Journal of Mechanical Engineering Research and Developments ISSN: 1024-1752 CODEN: JERDFO Vol.43, No.5, pp. 346-354 Published Year 2020
Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
Muna S. Kassim†, Firas A. Abbas‡, Israa Ali Abdulghafar‡†, Laith Jaafer Habeeb‡‡
†College of Engineering, Mustansiriyah University, Iraq-Baghdad ‡Gas filling company, Ministry of oil, Iraq-Wassit ‡†Middle Technical University, Iraq-Baghdad ‡‡Training and Workshops Center, University of Technology, Iraq-Baghdad
*Corresponding Author Email: [email protected], [email protected], [email protected]
ABSTRACT: Air flowing round model rockets by means of different nose geometries has been investigated during this study. The mathematical related computational fluid dynamics techniques applied for the investigation is presented and a computational model is developed using ANSYS FLUENT R 19.2 software. Pressure contours, airflow path lines, and drag coefficient depending on the rockets velocity are presented. The most suitable nose shape for the rocket is selected. Results of numerical simulation showed that the maximum drag coefficient was with spline nose in all velocities. It has been found that at all velocity ranges, the lowest drag coefficient is with elliptical nose.
KEYWORDS: 3D Simulation, Airflow, Drag coefficient, Nose shape, Pressure distribution, velocity distribution.
INTRODUCTION
A geometrical and creation factors and the ballistics features regarding with a rocket are customarily expected for particular rocket design. The variety of the rockets speeds can be quite varied. The current design required evolving 10 푚 110 푚 a rocket having 0.2365 meters length and 0.0217 meters diameter. The velocity ranges from ⁄푠 to ⁄푠. Various nose shapes has been investigated during the simulation, such as, conical, elliptical, spline shapes [1] and [3]. It is known that drag coefficients are vital parameters regarding with this application. Numerical procedures to simulate aerodynamic behavior regarding with various sophisticated geometries with complex flow forms showed acceptable phenomena [5].Thus, they broadly used to expect aerodynamic characteristics of rockets during various improvement phases [7]. During this study, three types of nose shapes with various aerodynamic aspects have been studied numerically by using CFD simulation.
MATHEMATICAL MODELING
Numerical model executes investigation of a system relating fluid mechanics, and related phenomena based on several disciplines of knowledge which comprises mathematics, physics to offer significant designing of fluid flow. ANSYS FLUENT R 19.2 package is accepted for accomplishing numerical models through a rocket using 3D model. The solution of conservation continuity, momentum equations has been utilized to investigate the flow domain around this model. Investigation of aerodynamic performance is carried out using finite element software mentioned above [7]. By using SST k-omega turbulence model, a two-equation eddy-viscosity model which is adopted for several aerodynamic applications. It represents hybrid model joining the Wilcox k-omega with k-epsilon models. blending function, F1, stimulates Wilcox model adjacent the wall besides the k-epsilon model at the free stream. Thus confirms that the proper model has been used through the flow field:
• k-omega model remains well-matched used for simulating flow of viscous sub-layer.
• k-epsilon model stands perfect for predicting flow behavior of areas away from a wall.
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Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
The model is given by the following main equations [7]:
Turbulence Kinetic
휕푘 휕푘 ∗ 휕 휕푘 + 푈푗 = 푃푘 − 훽 푘휔 + [(휈 + 𝜎푘휈푇) ] (1) 휕푡 휕푥푗 휕푥푗 휕푥푗
Specific Dissipations
휕휔 휕휔 2 2 휕 휕휔 1 휕푘 휕휔 + 푈푗 훼푆 − 훽휔 + [(휈 + 𝜎휔휈푇) ] + 2( 1 − 퐹1)𝜎휔2 (2) 휕푡 휕푥푗 휕푥푗 휕푥푗 휔 휕푥푖 휕푥푖
Where 푘: turbulence kinetic energy, 휔: turbulence frequency, 휈푇: turbulent viscosity.
(Blending Function)
4 √푘 500휈 4𝜎휔2푘 퐹1 = tanh {{푚푖푛 [푚푎푥 ( ∗ , 2 ) , 2]} } (3) 훽 휔푦 푦 휔 퐶퐷푘휔푦
Note that 퐹1 = 1 inside a boundary layer with 0 in the free stream.
