Demonstrating the Potential of Transitional CFD for Sailplane ...

The Pennsylvania State University

The Graduate School

Department of Aerospace Engineering

DEMONSTRATING THE POTENTIAL OF TRANSITIONAL CFD

FOR SAILPLANE DESIGN

A Thesis in

Aerospace Engineering

by

Christopher J. Axten

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

December 2019

ii

The thesis of Christopher J. Axten was reviewed and approved* by the following:

Mark Maughmer

Professor of Aerospace Engineering

Thesis Advisor

Sven Schmitz

Associate Professor of Aerospace Engineering

Amy Pritchett

Professor of Aerospace Engineering

Head of the Department of Aerospace Engineering

*Signatures are on file in the Graduate School

iii

ABSTRACT

Traditional computational fluid dynamics solvers either model the flow as laminar or with

assuming the presence of turbulence. If the flow is modeled with turbulence the initial influence of

turbulence is minimal, and the flow can be considered laminar-like, but as the flow develops the

amount of turbulence grows until it acts as a fully turbulent boundary layer. Neither approach

properly models flow dynamics for the flight regime of a sailplane.

To demonstrate the potential of using computational fluid dynamics for sailplane design a

racing sailplane is analyzed with computational fluid dynamics using a recently developed

transition model to accurately model viscous effects. The results of the analysis are validated

against a conventional sailplane analysis program and are found to agree well. Regions with

complex flows, such as the wing-fuselage juncture and the empennage juncture, are examined to

highlight the potential for utilizing computational fluid dynamics to refine junctures in ways not

possible with conventional design methods. Practical uses for computational fluid dynamics in

sailplane analysis, such as investigating the stall characteristics and evaluating the tailwheel and

pushrod fairing drags, are also discussed along with notable gains in aircraft performance. Two

computational fluid dynamics transition models are compared and found to predict similar lift and

drag characteristics but determine conflicting transition locations at high-speed, with the recently

developed model more closely matching the predictions of the conventional analysis program.

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TABLE OF CONTENTS

List of Figures .......................................................................................................................... v

Nomenclature ........................................................................................................................... vi

Acknowledgements .................................................................................................................. vii

Chapter 1 Introduction ............................................................................................................. 1

Motivation ........................................................................................................................ 1 Fundamentals of Sailplane Performance .......................................................................... 2 The Flight Regime of a Sailplane..................................................................................... 3 Conventional Analysis Methods ...................................................................................... 4 Previous Studies ............................................................................................................... 6 The Schempp-Hirth Ventus 3........................................................................................... 9 Research Objectives ......................................................................................................... 9 Contributions of this Work .............................................................................................. 10

Chapter 2 Modeling Tools ....................................................................................................... 11

Conventional Tools for Problem Setup ............................................................................ 11 Boundary-Layer Transition in CFD ................................................................................. 14 Amplification Factor Transport Model ............................................................................ 15 CFD Solver ...................................................................................................................... 17 Validation of Tools .......................................................................................................... 17

Chapter 3 Mesh Generation ..................................................................................................... 23

Trimmed Cell Mesher Model ........................................................................................... 23 Adjustments for Transition Modeling .............................................................................. 24 Volume Mesh Generation ................................................................................................ 26

Chapter 4 Discussion of Results .............................................................................................. 28

Amplification Factor Flow Visualizations ....................................................................... 30 Skin Friction Coefficient Flow Visualizations ................................................................. 32 Stall Characteristics .......................................................................................................... 40 Component Drag .............................................................................................................. 42 Transition Model Comparison ......................................................................................... 43

Chapter 5 Conclusion ............................................................................................................... 49

Future Work ..................................................................................................................... 49

References ................................................................................................................................ 51

v

LIST OF FIGURES

Fig. 1 Typical sailplane drag breakdown (Thomas [2]) ........................................................... 5

Fig. 2 Standard Cirrus speed polar comparison (Hansen [3]) .................................................. 7

Fig. 3 Trimmed hexahedral mesh (Hansen [3]) ....................................................................... 8

Fig. 4 Schempp-Hirth Ventus-3 [8] ......................................................................................... 9

Fig. 5 Ventus 3 drag polars for all flap settings ....................................................................... 13

Fig. 6 PSU 94-097 mesh for Re=1,000,000 ............................................................................. 19

Fig. 7 PSU 94-097 lift curves .................................................................................................. 20

Fig. 8 PSU 94-097 drag polar for high-speed flight ................................................................ 21

Fig. 9 PSU 94-097 drag polar for low-speed flight .................................................................. 21

Fig. 10: Trimmed cell mesher process ..................................................................................... 24

Fig. 11: Fuselage and wing surface meshes ............................................................................. 25

Fig. 12: Domain volume mesh ................................................................................................. 26

Fig. 13: Vortical structure volumetric refinement ................................................................... 27

Fig. 14 Ventus 3 drag polar comparison .................................................................................. 28

Fig. 15 Ventus 3 speed polar comparison ................................................................................ 29

Fig. 16 Amplification factor predictions on top (right) and bottom (left) of the Ventus 3 at

𝐶𝐿 = 0.62 ........................................................................................................................ 31

Fig. 17 Amplification factor predictions on left (top) and right (bottom) of the Ventus 3 at

𝐶𝐿 = 0.62 ........................................................................................................................ 32

Fig. 18 Skin-friction coefficient predictions for the top (right) and bottom (left) of the

Ventus 3 at 𝐶𝐿 = 0.62 using the AFT model .................................................................. 33

Fig. 19 Skin-friction coefficient predictions for the left (top) and right (bottom) of the






vi


Ventus 3 at 𝐶𝐿 = 1.5 using the AFT model .................................................................... 38


Ventus 3 at 𝐶𝐿 = 1.5 using the AFT model .................................................................... 39

Fig. 24 Q-criterion of the flowfield at the horizontal tail half span at 𝐶𝐿 = 1.5 ..................... 40

Fig. 25 Skin-friction coefficient predictions of the Ventus 3 at 𝐶𝐿 = 1.5 using the AFT

model with near fuselage streamlines .............................................................................. 41


Ventus 3 at 𝐶𝐿 = 0.62 using the 𝛾 model........................................................................ 44







vii

NOMENCLATURE

𝑐 = reference chord

𝐶𝐷 = aircraft drag coefficient

𝐶𝐿 = aircraft lift coefficient

𝐶𝐿𝑚𝑎𝑥 = maximum aircraft lift coefficient

𝑑 = distance to nearest wall

𝑁𝑐𝑟𝑖𝑡 = critical amplification factor

= transported envelope amplification factor

𝑆 = reference wing area

= modified strain-rate magintude

𝑢𝑗 = Cartesian velocity component

𝑣 = freestream airspeed

𝑊 = aircraft weight

𝑥𝑗 = Cartesian coordinate

𝛾 = flight path angle

𝜌 = density

𝜇 = dynamic viscosity

𝜇𝑡 = turbulent eddy viscosity

𝜈 = kinematic viscosity

𝜈 = modified eddy viscosity

Ω = vorticity magnitude

viii

ACKNOWLEDGEMENTS

I would first like to acknowledge my advisor, Dr. Mark Maughmer, for his support and

help over the past couple of years. This work would not have been possible without him. I need to

thank the Schempp-Hirth company for providing me with the geometry and data for the Ventus 3

so I could do this work. Acknowledgment also goes out to my parents, siblings, and friends for all

of their help in giving me the support I needed through researching and writing this thesis. The

biggest thanks go to my wife Rachel and daughter Emma for their constant love, patience, and

support through all of the ups and downs, travelling for internships, and “I’m almost done”’s.

