high velocity and shock structure effects, an improper design of the air intakes might have immense effects on the propulsion performance, when flying supersonically. Air inlets have to meet design objectives to provide a sufficient amount of air for the propulsion system, with highest reachable quality, and of course least cost. In addition, the inlet must be able to provide sufficient mass flow rate for all flight conditions of the inlet operation. The two major criteria of the inlet air quality are higher total pressure and lower distortion. Meanwhile, the cost of the entire inlet performance is described by its drag. This introduction suggests that these four quantities, mass flow rate, preserved total pressure, distortion, and drag are the most important objectives of an inlet that must be considered during its design process. The dimensionless forms of the mentioned parameters could be used as the main performance parameters of an air inlet.
*
Corresponding author. E-mail addresses: [email protected] (M. Farahani), [email protected] (M.M. Mahdavi). https://doi.org/10.1016/j.ast.2019.05.014 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.
In addition to the above parameters – which are mostly related to the steady performance of an inlet. Stability margin (buzz limit) is another significant issue in the performance of a supersonic inlet. As this paper is focused on the steady performance, this parameter will not be considered here; however, distinct studies have been carried out by the present authors in order to identify the buzz phenomenon in the supersonic inlets [1–7]. The present study is an effort to develop a new type of air intake for the supersonic flight regime, with an improved performance criterion. Same as many other performance improvement and optimization studies, this study is not capable of meaningfully improve all performance parameters too. Thus, it is inevitable to draft a “target performance parameter”. The main target of this investigation is to increase the total pressure of the captured air, through lowering the total pressure drop in the inlet flow. Shock waves and boundary layers are two major loss mechanisms of the total pressure at the inlet. Consequently, there exist two different trends for minimizing the total pressure drop of an air inlet. The first trend is a set of studies and methods to control the boundary layer growth and to prevent separation. A few samples of these studies and methods could be found in refs. [8–12]. The second trend, consists of investigations which aimed to lower the total pressure loss through manipulating both the shock structure and the flow geometry in order to make the inlet more efficient or to increase its robustness when flying in off-design conditions.
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Nomenclature
α D M P X Re
Half Angle of Compression Surfaces Maximum body diameter Mach number Pressure Axial position Reynolds number, based on maximum body diameter
Abbreviations AIP MFR RC
Aerodynamics Interface Plane Mass Flow Rate Ratio Ramped Cone
Total Pressure Recovery Ratio
TPR
Subscripts 1st step 2nd step 3rd step A B C r
∞
First Compression Step (First Shock Wave) Second Compression Step (Second Shock Wave) Third Compression Step (Third Shock Wave) Zone A Zone B Zone C Ramp Free Stream
Fig. 1. Schematic of inlet with imaginary heat source, proposed by Soltani et al. [19].
One of the first known innovations in this context was through the use of compression surfaces to increase the compression stages. This Idea has been proposed by Ferry and Nucci in 1946 [13] and increased the reachable total pressure, in comparison to the un-started internal compression. It should be mentioned that Ferry and Nucci actually proposed their method, for the conventional 2D and/or for conical supersonic inlets. A few other studies used optimization loops to reach an optimum performance in the so-called conventional inlet structures. These optimization codes aimed at various target parameters and have used various optimization variables. For example, Rodriguez [14] used 13 geometrical optimization variables to design an optimized inlet for four distinct sets of target functions and geometrical constraints, by using the simplex algorithm. In another example, Zha et al. [15] used the genetic algorithm with 6 geometrical constraints and 8 optimization variables to design an inlet with an optimized TPR. In addition to the above studies, other researchers have studied consequences of several unconventional conversions on the inlet geometry. Chernyavsky et al. [16] studied the effect of sweep angle in the ramp leading edge and were succeeded to increase the total pressure recovery. Their study was carried out for a range of Mach numbers M∞ = 3 − 8. It should be mentioned that their TPR for a free stream Mach number of 3 was the same as the TPR for the design point of the present study, 64 percent [16]. In another effort, Kim and Song [17] studied the effect of bump addition to the ramp surface of a 2D inlet. Their result showed a 3 percent improvement in the total pressure recovery ratio of the sample inlet for the design Mach number of M∞ = 2. Bump inlets are of interest both as an alternative compression surface and as a boundary layer diverter. Yu et al. [18] have provided an effective, inverse design method for the bump inlets. In another effort, Soltani et al. [19] placed an imaginary heat source in front of the cowl lip of an axisymmetric conical intake and studied its effects on the shock structure and on the inlet performance. They succeeded to decrease the intake drag coefficient by 18 percent. Fig. 1 shows a 3D Schematic of the proposed Idea of using an imaginary heat source. Utilization of a bypass duct in an intake is another Idea which has been proposed by Kim et al. [20]. The proposed inlet of their study intentionally captured a surplus amount of flow rate. This superfluity of the captured flow enables the inlet to bypass the
Fig. 2. TPR of core, bypass and net captured flow of air inlet of [20].