푪푫풌흎
1 휕푘 휕휔 −10 퐶퐷푘휔 = 푚푎푥 (2𝜌𝜎휔2 , 10 ) (4) 휔 휕푥푖 휕푥푖 Kinematic Eddy Viscosity
푎1푘 휈푇 = (5) 푚푎푥(푎1휔,푆퐹2)
퐹2 (Second Blending Function)
2 푘 500휈 퐹 = tanh {{푚푎푥 [( √ , )]} } (6) 2 훽∗휔푦 푦2휔
푃푘 ( Production Limiter)
휕푈푖 ∗ 푃푘 = min (휏푖푗 , 10훽 푘휔) (7) 휕푥푗
The drag coefficient of the rockets has been considered theoretically a the next procedure [6] and[12]:
퐶퐷,푇 = 퐶퐷,푁푇+ 퐶퐷,퐵+퐶퐷,퐹+퐶퐷,퐼+퐶퐷,퐿 (8)
Where: 3 1 3 퐿 − 퐶퐷,푁푇 = 1.02 {퐶푓,푡푢푟푏퐴푤,푁푇} {1 + ( ) 2} (9) 퐴푐 2 푑
퐶 0.029 푑 (10) 퐷,퐵= ( 푏 )3 푑 √퐶퐷,푁푇
1 푡 퐶퐷,퐹 = {2퐶푓,푙푎푚퐴푤,퐹} {1 + 2 } (11) 퐴푐 퐶푟
1 푡 퐶퐷,퐼 = {퐶푓,푙푎푚푛푑푐푟} {1 + 2 } (12) 퐴푐 퐶푟 Reynolds number for the nose cone and body tubes was defined as:
푈퐿𝜌 50∗0.2365∗1.225 푅푒 = = = 809524 (13) 푁푇 휇 0.000017894
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Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
And the Reynolds number for the fin:
푈푐 𝜌 50∗0.0271525∗1.225 푅푒 = 푎푣푒 = = 92941 (14) 퐹 휇 0.000017894
푆 Where 푐 = . 푎푣푒 푏 The surface area for the fin can be determined from the geometry that was generated.
1 푆 = (푐 + 퐿 sin 훼)퐿 cos 훼 − {퐿2 sin 훼 cos 훼 + 퐿2 sin 훽 cos 훽 + (퐿 cos 훼 − 퐿 cos 훽)(푐 − 푐 + 퐿 sin 훼 − 푡 푙 푙 2 푙 푡 푙 푡 푡 푟 푙 퐿푡 sin 훽) + 2퐿푡 sin 훽} (15) The skin friction coefficient can be approximated assuming fully turbulent flow across on nose cone and body tube.
0.0315 0.0315 퐶푓,푡푢푟푏 = 1 = 1 = 0.00451105 (16) 푅푒푁푇7 8095247 And for laminar boundary layer on the fin as:
1.328 1.328 퐶푓,푙푎푚 = 1 = 1 = 0.00435606 (17) 푅푒퐹2 92941 2 For an nose cone, the following relation was presented:
퐴 8퐿 +12퐿 푤,푁푇 = 푁 퐵 = 39.2012 (18) 퐴푐 3푑 The different drag coefficient and the total value becomes:
3 3 − 퐶 = 1.02 ∗ 0.00451105 ∗ 39.2012 {1 + (10.8986) 2} = 0.187 퐷,푁푇 2
0.029 0.0164 퐶퐷,퐵= ( )3=0.0262 √0.187 0.022
1 0.0007 퐶 = {2 ∗ 0.00435606 ∗ 0.00419} {1 + 2 } = 0.135 퐷,퐹 0.00037 0.0038
1 0.0007 퐶 = {0.00435606 ∗ 4 ∗ 0.0038 ∗ 0.0217} {1 + 2 } = 0.0053 퐷,퐼 0.00037 0.0038
퐶퐷,푇 = 0.187 + 0.0262 + 0.135 + 0.0053 = 0.3535 The value for the total drag coefficient 0.3535 according to the theory can be compared with the value 0.379. From ANSYS FLUENT simulations, a difference of 6.7 % has been obtained.
Numerical simulation
Conical, elliptical, spline nose shapes were investigated as shown in Fig.(1). The overall dimensions of present model are described in Fig. (2) and nomenclature table considering the same nose length for all configurations [2] and [4].
(a) (b)
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Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
(c)
Figure 1. Model of rocket with various shape nose: (a) Conical. (b) Elliptical. (c) Spline.
3D models of computational fields for the rockets were created by Design Modeler of ANSYS workbench as shown in Fig. (1). Finite element models for simulating airflow around the rockets has been produced in ANSYS FLUENT package. Half for each one is discretized by adopting symmetry boundary condition for computational time saving. The computational field for each rocket was meshed by using Fluid Fluent Meshing of same package. The highest size of tetrahedral elements has been fixed to 134 mm with a maximal face size of 268 mm. 5 inflation layers were created with automatic program controlled. The mesh with the amount of 303,309 elements was generated as shown in Fig. (3).
Figure 2. Geometry of model rocket
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Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
Figure 3. Computational grid cuts at different locations.
