analysis of transonic flow over an airfoil naca0015 using cfd

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:21 No:01 1

210301-8484-IJMME-IJENS © February 2021 IJENS I J E N S

Analysis of Transonic Flow over an Airfoil NACA0015

using CFD Dr. Iman Jabbar Ooda1, Kareem Jawad Kadhim2, Abdnoor Jameel Shaheed3,

Department of aeronautical Engineering, University of Baghdad, Baghdad-Iraq

*Corresponding author Email; [email protected]

Abstract-- The transonic flow has been studied in this paper

which is one of the most difficult types of flow because it is an

internal flow from the subsonic flow and supersonic flow which

shock waves penetrate it. The difficulty in predicting of the

behavior of this type of flow includes the non-linear equations

which cannot be solved mathematically. The aerodynamic

characteristics of NACA 0015airfoil such as lift Coefficient,

drag Coefficient, pressure coefficient and wall shear stress in

transonic regime have been analyzed and predicted using

Ansys-Fluent (14.5) at different velocities in the Transonic

range (𝑴∞ = 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2) at =2.5°.The

Transonic Compressible flow simulation has been done using

k-ω shear stress transport (SST) turbulence model. The

calculations show that The lift coefficient decreases and the

drag coefficient increases due to the formation of shock wave

behind the supersonic airfoil flow areas, which typically begin

to appear at (𝑴∞= 0.7) and the effect of wall shear stress

becomes more significant on the leading edge and on the

middle of the airfoil as M∞ increases. The theoretical results

were compared with previous published results of experimental work and good agreement was obtained.

Index Term-- Airfoil, NACA0015, Mach No., transonic flow.

INTRODUCTION

As an aircraft flies near a Mach number of one, the airflow

may approach or exceed the sound speed along the airfoils.

A shock wave will form when this happens that will disrupt

the airflow and cause a sudden and dramatic increase in

drag, the lift decreases, the moments acting on the aircraft

change abruptly, and the vehicle may shake or buffet. Those

shock waves will lose the aircraft's stability. These features of flight as well as the velocities at which they occur are

generally referred to as transonic. In transonic regime, the

flow is composed of mixed regions of local subsonic and

supersonic flows all with local Mach numbers close to 1,

usually between (0.6 or 0.7 to 1.2).

A number of researches have studied aerodynamics

characteristics for different types of airfoils in transonic

flow regime. Raad Shehab Ahmed [1] Studied Transonic flow over un swept and swept wings by solving transonic

potential flow equation for the inviscid compressible flow.

He replaced the shock waves with discontinuities in which

the entropy is retained and calculated the area of velocity

and pressure coefficients as a function of the Mach number.

Manoj Kannan G,et al.[2] designed transonic airfoil and

studied numerically its aerodynamic properties such as

Pressure distribution and Velocity distribution over the

upper and lower surfaces of airfoil and variations of shock

patterns at different Mach numbers in the transonic range

(M=0.8,0.9,1.0,1.1,1.2) by using CFD and analyzed to

determine the effect of drag divergence on the lift created by

the airfoil. Tapan et al. [3] developed an extremely time-

accurate Navier stokes solver for NACA0012 transonic

flow. To solve the Navier stock equation, the solver uses

explicit Runge-Kutta method and optimized upwind. Novel, K.S. and Imam, S.[4]studied variation in Angle of attack

and Mach number over NACA0012 Airfoil by simulating

the Transonic Compressible flow using Spalart-Allmaras

and kω turbulence model and PRESTO solution technique

to govern Euler and Navier-Stokes continuity principle.

Muhammad Umar Sohail and Asad Islam [5] Simulated

Transonic flow over the swept wing ONERA M-6 at angle

of attack of 3.06° at 𝑀∞ = 0.8395 using Spalart-Allmaras

turbulence model. The solver analyzed the position of the

shock waves and the supersonic area on the wing. Shamudra

Dey [6] studied numerically the 3D transonic flow around NACA 0009 airfoil using Ansys Fluent software at angle of

attack of 3°. He visualized a shock and separation of

boundary layer and investigated lift coefficient and drag

coefficient.

