Numerical Determination of Critical Mach number of a Three-Element Airfoil in Unbounded Flow

55 Pages·2017·2.51 MB·English

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McKelvey School of Engineering Theses &
McKelvey School of Engineering
Dissertations
Spring 5-19-2017
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Bowen Hu
Washington University in St. Louis
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WASHINGTON UNIVERSITY IN ST. LOUIS
School of Engineering and Applied Science
Department of Mechanical Engineering and Material Science

Thesis Examination Committee:
Ramesh Agarwal, Chair
Qiulin Qu
Swami Karunamoorthy

Numerical Determination of Critical Mach number of a Three-Element Airfoil in Unbounded
Flow and in Ground Effect

by
Bowen Hu

A thesis presented to
the School of Engineering and applied Science
of Washington University in
partial fulfillment of the
requirements for the degree
of Master of Science

May 2017
St. Louis, Missouri
© 2017, Bowen Hu
Table of Contents
List of Figures ................................................................................................................................ iv
List of Tables ................................................................................................................................. vi
Acknowledgments......................................................................................................................... vii
ABSTRACT OF THE THESIS ..................................................................................................... ix
Chapter 1: Introduction ................................................................................................................... 1
1.1 Motivation ........................................................................................................................ 1
1.2 Brief Review of Literature ............................................................................................... 2
1.3 Scope of the Thesis........................................................................................................... 3
Chapter 2: Methodology ................................................................................................................. 4
2.1 Geometry and Mesh Generation....................................................................................... 4
2.1.1 Geometry .....................................................................................................................4
2.2 Mesh Generation .............................................................................................................. 5
2.1.2 Ground Effect Flow Field..............................................................................................6
2.3 Simulation Method ........................................................................................................... 7
2.4 Turbulence Model ............................................................................................................ 8
Chapter 3 Determination of Critical Mach Number in Unbounded Flow .................................... 10
3.1 Lift Coefficient and Drag Coefficient ............................................................................ 10
3.2 Pressure Coefficient Contours ........................................................................................ 12
3.3 Velocity Magnitude Contours ........................................................................................ 14
3.4 Streamlines ..................................................................................................................... 16
3.5 Conclusions .................................................................................................................... 18
Chapter 4 Aerodynamics of 30P30N Airfoil in Ground Effect .................................................... 19
4.1 Lift Coefficient and Drag Coefficient ............................................................................ 19
4.2 Pressure Coefficients and Contours ............................................................................... 21
4.3 Velocity Contours........................................................................................................... 23
4.4 Streamlines ..................................................................................................................... 23
4.5 Conclusions .................................................................................................................... 24
Chapter 5 Determination of Critical Mach Number of 30P30N in Ground Effect ....................... 25
5.1 Lift Coefficient and Drag Coefficient ............................................................................ 25
ii
5.2 Pressure Coefficients and Contours ............................................................................... 28
5.3 Ground Effect at Freestream Mach number 0.4 ............................................................. 30
5.4 Ground Effect at Freestream Mach number 0.45 ........................................................... 33
5.5 Ground effect at Freestream Mach number 0.5 ............................................................. 36
5.6 Conclusions .................................................................................................................... 39
Chapter 6 Conclusions .................................................................................................................. 41
References ..................................................................................................................................... 42
Vita……………………………………………………………………………………………….43

