A CFD Based Sonic Boom Prediction Method and ...

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 99 (2015) 433 – 451

“APISAT2014”, 2014 Asia-Pacific International Symposium on Aerospace Technology, APISAT2014

A CFD Based Sonic Boom Prediction Method and Investigation on the Parameters Affecting the Sonic Boom Signature Lengyana,b,*,Qian Zhansena,b b

a AVIC Aerodynamics Research Institude, Shenyang, 110034, China Aviation Key Laboratory of Science and Technology on High Speed and High Reynolds Number Aerodynamic Force Research, Shenyang, 110034, China

Abstract Based on bodies of revolution, several flight and shape parameters are considered for investigating their effects on the sonic boom signature including overpressure and impulse. Here, the parameters include flight altitude, Mach number, cone half-angle, bluntness and fineness ratio. Mach numbers are varied from 1.41 to 4.63 due to publicized wind tunnel experimental data for reference. Near-field domain at the flight altitude is modeled by the conservative Euler equations, and the far-field region computations are carried out using the Thomas ray tracing method. According to the parametric analysis, it is found that sonic boom can be reduced by increasing flight altitude, decreasing cone half-angle, increasing fineness ratio or decreasing Mach number. However, with the increase of bluntness parameter, the overpressure on the ground decreases first and then rises, and the sonic boom impulse shows the similar trend as the overpressure when the Mach number is between 2.96 and 4.63, but for Mach number of 1.41 to 2.01, the impulse increases near linearly with the increasing of the bluntness parameter. © Published by Elsevier Ltd. This © 2015 2014The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA)

Keywords: sinic boom; overpressure; impulse; effect parameters

1. Introduction Supersonic commercial aircrafts are promising future airliners with the possibilities to meet the growing airlift demand and to liberate passengers from the pain due to the potential to reduce inter-continental travel time. For a

* Corresponding author. Tel.: +86-024-86566625. E-mail address: [email protected]

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA)

doi:10.1016/j.proeng.2014.12.558

434

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

supersonic aircraft, in the near-field flow there exist a series of complicated pressure waves, such as shock waves, contact discontinuities or expansion fans, which originate from various parts of the airframe and engine. At the vehicle nose, there is a rise in pressure followed by a steady decrease to negative pressure, and then rising to atmospheric pressure. When propagated to the ground, these waves coalesce into the characteristic N-shaped wave. The two large pressure changes create a “double boom” effect[1]. Figure 1 shows a schematic of the generation and propagation of sonic boom from the aircraft. The impact of the sonic boom is so large that the Federal Aviation Administration (FAA) has issued a noise policy in Federal Aviation Regulation (FAR) Part 91 item 817 for supersonic aircraft stating: "Since March 1973, supersonic flight over land by civil or private aircraft has been prohibited by regulation in the United States." In order to avoid negative impact of sonic boom on people, the same policy also states in other nations and regions. The sonic boom is one of the most important environment aspects that may affect the future development and the operation of the new generation supersonic transport aircraft, particularly, the second generation supersonic transport and the supersonic business jet. Nobody is expecting the future operation of supersonic transport aircraft, without solving this ecological problem.

Fig. 1. Sonic boom generation and propagation

Sonic boom minimization began with Busemann[2] who told us how to eliminate the wave drag and sonic boom due to the aircraft’s volume in 1955. Later, Seebass and coworkers[3-9] contributed in Sonic Boom mitigation which included midfield effects. In 1975, Darden[10] modified the Seebass-George method to consider standard atmosphere. Jones-Seebass-George-Darden theory is the cornerstone of sonic boom minimization, and has been employed in numerous studies of low-boom configurations. In late 2000, Defense Advanced Research Projects Agency (DARPA) initiated the Quiet Supersonic Platform (QSP) to examine the impact of advanced technology and innovative design approaches on supersonic aircraft. For the first stage, a joint industry/government team led by Northrop Grumman Corporation (NGC) works on “Shaped Sonic Boom Demonstrator” Program (SSBD)[11]. The purpose of SSBD is to mitigate sonic boom via specialized shaping techniques and produce a flat-top overpressure ground wave. The result has shown significant reduction in ground overpressure. In 2002, NGC publicized the project of the second stage[12]. It directed towards development and validation of critical technology for long-range advanced supersonic aircraft with substantially reduced sonic boom relative to current generation supersonic aircraft. Improved capabilities include supersonic flight over land without adverse sonic boom consequences with boom overpressure rising less than 0.3 psf. Delta wing geometry was optimized by Kandil and Ozcer using four design

