Comparative Study of Numerical Simulation of External Winding of
Arrow-Shaped Wing and Delta Wing
Weijun Feng
1a
,
Minghan Wang
2b
and Menglin Yang
3c
1
School of Intelligent Manufacturing, Chengdu Institute of Technology, Chengdu, 611700, China
2
School of Mathematics, Statistics and Mechanics, Beijing Institute of Technology, Beijing
,
100124 China
3
Yuanxuetong Education Group, Shanghai, 20005, China
Keywords: Delta Wing, Arrow-Shaped Wing, Numerical Simulation.
Abstract: With the rapid development of the aviation industry, the demand for aircraft performance optimization is
increasingly urgent in China. As a new type of aerodynamic layout, the arrow wing has become a key research
direction to improve the aerodynamic efficiency of aircraft because of its unique streamlined design and
potential drag reduction and efficiency. The objective of this research is to conduct an in-depth exploration
of the external flow characteristics of an arrowing within a complex flow field by means of a high-precision
numerical simulation approach, thereby providing a scientific foundation for optimizing wing design and
enhancing flight performance. In this paper, the computational fluid dynamics (CFD) approach is employed
to simulate the external flow features of an arrow wing. As a specially engineered airfoil for aircraft, the arrow
wing possesses distinctive aerodynamic performance. Through the establishment of a high-precision
calculation model and the application of advanced numerical algorithms, this paper conducts a detailed
analysis of the circumfluence phenomena of an arrow wing under various flight conditions. The key
parameters, such as velocity field, pressure field, and vortex structure, are compared and analyzed in contrast
to the corresponding parameters of the delta wing, thereby obtaining the advantageous aerodynamic
conditions of the arrow wing. This provides theoretical guidance for wing topology optimization and scientific
basis and technical support for design optimization, aerodynamic performance evaluation, and flow control
of arrowing.
1 INTRODUCTION
However, due to its complex flow field structure, it is
difficult for traditional experimental methods to fully
reveal its circumferential flow characteristics. As an
innovative aircraft design concept, the arrow wing
has attracted wide attention due to its unique
geometry and excellent aerodynamic performance.
Therefore, the use of numerical simulation
technology has become an important means of
studying the external flow around the arrow wing
(Gao, 2016) (Zhang, 2010). In this paper, the external
flow around the arrow wing is simulated and analyzed
in detail based on the CFD method (Yan,2011), and
compared with the corresponding external flow
around the delta wing simulation data to provide a
reference for the research and application in related
a
https://orcid.org/0009-0004-2630-1845
b
https://orcid.org/0009-0008-2767-0799
c
https://orcid.org/0009-0007-7217-9889
fields (Li,2016).
2 NUMERICAL SIMULATION
METHOD
2.1 Geometric Model and Meshing
This article is first based on the particle size and
geometry of the arrow wing, Three-dimensional
computational is accurate structured. Soon afterward,
this paper used advanced meshing technology, by
doing high-quality structuring or unstructured
meshing for this arrow wing. The fineness of the
mesh has a direct impact on the accuracy of the
simulation results, therefore, localized encryption
was performed in critical areas (e.g. wingtips, leading
Feng, W., Wang, M. and Yang, M.
Comparative Study of Numerical Simulation of External Winding of Arrow-Shaped Wing and Delta Wing.
DOI: 10.5220/0013444700004558
In Proceedings of the 1st International Conference on Modern Logistics and Supply Chain Management (MLSCM 2024), pages 505-512
ISBN: 978-989-758-738-2
Copyright © 2025 by Paper published under CC license (CC BY-NC-ND 4.0)
505
Figure 1: Three views of the tip-wing model and overview of the meshing.
edges,etc.) The breakdown is shown in fig.1 (Han,
2004).
2.2 Numerical Algorithms and
Turbulence Modelling
In this paper, a numerical algorithm based on the
finite volume method is used, a two-dimensional
Reynolds averaged equation (Cheng,2023)
(Rumesey,1988) (Spalart,1992).
The continuity equation describes the principle of
conservation of fluid mass, in the two-dimensional
case it can be expressed as:
+
+
= 0 (1)
Including, ρ is density, t is time, and u and v are the
velocity components of the fluid in the x and y
direction.
