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

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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 퐶퐿 = 0.62 ...... 31

Fig. 17 Amplification factor predictions on left (top) and right (bottom) of the Ventus 3 at 퐶퐿 = 0.62 ...... 32

Fig. 18 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at 퐶퐿 = 0.62 using the AFT model ...... 33

Fig. 19 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at 퐶퐿 = 0.62 using the AFT model ...... 35

Fig. 20 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at 퐶퐿 = 0.23 using the AFT model ...... 36

Fig. 21 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at 퐶퐿 = 0.23 using the AFT model ...... 37

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Fig. 22 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at 퐶퐿 = 1.5 using the AFT model ...... 38

Fig. 23 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at 퐶퐿 = 1.5 using the AFT model ...... 39

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

Fig. 25 Skin-friction coefficient predictions of the Ventus 3 at 퐶퐿 = 1.5 using the AFT model with near fuselage streamlines ...... 41

Fig. 26 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at 퐶퐿 = 0.62 using the 훾 model...... 44

Fig. 27 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at 퐶퐿 = 0.62 using the 훾 model...... 45

Fig. 28 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at 퐶퐿 = 0.23 using the 훾 model...... 46

Fig. 29 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at 퐶퐿 = 0.23 using the 훾 model...... 47

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NOMENCLATURE

푐 = reference chord

퐶퐷 = aircraft drag coefficient

퐶퐿 = aircraft lift coefficient

퐶퐿푚푎푥 = maximum aircraft lift coefficient

푑 = distance to nearest wall

푁푐푟푖푡 = critical amplification factor

푛̃ = transported envelope amplification factor

푆 = reference wing area

푆̃ = modified strain-rate magintude

푢푗 = Cartesian velocity component

푣 = freestream airspeed

푊 = aircraft weight

푥푗 = Cartesian coordinate

훾 = flight path angle

𝜌 = density

휇 = dynamic viscosity

휇푡 = turbulent eddy viscosity

휈 = kinematic viscosity

휈̃ = modified eddy viscosity

Ω = vorticity magnitude

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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.

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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

퐶 2푊 푣 = 퐷 √ (1) 푠푖푛푘 3 𝜌푆 퐶퐿2 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,

퐶 1 퐿/퐷 = 퐿 = (2) 퐶퐷 tan(훾) 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

퐿 퐶퐿 = 1 (3) 𝜌푣2푆 2

퐷 퐶퐷 = 1 (4) 𝜌푣2푆 2

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,

𝜌푣푐 푅푒 = (5) 푐 휇

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.

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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 훾 − 푅푒휃 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.

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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 훾 − 푅푒휃 model the calibrated application was turbomachinery. Therefore, since the 훾 − 푅푒휃 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.

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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.

12 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.

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1.8

1.6

1.4

Composite 1.2 Landing

1 3

2 CL 0.8 1 0 0.6 -1 -2 0.4 S

0.2

0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 CD

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.

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

휕푢 휏푤푎푙푙 = 휇 (6) 휕푦푤푎푙푙 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 푘 − 휔 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 푒푁 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 푒푁 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 푒푁 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

푈 ≈ 훺퐷(퐻 ) (7) 휃 12 where the 퐷(퐻12) 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

휕𝜌푛̃ 휕𝜌푢푗푛̃ 푑푛̃ 휕 휕푛̃ + = 𝜌Ω퐹푐푟푖푡퐹푔푟표푤푡ℎ + [𝜎푛(µ + µ푡) ] (8) 휕푡 휕푥푗 푑푅푒휃 휕푥푗 휕푥푗

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,

2 퐷휈̃ ̃ 푐푏1 휈̃ 1 휕 휕휈̃ 휕휈̃ 휕휈̃ = 푐푏1푆휈̃(1 − 푓푡2) − (푐푤1푓푤 − 2 푓푡2) ( ) + [ ((휈 + 휈̃) ) + 푐푏2 ] (9) 퐷푡 푘 푑 𝜎 휕푥푗 휕푥푗 휕푥푗 휕푥푗 and simply redefining the 푓푡2 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