435

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

variables; maximum thickness ratio, maximum camber ratio, nose angle and dihedral angle[13-14]. It was shown that some of these parameters have significant effect on sonic boom level on ground. In this paper, based on double cone configuration and bodies of revolution[15-16], several flight and shape parameters are considered for investigating their effects on the sonic boom signature including overpressure and impulse. Here, the parameters include flight altitude, Mach number, cone half-angle, bluntness and fineness ratio. Mach numbers are varied from 1.41 to 4.63 due to some wind tunnel experimental results are available for reference. Near-field domain at the flight altitude is modeled by the conservative Euler equations and the far-field region computations are carried out using the Thomas ray tracing method[17]. . 2. Computational investigations of effect parameters In the present investigation, the characteristics of sonic boom considered are maximum overpressure ( dp ) and impulse ( I ³ dp dx ) on ground. Based on a series of revolute body models, parameters including the flight Mach number and altitude, cone half-angle, fineness ratio and bluntness parameter are analyzed. Each model consists of a forebody which is assumed to have a reference length L 5.08cm and a circular cylinder afterbody approximately 20.32cm long, and has a reference cross-sectional area Aref 0.26cm2 . Three kinds of forebody shape are used, including cone, blunt and double-cone geometry. Cone and blunt forebody shape is used for the investigation of shape parameters, and double-cone configuration is used for flight parameters. In order to compare with measured signatures, the calculation conditions are the same as experimental in the process of near-field simulation, and the pressure distributions at zero angle of attack taken at h L 2,5 from the model, where h is the distance to the model. Considering far-field propagation with actual aircraft which is assumed to have a reference length of 10.16m, nearfield data need to multiply scale coefficient before propagating to the ground according to the similarity laws. For all the cases, the data at h L 2 are used as initial value for propagating to far-field, and the data at h L 5 are used to compare with experimental data. 2.1. Effect of cone half-angle To investigate the effect of the cone half-angle T on sonic boom, a series of CFD simulation are obtained by varying cone half-angle from 3.24 to 12.75 . The maximum cross-sectional area Amax is equal to reference Amax Aref 1.0 . The test models are given in figure 2 and all run cases are summarized in table 1.

Fig. 2. Models in cone series Table 1. All simulations cases for near-field Ma

Static temperature (Pa)

Static pressure (K)

Flight altitude (km)

1.41

21362.9

222.52

11.38

2.01

8675.815

172.0

16.66

2.96

3986.624

125.0

23.4

3.83

1713.198

87.5

28.7

4.63

1217.113

65.11

29.89

Signatures are compared against experimental data given in Ref. 15. More precisely, the P is defined as

436

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

( p  pf ) pf and X is x  x0 where x0 is the distance from the point where pressure curve crossed the x-axis for the first time. In general, the computational and the measured results are in good agreement for all the cases. They are depicted in figure 3. The variation of maximum overpressure and impulse on ground with cone half-angle at different Mach number is shown in figure 4 and 5. These data clearly indicate the strong influence of cone halfangle on the characteristic of the sonic boom. Figure 4 shows the trend toward increased maximum overpressure with increasing cone half-angle. Furthermore, this trend varies with Mach number. At the lower Mach number, the growth rate of maximum overpressure is reduced gradually with increasing cone half-angles. But for the higher Mach number, the maximum overpressure has basically direct relationship with cone half-angle. It is observed that at Ma 1.41 the maximum overpressure rises from 0.53psf ( T 3.24 ) to 0.72psf ( T 6.46 ), but the increase in overpressure is only 0.09psf when the cone half-angle varied from 6.46 to 12.75 . At Ma 4.63 the growth rate is 0.0023psf basically for any cone half-angle. Impulse has the similar trends with the maximum overpressure, Fig. 5. The impulse increases with the increasing of cone half-angle. And also, this trend varies with Mach number. 2.2. Effect of bluntness To investigate the effect of the bluntness on sonic boom, a series of body shapes with various degrees of nose bluntness parameter n is illustrated in figure 6. It should be noted that model 1 in Fig. 6 is identical to model 1 of n section 2.1. The bluntness parameter is defined by the equation r kx , where r is nose radius of model and x is distance along longitudinal axis from model nose, representing the body shape. Test cases for different bluntness parameter are the same as that in table 1.

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 3. Compared of experimental data to the present numerical solutions at

h L 5

437

438

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 4. Variation of ground maximum overpressure with cone half-angle at different Mach numbers

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

439

Fig. 5. Variation of ground impulse with cone half-angle at different Mach numbers

Fig. 6. Models in bluntness series

The comparison between the experimental and predicted signatures at h L 5 is shown in figure 7. It is observed that they are in good agreement for all the test cases. Figure 8 and 9 shows the variation of maximum overpressure and impulse on ground with bluntness parameter for Mach number from 1.41 to 4.63. These data clearly indicate the strong influence of bluntness on the characteristics of the sonic boom. In Fig. 8, results show that the overpressure decreases first and then increases with the increasing of bluntness parameter. So, it has optimal bluntness parameter for minimizing maximum overpressure. Optimal bluntness parameter is found to be sensitive with Mach number.