The momentum equation describes the change in
fluid momentum with time and the transfer of
momentum due to pressure viscous forces and
external forces such as gravity
The momentum equation of two-dimensional
RANS can be expressed as:
+
+
= -
+
+
+ ρf
(2)
+
+
= -
+
+
+ ρf
(3)
Two-dimensional Reynolds averaged equation
Including, ρ is density, 𝜏
is Components of the
viscous stress tensor( i,j=x,y ） , 𝑓
and 𝑓
is
external force per unit mass in the x and y direction.
The viscous stress direction is usually related to the
viscous coefficient μ and velocity gradient of the
fluid, such as:
𝜏
2𝜇
+ γ（
） (4)
𝜏
𝜏
u（
） (5)
𝜏
2𝜇
+ γ（
） (6)
The viscous stress direction including, λ is the
second annularity coefficient, for most fluids
including gases and water, can be considered as 𝜆
𝜇.
In the choice of turbulence model, considering the
complexity of practicing memory bypassing, the
RANS(Reynolds averaged equation) equations,
which are suitable for complex flow phenomena,
were chosen to be combined with the SST k-ω of the
turbulence model for solving. Ensure computational
efficiency while better capturing non-stationary and
turbulent features in the flow.
2.3 Boundary Conditions and Solution
Setup
Reasonable inlet and outlet boundary conditions and
surface conditions, as well as the original boundary
conditions, are set according to the actual flight
conditions of the practice memory Flight state (initial
value conditions) ： The specified thermodynamic
temperature T=300K, is kept constant Mach number
M=0.84 corresponds to the computed free-stream
velocity u
=291.64m/s , Air density
ρ=1.148kg/m
, corresponds to the computed fluent
pressure p ρRT=9.8858.97Pa
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506
3 SIMULATION RESULTS AND
ANALYSIS
3.1 Flow Field Characterisation
The flow field characteristics of an arrow-shaped
wing at a given flight speed and angle of attack are
obtained through numerical simulation. The results
show that the geometry of the arrow-shaped airfoil
leads to a unique vortex structure and pressure
distribution for its wrap-around flow phenomenon. In
the leading edge and wing tip regions, significant
vortex separation phenomena occur, and these
vortices significantly affect the lift and drag of the
wing. The highest static air pressure is found at the
leading edge of the wing, with a static ultra-low
pressure region at the front at about 1/5 to 2/5 of the
airfoil, and a static low-pressure region at 2/5 to 4/5
of the airfoil, and the air pressure in the rest of the
wing floats above and below the mean air pressure of
the flow field, and the specific distribution of the
static air pressure is shown in Fig. 2.
Considering again the nature of the flow field
outside the wing, the leading edge of the wing has a
relatively slow air flow rate compared to the other
regions due to the vortex separation generating
region, whereas in the static low-pressure region at
the upper edge of the wing at about 2/5 to 4/5 of the
airfoil, the airflow rate is generally higher than that at
the lower edge, as shown in Fig. 3.
Figure 2a: Arrow airfoil pressure distribution (3D overview).
Figure 2b: Arrow airfoil pressure distribution (2D profile).
Comparative Study of Numerical Simulation of External Winding of Arrow-Shaped Wing and Delta Wing
507
Figure 3: Arrow-shaped wing 2D profile of external bypass flow velocity map.
Figure 4: An overview of the three views of the delta wing model used for comparison and its meshing.
3.2
Pneumatic Performance Evaluation
(Without Expansion)
Based on the simulation results, the aerodynamic
performance of the arrow-shaped wing is evaluated.
The key parameters such as lift coefficient and drag
coefficient (Yan,2020) were calculated and compared
and analyzed with the delta wing (Schaeffler, 1998).
In this study, the wing of Mirage 2000 is chosen as
the control wing and its meshing with the same
conditions as the arrow-shaped wing is shown in Fig.
4.
Subsequently, this study also analysed the
pressure distribution of this delta wing with external
winding conditions under the same initial value
conditions, and the results are shown in Fig. 5.