NOMENCLATURE

Latin symbols

t time

CD Drag Coefficient

CL Lift Coefficient

Cp Pressure Coefficient

h Static enthalpy

p Static pressure

q Energy flux transferred by heat conductivity along

the coordinate xi

U velocity

k Turbulent kinetic energy

Greek symbols

α Angle of attack

ρ Density

mailto:[email protected]



µ Dynamic fluid viscosity

µt Dynamic eddy viscosity

ω Specific dissipation rate

Governing equations

The computational Fluid Dynamics is governed by the following equations [7]: the continuity equation :

𝜕𝜌

𝜕𝑡+

𝜕

𝜕𝑥𝑗

(𝜌𝑈𝑗) = 0 … … … … … … . (1)

Momentum equation:

𝜕

𝜕𝑡(𝜌𝑈𝑖) +

𝜕

𝜕𝑥𝑗

(𝜌𝑈𝑖𝑈𝑗) = −𝜕𝑝

𝜕𝑥𝑖

+𝜕𝜏𝑖𝑗

𝜕𝑥𝑗

… … … … … … … . . (2)

And the energy equation:

𝜕

𝜕𝑡(𝜌ℎ) +

𝜕

𝜕𝑥𝑗

(𝜌𝑈𝑗ℎ) =𝜕𝑝

𝜕𝑡+ 𝑈𝑗

𝜕𝑝

𝜕𝑥𝑗

+ 𝜏𝑖𝑗

𝜕𝑈𝑗

𝜕𝑥𝑗

−𝜕𝑞𝑖

𝜕𝑥𝑖

… … … … . (3)

Geometry & Grid Generation

The Ansys-Fluent 14.5 finite element program is used to analyze the NACA0015 airfoil with a chord of 1m. To create the airfoil

geometry, the coordinates were taken from [8] . For airfoil flow analysis, the C mesh domain was selected and a structured mesh

called "mapped face mesh" was generated. This method is very time-consuming to generate high-quality meshes and is not suitable for

complex meshes. As shown in figure (1), the dimension of the arc radius (R1) is set to 12.5m, while the sides of the other two squares

(H2) are set to 20m. The airfoil is discretized into 149,252 elements with 150268 nodes. The mesh model shown in Figure (2) and

Figure (3) and the mesh details shown in Table (1). Figure 3 shows a mesh of airfoil with C domains. The mapped mesh is created on the entire domain. The cross section near the airfoil is developed to be fine and coarser at the farther away from the airfoil. For this

kind of airfoil, a quadratic element is used. In some areas away from the airfoil, the mesh must also be fine.

Fig. 1. Computational Domain



Fig. 2. Full Domain Mesh

Fig. 3. Close-up Mesh around Airfoil.

Table I

Details of mesh

Physics Reference CFD Smoothing High

Solver Reference Fluent Span Angle Center Fine

Relevance 100 Curvature normal angle 12

Use advanced size function On curvature Growth Rate 1.1

Relevance Center Fine

Inputs and Boundary Condition

The boundary conditions of the Airfoil surface may also be used (provided in the mesh section by naming the portion of the modeled

Airfoil i.e. upper wall, lower wall, fluid(air) and All the outer boundaries are considered to be the "Pressure Far Field" as shown in

Figure (4). Table (2) shows The boundary conditions values of the Airfoil.

Fig. 4. Geometric Modeling of airfoil



Table II

The boundary Condition value for Airfoil.

Total Temperature 300K Cp 1006.43

Mach number 0.6-1.2 Thermal Conductivity 0.0242

Angle of Attack 1.5 , 2.5 Viscosity 1.7894e-05

Density Ideal Gas Molecular Weight 28.966

Turbulence Model

Transonic compressible flow simulation has been done using the k-ω shear stress transport (SST) turbulence model. The (SST) model

is a combination of the k-ω model and the k-ε model. The k-ω (SST) model shows good behavior in adverse pressure gradients and

flow separation and the k-ω (SST) model produces some significant turbulence rates in regions with high normal strain, such as

stagnation regions and regions of high acceleration. The k-ω shear stress transport SST model has the ability to account the transport

of the main shear stress in the gradient of adverse pressure in the boundary layer.The k-ω (SST) turbulence model [9] is a two-

equation eddy-viscosity model

𝜕

𝜕𝑡(𝜌𝑘) +

𝜕

𝜕𝑥𝑖

(𝜌𝑘𝑢𝑖) =𝜕

𝜕𝑥𝑖

[(𝜇 +𝜇𝑡

𝜎𝑘

)𝜕𝑘

𝜕𝑥𝑗

] + 𝐺�̃� − 𝑌𝑘 + 𝑆𝑘

𝜕

𝜕𝑡(𝜌𝜔) +

𝜕

𝜕𝑥𝑖

(𝜌𝜔𝑢𝑖) =𝜕

𝜕𝑥𝑗

[(𝜇 +𝜇𝑡

𝜎𝜔

)𝜕𝜔

𝜕𝑥𝑗

] + 𝐺𝜔 − 𝑌𝜔 + 𝐷𝜔 + 𝑆𝜔

where 𝐺�̃�represents the generation of turbulent kinetic energy the arises due to mean velocity gradients, 𝐺𝜔 is generation of ω , 𝑌𝑘 and

𝑌𝜔 represent the dissipation of k and ω due to turbulence. 𝜎𝑘 and 𝜎𝜔 are the turbulent Prandtl numbers for k and ω respectively and

𝑆𝜔 and 𝑆𝑘 are source terms defined by the user. 𝐷𝜔 is the cross diffusion term.