excess mass flow rate with lower TPR losses. This idea is more effective to remove the bow shock effects from the core flow through spillage. Fig. 2 shows the resulting total pressure recovery for various mass flow rates. As it is evident, the core flow seems to have a more efficient and a more robust performance in preserving the total pressure ratio, in comparison to the net captured air of the core plus bypass flow. Similar to the Kim et al. [20] proposal several other studies, have focused on ideas to make inlets more robust in the case of the off-design flight conditions. The throat area and the cowling position angle are the two usual parameters for controlling the off-design spillage which results in deterioration of both TPR and MFR. For conical inlets, these parameters, TPR and MFR, are varied by the axial position of the spike. Maru et al. [21] proposed a new spike design through employing several rows of cone frustums. Their technique ensured that the throat area and cowling position did not have significant effects on the TPR or MFR. In another study, Weir et al. [22] suggested a canaled center-body which provided an alternate mechanism to control the throat area, instead of varying the spike position. 2. The proposed inlet A supersonic inlet could yield more TPR as its number of shock wave compression stages are increased. This fact has motivated designers to implement several ideas to improve the shock structure of supersonic inlets. The present study, however, proposes a new idea and its implementation will result in a new inlet type. The main idea is to study whether appendation of two transverse oblique shocks with increase the TPR of a conical shock structure formed instead of a conventional axisymmetric external-compression inlet. The aforementioned oblique shocks will increase compression stages on the inlet flow and a resultant increase in the final TPR value is expected. For convenience, this new type of inlet is called “RC inlet” in the present paper (the term
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Fig. 3. A generic geometry, simulating RC-inlet for zero-dimensional analysis. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
“RC inlet” has been adopted as an abbreviation of “a ramped-cone inlet”). The study started with a generic geometry, composed of two transverse ramps and a chasing cone. Fig. 3 depicts this schematic geometry with arbitrary lengths and angles. The backward boundary of the domain of this figure is a pressure contour on an assumed cross plate, where the conical shock trace (red zone) is completely inscribed inside the oblique shocks intersection (turquoise zone). A hypothetical axisymmetric cowl behind the cone in the above geometry has been assumed in order to create a hypothetical normal shock. Accounting to this normal shock, the shock structure on the above geometry – in its zero-dimensional form, would be approximately similar to that of the generic RC inlet. However, the above geometry, with its infinite ramp span, is not a realistic design for the compression surfaces of an inlet. It is, therefore, beneficial to run the zero-dimensional analysis for the corresponding RC inlet. This zero-dimensional analysis is based on the shock-expansion theory. The so called “conical-shock on lip” assumption for a hypothetical cowl lip means that the cowl lip is of a circular type on which the conical shock lies. In this shock structure, it is assumed that almost all of the captured mass flow will pass through the four distinct shock waves. The first confronting shock wave is an oblique shock rooted from the closest ramp. This shock turns the horizontal upstream flow through a turning angle of “αr ”, upward of the first ramp which is equal to the half angle of the ramp. This turning angle, assigns the flow direction in the affected zone of the first shock, called “zone A” in this paper. Moreover, this angle determines values of both Mach number and total pressure in this zone, zone A. It should be mentioned that the above shock structure has two distinct zones, shown as “zone A” in Fig. 3, owing that the codename of zone A, is defined on the basis of the “closest ramp” where the free stream particles first encounter. These two zones will intersect with each other, turquoise zone of Fig. 3, and create other zone called “zone B”. The flow in this zone, zone B, has been influenced by both ramps i.e. zone B is the region behind both oblique shocks. After confronting the second oblique shock wave, the flow direction of zone A turns in a manner to satisfy the second ramp tangency condition. The corresponding turning angle of the second shock could be determined from a simple geometrical analysis as:
α2nd = arctg sin (αr )
(1)
in which the term αr denotes the half angle of the ramps. The above turning angle, as well as the flow Mach number in zone A, define the flow characteristics in zone B.