440

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Optimal bluntness parameter varies from about 0.62 to 0.49, 0.4, 0.36 and 0.38 with Mach number of 1.41, 2.01, 2.96, 3.83 and 4.63 respectively. In fig. 9, one can observe that impulse has nearly linearly increased with the increase in Mach number with the case of Ma 1.41 and 2.01. Then, the trend of it is similar to maximum overpressure with the variation of Mach number from 2.96 to 4.63. There also exists optimal bluntness parameter for minimizing impulse. The value of optimal bluntness parameter for minimizing impulse varies from about 0.36 to 0.41and 0.43with Mach number of 2.96, 3.83 and 4.63 respectively.

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 7. Compared of experimental data to the present numerical solutions at

h L 5

441

442

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 8. Variation of ground maximum overpressure with bluntness at different Mach numbers

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 9. Variation of ground impulse with bluntness at different Mach numbers

443

444

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

2.3. Effect of fineness ration In the present work, fineness ratio is defined by base area ratios ( Amax Aref ). To investigate the effect of fineness ratio, models of each forebody shape were constructed having area ratio of 1.0 and 4.0 under the condition of the same bluntness parameter. The test models are illustrated in figure 10 and all test cases are also as shown in table 1. It should be noted that model 1, 2 and 3 of this investigation is identical to models of section 2.1.

Fig. 10. Models in fineness ratio

Similar to the previous study, figure 11 shows the predicted solution at h L 5 versus that of the experimental data given in Ref. 16. In general, they are in good agreement for all the cases. Figures 12 and 13 show the trend toward linearly increased maximum overpressure and impulse with increasing fineness ratio. Furthermore, the growth rate varies with Mach number and bluntness parameter. With Mach number of 1.41 and bluntness parameter of 0.5, the maximum overpressure of area ratio of 1.0 is 0.36psf, while that with area ratio of 4.0 shows a value of 0.9psf. The growth rate is 0.18psf. If just changing Mach number to 4.63 and holding the bluntness parameter unchanged, the maximum overpressure reduces from 0.2psf for area ratio of 4.0 to 0.1psf for area ratio of 1.0. The growth rate is about 0.03. So, there is significant reduction in growth rate with Mach number increasing. Compared Fig. 12 to Fig. 13, signature impulse has the similar trends as the maximum overpressure.

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

445

446

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 11. Compared of experimental data to the present numerical solutions at

h L 5

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 12. Variation of ground maximum overpressure with fineness ratio at different Mach numbers

447

448

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 13. Variation of ground impulse with fineness ratio at different Mach numbers

2.4. Effect of flight Mach number and altitude Double-cone geometry is shown in figure 14 and the near-field simulation conditions are illustrated in table 2. The model is defined analytically by: 0.08

r

x

r

x

r

2 2 2

(0 d x d 0.25L)

S 0.02

(0.25L d x d 0.75L)

S 0.04

S

(x 

2 2 ) 2

(1)

(0.75L d x d L)

Fig. 14. Side-View of the double-cone configuration Table 2. Near-field simulations cases for double-cone Test

Altitude (km)

Static Temperature (Pa)

Static Pressure (K)

Flight Mach

1

11.38

21362.9

222.52

1.41ˈ2.01ˈ2.96ˈ3.83ˈ4.63

2

16.66

8675.815

216.65

1.41ˈ2.01ˈ2.96ˈ3.83ˈ4.63

3

23.4

3986.624

216.65

1.41ˈ2.01ˈ2.96ˈ3.83ˈ4.63

Signature got in test 1 with Mach number of 1.41 is compared against experimental data and shown in figure 15. The computational solutions and the measured results are in good agreement generally. Figure 16 illustrates that the characteristic of sonic boom is reduced gradually with flight altitude increasing which has already been identified in Ref.18. At the Mach number of 1.41, in comparison with the maximum overpressure of the test case 1 (0.59psf), the overpressure of the test case 2 is 0.28psf. This represents 53% decrease in the sonic boom ground signature. At the same time, comparing test case 2 with test 3 (0.16psf), overpressure has reduced by 44%. It is observed that the growth rate is lower than before when the flight altitude is above 17km. This trend is identical fo r all the Mach number calculated in the present study. Impulse has the same trend with overpressure. Figure 17 shows that the characteristic of sonic boom is increased gradually with increasing flight Mach number. At the flight altitude of 11.38km, the rise in overpressure is 11% with Mach number going up from 1.41 to 4.63, and impulse has significant

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

rise about 2.5 times. So, impulse is more sensitive to Mach number.