Table III

Fluent Solver Description

Solver gradient Least square cell based Turbulent kinetic energy Second order upwind

Momentum Second order upwind Turbulent dissipation Second order upwind

RESULTS AND DISCUSSION

1-Convergence of solution

Figure 5. shows the CD and CL convergence history respectively. The Drag coefficient CD and Lift coefficient CL has been

investigated for 2D transonic flow over NACA 0015 airfoil for = 2.5° and 𝑀∞=0.6 and it is calculated to be 8.50E-03and 0.33 respectively.

Fig. 5.Convergence of CL and CD Plots against Number of Iterations

https://www.cfd-online.com/Wiki/Two_equation_turbulence_models

https://www.cfd-online.com/Wiki/Two_equation_turbulence_models

https://www.cfd-online.com/Wiki/Eddy_viscosity



2- EFFECT OF 𝑀∞ ON THE FLOW AROUND AN AIRFOIL

Figure 6. illustrates the creation of shock with increasing a

free-stream number of Mach around an airfoil. Up to a free-

stream number of Mach of approximately 0.7

compressibility effects have only minor influence on the flow pattern and drag and the entire wing experiences

subsonic airflow As the flow must accelerate as it travels

around the airfoil, Local flow is sonic at a single point on

the top surface where the flow peaks locally and indicates

that the flow has exceeded the critical Mach number at that

point. The velocity has continued to grow beyond the

critical number of Mach, and the normal shock wave has

passed far enough aft that significant separate ion of airflow

occurs and a supersonic area and shock wave also forms at

the lower surface. The velocity increased to the point that all

the shock waves at the upper and lower surfaces of the

airfoil moved to the back and attached to the trailing edge. On a freestream Mach number greater than 1, a bow shock

occurs around the airfoil nose. The airfoil still in supersonic

flow and the flow begins to reline itself, and settles parallel

to the body's surface.

Fig. 6. creation of shock with increasing Mach number around an airfoil

M=0.9 M=1.0 M=0.9

M=0.6 M=0.7 M=0.8

M=1.0 M=1.1

M=1.2



3- PRESSURE COEFFICIENT

Figure 7. demonstrates the distribution of pressure coefficient (cp) on both surfaces of Airfoil at =2.5°. At 𝑀∞ = 0.6, the flow

extends along the leading edge and then begins to slow down, which is the typical subsonic behavior. At 𝑀∞ = 0.7 the flow continues

to expand after going around the leading edge, and it returns to subsonic speed through a shock wave on the upper side at (x/c=0.348)

a cross which there is an extremely rapid rise in pressure coefficient., the shock moves aft, becoming much stronger as 𝑀∞ increases

further. This leads to formation of bow shock, where the pressure coefficient is high compared to other region.

Fig. 7. distribution of Pressure coefficient (Cp) on the upper and lower sides of the Airfoil NACA0015 at =2.5°

3.WALL SHEAR STRESS

Figure 8. shows Effect of increasing 𝑀∞on the wall shear stress at =2.5°.It can be seen that the shear stress of the wall is proportional to the gradient of speed at the wall. This means that higher speeds cause greater shear stress on the wall. Consequently, the suction

area (upper surface) generates more shear stress on the wall than the pressure area (lower surface) of the airfoil. As the 𝑀∞increases,

the effect of wall shear stress on the leading edge and on the middle of the airfoil is more significant.

Fig. 8. Effect of increasing 𝑀∞on the wall shear stress at =2.5°

4- LIFT AND DRAG COEFFICIENTS

Figure 9. shows the effect of increasing 𝑀∞ on lift coefficient at =2.5°. It can be noticed that the lift coefficient decreases due to the formation of shock wave, while lift increases again on intrados. The loss of lift is due to the separation of the boundary layer on the

upper surface of airfoil. As the 𝑀∞ increases, the shock wave moves the back and attached to the trailing edge, the amount of

separation decreases, and the airfoil recovers part of its lift, until the free stream becomes supersonic, after this point, the lift gradually

decreases again.



Fig. 9. Effect of increasing 𝑀∞ on lift coefficient at =2.5°

Figure 10. shows the Effect of increasing 𝑀∞ on CD

coefficient at =2.5°.The increasing in drag coefficient is due to the normal shock wave behind the supersonic airfoil

flow areas, which typically begin to appear at (𝑀∞= 0.7). It

is clear that the drag coefficient is relatively high near

(𝑀∞=0.9). There are two reasons that can cause to increase

drag; firstly, a shockwave causes increase in static pressure,

higher Mach number, higher increase in static pressure.