1

Chapter 1

Introduction

Motivation

The sport of soaring dates back to the 1920s, with the first World Gliding Championship

being held in 1937. Since then sailplane designers have continually pushed the bounds of aircraft

performance to out fly their competition. Due to the need to innovate, some of the most

significant improvements to aircraft design were original to, or made popular by, sailplanes. A

few examples are the D-tube structure, designing for laminar flow, the use of composites

materials, cruise flaps to minimize trim drag, and winglets to minimize induced drag. However,

one technology that has not been widely adopted by the sailplane community is the use of

computational fluid dynamics (CFD) for design and analysis. CFD provides an analysis tool that

can model every component of an aircraft together to capture the interactions between them. A

challenge to modeling sailplanes in CFD has been that traditional Reynolds-Averaged Navier-

Stokes (RANS) CFD analysis methods were initially developed for high Reynolds number flows

for which it was not necessary to accurately account for the transition process, as at the Reynolds

number of transport and military aircraft, the flow is predominantly turbulent. For CFD to

accurately model the flow physics, a boundary layer transition model needs to be coupled with

the chosen turbulence model. Accurate flow modeling will allow future sailplane designers to

identify regions for improvement and optimize these regions. This study focuses on CFD analysis

for a sailplane, but the methodology is critical for accurately modeling any aircraft with Reynolds

numbers low enough to support laminar flow, including UAVs, general aviation aircraft,

rotorcraft, and business jets.

2

Fundamentals of Sailplane Performance

Not having a direct form of propulsion, sailplanes utilize various forms of updrafts to stay

aloft after being towed or launched to altitude. In competitive soaring, the most common

mechanism for sustaining and gaining altitude is pockets of rising air called thermals. Thermals

allow the sailplane to climb if the air is rising in the thermal faster than the sailplane is sinking

relative to the air. The sailplane sink rate is calculated using

𝑣𝑠𝑖𝑛𝑘 =𝐶𝐷

𝐶𝐿32

√2𝑊

𝜌𝑆 (1)

for a given flight condition. On the other hand, competitions are won by flying the furthest

distance in the least amount of time, so time spent climbing wants to be minimized as it does not

contribute to distance covered. This leads to desire for sailplanes to be able to fly large distances

before needing to stop and regain altitude. The distance a sailplane can fly from a given altitude

in smooth air is based on the aircraft lift to drag ratio,

𝐿/𝐷 =𝐶𝐿

𝐶𝐷=

1

tan(𝛾) (2)

for a given flight condition. Integrating the outcomes of equation (1) and equation (2) is the key

to designing a high-performance sailplane that can both climb and cruise well. In both of these

equations, however, is a dependence on the aircraft lift and drag coefficients, which are

respectively defined as

𝐶𝐿 =𝐿

1

2𝜌𝑣2𝑆

(3)

𝐶𝐷 =𝐷

1

2𝜌𝑣2𝑆

(4)

In most engineering analysis the aircraft is considered in trim, meaning the aircraft is in steady

flight as all of the forces and moments balance. So, for a trim state the lift coefficient is generally

dictated by a given airspeed and necessity for lift to equal weight. This limits the designer’s

3

ability to use the lift coefficient to improve a sailplane’s performance. However, the designer can

focus on reducing the drag coefficient to produce lower sink rates and higher lift to drag ratios.

But, before the designer can attempt to minimize drag, they must first understand the flow regime

in which a sailplane operates.

The Flight Regime of a Sailplane

One of the most important flow quantities in sailplane design is a nondimensional ratio of inertial

forces to viscous forces, called the Reynolds number. For external aerodynamics the Reynolds

number provides qualitative and quantitative insight into the state of the boundary layer on a

body, such as a wing. In wing and airfoil analysis, the Reynolds number is generally based on the

chord of the wing,

𝑅𝑒𝑐 =𝜌𝑣𝑐

𝜇 (5)

The Reynolds plays an especially large role in sailplane design as it is one of the main factors that

dictates where the boundary layer along a body will transition from laminar to turbulent.

Boundary layer transition is critical in sailplane design and analysis for several reasons. Laminar

flow is desired as it has much lower wall shear stress, and thus much lower skin friction drag,

than a turbulent boundary layer. This reduction in skin friction drag equates to better

performance. On the other hand, turbulent boundary layers are generally more resistant to

separation than laminar ones due to their ability to convect momentum from the outer part of the

boundary layer (the freestream air) to the inner part (near the wall), which is beneficial when the

aircraft is at a high angle of attack during landing and climbing. The sailplane aerodynamic

design ends up being a compromise of these requirements: achieve as much laminar flow as

possible, but cause the laminar boundary layer to transition before it separates. So, the transition

4

mechanisms and location must be accurately predicted since the design and performance depend

so heavily on it.

Conventional Analysis Methods

The conventional approach of predicting the performance of a sailplane, or any fixed

wing aircraft, is to break the drag down by components so that each component can be analyzed

individually and then added together for the total drag. The wing drag, which is main source of

drag on a sailplane, is decomposed into the lift-induced drag and profile drag. The lift-induced

drag comes from the need for the wing to push incoming air downward to generate lift as an equal

and opposite reaction. It is predicted using one of several analytical or numerical methods, such

as a lifting-line, vortex lattice, or panel methods. Generally, a strip theory approach is used to

estimate the profile drag on the wing, which correlates local angles of attack along the span of the

wing, usually extracted from the method used to predict the lift-induced drag, to airfoil sectional

data. The sectional drag comes from airfoil wind-tunnel tests or analytical methods that iterate

integral boundary layer properties with potential flow solutions, such as the XFOIL code [1]. The

drag on other lifting surfaces, like the empennage surfaces, are computed the same way as the

wing, although iteratively if the airplane is being analyzed in the trimmed condition. Drag on

non-lifting components (e.g. fuselage, landing gear, etc.) can be estimated with a host of

empirical and analytical methods based on shape, Reynolds number, and “rules of thumb”. With

the drag of every component tallied, they can be added together and scaled by another “rule of

thumb” factor to account for any drag not being directly estimated, such as interference drag.

Some version of this process has been used to design and analyze sailplanes for about as long as

sailplanes have been flying, so it has become very tuned to the problem. A representation of the

drag breakdown for a typical sailplane from is shown in Fig. 1.

5

Fig. 1 Typical sailplane drag breakdown (Thomas [2])

However, there are some assumptions and deficiencies to the conventional design methods that

could be better handled by CFD.

One assumption of the conventional design methods is that the flow on the wing is

effectively two dimensional along the span. For most fixed wing aircraft, especially sailplanes,

this is generally a valid assumption except very close to the tip of the wing where spanwise

pressure gradients are high, or at high lift flight conditions. The “rule of thumb” approach for the

drag of certain components and drag from interference generally works well since it has been

calibrated with the flight tests of many sailplanes; however, it lacks the ability to lead the

designer in ways to reduce these forms of drag and provides little insight into how to analyze new

configurations. Thus, provided that an accurate transition prediction capability is employed, there

is potential for RANS CFD to be of value during the sailplane design process.