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Two lax, but acceptable assumptions has been made in this procedure. The first one neglects particles that exist in the proximity of the bisector plane of the inter-ramps space. The previous two-stages model of the transverse oblique shocks is valid only for particles which are adequately away from the bisector plane. Particles that are in the vicinity of the bisector plane sense the presence of both ramps simultaneously, which means that these particles would be transferred to zone B via a single oblique shock wave, third oblique shock. This oblique shock is stronger than the previous two oblique shocks. This clearly indicate that the third oblique shock, causes a higher total pressure loss and the corresponding Mach number of the flow in this region would be low. However, zone B covers only a thin frontal area and the losses of total pressure and Mach number in this region do not cause significant effect on the average Mach number and on the total pressure of the final captured flow. Based on this argument, it is assumed that the third oblique shock can be neglected and the entire influence of ramps on the shock structure, could be modeled by a two-stage oblique shocks model. The second so-called lax assumption is the uniformity of the flow in zone B. The third oblique shock has significant effect on this assumption, but as state into previous section, this shock wave could be neglected in the first assumption. Thus the uniformity of flow in zone B is a fair assumption. By justifying these two assumptions, the two-stage shock model is capable of determining all flow variables in zone B, Mach number, total pressure, and velocity direction. The remaining two shock waves, a conical shock and a hypothetical normal shock, might be treated in a similar manner as the first oblique shock was handled. The conical shock wave is propagating only in zone B hence its affected zone called “zone C”, red zone in Fig. 3, could be determined from the Taylor-Maccoll method [23]. The following hypothetical normal shock wave, which lies in zone C, could be treated by the normal shock relations. An alternative way to model these two shocks is to consider them as waves that would be generated in a complete conical external compression intake. Connors and Meyer [24] published a paper which applies similar assumption, hence their result could be utilized to model the previous two shock waves simultaneously. Their paper analytically determines the maximum reachable TPR for each Mach number and the corresponding cone angle for a generic conical intake. Table 1 presents the steps of the zero-dimensional analysis of the shock structure, used in this investigation. In each step of the procedure shown in Table 1, the fraction of the total pressure loss is calculated. Three steps mentioned in the above table results in some percentages of total pressure drop. The final total pressure recovery ratio of the shock structure is then determined from the following equation:
TPRfinal
= TPR1st step (M∞ , αr ) ∗ TPR2nd step (MA , αr ) ∗ TPR3rd step (MB ) (2) where
MA = f1 (M∞ , αr )
(3)
MB = f2 (MA , αr )
(4)
The above equation suggests that by utilizing this procedure, the maximum reachable TPR of the final shock structure for any given free stream Mach number, could be determined as a function of ramp angle. Fig. 4a shows the TPR results as a function of ramp angle obtained from equation (2) for various free stream Mach numbers.
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Table 1 Summary of three steps of compression by shock waves in zero-dimensional analysis. Step
1 2 3
Step definition
First oblique shock Second oblique shock Conical + normal shock
Neighboring zones Upstream
Downstream
Free stream Zone A Zone B
Zone A Zone B Hypothetical subsonic diffuser
Ramp/cone effective angle
Determination procedure
αr
Oblique shock relations Oblique shock relations See ref. [24]
Arctg(sin (αr )) Optimized cone angle for Mach number of zone B
Fig. 4. Results of effectiveness investigation of appending the ramps. TPR of zero-dimensional RC-inlet as function of ramp angle, in various Mach numbers. a) In raw form. b) In normalized form.