It is evident from Fig. 6 that the wind drag
coefficient (Cd) of the arrow wing, relative to the
delta wing, decreases rapidly for the initial few
iterations, then gradually levels off and eventually
converges at a lower value (the delta wing converges
at a higher value). At the beginning of the iterations
(about the first 10 iterations), the wind resistance
decreases rapidly, from 0.0900 to about 0.0200. after
about 40 iterations, the wind resistance stabilizes at
about 0.0200. On the contrary, in the first 50
iterations of the delta wing, the wind resistance
fluctuates greatly and shows an upward trend, and
after about 75 iterations, it gradually decreases from
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508
Figure 5a: External bypass flow velocity maps for the delta wing model used for comparison.
Figure 5b: Pressure distribution of delta wing models used for comparison.
Figure 6a: Variation of wind drag coefficient of the arrow-shaped wing with an increasing number of iterative calculations.
Comparative Study of Numerical Simulation of External Winding of Arrow-Shaped Wing and Delta Wing
509
Figure 6b: Variation of wind drag coefficient of a delta wing with an increasing number of iterative calculations.
Figure 7a: Variation of lift coefficients of the arrow-shaped wing with an increasing number of iterative calculations.
Figure 7b: Variation of lift coefficient of a delta wing with an increasing number of iterative calculations.
MLSCM 2024 - International Conference on Modern Logistics and Supply Chain Management
510
0.0475 to about 0.0425 and tends to stabilize, and the
wind resistance is higher than that of the arrow-
shaped wing
It is obvious from Fig. 7 that, relative to the delta
wing, the lift coefficient (Cl) of the arrow wing rises
rapidly within the initial 10-step iteration, and there is
an increase to a decrease within the 10-step to 20-step
iteration, followed by a gradual levelling off, and
ultimately converges at a higher value, in the early
iteration, the lift coefficient rises rapidly to 0.2620,
and then decreases gently to about 0.2500 and
stabilises, in contrast to the delta wing, which has a
greater fluctuation in the On the contrary, the lift
coefficient of delta wing, within the first 50 steps of
iteration, fluctuates with a larger amplitude and
shows an overall upward trend, and after about 75
steps of iteration, it gradually decreases from 0.0225
to about 0.0205 and tends to be stable, and the lift
coefficient is obviously lower than that of the arrow-
shaped wing.
Figure 8a: Variation of the velocity of the arrow-shaped wing with an increasing number of iterative calculations.
Figure 8b: Velocity of a delta wing with an increasing number of iterative calculations.
Comparative Study of Numerical Simulation of External Winding of Arrow-Shaped Wing and Delta Wing
511
It is obvious from Fig 8 that, relative to the delta
wing, the lift coefficient (Cl) of the arrow wing rises
rapidly within the initial 10-step iteration, and there is
an increase to a decrease within the 10-step to 20-step
iteration, followed by a gradual leveling off, and
ultimately converges at a higher value, in the early
iteration, the lift coefficient rises rapidly to 0.2620,
and then decreases gently to about 0.2500 and
stabilizes, in contrast to the delta wing, which has a
greater fluctuation in the On the contrary, the lift
coefficient of the delta wing, within the first 50 steps
of iteration, fluctuates with a larger amplitude and
shows an overall upward trend, and after about 75
steps of iteration, it gradually decreases from 0.0225
to about 0.0205 and tends to be stable, and the lift
coefficient is obviously lower than that of the arrow-
shaped wing.
4 CONCLUSION
In this paper, the numerical simulation of the external
winding flow of an arrow-shaped wing is carried out
by CFD method, and the aerodynamic characteristics
and flight performance of the arrow-shaped wing and
delta wing in a fixed flow field are compared and
analysed, and the advantageous flight conditions of
the arrow-shaped wing are obtained, which reveal its
unique flow field characteristics and aerodynamic
performance, and its advantages and disadvantages
relative to that of the delta wing. The results provide
a scientific basis and technical support for the design
optimization, aerodynamic performance evaluation,
and flow control of the arrow-shaped wing. In the
future, explore more accurate turbulence models,
develop adaptive mesh technology, and strengthen
the close integration of experimental validation and
numerical simulation. to more comprehensively
reveal the flow characteristics of the arrow-shaped
airfoil and promote the development and application
of related technologies.
AUTHORS CONTRIBUTION
All the authors contributed equally and their names
were listed in alphabetical order.
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