6

Previous Studies

Relatively few academic studies have been published dealing with the analysis and/or

design of a sailplane using CFD. Those that have been done showed promise, but none fully

demonstrated the capabilities as none analyzed a complete sailplane and/or used transition models

that lacked the fidelity of a physics-based model. An early work was done by Bosman [2] with

the analysis of the Jonkers JS-1 sailplane. Bosman demonstrated the utility of CFD by shifting the

location of the wing, assessed the gain of using active flow control near the wing-fuselage

juncture, and completely faired the rudder pushrod, which is generally only partially faired, to

gain a fairly substantial increase in L/D of about 3 increments. However, for simplicity and to

minimize cell count Bosman only modeled from the centerline of the aircraft to mid-span,

neglecting the tip and the flow domain beyond the tip. The domain reduction likely had little

effect on the juncture results, but not modeling the entire aircraft leaves the total performance to

be assumed and neglects understanding of the wing flowfield. Bosman also used an algebraic

boundary layer transition model which is limited in its fidelity compared to models based on one

or two transport equations.

Another analysis was conducted by Hansen [3] on the Schempp-Hirth Standard Cirrus.

Hansen used the solver STAR-CCM+ with the 𝛾 − 𝑅𝑒𝜃 transition model, which is a two equation

correlation-based transition model developed by Menter and Langtry et al. [4]. The results were

compared with flight test results from the Idaflieg summer meeting and overall agreed reasonably

well, as seen in Fig 2.

7

Fig. 2 Standard Cirrus speed polar comparison (Hansen [3])

Hansen had a consistent, slight underprediction in sink rate that is attributed to neglecting leakage

from the canopy seam, neglecting trim drag from not deflecting the elevator, and not including

the tail and wing skids. Hansen also does not model the entire aircraft in a single domain, but

models the entire aircraft by separating the wing and forward fuselage from the aft fuselage and

empennage, using the flow downstream of the wing and forward fuselage solution as the inflow

for the empennage section. The transition model Hansen uses is a correlation-based model,

meaning it is fundamentally based on the boundary layer transition properties for a certain

application. For the 𝛾 − 𝑅𝑒𝜃 model the calibrated application was turbomachinery. Therefore,

since the 𝛾 − 𝑅𝑒𝜃 model is a correlation-based model, rather than physics based and was

calibrated for transition in turbomachinery, it was not used as the primary transition model in the

current study. However, as Hansen demonstrated, the model can be calibrated to perform analysis

on external aerodynamics. Hansen’s study provided additional value at the start of this work

because it utilized the same solver and meshing approach as Hansen, so images like Fig. 3 were

8

useful in understanding the mesh sizing and growth rates necessary for other transition models,

which provided a starting point for the transition model used in this study.

Fig. 3 Trimmed hexahedral mesh (Hansen [3])

A more recent study was published by Maughmer et al. [5] on the analysis of a Discus 2

wing, as well as the winglets on the aircraft being analyzed in this study, the Ventus 3. The study

used a transition model developed by Coder and Maughmer [6], an earlier version of the same

model used in this study, and was implemented into the solver OVERFLOW [7]. Analysis of the

wing showed the two-dimensionality of the flow along a sailplane wing, essentially validating

one of the assumptions of conventional analysis methods, while showing three-dimensionality of

the flow on a winglet. The analysis of the Ventus 3 winglet provided insight that the winglet was

dropping out of the drag bucket at low lift coefficients, so the winglet was redesigned to perform

better at those flight conditions. Since analysis was only conducted on the Discus 2 wing and the

Ventus 3 winglet, much was left to be gained by analyzing the full aircraft.

9

The Schempp-Hirth Ventus 3

The aircraft used for the study was the Schempp-Hirth Ventus 3, as seen in Fig. 4, which

represents the latest in sailplane design.

Fig. 4 Schempp-Hirth Ventus-3 [8]

The Ventus 3 is produced in four models: the sport and performance editions with either a 15-

meter or 18-meter wingspan. For this study, the 18-meter version of the sport edition was used

throughout. It was also assumed that the aircraft was loaded to its maximum weight of 600kg for

all flight conditions.

Research Objectives

The goal of this work is to demonstrate that, with the inclusion of a boundary layer

transition model, RANS CFD is a valuable tool to the sailplane designer for analyzing the entire

10

vehicle. Several research objectives were formulated to support this goal. The first objective was

to verify the boundary layer transition model used and understand the meshing and modeling

characteristics necessary for it to function properly. Next, several CFD models of the Ventus 3

were created for various flight conditions in order to understand the meshing challenges, as well

as used later in CFD analysis. After the CFD analysis, the results were quantitatively compared

with an in-house sailplane performance tool to provide a method for validating the results.

Aspects of the CFD results not captured by the in-house code were identified to highlight the

utility of CFD. The stall buffet behavior and the drag on the tailwheel and a fairing for the rudder

pushrod were evaluated to demonstrate two practical applications of CFD. Lastly, two flight

conditions were analyzed with and compared against another transition model to provide insight

on the advantages and disadvantages of each model.

Contributions of this Work

This work seeks to contribute to two developing fields: the use of CFD in sailplane

design and transition modeling in CFD. Sailplanes are among the most aerodynamically refined

flight vehicles in the world, so improvements over past designs can become limited when the

tools available are not evolving as well. This study is the first published CFD analysis of a

complete sailplane, known to the author. It is hoped that this work demonstrates that the

computational models are mature enough be used for sailplane design. Recent developments in

CFD transition modeling are the primary reason CFD has become a viable sailplane design tool,

and this study provides another set of data for further validation and refinement of those models.

This is critical as many classes of aircraft, from UAV’s to general aviation to laminar flow

commercial aircraft concepts, which require accurate modeling of the boundary layer transition

process to produce physical and accurate results.

11

Chapter 2

Modeling Tools

Generally, profile drag is estimated by assuming the streamlines over the wing are

relatively straight and parallel. This assumption holds well over most of an aircraft wing,

especially on wings with large aspect ratios, but this assumption begins to break down near the

wingtip as three-dimensional pressure gradients pull the streamlines near the wingtip on the lower

surface toward the tip and push the streamlines towards the fuselage on the upper surface. While

non-viscous methods can account for three-dimensional effects in the outer flow, doing so in the

boundary layer is generally only accomplished with CFD, wind tunnel testing, flight testing.

Three-dimensional boundary layer models have been recently developed, although have not

expanded to wide use and would not handle junctures as well as CFD. Winglets operate entirely

in a region affected by spanwise flow, thus making it difficult to accurately estimate their

performance without utilizing CFD or testing experimentally.

Conventional Tools for Problem Setup

When airfoils and aircraft are analyzed with CFD, they are run through angle of attack

sweeps with varying airspeeds and atmospheric conditions to provide results through a range of

Reynolds and Mach numbers. For this study it was decided that the Ventus 3 would only be

analyzed at various trim states, as it has eight flap settings to precisely control the aircraft

performance depending on the flight conditions. The flap deflections corresponding to each flap

setting are shown in Table 1.

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Table 1 Ventus 3 flap settings and deflections

Flap Setting Inboard Flap Deflection (°) Outboard Flap Deflection (°)

Landing 20 9

3 13.5 9

2 9 9

1 2 2

0 0 0

-1 -2 -2

-2 -4 -4

S -6 -6

A Penn State in-house code called PGEN [9] has the capability to optimally determine

flap settings as these depend on velocity. Data from PGEN can be seen in Fig. 5, where the

Ventus 3 is analyzed by first holding each flap setting constant, and then allowing PGEN to

optimize the drag polar with the available flap settings, generating the composite polar.