This figure shows the maximum reachable TPR for any ramp angle for each free stream Mach number. It is clearly seen that appending the ramps has improved TPR value. In addition, an optimal ramp angle can be deduced for each free stream Mach number from the maximum value of the corresponding TPR. Fig. 4a shows that, for a free stream Mach number of 3, the shock structure for the hypothetical intake which has compression surfaces similar to that of Fig. 3, and a ramp angle of 11 degrees, can reach a total pressure recovery ratio of 0.84. In addition, the cone angle for this optimized design would be 28 degrees which has been determined in accordance with Connors and Meyers procedure [24]. Fig. 4b illustrates similar data normalized to the zero ramp angle case. From this figure it is seen that by means of appending the ramps, the corresponding values of TPR of a conical external compression inlet has been increased about 42 percent for M∞ = 3, 68% for M∞ = 3.5 and finally 95% for M∞ = 4. This result suggests that these ramps become more effective as the upstream Mach number is increased. The above results display the level of effectiveness of the ramps and the optimum ramp angle; however, this zero-dimensional analytical simulation of the RC-intake performance, does not show any details involved in the geometrical optimization of each component i.e. ramp sweep angle, the distance between the cone and the ramp’s apex, and the optimized shape of the cowl lip. This insufficiency would be eliminated by means of a three-dimensional design optimization loop in which a full 3D geometry of the final RC-type inlet could be extracted. Fig. 5 shows the corresponding final intake geometry. 3. Numerical simulation As the final step of this study, the performance of the final geometry of the resulting optimized RC-inlet has been numerically simulated in order to verify the effectiveness of the proposed method. These sets of simulations are used to calculate the total pressure recovery of the present RC-inlet operating at its design point. In addition, variation of mass flow rate ratio, Mach number and angle of attack on the performance of the inlet are investigated. The final results are compared with the corresponding TPR outputs of multi-cone inlets which had been experimentally stud-
Fig. 5. 3D view of the final RC-inlet geometry (cut through a symmetric plane).
ied by Connors and Wise [25]. In addition, analytical computations of Connors and Meyers [24] have been used to compare performance of the present RC-inlet for its designed condition with a maximum reachable TPR with a few other 2D and axisymmetric inlets. 3.1. Simulation setup The simulations of flow field around the RC-inlet, has been performed from the well-known Ansys Fluent CFD code. The solutions are focused on the steady-state behavior of the inlet. The Flow equations have been solved in density-based form by using the implicit Roe-FDS formulation. According to the 4-plane-symmetrical nature of the RC-inlet and in order to reduce the computational costs, an octant slice of the full scale inlet geometry has been used to run the simulations which is an appropriate condition for the zero degrees angle of attack condition. The numerical domain of each octant of the inlet has been discretized by 250,000 cells. In this case, the rest of the inlet has been modeled by the symmetry planes which are the side boundaries of the numerical domain. The upstream flow is modeled by the “pressure far-field” boundary condition and the AIP at the end of the inlet duct has been modeled by the “pressure outlet” boundary condition. Fig. 6a depicts a cut view of the structured mesh on a symmetry plane of the present RC-inlet.
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Fig. 7. Effect of Reynolds number on the TPR for a sample inlet geometry.
Fig. 8. The supersonic inlet used for validation.
Fig. 9. Location of pressure ports on the validation inlet.
Fig. 6. Generated numerical mesh. a) On a symmetric plane. b) On a symmetric plane and half geometry walls.
For the case of the flow simulations used to investigate the intake performance for non-zero angles of attack, a half slice of the full geometry must be used. This half geometry consists of four similar octants and is shown in Fig. 6b. This figure provides an insight into to the full structure of the generated numerical grid. It should be mentioned that the present simulations are based on the inviscid assumption. This assumption would clearly result in an over-estimation of the total pressure recovery, but it has been assessed to be helpful to eliminate the size effects on the TPR. Note that the size effects should be eliminated in the present simulations because this study is focused on a maximum reachable TPR for the new inlet type, not for a certain inlet with a specific size. To compensate for the effects of the over-estimation of TPR in the present RC-inlet performance, its total pressure recovery output at the design-point has been compared to the inviscid analytical calculations of Connors and Meyers. [24] The other benchmark which has been used in this study for comparison is the experimental performance data of two axisymmetric inlets, provided by Connors and Wise [25], however, these performance data count for the viscous losses in TPR. However, it is noted that TPR output of these inlets based on the viscous losses are sufficiently close to that inviscid values. This viscous independency is mainly due to the correlation of TPR and Reynolds number of the inlet which as depicted in Fig. 7.
