Relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body

DONG Su-rong

(College of Mechatronic Engineering, North University of China, Taiyuan 030051, China)

董素榮

(中北大學 機電工程學院， 山西 太原 030051)

?

Relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body

DONG Su-rong

(CollegeofMechatronicEngineering,NorthUniversityofChina,Taiyuan030051,China)

Synthetic analysis is conducted to the wind tunnel experiment results of zero lift drag coefficient and lift coefficient for large aspect ratio winged rigid body. By means of wind tunnel experiment data, the dynamics model of the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body is amended. The research indicates that the change trends of zero lift drag coefficient and lift coefficient to Mach number are similar. The calculation result and wind tunnel experiment data all verify the validity of the amended dynamics model by which to estimate the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body, and thus providing some technical reference to aerodynamics character analysis of the same types of winged rigid body.

winged rigid body; zero lift drag coefficient; lift coefficient; wind tunnel experiment; dynamic characteristics

0 Introduction

The research on relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body is crucial to analysis of motion characteristics of large aspect ratio winged rigid body. On account of uncertainty factors effect such as systematic constraint condition on the motion of large aspect ratio winged rigid body, stochastic environment variation, diversity of configuration as well as motion velocity and attitude[1-3]. In addition, the high altitude aerodynamic characteristics of rigid motion along with the change of the height of sea dials have large differences[4]. The existing dynamics models which estimate the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body have some limitations and errors[5].

Currently, the general practice in obtaining the accurate data of zero lift drag coefficient and lift coefficient is based on of wind tunnel experiment[6-9]. However, the expense of wind tunnel experiment for large aspect ratio winged rigid body often results in lack of the data to modify the dynamics model. This paper combines theoretical analysis, numeric simulation with wind tunnel experiment to investigate the relationship between the lift coefficient and zero lift drag coefficient of large aspect ratio winged rigid body to Mach number. On the basis of wind tunnel experiment data of large aspect ratio winged rigid body, it amends its dynamics model which may provide technology reference to the aerodynamics feature study of the same product.

1 Aerodynamics feature analysis

1.1 Aerodynamics feature analysis

A large aspect ratio winged rigid body is generally composed of two components, as shown in Fig.1. A flying winged rigid body receives action of air drag on the surface whose magnitude rests on configuration, motion velocity and attitude, and action of stochastic environment load[10-11]. The action of aerodynamic force on a winged rigid body will affect the motion distance and stability.

To investigate aerodynamics feature of a rigid body, lift coefficient and zero lift drag coefficient are studied firstly since they are the parameters characterizing the aerodynamics feature. In general, it is required to study separately aerodynamic parameters of every component firstly, and then to take into consideration the interference between components, lastly, to find out the aerodynamics feature parameters of assembly.

Fig.1 Large aspect ratio winged rigid body

1.2 Lift coefficient aerodynamics model of winged rigid body

Suppose a winged rigid body is composed of the body and the wing-tail-body.

1) The lift coefficient of the body,CYB

In subsonic range, i.e.M<1, the lift coefficient of the body,CYB, is approximately a constantCYB=δ, while in supersonic range, i.e.M≥1, the lift coefficient of the body is also approximately a constantCYB=2.4δ. Here,Mis Mach number;δis attack angle.

2) The lift coefficient of wing-tail-body,CYW

(1)

(2)

(3)

(4)

The lift efficiency depends on configuration parameters and motion feature[12-14]. In addition, due to the aerodynamic force interference between two components of winged rigid body, the aerodynamic feature of the wing-tail-body in adjacent area of the body will be affected by the aerodynamic feature in the body area, and vice versa. Consequently, the computation of the lift coefficient of assemblyCYBWshould take into consideration the lift coefficient in the bonding district of two components. We may just as well use an interference modified coefficientCKyto represent the lift coefficient in the bonding district.

By combining the theoretical analysis with experiment modification, the interference modified coefficient formula ofCKycould be obtained by

(5)

whereDis the diameter of cross section of the body;Dbis the bottom diameter of the body, thus, the lift coefficient of assembly is

(6)

1.3 Zero lift drag coefficient aerodynamics model of winged rigid body

Zero lift drag coefficient of winged rigid body is the drag coefficient when the attack angle is zero.