Therefore, by definition of drag, increase in static pressure will cause to increase drag . Secondly, Shockwaves can

cause separation in the flow, it means that the smooth flow

over the body is disturbed and flow is no more attached to

body neatly. This results in decrease in lift. The flow is

disturbed due to sudden drop in velocity and decrease in

velocity means decrease in energy of the flow. Just a

background on separation: when flow is going around a

body, it loses energy because it has to overcome skin

friction. If the energy decreases by decreasing velocity then

the drag will be increased because velocity and pressure are

inversely related, decrease in velocity causes increase in

pressure which causes increase in drag. As 𝑀∞increases, the

flow is supersonic all around the body (with the exception

of a small area near the stagnation point on the leading edge). There is a bow shock wave around the airfoil nose,

most of the airfoil is in supersonic flow. The flow begins to

be realigned parallel to the body surface and stabilizes, and

the shock-induced separation decreases. This condition

results in a lower drag-coefficient.

Fig. 10. Effect of increasing 𝑀∞ on CD coefficient at =2.5°

Validation of the Simulation process

In order to validate the computational results obtained in this study, Pressure coefficients at (=0°,-4°) and (𝑀∞= 0.675, 0.777, 0.702) are compared with the results of experimental work [10] as shown in figure 11. It can be seen that there is a good agreement between

the computational and experimental results. The small variation in results is due to variation in grid sizing, operating condition,

geometrical parameters, etc. but the obtained result shows the same trend so that the results are suitably verified.

Figure 11. Comparison of Cp values between computational and experimental results for Cp for NACA 0015.

CONCLUSIONS

It is evident form the data obtained from the simulated flow

over airfoil NACA 0015 is that:

1- As the 𝑀∞increases, shock waves appear in the

flow region. When 𝑀∞ increases further, the shock

becomes much stronger and moves aft rapidly

leading to the creation of bow shock, where the



pressure coefficient is high compared to other

region.

2- The lift coefficient decreases and the drag

coefficient increases due to the formation of shock

wave behind the supersonic airfoil flow areas,

which typically begin to appear at (𝑀∞= 0.7).

3- With the increase of M∞, the influence of wall

shear stress on the leading edge and middle of the

airfoil becomes more significant.

4- The comparisons between computational and

experimental results showed excellent agreement

with the predicted pressure coefficient.

REFERENCES [1] Raad Shehab Ahmed,” Aerodynamic Parameters Analysis of

Transonic Flow Past Unswept and Swept Wings”,Eng. &

Tech. Journal, Vol. 29, No.5, 2011

[2] Manoj Kannan G1, Dominic Xavier Fernando2 and Praveen

Kumar R3” Study on the Shock Formation over Transonic

Aerofoil “,Advances in Aerospace Science and Applications.

ISSN 2277-3223 Volume 3, Number 2 (2013), pp. 113-118 ©

Research India Publications

http://www.ripublication.com/aasa.htm

[3] Tapan, K., Bhole, A. and Sreejith N.A. (2013), ‘Direct

numerical simulation of 2D transonic flows around airfoils’,

Computers & Fluids, Volume 88, pp. 19-37.

[4] Novel, K.S. and Imam, S. (2015), ‘Analysis of Transonic Flow

over an Airfoil NACA0012 using CFD’ International Journal of

Innovative Science, Engineering & Technology, Vol. 2, Issue 4.

[5] Muhammad Umer Sohail , Asad Islam.” Verification and

Validation of Flow Over a 3D ONERA Wing using CFD

Approach”,Journal of Space Technology, Vol 7, No 1, July

2017.

[6] Shamudra Dey, “Numerical Simulation of 3D Transonic Flow

over NACA 0009 Airfoil Geometry “,”Proceedings of the 5th

International Conference on Engineering Research, Innovation

and Education ICERIE 2019, 25-27 January, Sylhet,

Bangladesh .

[7] Dhruva Koti & Ayesha Khan M.” Numerical Analysis of

Transonic Airfoil”, International Journal of Engineering

Research & Technology (IJERT) ISSN: 2278-0181 ,Vol. 7 Issue

05, May-2018.

[8] http://airfoiltools.com/airfoil/naca4digit

[9] Menter, Florian R. “Improved two-equation k-omega turbulence

models for aerodynamic flows.” (1992).

[10] Friedrich Wilhelm Riegels,” Aerofoil Sections Results From

Wind-Tunnel Investigations Theoretical Foundations ”, London

Butterworths 1961.

http://airfoiltools.com/airfoil/naca4digit

analysis of transonic flow over an airfoil naca0015 using cfd

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