This figure shows that the total pressure recovery ratio of any inlet approaches its inviscid limit for large scales, high Reynolds number. Furthermore, TPR approaches its creeping limit for very low Reynolds number. Note that the inlets of Connors and Wise have been tested at a Reynolds number of 2.5 × 106 , hence, their output TPR could be assumed to be close to its inviscid value. 3.2. Validation The simulation setup has been validated, using experimental performance data of an axisymmetric, single-cone inlet. This inlet has been designed for a free stream Mach number of M∞ = 2. Experimental performance study of this inlet has been performed by the authors and further detail of the experimental data and setup has been presented in ref. [26]. Fig. 8 shows the wind tunnel model of this inlet. The static pressure distribution over both the spike and the outer cowl surfaces has been measured for this intake. The pressure distribution on these two surfaces is used to validate the simulation setup on the same geometry. Fig. 9 shows the location of static pressure ports on the spike and on the outer cowl surfaces of this intake. There are 16 pressure taps on the outer cowl surface and 27 ports on the spike surface of the model. Moreover, three total pressure rakes has been embedded in this intake; however, the output of these rakes are not used in this validation procedure. The inaccuracy of the experimental measurements for the inlet shown in Fig. 8, has been investigated and reported in ref. [26] and are presented in Table 2. Moreover, all measurements were
Table 2 Measurement inaccuracies at the validation experimental test.
P0∞ /P0∞
P0 /P0
P/P
(P/P∞ )/(P/P∞ )
M/M
T0∞ /T0∞
T/T
0.01%
0.73%
0.74%
1.04%
0.8%
0.03%
1%
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Fig. 10. Comparison of the numerical prediction of the pressure on the spike surface, with experimental data.
Fig. 12. Comparison of the numerical prediction of the pressure on the external cowl surface, with experimental data.
Fig. 11. Center-body of the validation inlet.
repeated several times to ensure the repeatability of the measurements. The result shows that the maximum differences in successive measurements of a sample parameter (P/P∞ ) is about 1.04%. Fig. 10 shows both the measured and predicted static pressure distribution on the spike surface. The numerical simulations were performed at the same conditions of the numerical case, i.e. both the free stream condition and inlet back pressure were exactly the same for the two cases. As it is shown in Fig. 10, the conical shock wave increases the static pressure up to 2.65 times that of the free stream pressure. Then the first normal shock increases the static pressure to nearly 5 times larger than the free stream pressure. After that, nearly linear decrease in the static pressure occurs which continues until X = 1.5 and just a local pressure increase near the throat ( DX ∼ 1) D disrupts it. This pressure jump had been formed by the viscosity dominance in the throat region where the inviscid numerical solution has failed to simulate it. Moreover, the experimental model used four struts to hold the spike which the present simulation scheme did not model then. However, this model inaccuracy resulted in a 25 percent error in the calculation of the static pressure at the throat, which could be acceptable, since it had a negligible effect on the total performance of the intake. Fig. 11 shows an image of the center-body of this inlet, the mentioned struts are reviled in this figure. The second notable error in the numerical result of Fig. 10 is related to the downstream value of the pressure at the second norX mal shock ( D = 1.5). The numerical solution has over-estimated the static pressure downstream of this shock wave by about 15 percent. In the same manner, Fig. 12 shows the static pressure distribution on the external cowl surface. According to this figure, the main trend of the numerical result and the experimental data are similar.
Fig. 13. A sample Mach number contour on the ramp surface and the symmetry planes of the RC-inlet.
4. Results 4.1. Flow structure around an RC-inlet as seen the new RC-inlet has a significantly unconventional geometry, therefore, would be convenient to make a perception to its flow structure before proceeding the performance-study. Fig. 13 depicts a cross view of the present inlet and its Mach number contour. The Mach number contour is illustrated for a free stream Mach number of 3, zero degrees angle of attack and in the presence of some flow spillage. For legibility of this figure, both the spike and the cowl surfaces are colored in solid gray and the Mach number contour has been shown on the both ramp surfaces and the symmetry planes. Orange color on the ramps shows a reduction in the Mach number over ramp surfaces as a result of the presence of oblique shocks which are rooted from the ramp leading edges. The green region surrounded the spike represents Mach number reduction due to the conical shock wave rooted from the spike apex. At last, the blue region represents the subsonic zone following the spillage bow shock. As it is clearly shown in Fig. 13, the spillage bow shock is located behind the cowl lip protrusion. This suggests that some parts of the cowl lip are submerged in the spilled subsonic zone, while other parts of the cowl lip are exposed to the supersonic flow. This result unveils the characteristic procedure of spillage in the RC-inlets. In the case of low spillage rates in RC-inlets, the spilled flow is limited to a small region at the intersection of the cowl lip and the ramp surface. As the spillage rate is increased, this small region grows and the subsonic zone covers a larger area on the cowl lip. Finally, just for the extreme spillage conditions, the cowl lip would be submerged in the subsonic region completely.