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List of Figures
Fig 2.1 Definitions of gap, overlap, and deflection angles in a three-element airfoil.
Fig. 2.2 Sketch of 30P30N airfoil in GE.
Fig 2.3 Computational domain and structured mesh layout in unbounded flow
Fig 2.4 Computational domain and structured mesh layout in ground effect
Fig 3.1 Variation of lift coefficients of 30P30N and RAE2822 airfoils with Mach number in
unbounded flow
Fig 3.2 Variation of drag coefficient of 30P30N and RAE2822 airfoils with Mach number in
unbounded flow
Fig 3.3 Lift coefficient of complete airfoil, slat, main and flap of 30P30N in unbounded flow
Fig 3.4 Pressure coefficient contours of 30P30N at freestream Mach number = 0.2, 0.3, 0.33,
0.35, 0.4 and 0.5
Fig 3.5 Velocity magnitude contours of 30P30N at freestream Mach number = 0.2, 0.3, 0.33,
0.35, 0.4 and 0.5
Fig 3.6 Streamlines around 30P30N at freestream Mach number = 0.2, 0.3, 0.33, 0.35, 0.4 and
0.5
Fig 4.1 Lift coefficient of 30P30N at different ride heights at freestream Mach number = 0.2
Fig 4.2 Drag coefficient of 30P30N at different ride heights at freestream Mach number = 0.2
Fig 4.3 Lift coefficient of complete airfoil, slat, main and flap of 30P30N at different ride heights
with freestream Mach number = 0.2
Fig 4.4 Pressure coefficient distributions at different ride heights at freestream Mach number =
0.2
Fig 4.5 Pressure coefficient contours at h/c=0.1, 0.2 for 1 when freestream Mach number = 0.2
Fig 4.6 Velocity contours at h/c=0.1, 0.2 and 1 at freestream Mach number = 0.2
Fig 4.7 Streamlines at h/c=0.1, 0.2 and 1 at freestream Mach number = 0.2
Fig 5.1 Variation in lift coefficient of 30P30N with freestream Mach number at different ride
heights
iv
Fig 5.2 Variation in drag coefficients of 30P30N with freestream Mach number at different ride
heights
Fig 5.3 Variation in lift coefficient with ride height at various freestream Mach numbers
Fig 5.4 Variation in drag coefficient with ride height at various freestream Mach number
Fig 5.5 Pressure coefficient distributions at different heights at freestream Mach number = 0.2
Fig 5.6 Pressure coefficient distributions at different heights at freestream Mach number = 0.3
Fig 5.7 Pressure coefficient distributions at different heights at freestream Mach number = 0.4
Fig 5.8 Pressure coefficient distributions at different heights at freestream Mach number = 0.5
Fig 5.9 Pressure coefficient contours at freestream Mach number = 0.4 at different ride heights
Fig 5.10 Velocity magnitude contours at freestream Mach number = 0.4 at different ride heights.
Fig 5.11 Streamlines at freestream Mach number = 0.4 at different ride heights
Fig 5.12 Pressure coefficient contours at freestream Mach number = 0.45 at different ride heights
Fig 5.13 Velocity magnitude contours at freestream Mach number = 0.45 at different ride heights.
Fig 5.14 Streamlines at freestream Mach number = 0.45 at different ride heights
Fig 5.15 Pressure coefficient contours at freestream Mach number = 0.5 at different ride heights
Fig 5.16 Velocity magnitude contours at freestream Mach number = 0.5 at different ride heights.
Fig 5.17 Streamlines at freestream Mach number = 0.5 at different ride heights
Fig 5.18 Variation in critical Mach number with ride height

v
List of Tables
Table 2.1 Geometric parameters (gap and overhang values are specified as percentage of stowed
chord, c).

vi
Acknowledgments

First of all, I would like to thank my advisor Dr. Ramesh Agarwal. I have learned a lot of
professional knowledge from him in aerodynamics and computational fluid dynamics. More
importantly, his patience and persistence in providing research guidance have deeply touched me.
For me, Dr. Ramesh Agarwal is not only a professor but also a mentor in my life.

I would also like to thank everyone who helped me with the thesis. Thanks to Dr. Qiulin Qu for
his guidance in my research and his continuous encouragement. Thanks to Junhui Li for his
patience in answering my questions. Thanks to Boshun Gao for the help he provided when I met
with problems in my research. Thanks to Ning Deng and Pan Du for helping me with the mesh
generation. Thanks to Xu Han for teaching me how to set parameter in the simulations. I am also
thankful to all my colleagues in CFD lab for their continuous help and good company.

Finally, I would like to acknowledge my committee members, Dr. Peters and Dr.
Karunarmoorthy, for taking the time to read the thesis and attend its defense.

Bowen Hu

Washington University in St. Louis
May 2017

vii
Dedicated to my parents

I want to dedicate this thesis to my parents (Yingzhong Hu and Qun Wang) and grandparents for
their life-time guidance, love and support.

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