휈̃ 2 푓 = 푐 {1 − 푒푥푝[2(푛̃ − 푁 )]}푒푥푝 [−푐 ( ) ] (10) 푡2 푡4 푐푟푖푡 푡4 휈 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

0.38푐 훿 = 1 (11) 푅푒푐5 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 푦1 spacing, typically presented in 푦 units. A

+ target 푦1 value of 0.67 푦 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

0.026 푐푓 = 1 (12) 푅푒푐7 to calculate a wall shear stress

2 휏푤 = 0.5푐푓𝜌푣 (13)

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

휏 푢 = 푤 (14) ∗ 𝜌 that is finally used with the desired 푦+ to calculate a first cell height

+ 푦 푑푒푠푖푟푒푑휇 푦1 = (15) 𝜌푢∗

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 푁푐푟푖푡 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.

1.8

1.6

1.4 LSLT Re=1,000,000 1.2 LSLT Re=800,000 1.0 LSLT Re=600,000

cl 0.8 LSLT Re=400,000 STAR-CCM+ Re=1,000,000 0.6 STAR-CCM+ Re=800,000 0.4 STAR-CCM+ Re=600,000 0.2 STAR-CCM+ Re=400,000

0.0 -10.0 -5.0 0.0 5.0 10.0 15.0 -0.2 cd

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.

21

LTST Re=1,000,000 LTST Re=800,000 STAR-CCM+ Re=1,000,000 STAR-CCM+ Re=800,000 1.8 1.6 1.4 1.2 1.0

cl 0.8 0.6 0.4 0.2 0.0 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 -0.2 cd

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

LTST Re=600,000 LTST Re=400,000 STAR-CCM+ Re=600,000 STAR-CCM+ Re=400,000 1.8 1.6 1.4 1.2 1.0

cl 0.8 0.6 0.4 0.2 0.0 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 -0.2 cd

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

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 2푛 (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 푦+ 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 푁푐푟푖푡 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.

PGEN Composite STAR-CCM+ Composite

1.6

1.4

1.2

1 CL 0.8

0.6

0.4

0.2

0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 CD

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

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.

PGEN Composite STAR-CCM+ Composite

Airspeed (km/h) 0 50 100 150 200 250 300 0

0.5

1

1.5 Sink(m/s) Rte 2

2.5

3

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

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

퐶퐿 = 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

퐶퐿 = 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

퐶퐿 = 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

퐶퐿 = 0.62 using the AFT model

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.

Fig. 20 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at

퐶퐿 = 0.23 using the AFT model

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

Fig. 21 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at

퐶퐿 = 0.23 using the AFT model

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.

Fig. 22 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at

퐶퐿 = 1.5 using the AFT model

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

39

Fig. 23 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at

퐶퐿 = 1.5 using the AFT model

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 퐶퐿 = 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 퐶퐿 = 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

퐶퐿 Tailwheel + Fairing 퐶퐷 Pushrod Fairing 퐶퐷 ∆ 퐿/퐷 ∆ 퐿/퐷 (%) 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 훾 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 훾 − 푅푒휃 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 훾 model is that since it requires a much finer mesh than the 훾 − 푅푒휃 model, which can properly function using a mesh about as coarse as the general best practices. However, mesh requirements for the 훾 model are similar to the AFT model, so for fairness and convenience, the 훾 model cases were analyzed using the same mesh as the equivalent AFT cases presented above. The 훾 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 훾 models

퐶퐿 AFT 퐶퐷 훾 퐶퐷 AFT 퐿/퐷 훾 퐿/퐷 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 훾 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.

Fig. 26 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at

퐶퐿 = 0.62 using the 훾 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.

Fig. 27 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at

퐶퐿 = 0.62 using the 훾 model

The 훾 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 훾 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.

Fig. 28 Skin-friction coefficient predictions for the top (right) and bottom (left) of the Ventus 3 at

퐶퐿 = 0.23 using the 훾 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

Fig. 29 Skin-friction coefficient predictions for the left (top) and right (bottom) of the Ventus 3 at

퐶퐿 = 0.23 using the 훾 model

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 훾 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 훾 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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