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Fig. 15. Comparison of TPR of present RC-inlet in design point, with maximum reachable TPR of 4 axisymmetric inlet types (curves from Connors and Meyers [24]).
Fig. 16. TPR of the present inlet and axisymmetric inlets of Connors and Wise [25], as function of MFR.
Fig. 14. Mach number contours of several cross plane around the present RC-inlet.
In order to make a perspective insight, Fig. 14 shows the Mach number contour of the present RC-inlet on an identically spaced cross planes. These contours are extracted for the same flight conditions of Fig. 13 and the Mach number range is the same too. Fig. 14a shows the Mach number contour on a cross plane, located 0.3D behind the apex point of the ramps. As seen from this figure, every pair of the neighboring ramps, form a complicated shock wave with the triangular cross-section on this plane. The first cross plane, Fig. 14a, is located ahead of the spike surface, thus it does not encompass the influence zone of the spike. In return, propagation of the conical shock (rooted from the spike apex) is shown in Fig. 14b as small green regions. Fig. 14c shows a crossplane which crosses the cowl lip of the inlet. This figure shows the subsonic captured flow as well as the spillage regions in the corners of the cowl section. In summary, Fig. 14d and Fig. 14e show the shock structure on the rest of the inlet and transition of the complicated shock structure to a nearly conical sonic boom. 4.2. RC-intake performance in design point One of the first touchstones to umpire the performance of the new RC-inlet is to compare its TPR at design point with the maximum reachable TPR of other inlet at the same free stream condi-
tion. Fig. 15 shows the results of this comparison. The TPR output of the present RC-inlet has been predicted from the CFD simulation and is equal to 76. The zero-dimensional analysis, had previously predicted the same parameter to reach 84 percent, the difference in the values is obviously due to the different levels of the fidelity between the 3D flow simulation and the zero dimensional analysis. These values are compared to the analytical calculation of the maximum reachable TPR of a few inlets [24] in Fig. 15. It should be noted that the fidelity of the analytical curves is the same as that of the zero dimensional calculation of the TPR of the present inlet. As seen from Fig. 15, data compares very well with each other. However, Fig. 15 shows that the present inlet yields more TPR in comparison to other inlet types at the same free stream Mach number of M∞ = 3. 4.3. Mass flow rate dependency It is known that in off design operation mass flow rate has significant effect on the TPR and any reduction of the mass flow rate leads to the subcritical operation of the inlet and results in a spillage. This spillage usually dictates a bow shock wave which deteriorates the shock structure design and decreases the total pressure recovery ratio significantly. Fig. 16 shows the effect of TPR on the mass flow rate ratio, for the present inlet and for two other inlets which were experimentally studied by Connors and Wise [24]. According to Fig. 16, the present intake has a reasonable correlation between TPR and MFR, further it has higher total pressure recovery ratio for all MFRs considered here when compared to two other inlets. Fig. 17 shows the Mach number contours for several values of the spillage flow. The first contours, Fig. 17a represents the supercritical condition of the RC-inlet and the following three contours, represent the subcritical conditions with approximately 5 percent
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Fig. 18. Drag coefficient of the present inlet, versus normalized MFR.
Fig. 19. TPR of the present inlet and axisymmetric inlets of Connors and Wise [25], as function of MFR.
MFR Fig. 17. Mach number contour for four values of MFR . a) 1, b) 0.95, c) 0.85, d) max 0.76. (Left: contour on the ramp-side symmetry plane and corresponding ramp. Right: contour on the ramp-far symmetry plane.)
