CFD Final Report-2

Group # 9

Subsonic BWB

Computational Fluid Dynamics

Submitted by:

Dane Irwin

Dwight Nava

Evan Johnson

Nick Z.

California State Polytechnic University Pomona

Department of Aerospace Engineering

Abstract

The objective of this project was to obtain aerodynamic coefficients and analyze subsonic

flow over a 3-D model of a blended wing body (BWB). The BWB model analyzed in this project

was based out of an aerodynamically scaled Lockheed Martin’s X-56A/MUTT. In order to

generate accurate aerodynamic results, the model was redefined to have smooth contours,

leading and trailing edge precision, and a symmetry plane to reduce computational time. The

uniform air flow was replicated by enclosing the half model with a rectangular box each

spanning at least 10 times the span of the aircraft in each directional axes. The flow was set to be

a constant of Mach 0.3 while the angle of attack was sweep for angles of 0, 5, and 10 degrees. In

good practice, the model was analyzed with inviscid runs and once adequate results were

observed, viscous flows were performed.

Introduction

In this project, a blended-wing-body model based on Lockheed Martin X-56A/MUTT is

analyzed in subsonic, viscous, and compressible flow regime to obtain an accurate computational

fluid dynamics stimulation of the lift and drag forces generated by the aircraft at various angles

of attack.

The CFD analysis was performed using the AnSYS FLUENT pressure-based solver. The

ideal gas model was used to simulate compressibility effects in the test volume. Upstream of the

model, a velocity inlet boundary condition was applied with an inlet velocity of M = 0.3 SSL

and downstream a pressure outlet was applied, the remaining four walls of the enclosure box

were assigned symmetry boundary conditions, preventing viscous effects and surface shear from

being simulated.

Ultimately, the underlying goal of this analysis is to obtain lift and drag coefficients in

the low subsonic flow regime in order to validate and modify existing panel method estimations

these parameters. The lift curve slope (𝐶𝐿𝑎𝑙𝑝ℎ𝑎) was also calculated in order to compare its value

to the one generated and used by AVL. This is all part of an ongoing research project involving

the design of a stability augmentation system for a tailless blended wing body aircraft.

In order to achieve reasonable, accurate, converging results, the mesh generated for the

finite volume analysis was extremely complicated, containing roughly 4.5 million tet elements

(around 1 million nodes). Only three simulations were able to be completed in the allotted time

frame of this project, due to the computationally intensive nature of the simulation. Convergence

took between 4 and 8 hours for each of the three runs.

Governing Equations

The governing equations of the flow are dependent on the type of flow that is occurring.

The first type of flow that was analyzed is inviscid flow, which is best described by Euler’s

equation shown below, which are nonlinear and hyperbolic.

𝜕�⃗⃗�

𝜕𝑡+

𝜕𝐹

𝜕𝑥+

𝜕𝐹

𝜕𝑦+

𝜕𝐹

𝜕𝑧= 0

where

�⃗⃗� = {𝜌𝜌𝑢𝐸

} and 𝐹 = {

𝜌𝑢

𝜌𝑢2 + 𝑝𝑢(𝐸 + 𝑝)

}

The first element represents that for mass, the second for momentum, and the third for energy.

As can be seen there is no term that includes viscosity, which forces the equation to be valid only

for inviscid flow.

The other governing equation is that which is used for turbulent viscous flow is the

Navier-Stokes equation given as:

𝜌 (∂v

∂t+ v ∙ ∇v) = −∇p + ∇T + f

where T is the total stress tensor and f is the body forces acting on the fluid element. Along with

the Navier-Stokes equation, there are two addition equations for the turbulent kinetic energy, k,

and the dissipation, ε.