13

Fig. 5 Ventus 3 drag polars for all flap settings

For this study PGEN was used to determine the flap setting for minimum drag at various

lift coefficients so those flight conditions could be further explored. PGEN does not output some

of the parameters necessary for a CFD analysis, such as angle of attack or elevator trim

deflection, so the aircraft was also analyzed using the Athena Vortex Lattice (AVL) [10] program

to determine the values for trim corresponding to each flight condition. Generally, vortex lattice

methods do not model fuselages and pods well, one of the advantages of CFD, so a “rule of

thumb” value was used to estimate the fuselage pitching moment in order to approximately trim

the aircraft with the fuselage.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

CL

CD

Composite

Landing

3

2

1

0

-1

-2

S

14

Boundary-Layer Transition in CFD

Historically, CFD turbulence models are designed for high Reynolds number flows so

they very loosely model, or ignore altogether, the process of boundary layer transition. For

example, the eddy-viscosity branch of RANS models represents the effects of turbulence as a

form of viscosity called the turbulent viscosity. Since the wall shear stress

𝜏𝑤𝑎𝑙𝑙 = 𝜇𝜕𝑢

𝜕𝑦𝑤𝑎𝑙𝑙 (6)

is dependent on the viscosity, eddy-viscosity models would calculate it with an effective viscosity

from the sum of the local turbulent viscosity and the dynamic viscosity. Early on, the boundary

layer is treated as “laminar like” with initially low amounts of turbulent viscosity and then, as the

boundary layer continues downstream the turbulent viscosity gradually grows until it plateaus, at

which point the boundary layer is fully turbulent. This approach predicts significantly worse

performance on sailplanes as, in reality, the boundary layer should have no turbulent viscosity

until the point of transition, since the laminar boundary layer only has dynamic viscosity, where it

then should have a significant jump in turbulent viscosity. The gradual building of turbulent

viscosity raises the skin friction in regions where a laminar boundary layer, with no turbulent

viscosity, physically exists and thus artificially raises the drag.

One of the first widely accepted CFD transition model was the Langtry and Menter

Correlation-Based transition model [11]. It was released in 2009 and has been implemented in a

number of government and commercial solvers, including OVERFLOW [7] and STAR-CCM+.

An alternative model, called the Amplification Factor Transport (AFT) model, was developed by

Coder and Maughmer [6] and refined by Coder [12–14], that is based on Linear Stability Theory

rather than a correlation based approach. In practice, both of the models work the same way by

coupling with a turbulence model, the 𝑘 − 𝜔 SST turbulence model for the Langtry and Menter

transition model and the SA turbulence model for the AFT model, and then acting as an “on or

15

off” logic for the production of turbulence in the turbulence model based on criterion of the

transition model. However, as discussed in Chapter 1, accurately modeling the boundary-layer

transition process and its location are of key importance when modeling the flow over a sailplane.

For this reason, the more physics based AFT model was chosen as the primary transition model

for this study, although a couple of cases were run with the Langtry and Menter model for

comparison.

Amplification Factor Transport Model

The Amplification Factor Transport transition model is based on the 𝑒𝑁 method of linear

stability theory and adapts it to be used in the context of CFD. Many details of the method are

based on Drela and Giles’ [15] implementation of the, so called, approximate envelope method.

This method takes the general 𝑒𝑁 method and only tracks the maximum amplitudes of the

frequencies being most amplified rather than the full envelope of amplitudes and frequencies.

This reduces the scope of 𝑒𝑁 to just checking if the worst-case scenario meets the transition

criterion, which greatly reduces the computational requirements of predicting transition. It is the

transition method used in the widely popular XFOIL [1] tool.

The primary difficulty with translating Drela and Giles’ implementation into CFD is that

many of the necessary parameters are based on values that are predicted using integral boundary-

layer (IBL) theory. This is fundamentally different than CFD in which the boundary layer

velocity profiles are actually calculated, so to utilize Drela and Giles’ method the IBL properties

need to be either extracted or estimated as the flow solution is being converged. Coder and

Maughmer do this with an estimation based on a scaling of the dimensions of vorticity,

16

𝑈

𝜃≈ 𝛺𝐷(𝐻12) (7)

where the 𝐷(𝐻12) term is based on calibration of the model. Using the approximated IBL values,

the calculation of the approximate envelope factor is presented in a form compatible with CFD

modeling, namely a transport equation. The derived transport equation is

𝜕𝜌

𝜕𝑡+

𝜕𝜌𝑢𝑗

𝜕𝑥𝑗= 𝜌Ω𝐹𝑐𝑟𝑖𝑡𝐹𝑔𝑟𝑜𝑤𝑡ℎ

𝑑

𝑑𝑅𝑒𝜃+

𝜕

𝜕𝑥𝑗[𝜎𝑛(µ + µ𝑡)

𝜕

𝜕𝑥𝑗] (8)

The final aspect of integrating the transition model into CFD is coupling it with a

turbulence model. The AFT model is most commonly coupled with the Spalart-Allmaras (SA)

turbulence model, which is a one equation eddy viscosity model that is generally favored for

external aerodynamics. The AFT model is implemented by maintaining the SA governing

transport equation,

𝐷

𝐷𝑡= 𝑐𝑏1(1 − 𝑓𝑡2) − (𝑐𝑤1𝑓𝑤 −

𝑐𝑏1

𝑘2𝑓𝑡2) (

𝑑)2+

1

𝜎[𝜕

𝜕𝑥𝑗((𝜈 + 𝜈)

𝜕

𝜕𝑥𝑗) + 𝑐𝑏2

𝜕

𝜕𝑥𝑗

𝜕

𝜕𝑥𝑗] (9)

and simply redefining the 𝑓𝑡2 term. In the original model this term was used to transition the

boundary layer when a trip point was defined. Originally the trip point has to be known

beforehand, so the term provides a mechanism to control transition when the SA model is

generating turbulence, and thus can be used to trip the boundary layer when dictated by the AFT

model.

Coder designates the original model as the AFT2014 model and follows it with several

evolutions: the AFT2017a, [12], AFT2017b, [13], and AFT2019 [14] models. The evolutions

include relations based on better calibrations and increased robustness. In the AFT2014 and

AFT2017a models, an algebraic equation for intermittency is used to provide the SA model the

“on or off” logic depending on if the flow has locally met the transition criterion. The algebraic

intermittency equation in the AFT2017b and AFT2019 models is further enhanced to become a

second transport equation to provide a more robust “on or off” logic. Due to implementation

17

issues, the AFT2017a algebraic intermittency model was used for this study, for which the

relation

𝑓𝑡2 = 𝑐𝑡41 − 𝑒𝑥𝑝[2( − 𝑁𝑐𝑟𝑖𝑡)]𝑒𝑥𝑝 [−𝑐𝑡4 (

𝜈)2] (10)

was used to couple the amplification factor transport equation with the SA model. Beside the

algebraic intermittency equation, the model used in this study implemented the most recent

relations and calibrations available.

CFD Solver

The CFD solver used for the study was version 12.06.11 of STAR-CCM+ by CD-

Adaptco [16]. The simulations were solved using the Semi-Implicit Method for Pressure Linked

Equations (SIMPLE) algorithm with a constant density assumption to speed up the time per

iteration. The SA turbulence model was used since the transition model employed can be coupled

to it and the advantages it offers for streamlined external aerodynamics.

Validation of Tools

The AFT model has been incorporated into several solvers, with OVERFLOW being the

primary one. The implementation in OVERFLOW has been verified against experimental data by

Coder for several airfoils and three dimensional configurations [17]. However, to verify the

meshing techniques and implementation of the AFT model in STAR-CCM+ used in this study, a

winglet airfoil, the PSU-94-097, was analyzed at various flight scale Reynolds numbers and

compared to published wind-tunnel data [18].