RESULTS AND DISCUSSIONS
The numerical simulation outcomes for the airflow around the rockets was achieved. Fig. (4) shows pressure contour at the surface of the rocket and its cross-section plane. Fig. (5) and Fig. (6) represents the velocity and path lines 푚 contours for the rocket at 50 ⁄푠. Fig. (7) shows the variation between air velocity and the drag coefficient for each rocket model. Drag is the main concern of aerodynamic sizing of a free flying rocket. The drag resultant consequence on the ballistic coefficient have a straight effect upon the ballistic trajectory flown by a rocket using a certain energy management arrangement. The aerodynamic drag of the whole rocket is the most significant factor affecting accuracy. Various techniques can be used for decreasing the drag on rocket vehicle in flight. Drag of nose- body shape depends mainly on nose ranges of velocities. Therefore, the choice of nose shape comprises trade-off assessments for a specific application. The minimum drag configuration is usually chosen regarding with specific nose configurations. The nose cone of a rocket are planned to minimize drag and to provide its strength and control. The leading point that encounters the air is the nose cone, thus optimizing the best nose cone will help to achieve minimum drag coefficient Subsequently, good aerodynamic performance will be attained. It can be seen that the maximum drag coefficient was with spline nose in all velocities. This figure reveals that the drag coefficient for conical and spline nose is similar. It is obvious that at all velocity ranges, the lowest drag coefficient is with elliptical nose. According to above analysis, elliptical nose shape has been selected for further aerodynamic study of the rocket target.
(conical)
(elliptical)
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Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
(spline) 50 푚 Figure 4. Pressure distribution of cross section plane at ⁄푠 .
(conical)
(elliptical)
(spline) 50 푚 Figure 5. Velocity distribution of cross section plane at ⁄푠
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Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
(conical)
(elliptical)
(spline) 50 푚 Figure 6. Velocity path lines of cross section plane at ⁄푠 .
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Numerical Analysis of Nose shape on the Aerodynamic Characteristics of Rocket
Figure 7. The variation between air velocity and the drag coefficient for each rocket model.
CONCLUSION
Numerical simulation of various aerodynamic characteristics of model rocket with different nose shapes is performed during this study. Pressure contours, airflow path lines, and drag coefficient depending on the rockets velocity are presented. Results show that the maximum drag coefficient was with spline nose in all velocities. It is noted that the drag coefficient for conical and spline nose is very close. Depending on the above discussion of the contribution of the nose section on the normal force, it has been found that at all velocity ranges, the lowest drag coefficient is with elliptical nose.
ACKNOWLEDGMENT
The authors desire to direct their deep thanks and appreciation to the support delivered by (Al - Mustansiriyah University) to complete the present work.
NOMENCLATURE
훼: fin leading edge sweep angle 50° 훽: fin trailing edge angle 15° 푑 (푚) : body tube diameter 0.0217 푚
푑푏: base diameter( 푚) 0.0164 푚 퐿 (푚): length of nose and body 0.2365푚
퐿퐵 (푚) : body tube length 0.165 푚 퐿푁 (푚) : nose length 0.0715 푚 퐿푙 : length of leading edge of fin (푚) 0.060 푚 퐿푡 : length of trailing edge of fin (푚) U 0.033 푚 푛 : number of fins 4 푡 (푚) : thickness of fin 0.0007 (푚) 푘푔⁄ 푘푔⁄ 𝜌 푚3 density of air 1.225 푚3 푘푔 푘푔 휇 ( ⁄푚. 푠) dynamic viscosity of air 0.000017894 ⁄푚. 푠 2 2 퐴푐(푚 ) : cross sectional area for body tube 0.000369836 푚 2 2 퐴푤,퐹(푚 ) : total area wetted surface for all fins 0.00418879 푚 2 2 퐴푤,푁푇(푚 ) : area wetted surface for nose and body tube 0.014498 푚 b (푚) : span for the fin 0.0385673 푚
푐푎푣푒(푚) : average fin chord length 0.0271525 푚 푐푟(푚) : root fin chord length 0.038 푚 푐푡(푚) : tip fin chord length 0.010 푚 퐶퐷,푁푇: nose & drag coefficient for body tube -
퐶퐷,퐵 : drag coefficient for the base -
퐶퐷,퐹 : drag coefficient for the fin -
퐶퐷,퐼 : drag coefficient for the interference -
퐶퐷,푇 : total drag coefficient -
퐶푓,푙푎푚 : skin friction coefficient of laminar -
퐶푓,푡푢푟푏: skin friction coefficient of turbulent -
푅푒퐹 : Reynolds number for the fin - 푅푒푁,푇 : Reynolds number for nose cone and body tube - 푆 (푚2) : area for fin 0.00100472 푚2 푚 푈 ( ⁄푠) : free stream velocity -
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