𝜕

𝜕𝑡(𝜌𝑘) +

𝜕

𝜕𝑥𝑖

(𝜌𝑘𝑢𝑖) =𝜕

𝜕𝑥𝑗[(𝜇 +

𝜇𝑡

𝜎𝑘)

𝜕𝑘

𝜕𝑥𝑗] + 𝑃𝑘 + 𝑃𝑏 − 𝜌𝜖 − 𝑌𝑀 + 𝑆𝑘

𝜕

𝜕𝑡(𝜌𝜖) +

𝜕

𝜕𝑥𝑖

(𝜌𝜖𝑢𝑖) =𝜕

𝜕𝑥𝑗[(𝜇 +

𝜇𝑡

𝜎𝜖)

𝜕𝜖

𝜕𝑥𝑗] + 𝐶1𝜖

𝜖

𝑘(𝑃𝑘 + 𝐶3𝜖𝑃𝑏) − 𝐶2𝜖𝜌

𝜖2

𝑘+ 𝑆𝜖

where, C1ε, C2ε, C3ε, σk, σε, are constants. The Navier-Stokes equations are nonlinear and a

mixed set of hyperbolic-parabolic. The equation also provides all of the necessary information to

accurately describe turbulent viscous flow over the three-dimensional body/wing configuration.

Numerical Methods

In order to perform a finite

volume flow analysis of the X-56 test

model, significant changes to the

geometry had to be made to simplify

the model. Among these simplifications

was the removal of all leading and

trailing edge control surfaces along the

wing, as well as the removal of the

rudder control surface on the vertical

stabilizer / winglet. The body flap

which serves as an elevator for our

blended wing body design was also

simplified for the purpose of the

simulation. Once this was completed, a

semi-span version of the model was generated and imported into AnSYS for meshing. The idea

behind splitting the model into a semi-span model was to reduce the computational overhead

required to perform a static simulation. Due to the fact that our aircraft (and almost all aircraft) is

symmetrical about the Y-axis, this allows us to greatly reduce simulation time required while

obtaining results of the same accuracy provided there is no sideslip angle to the flow.

Figure 2- Mirrored top view of test geometry showing full span and planform surface.

Figure 1- Semi Span model of the X-56 blended wing body aircraft.

Figure 3 - Mirrored frontal view of the AnSYS test model.

Semi- Span

(m)

Mean Aerodynamic

Chord (m)

Planform Area

(m^2)

0.457317073 0.127 0.11017357

Table 1 - Model geometry data (all semi span).

Once the model geometry was

imported into AnSYS, a finite volume

enclose was created around it. The sizing

of the enclosure was made significantly

larger than the model in order to prevent

any unwanted wall interactions. The

dimensions of the enclosure were 340 in. x

170 in. x 110 in. which were found to be

adequately large to simulate free flight

conditions. At this point, a Boolean

operation was performed in order to

remove the semi-span model from the

enclosure, thus creating a volume of all of

the regions surrounding the model. Once

this operation was finished, the model was ready to be meshed in preparation for the simulation.

The meshing process was rather straightforward, as AnSYS takes care of most of the

work given a few parameters. Initial attempts to mesh the model automatically failed, and it was

decided after research to go with a tetrahedron based mesh. The mesh generation scheme was

non patch-conforming, with a surface sizing control on both the upper and lower surface of the

wing bringing the edge length of elements down to 0.01 in. for increased resolution and

accuracy. Finally, once the mesh was generated, a post-mesh inflation layer was added around

Figure 4 - Image of the finite volume enclosure used for the simulation runs.

the entire model. This inflation layer adds more cells closer to the surface of the aircraft in order

to more accurately represent the boundary layer effects. The resulting mesh was incredibly

detailed and contained between 4-5 million cells.

Figure 5 - Trimetric view of mesh showing the finite volume enclosure.

Figure 6 - Section cut across X-Y plane of mesh revealing the cells surrounding the model.

Figure 7 - Close up view of mesh surrounding model at line of symmetry. The inflation layers can be seen along the edges of the airfoil profile.

Once the meshing of the model was completed, the boundary conditions and model

parameters were set up within AnSYS. For this series of tests, a viscous, compressible pressure-

based model was chosen for the analysis. For compressibility, the ideal gas model was chosen in

order to simplify setup and decrease simulation time. The k-epsilon boundary layer transition

model was chosen for the viscous flow model because of its computational efficiency and

accuracy in simulating realistic boundary layers.

The boundary conditions used for this simulation were as follows: A velocity inlet was

created upstream of the model. This velocity inlet was set to an atmospheric pressure of 1 atm.

(SSL) and a velocity of M = 0.3 (102.08 m/s). Downstream of the model, a pressure outlet was

placed; this pressure outlet was also set to a pressure of 1 atmosphere at sea level. The remaining

four sides to the enclosure were all given symmetry boundary conditions.