Generating meshes in STAR-CCM+ begins with specifying values for near the body

grids that are meant to capture boundary layers. The values specified include the desired number

18

of cells in the grid, the grid thickness, and the thickness of the first cell away from the wall. For

the validation study and the full Ventus 3 analysis the meshes were generated with 25 cells in the

near body grid using a hyperbolic tangent distribution to meet the desired growth rate of 1.3. The

boundary-layer thickness was estimated using the relation

𝛿 =0.38𝑐

𝑅𝑒𝑐15

(11)

for the turbulent boundary layer thickness on a flat plate [19]. Assuming the same Reynolds

number, laminar boundary layers tend to be thinner than turbulent ones, so estimating the

boundary layer thickness based on an entirely turbulent flow is a conservative approach in

estimating the boundary layer thickness. In practice the boundary layer at the trailing edge is

close to the thickness of the near body grid due to airfoil adverse pressure gradient growing the

turbulent boundary layer faster than does a turbulent boundary layer on a zero-pressure gradient

flat plate. The last important property in modeling boundary layers is the wall normal spacing of

the first cell in a boundary layer, known as the 𝑦1 spacing, typically presented in 𝑦+ units. A

target 𝑦1 value of 0.67 𝑦+ units is used for the PSU 94-097 validation. The process of calculating

the first cell height starts with estimating a representative local skin friction coefficient for the

problem, which was done by using the turbulent flat plate local skin friction coefficient, based on

the chord length,

19

𝑐𝑓 =0.026

𝑅𝑒𝑐17

(12)

to calculate a wall shear stress

𝜏𝑤 = 0.5𝑐𝑓𝜌𝑣2 (13)

The wall shear stress is divided by the density to determine a friction velocity

𝑢∗ =𝜏𝑤

𝜌 (14)

that is finally used with the desired 𝑦+ to calculate a first cell height

𝑦1 =𝑦+𝑑𝑒𝑠𝑖𝑟𝑒𝑑𝜇

𝜌𝑢∗ (15)

An example of the mesh used for the airfoil studies is presented in Fig. 6.

Fig. 6 PSU 94-097 mesh for Re=1,000,000

The specified boundary-layer properties also create a boundary layer grid that transitions

smoothly to the core mesh, which is also an important quality in boundary-layer meshing.

Downstream of the airfoil, a refinement was used to capture the flow structures and wake of the

airfoil.

Overall, the mesh used for the PSU 94-097 validation was a somewhat coarse 40,000

cells when compared to other transitional CFD studies. Part of the validation was to determine the

minimum cell count required to get high fidelity results, so these meshing values can be used to

minimize the cell count for the aircraft analysis.

As discussed in the previous section, the AFT model requires a user defined value of

amplification ratio at which boundary layer transition is said to occur. For the validation of tools,

20

an 𝑁𝑐𝑟𝑖𝑡 of 9 was used, as it has been shown to produce results that compare well with those from

low turbulence wind tunnels [20], such as the Penn State Low-Speed Low-Turbulence (LSLT)

tunnel. Additionally, the far field turbulent eddy viscosity ratio was set to 0.1 as dictated by

Coder [14].

Comparison between the CFD results and those obtained experimentally show good

agreement between the lift curves except for overprediction of the maximum lift coefficient, as

seen in Fig. 7.

Fig. 7 PSU 94-097 lift curves

This behavior is common among comparisons between experiment and RANS CFD,

independent of if a transition model is used, because RANS turbulence models tend to

overestimate the conditions for a turbulent boundary layer to stay attached. The drag polars

equating to high-speed and low-speed flight conditions also show good agreement within the

primary operating conditions of the airfoil, although some discrepancies are seen near the edges

of the operating range, especially with the same overprediction in the maximum lift coefficient.

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

-10.0 -5.0 0.0 5.0 10.0 15.0

cl

cd

LSLT Re=1,000,000

LSLT Re=800,000

LSLT Re=600,000

LSLT Re=400,000

STAR-CCM+ Re=1,000,000

STAR-CCM+ Re=800,000



21

Fig. 8 PSU 94-097 drag polar for high-speed flight

Fig. 9 PSU 94-097 drag polar for low-speed flight

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350

cl

cd

LTST Re=1,000,000 LTST Re=800,000

STAR-CCM+ Re=1,000,000 STAR-CCM+ Re=800,000

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350

cl

cd

LTST Re=600,000 LTST Re=400,000

STAR-CCM+ Re=600,000 STAR-CCM+ Re=400,000

22

Aside from the over prediction of the maximum lift coefficient, the transition model

slightly underpredicts the drag at lower lift coefficients. This tends to happen at negative angles

of attack where, as can be observed in Fig. 7, a lift coefficient of 0.5 occurs at an angle of attack

of zero degrees. Accurate predictions in this region for cambered airfoils can be difficult for CFD

and other analysis methods because, as with the overprediction of the maximum lift coefficient,

the flow models generally delay the separation point of a turbulent boundary layer. So, as the

angle of attack becomes negative the transition point quickly moves to the leading edge due to the

pressure gradient on the lower surface becoming adverse. Then, as angle of attack is further

reduced, the turbulent lower surface boundary layer separation moves from the trailing edge

forward toward the leading edge. This creates a large drag increase, but since the turbulence

model delays the separation point moving forward, it also delays the drag rise.

In this situation, it is possible refining the mesh may improve the results, but part of the

objective of this airfoil analysis was to find the coarsest mesh characteristics that allow the

transition model to function properly and demonstrate good agreement across the general

operating envelope, which was achieved with this mesh configuration. The specific surface and

volume mesh values will be described in greater depth in Chapter 3.

23

Chapter 3

Mesh Generation

As with all computational methods, RANS CFD requires a flow domain to be discretized

into finite elements before the governing equations can be solved numerically. This leads to the

discussion of how the domain should be discretized so that the discretization does not artificially

affect the solution. Depending on the approach, many factors have to be considered to produce a

solution that is minimally to completely not influenced by mesh being used. For this study the

mesh was generated with the trimmed cell mesher within STAR-CCM+, and a series of volume

and surface refinements were made to ensure the flow physics were modeled as realistically as

possible.

Trimmed Cell Mesher Model

The unstructured meshing package in STAR-CCM+ was used for mesh generation. Both

of the meshers available in STAR-CCM+, the polyhedral and trimmed cell meshers, were initially

considered for the study. The polyhedral mesher inherently has smooth cell growth, generally has

a lower cell count and can converge faster; however, after several iterations of both approaches,

the trimmer mesh was chosen due to its much faster meshing time. The general process for the

trimmed cell mesher is to take a given surface or volume and overlay the body with a mesh of

prescribed size, as shown in Fig. 10.

24

Fig. 10: Trimmed cell mesher process

The images represent the process of how the majority of the volume mesh is generated.

The main values specified by the user are the base target size, the input body boundary targets

sizes, surface growth rates, volume growth rates, and blending ratios. The mesher takes these

values and creates a mesh completely made up of hexahedrals that are a factor of 2𝑛 (i.e.

multiples of 1, 2, 4, … or ½, ¼, …) of the specified base target size.

Adjustments for Transition Modeling

The general practices for meshing aircraft are relatively well understood and provide a

good starting point for a sailplane, although, some differences exist. The largest difference is in

the streamwise spacing, as transition models are particularly sensitive to this. A common, and

valuable, reference is the best practices in gridding published by Chan [21] for leading edge,

trailing edge, and chordwise spacings on airfoils in percent of chord. The paper is intended for

structured, overset gridding, although the values work just as well for unstructured meshing. Chan

recommends using a 0.1% spacing for the leading edge, 0.2% for the trailing edge, and 101 points

along both the upper and lower surface. For standard turbulence models these spacings provide

reasonable answers without the necessity for substantial computational resources; however,

transition models require a much finer mesh than the standard RANS models. STAR-CCM+

validation cases for a built-in transition model called the Gamma model, based on the Langtry-

25

Menter transition model [11], show that for the Gamma model requires a target spacing of 0.5%

of chord, or about 200 points, along both the upper and lower surface. The leading edge spacing

is also halved from Chan’s recommendations.