Fig. 15. Compared of experimental data to the present numerical solutions at

h L 5

Fig. 16. Variation of ground overpressure and impulse with flight altitude

449

450

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451

Fig. 17. Variation of ground overpressure and pulse with Mach number

3. Conclusion For the ground sonic boom prediction, near-field domain at the flight altitude is modelled by the conservative Euler equations, and the far-field region computations are carried out using the Thomas ray tracing method. Based on bodies of revolution, several flight and shape parameters are considered for investigating their effects on the sonic boom signature including overpressure and impulse. Here, the parameters include altitude, Mach number, cone half-angle, bluntness parameter and fineness ratio. Mach numbers are varied from 1.41 to 4.63 due to publicized wind tunnel experimental results are available for reference. According to the parametric analysis, it is found that: z Solutions clearly indicate the influence of cone half-angle on the characteristics of the signature. It shows the trend toward increased maximum overpressure with increasing cone half-angle. Furthermore, the increasing ratio varies with Mach number. z Bluntness has an effect on the characteristics of the signature. Calculation results show that the overpressure decreases first and then increases with the increase of bluntness. z Fineness ratio has an impact on the characteristics of the signature. Solutions show that the overpressure decreases with the increase of fineness ratio. z Results show the variation of the maximum overpressure with flight altitude and Mach number. In the case of the same Mach number, the overpressure decreases with increasing flight altitude quickly; and in the case of the same flight altitude, the overpressure increases with increasing Mach number. So, flight altitude is more important in contrast with Mach number. References [1] Maglieri D J, Plotkin K J. Sonic boom, chapter 10, aeroacoustics of flight vehicles[ R]. NASA RP-1258, 1991, 1: 519-561. [2] Busemann, A., The Relation between Minimizing Drag and Noise at Supersonic Speeds, Proceedings, High Speed Aerodynamics, Polytechnic Institute of Brooklyn, pp. 133-144, 1955. [3] Jones, L. B., Lower Bounds for Sonic Bangs. Journal of the Royal Aeronautical Society, Vol. 65, June 1961, pp. 433-436. [4] Carlson, H. W., The Lower Bound of Attainable Sonic-Boom Overpressure and Design Methods of Approaching This Limit. NASA TND1494, Oct. 1962. [5] Carlson, H. W., Influence of Airplane Configuration on Sonic Boom Characteristics, J. Aircraft 1, No. 2, 82-86, 1964. [6] McLean, F. E. and Shrout, B. L., Design Methods for Minimization Of Sonic Boom Pressure-Field Disturbances, Journal of the Acoustical Society of America, 39, 5, Part 2, 1966, pp. S19-S25. [7] Ferri, A., Airplane Configurations for Low Sonic Boom, NASA SP-255, Oct. 1970, pp. 255-275. [8] Hayes, W. D., Haefili, R. C., and Kulsvud, H. E., Sonic Boom Propagation in a Stratified Atmosphere, With Computer Program, NASA CR1299, 1969. [9] George, A. R. and Seebass, R., Sonic Boom Minimization Including Both Front and Rear Shocks, AIAA Journal, Vol. 9, No. 10, Oct. 1971, pp. 2091-2093. [10] Darden, C. M., Minimization of Sonic Boom Parameters in Real and Isothermal Atmospheres, NASA TND-7842, 1975.

Lengyan and Qian Zhansen / Procedia Engineering 99 (2015) 433 – 451 [11] Pawlowski J. W., Graham D. H., Boccadoro C. H., Coen P. G., Maglieri D. J., origins and Overview of the Shaped Sonic Boom Demonstration Program, AIAA 2005-5, 2005. [12] Guo R, Study Progress of Boomless Configuration Theory, Advances in aeronautical science and engineering, 2010, 1(4):341 -346(in Chinese). [13] Kandil O. A., Khasdeo N. and Ozcer I. A., Sonic Boom Mitigation through Thickness, Camber and Nose A ngle Optimizations for a Delta Wing, AIAA-2006-6636, 2006. [14] Khasdeo N., Kandil O. A. and Ozcer I. A., Optimization of Delta Wing Geometry parameters for Sonic Boom Mitigation, AIAA-2007-4109, 2007. [15] Carlson H. W., Mack R. J. and Morris O. A., A Wind-Tunnel Investigation of the Effect of Body Shape On Sonic-Boom Pressure Distributions, NASA TN D-3160,November 1965. [16] Sbrout B. L., Mack R. J. and Dollybigb S. M., A Wind-Tunnel Investigation of Sonic-Boom Pressure Distributions of Bodies of Revolution at Mach 2.96, 3.83, and 4.63, NASA TN D-3160, November 1965. [17] Thomas C., Extrapolation of sonic boom pressure signatures by the waveform parameter method, TND-6832, 1972. [18] Dan D, Yang W, Supersonic Business Jet Sonic Boom Computation and Layout Discussion, Advances in aeronautical science and engineering, 2012, 3(1):7-15(in Chinese).

451