Flow Velocity (m/s)

Flow Turbulence

(%)

Flow Density

(kg/m3)

Flow Dynamic

Pressure (Pa)

102.08 5 1.225 6382

Table 2 - Flow conditions used for simulation runs.

Each test run was initialized using a hybrid initialization scheme; the hybrid initialization

was chosen because in general it was shown to reduce the number of iterations required to

achieve convergence due to its more accurate calculation of initial conditions.

In addition to the typical residuals monitored during iterations, it was chosen to also

monitor CL and CD during each of the three simulations in order to get a better overall idea of

whether convergence was occurring. This proved to be invaluable in deciding when to end

iterating for each of the simulations. The residuals displayed are scaled, meaning that aside from

being displayed in a logarithmic plot; they are also measurements of how many orders of

magnitude the error fluctuation has decreased between runs. The simulation never met its

convergence parameters of 1.0 e-3 and declared that a simulation had “converged” because the

continuity residual only fell by two orders of magnitude.

Upon researching this issue, it was determined that the overall mas imbalance (the

parameter that is monitored and displayed as the continuity residual) was very low (1.0e-9 –

1.0e-9) from the first iteration, meaning that it could not diminish by three orders of magnitude.

Due to this issue, monitoring the drag and lift coefficients allowed for the convergence of these

parameters to be monitored. Each simulation ran for a different number of iterations because of

this approach to manually determining convergence. All three runs were allowed to iterate until

the fluctuations in CD and CL were below 1% of their respective values; this resulted in the

0°, 5°, and 10° angle of attack simulation converging after 950 iterations, 1450 iterations, and

1150 iterations respectively. The residual plots for each of the three simulation runs can be seen

below in Figure 8 through Figure 10.

Figure 8 - Residual plot for the 0 deg. AOA run.

Figure 9 - Residual plots for the 5 deg. AOA run.

Figure 10 - Residual plots for the 10 deg. AOA run.

Results and Discussion

After convergence was achieved for each of the three cases, the results were loaded into

the postprocessor for analysis and plotting. The surface relative pressure contours of the model

were plotted and are shown in Appendix A-4 the plots show the pressure changes that occur over

the entire blended wing body model in order to produce lift.

One of the unique aspects about the shape and airfoil design of our aircraft, is that it has

what is called reflex camber. Typical cambered airfoils have positive camber in order to increase

lift coefficient at zero AOA. The reflex camber airfoil present in both the body and outboard

wing of our X-56 research model does exhibit this positive camber as well; the reflex camber

comes into play at approximately 0.6 − 0.8 ∗ 𝑐𝑙𝑜𝑐𝑎𝑙. At this point of the section chord, the

camber changes sharply from positive to negative camber.

The motivation behind reflex camber is to alleviate some of the adverse pitching

inherently present in tailless aircraft. The reflex camber increases the pressure along the lower

surface of the wing near the trailing edge in order to apply a restoring moment counteracting the

divergent moment generated from the rest of the airfoil. This effect is well illustrated in the Y-

sweep of pressure contours displayed in Appendix A-3

Angle of Attack (deg.)

Drag (N): Lift (N): Moment (N*m): CL: CD: CM: L/D:

0 6.22 22.167 0.2336 0.031524 0.008846 0.000332 3.563826

5 9.145 133.66 2.717 0.19008 0.013005 0.003864 14.61564

10 15.64 188.63 3.294 0.268254 0.022242 0.004685 12.06074

Table 3 - Summary of aerodynamic forces and moments at various angles of attack.

The aerodynamic force and moment coefficients shown in Table 3 above are all within a

reasonable and expected range. The blended wing body exhibits a much higher overall lift to drag

ratio than most conventional aircraft designs. At its top L/D of 14.61 at 5 degrees angle of attack,

the body exhibits a drag coefficient of only 0.013 and a lift coefficient of 0.190. This validates the

theory and motivation behind blended wing body aircraft design, which is increasing overall

aerodynamic efficiency.