It was found that the STAR-CCM+ recommended spacings were adequate for the AFT

transition model, but similarly were the minimum spacing possible before “mesh induced”

transition occurred and triggered the model at unphysical locations. Found to be equally

important was smooth growth between fine and coarse regions, such as between the wing leading

edge and further aft, or between the fuselage nose and fuselage body. Due to how the trimmed

cell mesher grows by doubling the cell size, care had to be taken to ensure the amplification

factor solution was “established” on a constant size, fine mesh before allowing the surface mesh

size to grow. This was accomplished by using a surface growth rate of 1.05 on most of the

aircraft, and 1.03 on the fuselage as the gradient of the flow partially stagnating on the fuselage

nose required very smooth growth for the solution to hold. An example of the resulting mesh can

be seen in Fig. 11.

Fig. 11: Fuselage and wing surface meshes

26

Volume Mesh Generation

The volume mesh generation was somewhat standard to the best practices for fixed wing

aircraft. Since the analysis was a subsonic simulation, a “bullet” shaped domain was used to

provide additional distance downstream of the aircraft for wake development. The upstream inlet

boundary was placed 200 meters away, approximately 10 spans for the 18m glider, and the

downstream outlet was placed 225 meters away to give more space for wake resolution. The far

field mesh size was targeted as about 4 meters, which is less than the body length of the aircraft.

A representation of the domain is shown in Fig. 12

Fig. 12: Domain volume mesh

27

The same boundary layer mesh characteristics mentioned in the validation of tools

section were also used on all of the aircraft configurations, namely a target 𝑦+ of 0.67 and growth

rate of 1.3. Similar to Fig. 6, a refinement was used downstream of the wing to capture the flow

structures and wake.

Aside from the standard volume meshing controls, additional volumetric refinements

were added to capture the various vortical structures shed by the aircraft at lifting surface tips and

planform breaks. The bodies used for volumetric refinement can be seen in Fig. 13, and they were

rotated based on angle of attack to properly capture vortical structures.

Fig. 13: Vortical structure volumetric refinement

In total, each flight condition produced a mesh with between 170-225 million cells, with

some variance between flap settings. To the seasoned meshing specialist this may sound like an

overly dense mesh for this aircraft in a RANS simulation; however, high cell count was mostly

due to the type of mesher being used in conjunction with the required fineness for the transition

model to produce valid results.

28

Chapter 4

Discussion of Results

Overall, the CFD results with the AFT transition model compare well with those from

PGEN. An 𝑁𝑐𝑟𝑖𝑡 of 12 was used for all of the aircraft simulations, as this value has been

historically associated with sailplane analysis and is suggested in the XFOIL User Manual [1]. A

comparison of the Ventus 3 drag polars is shown in Fig. 14.

Fig. 14 Ventus 3 drag polar comparison

Over the entire profile, the CFD predicted a slightly higher drag coefficient for a given

lift coefficient. At lower lift coefficients, the two predicted results are close, with the difference

being about four drag counts, while at higher lift coefficients the offset increases to about thirty-

five drag counts. The offset is so large at higher lift coefficients because of how the number of

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

CL

CD

PGEN Composite STAR-CCM+ Composite

29

CFD cases was discretized. Most of the flight conditions investigated were below a lift coefficient

of 1.0, since this value is representative a lift coefficient for climbing and values for flying

between thermals are considerably lower. A low-speed case for landing was analyzed, which is

the case at the top of polar with a lift coefficient of 1.5. Since the drag starts to rise severely

above a lift coefficient of 1.4, and no flight conditions were investigated between 1.0 and 1.5, the

agreement between the drag polars would likely be better at the higher lift coefficients than is

seen in Fig. 14.

The aircraft speed polar is shown in Fig. 15, which plots sink rate versus airspeed.

Fig. 15 Ventus 3 speed polar comparison

The speed polar shows an offset between the predicted results of 0.03 meters per second at low-

speed and 0.05 meters per second at high-speed. The speed polar also represents the agreement

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300

Sin

k R

te (

m/s

)

Airspeed (km/h)

PGEN Composite STAR-CCM+ Composite

30

between the methods better than the drag polar since the CFD data points are discretized evenly

by airspeed, as opposed to being clustered to lower lift coefficients on the drag polar.

Amplification Factor Flow Visualizations

The ability to visualize the flow on an aircraft and where the interference drag occurs is a

valuable tool to the designer, as it provides a direct understanding of the flow physics and, if the

flow can be understood, it can be optimized. To demonstrate this utility, representations of

various flight conditions are shown below, first using the local amplification factor and then the

local skin friction coefficient.

Representations of the local amplification factor on the Ventus 3 near the maximum lift

to drag condition are shown below in Fig. 16 and Fig. 17. Fig. 16 shows the top and bottom of the

aircraft, side by side, while Fig. 17 shows the aircraft from the left and right sides. For the images

of the top and bottom of the aircraft, the flow is going down the page while the flow is essentially

in the positive “X” direction for the side images. In both images the laminar boundary layer is

blue and turbulent boundary layer is red, with transition appearing from light blue to yellow.

31

Fig. 16 Amplification factor predictions on top (right) and bottom (left) of the Ventus 3 at

𝐶𝐿 = 0.62

Streamlines and vortex cores also provide valuable insight for extracting qualitative

understanding from visualizations. For Fig. 16 through Fig. 29 the black lines on the aircraft are

constrained streamlines, or streamlines that show the direction of the flow near the body, while

the gray lines trailing the aircraft are the cores of strong vortices. In Fig. 16 the streamlines along

the wing and horizontal tail are relatively straight, showing that the flow is well behaved and two-

dimensional. Two-dimensional flow is one of the fundamental assumptions of the conventional

analysis methods, so observing the streamlines in Fig. 16 indicates that this assumption is valid

for a sailplane. One could even propose that since the flow is two-dimensional, CFD does not add

significant value to sailplane design, although Fig. 17 demonstrates some important flow features

not captured by conventional models, such as the flow around the wing-fuselage juncture, as

shown in the upper image of Fig. 17.

32

Fig. 17 Amplification factor predictions on left (top) and right (bottom) of the Ventus 3 at

𝐶𝐿 = 0.62

The constricting of the streamlines around the wing-fuselage juncture shows that the flow is

accelerating through that region, which in turn increases the skin friction as will be discussed

later, and influences the transition point on the fuselage.

Skin Friction Coefficient Flow Visualizations

Visualizing the amplification factor over the surface of the aircraft provides valuable

insight into how and where the boundary layer has transitioned; however, the local amplification

33

factor at the wall is generally not the highest value locally as it can reduce after transition has

occurred, such as downstream of the wing upper surface laminar separation bubble, even though

the model continues to treat the flow as turbulent. For these reasons and to compare with the

Gamma transition model, which does not use the amplification factor to predict transition, the

local skin friction coefficient was instead used to visualize the results. The skin friction

coefficient is a common method for examining the transition and separation locations in CFD

solutions as it clearly shows laminar flow with low values, turbulent flow with a jump in value,

and separated regions with a near zero value. For the same flight condition and aircraft

orientations as above, the skin friction distribution for the Ventus 3 is seen in Fig. 18 and Fig. 19.