1) Zero lift drag coefficient of the bodyCXOB

When the assembly flies at supersonic speed, the zero lift drag coefficient of the bodyCXOBis composed of its head section wave drag coefficientCXln, tail section wave drag coefficientCXlt, bottom section drag coefficientCxlb, friction drag coefficientCXfBand increased drag coefficient ΔCXFfrom the head section variation of the body, where the configuration in the tail section is the principal factors affecting the tail section drag[15-17]. When the assembly flies at subsonic speed, zero lift drag coefficient of the body,CXOB, has no head section wave drag and tail section wave

(7)

where

(8)

(9)

(10)

(11)

(12)

2) Zero lift drag coefficient of the wing-tail-body,CXOW

WhenM≥1, zero lift drag coefficient of wing-tail-bodyCXOWis composed of profile drag coefficientCXfWand thickness wave drag coefficientCXPW; whenM<1, the thickness wave drag coefficient will not exist.

(13)

(14)

(15)

The zero lift drag coefficient of assemblyCX0is the sum of zero lift drag coefficients of the body and the wing-tail-body. The drag which the wing-tail-body provides to the assembly is proportional toN, which is the pair number of the wing-tail-body.

The zero lift drag coefficient of the assembly formula is

(16)

2 Calculation examples, result analysis and experiment verification

This paper takes a kind of large aspect ratio winged rigid body as an example to calculate its lift coefficient and zero lift drag coefficient. The comparison results of the calculation result and the wind tunnel experiment data are shown in Figs.2 and 3.

Fig.2 Relationship between zero lift drag coefficient of assembly and Mach number

From the figures, the calculation results and the wind tunnel experiment data indicate that the change trends of zero lift drag coefficient and lift coefficient of assembly to Mach number are similar. In transonic region, the zero lift drag coefficient and lift coefficient all present sharp mutations. While in subsonic and supersonic regions, the changes are relatively stable, especially in the region of 1.5Ma to 3.5Ma, the received load of assembly descends in relatively stable mode.

Fig.3 Relationship between lift coefficient of assembly and Mach number

In supersonic region of 1.5Ma to 3.5Ma, the calculation results reflecting the relationship of zero lift drag coefficient and lift coefficient of assembly to Mach number bear fairly good coincidence to the wind tunnel experiment result; While in subsonic and transonic regions, the calculation results have big error compared with the wind tunnel experiment result, because the received load change of assembly and the effect of airflow disturbance change are fairly complex while the existing dynamics model of zero lift drag coefficient and lift coefficient do not take into account reasonably of the received load change of assembly and the effect of airflow disturbance change.

3 Conclusion

The research has indicated that in the region of 0.5Ma to 3.5Ma the change trends of zero lift drag coefficient and lift coefficient of assembly to Mach number are similar, and the theoretical analysis and the wind tunnel experiment results verify the conclusion.

By means of wind tunnel experiment data, the dynamics model of zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body is amended. The calculation results and the wind tunnel experiment results all verify the validity of the amended dynamics model. Consequently, under the condition of lack of aerodynamics experiment data, it is possible to utilize the configuration parameters to amend the theoretical model for estimaion of the aerodynamics character, which can provide some technical reference to aerodynamics design for the same types of the large aspect ratio winged rigid body[18-19].

[1] ZHA Ge-cheng, Smith D, Schwabacher M, et al. High-performance supersonic missile inlet design using automated optimization. Journal of Aircraft, 1997, 34( 6): 697-705.

[2] Jameson A. Automatic design of transonic airfoils to reduce the shock induced pressure drag. In: Proceedings of the 31st Israel Annual Conference on Aviation and Aeronautics, 1990.

[3] ZHANG Bo, XU Yu-xin, CAO Meng-yu, et al. Design and research of wind tunnel test for deflectable nose. Research and Exploration in Laboratory, 2014. 33(4): 18-21.

[4] ZHAI Ying-cun, TAO Guo-hui, DANG Ming-li. The research on aerodynamic characteristics and ballistic characteristics of fin-stabilized rocket at high altitude. Journal of Projectiles, Rockets, Missiles and Guidance, 2011, 31(2): 142-144.