All of the simulation runs were viscous and therefore had two fundamental contributors to

drag: skin friction, and pressure drag. Shown below in Table 4 is the breakdown of drag forces and

coefficients for each of these two categories. These results further validated the accuracy of the

simulation as they showed that the skin friction coefficient varied by only 6% over the course of a

10 degree change in angle of attack. At zero angle of attack, the wing exhibited an incredibly low

drag coefficient of only 0.0089, once again showing its efficiency over traditional aircraft design.

AOA (deg.) Skin Friction: Pressure Drag: Total Skin Friction: Pressure Drag: Total:

0 3.646 2.583 6.229 0.0052 0.0037 0.0089

5 3.627 5.514 9.141 0.0052 0.0078 0.0130

10 3.2813 12.359 15.6403 0.0047 0.0176 0.0222

Drag Forces (N) Drag Coefficient (CD)

Table 4 - Breakdown of aerodynamic drag forces and coefficients for the model at various angles of attack.

Figure 11 - Plot of Drag Coefficient vs AOA

Figure 12 - Lift coefficient vs AOA

y = 0.0013x + 0.0080

0.005

0.01

0.015

0.02

0.025

0 2 4 6 8 10 12

Dra

g C

oef

fici

ent


Drag Coefficient vs. Angle of Attack

y = 0.0237x + 0.0449

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12

Lift

Co

effi

cien

t


Lift Coefficient vs. Angle of Attack

Figure 13 - Pitching moment vs AOA

Figure 14 - Drag polar for the blended wing body test model.

y = 0.0004x + 0.0008

0

0.001

0.002

0.003

0.004

0.005

0.006

0 2 4 6 8 10 12

Pit

chin

g M

om

ent

Co

effi

cien

t


Pitching Moment Coefficient vs. Angle of Attack

y = 16.14x - 0.0739

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.005 0.01 0.015 0.02 0.025

Lift

Co

effi

cien

t

Drag Coefficient

Drag Polar (CL vs CD)

Conclusion

A successful viscous, compressible, subsonic 3D flow analysis was performed on a

scaled version of the experimental X-56A blended wing body aircraft. The results obtained

through this static simulation in FLUENT all appear to be realistic and valid values, however the

comparison still needs to be made between the CFD results and experimental results in the

subsonic wind tunnel. The X-56 test model which will serve this purpose is currently in the

process of being fabricated, and when conclusive wind tunnel tests are completed, the true

accuracy of these CFD results will be established.

A-1 Pressure Contours at 0 degree Angle of Attack at Various Spanwise Stations:

y = 0

y = 0.05m

y = 0.1m

y = 0.15m

y = 0.20m

y = 0.25m

y = 0.30m

y = 0.35 m

y = 0.4m

A-2 Pressure Contours at 5 degrees Angle of Attack at Various Spanwise Stations:

y = 0m

y = 0.05m

y = 0.1m

y = 0.15m

y = 0.2m

y = 0.25m

y = 0.3m

y = 0.35m

y = 0.4m

A-3 Pressure Contours at 10 degrees Angle of Attack at Various Spanwise Stations:

y = 0m

y = 0.05m

y = 0.1m

y = 0.15m

y = 0.2m

y = 0.25m

y = 0.3m

y = 0.35m

y = 0.4m

A-4 Pressure Contours on Surface of Model:

Surface Pressure Contour at 0 Degree AOA



Surface Pressure Contour at 0 Degree AOA (bottom surface)



Surface Pressure Contour at 0 Degree AOA (frontal view)



A-5 Velocity Contours at 0 degrees Angle of Attack at Various Spanwise Stations:

y = 0.0m

y = 0.15m

y = 0.3m

A-6 Velocity Contours at 5 degrees Angle of Attack at Various Spanwise Stations

y = 0.0m

y = 0.15m

y = 0.3m

A-7 Velocity Contours at 10 degrees Angle of Attack at Various Spanwise Stations:

y = 0.0m

y = 0.15m

y = 0.3m

As mentioned previously, due to time constraint, we are not yet able to generate enough coefficient

of lift at various angles of attack to determine Clalpha. This will be completed out of the scope of

this project.

A-9 Turbulent Kinetic Energy Volume Plots at Various AOA

0 Degree AOA

5 Degrees AOA

10 Degrees AOA

Documents

CFD Final Report-2