Fig. 18 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at

𝐶𝐿 = 0.62 using the AFT model

The red represents regions of high skin friction, such as the leading-edge spike on an

airfoil or where the flow has just transitioned from laminar to turbulent, and the blue represents

regions of low to no flow (i.e. local separation). Fig. 16 and Fig. 18 are seen to compare well with

regards to the transition location on the wing and horizontal tail based on the rise in amplification

factor and skin friction coefficient at approximately the same chordwise location on both

components. Transition at these locations happens through a laminar separation bubble so the rise

34

in skin friction coefficient is slightly aft of the observed amplification factor transition point

because the skin friction rises where the bubble reattaches and the amplification factor rises in the

bubble.

Another advantage to using the local skin friction coefficient for flow visualization is that

regions of high flow gradients, which can be large contributions to drag, can be visualized

regardless of whether the location is laminar or turbulent. For example, the flow on the fuselage

in Fig. 19 can be seen to transition just upstream of the wing-fuselage juncture where the surface

turns from blue to green.

35

Fig. 19 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at


However, the high skin friction is only partially coming from the turbulent boundary layer, as the

real cause is the juncture causing the flow to accelerate to a high velocity. This translates into a

non-negligible amount of drag on the aircraft. A sailplane designer could use this information to

reshape the juncture so that the flow does not accelerate as strongly around the juncture, thereby

reducing the skin friction drag.

Another feature only captured in CFD is a vortex that forms on the aft part of the tail

juncture in Fig. 19 due to interaction between the tail surfaces. Utilizing the vortex cores feature

and investigating the streamlines indicates that the vortex from this juncture is fairly strong, so

36

utilizing CFD to design the fillets between tail surfaces could provide a substantial increase in

performance. This vortex is seen in every visualization, varying in strength, so it could have a

large impact on the aircraft performance, although designers could also utilize tools like

Quadratic Constitutive Relations (QCRs), which better model regions with secondary gradients or

strong streamline curvature, to get a better understanding of this flow feature.

The streamlines on the lower surface of the winglet, seen the lower image of Fig. 19,

have some highly three-dimensional behavior, again only captured in CFD. Although, the skin

friction does not seem to drop to zero, indicating that the boundary layer does not separate on the

lower surface until the trailing edge, which is fortunate as separation would create a large increase

in pressure drag.

The top and bottom views of the Ventus 3 for a high-speed case are shown in Fig. 20.



Comparing with the representation for the maximum lift to drag case in Fig. 18, Fig. 20

looks relatively similar with the expected two-dimensional behavior on the wings and horizontal

tail with similar transition locations. However, the side views of the aircraft in Fig. 21 have some

differentiating features.

37



The most notable differences between the cases is that the high skin friction region

around the wing-fuselage juncture is notably less red and the streamlines appear less constricted

than in Fig. 19. This likely results in a drag coefficient reduction for the fuselage as compared to

the maximum lift to drag case.

It is also worth noting that the streamlines on the underside of the winglet in Fig. 21 are

much more two-dimensional; however, it seems the boundary layer has transitioned earlier based

on the color changes.

Comparing the maximum lift to drag and high-speed cases of Figs. 16-21 with the low-

speed case in Fig. 22 highlights some of the features in the low-speed case that are only captured

38

by CFD. First, boundary layer transitions much earlier in the low-speed case, not that this isn’t

observed with conventional methods, but especially near the root of the wing the transition

location moves substantially forward from the fuselage and wing interaction. Additionally, some

three-dimensional effects are observed on the wing near the root and at the two-thirds span flap

break with the curving of the streamlines. This amount of three-dimensionality is not enough to

invalidate conventional methods for this case; however, it shows that high-lift conditions can be

better handled by CFD than by conventional methods as the two-dimensionality assumptions start

to break down.



The side views of the low-speed case in Fig. 23 also show significantly different flow

patterns than the other cases.

39



For example, the wing-fuselage juncture has a very large region with high skin friction

coefficients, showing the influence of the juncture at low speed. The streamlines along the

fuselage are also very interesting as they indicate the flow is spiraling around the fuselage, again

demonstrating the three-dimensionality of the flow even on the fuselage.

For Figs. 22 and 23, the vortex cores were made black and the line width increased to

more clearly show the various vortices and track their paths. One example is the vortex from the

most inboard flap break, near the root. The vortex from this flap break drifts up to interfere with

the vertical tail and is the cause of increased skin friction on the lower part of the vertical fin. The

40

higher region of increased skin friction results from the fuselage’s turbulent boundary layer

flowing over the vertical tail. The outer part of the fuselage boundary layer is turbulent with high

momentum, so it creates a large amount of skin friction when it encounters the tail.

Surprisingly, the streamlines on the winglet indicate that the flow is relatively well

behaved and two-dimensional. This attests to the design of the winglet to spread out and move the

wingtip vortex so it does not have as strong of an influence on the wing.

Stall Characteristics

Sailplanes generally have a flight characteristic that when the aircraft is at, or near, stall

conditions separated flow from the wing-fuselage juncture begins to buffet the horizontal tail. It

has been reported that the Ventus 3 does not have this characteristic so CFD provides a method to

understand the flow at high-lift conditions, and to potentially develop a mechanism that alerts the

pilot to the stall in a similar way to the buffeting on other sailplanes. The Q-Criterion is used in

Fig. 24 to represent the wake of the wing at half of the span of the horizontal tail.

Fig. 24 Q-criterion of the flowfield at the horizontal tail half span at 𝐶𝐿 = 1.5

41

The wake from the wing in Fig. 24, where the Q-criterion is higher, is seen to not drift near the

horizontal tail, hence why the horizontal tail may not buffet from the separated wake of the wing.

The cut plane in Fig. 24 was placed at the half span of the horizontal tail because as the plane was

moved inboard the boundary layer of the vertical tail began interfering with the desired

visualization of the wake from the wing-fuselage juncture; however, it is possible that the wake

from the wing-fuselage juncture did not drift outboard enough to be visualized in Fig. 24. Thus,

streamlines were placed near the aircraft with give another visualization of the wake, which is

shown in Fig. 25.

Fig. 25 Skin-friction coefficient predictions of the Ventus 3 at 𝐶𝐿 = 1.5 using the AFT model

with near fuselage streamlines

The streamlines in Fig. 25 indicate that the flow near the wing-fuselage juncture is not

separated for this flight condition. The inboard flap break creates a strong vortex that influences

the flow over vertical tail, but the horizontal tail is not effected.

42

Future studies, utilizing the mentioned QCR model, at higher lift coefficients could

provide better insight into the stall characteristics of the Ventus 3 so methods could potentially be

developed to alert the pilot as they approach stall.

Component Drag

Aside from the flow visualization, CFD also provides quantitative values to the drag on

certain components. The drag on components like the tailwheel and pushrod fairing is difficult to

estimate with classic methods due to their largely separated wake. For tailwheels, a value can be

estimated from published wind-tunnel data on an assorted of tailwheel configurations. The drag

due to the pushrod fairing is not as straight forward, of an approach but methods of predicting the

drag using the frontal area do exist. However, one assumption with using these approaches is that

the flow coming into the component is clean and smooth. Both the tailwheel and the pushrod

fairing are on the aft section of the fuselage, so the incoming flow is the turbulent boundary layer

of the fuselage.

CFD provides a method that can decently model the separated wake and can estimate the

drag of the component when the component is integrated into the aircraft. Examples of drag

coefficients for various components, referenced to the aircraft’s wing area of 10.84 square meters,

and their impact on lift to drag ratio can be seen in Table 2.