[5] XU Shao-jie, CHEN Xiong, HU Shao-qin.The research of rocket aerodynamic calculation model of engineering algorithm. Journal of Projectiles, Rockets, Missiles and Guidance, 2012, 32(3): 167-170.

[6] Joshi M V, Reddy N M. Aerodynamic force measurements over missile configurations in IISc shock wind tunnel at M=5.5. Experiments in Fluids, 1986, 4(6): 338-340.

[7] Washington W D, Miller M S. Experimental investigations of grid fin aerodynamics a synopsis of nine wind tunnel and three flight tests. In: Proceedings of the RTO AVT Symposium on Missile Aerodynamics, Italy, 1998.

[8] Birch T J, Cleminson J R. Aerodynamic characteristics of a square cross-section missile configuration at supersonic. In: Proceedings of the 22nd Applied Aerodynamics Conference and Exhibit, Rhode Island, 2004.

[9] Birch T J, Prince S A, Simpson G M. An experimental and computational study of the aerodynamics of a square cross-section. In: Proceedings of the RTO AVT Symposium on Advanced Flow Management: Part A-Vortex Flows and High Angle of Attack for Military Vehicles, Norway, 2001.

[10] LEI Juan-mian, WU Jia-sheng. Coning motion and restrain of large fineness ratio unguided spinning rocket stabilized with tail fin. Acta Aerodynamica Sinica, 2005, 23(4): 455-457.

[11] DONG Su-rong, ZHAO Man. Study on dynamic characteristics of spread variable thickness arc-shaped fin. Journal of Projectiles, Rockets, Missiles and Guidance, 2004, (S1): 162-164.

[12] CHEN Nong, JIA Qu-yao. Study of wrap-around fins dynamic characteristics. Acta Aeronautica et Astronautica Sinica, 2002, 23(4): 321-323.

[13] Rossow V J. Lift enhancement by an externally trapped vortex. Journal of Aircraft, 1978, 15(9): 618-625.

[14] Morris S J. Design and flight test results for micro-sized fixed-wing and VTOL aircraft. In: Proceedings of the First International Conference on Emerging, 1997.

[15] Viswanath P R, Patil S R. Zero-lift drag characteristics of afterbodies with a square base. Journal of Spacecraft and Rockets, 1997, 34 (3): 290-293.

[16] Viswanath P R. Drag reduction of afterbodies by controlled separated flows. AIAA Journal, 2001, 39(1): 73-78.

[17] Cox J W, Smith M S, Driggers H H. High lift low drag wing and missile airframe. United States Patent, No. 5154370. 1992.

[18] Sahu J, Edge H L, Heavey K R, et al. Computational fluid dynamics modeling of multibody missile. In: Proceedings of the RTO AVT Symposium on Missile Aerodynamics, Italy, 1998.

[19] Reisenthel P H, Love J F, Lesieutre D J, et al. Innovative fusion of experiment and analysis for missile design and flight simulation. In: Proceedings of the RTO Symposium on Innovative Missile Systems, Amsterdam, 2006.

大長徑比帶翼剛體的零升阻力系數和升力系數與馬赫數的相關性

對大長徑比帶翼剛體的零升阻力系數和升力系數的風洞試驗數據進行了綜合分析， 利用風洞試驗數據修正了帶翼剛體升力系數和零升阻力系數的動力學模型。 研究結果表明， 大長徑比帶翼剛體的零升阻力系數和升力系數隨馬赫數的變化趨勢基本相似， 數值計算數據與風洞試驗數據都驗證了修正后的動力學模型對于估算大長徑比帶翼剛體的升力系數和零升阻力系數是可行的,為同類型帶翼剛體的空氣動力特性分析提供了技術參考。

帶翼剛體； 零升阻力系數； 升力系數； 風洞試驗； 動力學特性

DONG Su-rong. Relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body. Journal of Measurement Science and Instrumentation, 2015, 6(3)： 270-274.[

董素榮

(中北大學 機電工程學院， 山西 太原 030051)

10.3969/j.issn.1674-8042.2015.03.012]

DONG Su-rong (zhydsrtt@nuc.edu.cn)

1674-8042(2015)03-0270-05 doi： 10.3969/j.issn.1674-8042.2015.03.012

Received date： 2015-04-22

CLD number： V211 Document code： A