(Fig. 17b), 15 percent (Fig. 17c) and 26 percent (Fig. 17d) of flow spillage in their captured flow. The spilled amount of the inlet flow is characterized by the percentage of the drop in MFR, compared to the corresponding supercritical MFR case (MFRmax ). In addition to the above data, dependency of the drag coefficient of the present inlet to mass flow rate ratio might be of interest. Fig. 18 shows the pressure drag coefficient of the present inlet as a function of normalized MFR. This curve has not been compared to experimental inlets, because the net pressure drag in the experimental data of Connors and Wise [24] are not exact. However, to make a comparative sense, it should be noted that the approximation of the pressure drag coefficient in the first experimental inlet is a linear interpolation between CD = 0.4 at a normalized MFR of 0.7 and CD = 0.165 at a normalized MFR of 1. 4.4. Mach number dependency The effect of variation of the free stream Mach number on TPR is another important criterion in the off-design analysis. Similar to the previous section, this dependency on the present RC-inlet has been studied and the results are compared with the experimental data of the inlets of Connors and Wise [24]. Fig. 19 depicts the total pressure recovery ratio of these inlets for various Mach numbers.
Fig. 20. Normalized supercritical MFR of the mentioned inlets, as function of Mach number.
Inlet mass flow rate (MFR) is another performance parameter which varies with variation of the free stream Mach number. Fig. 20 shows the corresponding variations for the supercritical operation of the present inlet and the data is compared with the experimental inlets of Connors and Wise. Note that the curves in this figure have been normalized with the supercritical MFR for the design Mach number (M∞ = 3). Fig. 20 shows that the supercritical MFR of the present inlet has more coherence with the free stream Mach number than the other two inlets of ref. [25]. This severe sensitivity to the Mach number variation is rooted in small throat area which had been obtained by the TPR optimization and causes intense spillage in below-design Mach numbers. Further studies incorporating a multidisciplinary optimization of RC-inlet is expected to alleviate this problem. As a supplement to the Mach number dependency of the present inlet, the off-design performance at a subsonic Mach number of 0.7 had been simulated. The results showed that the present
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Fig. 21. Supercritical MFR of RC-inlet as a function of angle of attack, normalized by its value in zero angle of attack.
inlet yields 0.99 percent TPR, while the normalized MFR in this Mach number drops down to 0.35 percent 4.5. Angle of attack dependency The other off-design condition to be studied on the new inlet type is its operation at non-zero angle of attack. The main parameter studied in accordance to angle of attack variations, is the robustness of the captured mass flow rate ratio. Fig. 21 shows the supercritical MFR of the present inlet in various angles of attack, alongside of the aforementioned inlets of Connors and Wise. All three curves in this figure, have been normalized by the critical MFR at zero degrees angle of attack (i.e. MFRmax ) in order to demonstrate the percentage of MFR drop of each inlet geometry, at each angle of attack. According to this figure, the MFR drop trend in RC-inlet is almost similar to the second intake of Connors and Wise [25]. Fig. 22 shows the flow structure on the RC-inlet, exposed to a ten degrees angle of attack. Note that the back pressure has been set to zero, in order to measure the supercritical MFR; thus the termination shock has been completely swallowed.
Fig. 22. Mach number contour on a) symmetry plane and b) its perpendicular plane.
Declaration of Competing Interest There is no competing interest for authors in this paper. References
5. Conclusions A new configuration for a supersonic air inlet has been proposed. The novel idea of this new configuration was through the simultaneous use of a cone and four ramps as compression surfaces. This new configuration suggests a new type of supersonic inlet. A sample version of this new inlet type has been designed for a free stream Mach number of 3 and its performance has been studied by a numerical simulation for both design-point and offdesign operations. The design-point performance has been compared with the analytical predictions of Connors and Meyers [24] for the maximum reachable TPR of a few conventional conical inlet types. In addition, the off-design performance has been compared to the experimental results of two conical inlets, published by Connors and Wise [25]. Both design-point and off-design results, show an acceptable performance with a higher reachable TPR when compared with similar inlets and with a few conical inlet types. The results suggest that the simultaneous utilization of cone and ramps as compression surfaces would lead to a notable increase in the reachable total pressure recovery of the air inlet. Introduction of the new RC-inlet type is the main conclusion of the present paper. Further studies on this proposed inlet type, include to design of a new optimized sample of this inlet type and study its unsteady behavior and instability characteristics at various conditions.
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