Table 2 Component drag coefficients and aircraft lift to drag improvements without the

components for various flight conditions

𝐶𝐿 Tailwheel + Fairing 𝐶𝐷 Pushrod Fairing 𝐶𝐷 ∆ 𝐿/𝐷 ∆ 𝐿/𝐷 (%)

0.23 0.000049 0.000040 0.37 1.2

0.62 0.000048 0.000042 0.35 0.7

1.50 0.000047 0.000055 0.10 0.3

43

Table 2 shows there is the potential for notable gains during high-speed flight if the tailwheel and

pushrod drag could be removed, such as by retracting the tailwheel and streamlining the pushrod

fairing. The ability to quantify the drag on these components gives the designer the power to

optimize the shape of the component for further drag reduction or perform a trade study to decide

if can be made and are warranted.

Transition Model Comparison

As previously discussed in Chapter 2, versions of the Langtry-Menter correlation-based

transition model have been implemented into several government and commercial CFD solvers.

Currently, due to its wide distribution, the Langtry-Menter model is likely the most accepted

transition model in the CFD community. Thus, comparing the AFT model and a Langtry-Menter

model is valuable in providing an initial understanding of the differences between them and

which model is superior.

The 𝛾 transition model was the implementation chosen for the comparison. It is a one-

equation implementation of the original Langtry-Menter model and is available in STAR-CCM+

[22]. It has several advantages over the 𝛾 − 𝑅𝑒𝜃 used by Hansen, such as it tends to require less

time per iteration, since the model solves one less transport equation and it does not require the

user to set up extra procedures for the model to work correctly. One disadvantage of the 𝛾 model

is that since it requires a much finer mesh than the 𝛾 − 𝑅𝑒𝜃 model, which can properly function

using a mesh about as coarse as the general best practices. However, mesh requirements for the 𝛾

model are similar to the AFT model, so for fairness and convenience, the 𝛾 model cases were

analyzed using the same mesh as the equivalent AFT cases presented above. The 𝛾 model

requires different far field conditions than the AFT model so a turbulent viscosity ratio of 10 and

44

a turbulence intensity of 0.1% were used as suggested according to the STAR-CCM+ best

practices and Hansen’s study, respectively.

The aircraft drag coefficients and lift to drag ratios are shown in Table 3 resulting from

both transition models.

Table 3 Comparison of force coefficients for the AFT and 𝛾 models

𝐶𝐿 AFT 𝐶𝐷 𝛾 𝐶𝐷 AFT 𝐿/𝐷 𝛾 𝐿/𝐷

0.23 0.00750 0.00817 30.4 28.4

0.62 0.01262 0.01318 49.2 47.6

Considering the differences between the AFT model and PGEN, the AFT and 𝛾 models are

somewhat in agreement on the aircraft performance. That being said, the gap is large enough that

if more cases were considered and showed the same trend, the AFT model would be the general

recommendation for a designer since it is closer to the “proven” method.

The same aircraft orientations as shown for the AFT model are shown below.


𝐶𝐿 = 0.62 using the 𝛾 model

45

Comparing Fig. 18 and Fig. 26, the pictures are generally very similar. The transition

location on the wing looks almost identical at approximately 75% of the chord. The side views in

Fig. 27 are also very similar to the AFT model case.



The 𝛾 model even predicts the same vortex at the tail juncture and three-dimensional flow

over the winglet as in Fig. 19. One notable difference is the transition pattern and location on the

fuselage. In Fig. 19 it can be seen that the transition location is defined on the lower part of the

fuselage, but blurry on the upper part and near the juncture. In Fig. 27 the transition location is

well defined and smooth before and after. This could be from the AFT intermittency method

46

used, meaning the AFT2019 intermittency method would likely have a much cleaner transition

near the juncture. Although, the transition location in Fig. 27 occurs slightly earlier than in Fig.

19, so further investigation to know which model better handles transition on fuselages would be

valuable.

The top and bottom of the Ventus 3 for the high-speed case with the 𝛾 model appear

almost identical to the predictions with the AFT model. The transition location and smoothness of

the contours in Fig. 28 are very similar to Fig. 20. The agreement is encouraging in that it

demonstrates the validity of the AFT model against one of the most current transition models, and

at the same time shows that a correlation-based method can be tuned to be potentially as effective

as a more physical model like the AFT model.



The side views of the aircraft in Fig. 29, however, show some large differences between

the two models on predicted transition locations when compared with the results predicted using

the AFT model.

47



One of the largest differences between the methods is the transition location on the

fuselage for the case with a lift coefficient of 0.23. Comparing the change from blue to green in

Fig. 21 and Fig. 29, it is obvious that the 𝛾 model predicts a much earlier transition point on the

fuselage. Initially it was considered that the early transition point could have been caused by a

step up in mesh size or the flow solution was not fully converged. With closer inspection, it is

seen that the surface mesh size around the location of transition is completely isotropic so the

transition location was unlikely the result of mesh induced transition, where a fast change in mesh

size or a coarse mesh can prematurely trigger the transition model. The simulations in this study

48

were set up to output images of the skin friction coefficient every 200 iterations to ensure the

simulations had reached convergence at the end of the iteration limit. Viewing the skin friction

coefficient over the last few hundred iterations showed essentially no change in transition

location. Since there currently is not a simulation related issue, it must be assumed the 𝛾 model

transitioned as per its criterion. However, the transition location seems farther forward than

expected so it warrants further investigation.

49

Chapter 5

Conclusion

The goal of this study was to demonstrate the potential of CFD for sailplane design and

analysis. Conventional RANS CFD turbulence models do not include mechanisms to predict

boundary layer transition, which is essential in analyzing a sailplane, so the AFT transition model

was implemented to account for the transition process. To ensure valid results, the AFT model

implementation and meshing methodologies were verified against experimental data with strong

agreement. The aircraft meshing methodologies were then discussed and the differences between

the standard best practices and transition meshing requirements were noted. Comparisons

between a proven, conventional sailplane design tool and CFD were presented with good

agreement. Several flight conditions were explored in further detail to show the capability for

visualizing the complexity inherent in three-dimensional viscous flows. Also, the coefficient of

drag on components that were traditionally difficult to estimate were presented to demonstrate the

capability of CFD in handling bodies that are not streamlined. Overall, it was shown that CFD

can be a valuable asset to the sailplane designer since it can be used to provide insight and

capability just as accurate as the conventional methods.

Future Work

The potential for future work can be classified into two categories: further development

and validation of the transition modeling, and implementing other CFD methods to further exploit

the advantages of CFD. Future analysis could continue to investigate the practical differences

between transition models and use available experimental data to determine which model is the

most accurate and efficient tool for the designer.

50

One of the disadvantages of CFD is that the drag is just referenced as the skin friction and

pressure drags on a component. With conventional design methods, the drag components are

bookkept separately from one another, and it is well understood how to minimize each

contribution. However, if the designer does not explicitly know the induced drag and where it is

coming from, for example, it can be difficult to reduce. Due to the significance of induced drag

on sailplane design, a potential area for improvement is being able to extract the induced drag on

the aircraft from the downstream pressure field. The tool could be built on the work of Coder and

Schmitz [23]. A combination of the AFT model with a tool to estimate the induced drag could

provide a powerful package of tools to the sailplane, or any fixed-wing aircraft, designer.

Similarly, other methods to decompose the drag results from CFD could be developed so the

current understanding of how to minimize the drag of each component can be utilized.

51

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