Design of Flying Wing UAV and Effect of Winglets on its Performance

International Journal of Emerging Technology and Advanced Engineering

414

Design of Flying Wing UAV and Effect of Winglets on its

Performance

Rishabh Dagur

, Vikrant Singh

, Shabir Grover

, Nikhil Sethi

, Dr. B.B. Arora

1,2,3,4

Undergraduate Student, Dept. of Mechanical Engineering, Delhi Technological University, India

Abstract- In the present work, a Flying wing body was designed that can be used for surveillance and reconnaissance. The UAV is highly portable and can be launched for a mission from almost anywhere. A Design space was mathematically plotted by defining parameters: cruising speed, stall speed, GTOW, aspect ratio etc. After defining design requirements, these values are used t o stipulate parameters in designing equations of UAV sizing and airfoil selection. During the design phase, it was understood that a UAV with increased endurance will be more helpful in practical use. Our study made us realize that winglet configuration can play a major role in reducing the drag of the body and, finally increasing the overall mission time of the UAV. Previously, not much work has been done on winglet design of Hand-Launched UAVs and the vorticity analysis. Therefore, we have taken up this as the main subject for our paper. The parameters for winglets were calculated using the standard values from the previous research. Both the flying wing geometries i.e., with and without winglets were modeled and solved in CFD code. Both the models were compared to see the effect of winglets in drag reduction which ultimately agreed to increase the lift and endurance efficiencyof the flying wing body with the application of winglet. Also, a detailed analysis of vortex formation across the wingtip for both the scenarios was performed. Five Angle of Attacks were considered for both the cases.

Keywords: Unmanned Aerial Vehicles, Flying wing body, Winglets, Tailless-UAV, Computational Fluid Dynamics.

I. NOMENCLATURE

a Coefficient of GTOW

b Coefficient of empty weight

equation

Maximum Take-Off weight

Weight of Payload

Crew Weight Empty Weight

Fuel Wight

Vs Stall speed

Vmax Maximum speed

ROCmax Maximum rate of climb

STO Take-off run

Density of air

Friction Coefficient

Maximum coefficient of lift

Maximum speed

Engine/Motor Power

Drag Coefficient at 0 Angle of

Attack Air Density

Coefficient of Drag at Ground

Lift Coefficient at Take-Off

K Induce Drag Factor

Propeller Efficiency

AC Aerodynamic Code

Air density Ratio

B Wing Span

S Surface Area

Coefficient of lift Coefficient of drag Coefficient of drag

⁄ Wing Loading

International Journal of Emerging Technology and Advanced Engineering

415 II. INTRODUCTION

he aircraft industry is unconventionally breaching new

horizons of research. One of the major sectors of development is Unmanned Aerial Systems (UAVs). UAVs are

flying vehicles which can be remotely controlled from large distances (sometimes even from different continents). UAVs

are divided on behalf of their size, endurance, number of

motors, take-off and landing capabilities. A tailless flying wing UAV was designed under this research project. Fuselage

geometry was maintained same as the airfoil along the wing. Our major aim in this research project is to make the aircraft

endurance-efficient by decreasing drag on the body. After going through several research papers, the addition of winglets

was taken up as the most elementary solution for our need. This also prevented any alterations in the design and added

versatility. Winglets are vertically extruded wing tips

incorporated to reduce lift induced-drag. Winglets are the part of the wing that which can be mathematically understood as

the result of increased aspect ratio(given a constant area).

III. Literature Review

The concept winglet was coined by Dr. Whitcomb in 1976 [1] who at NASA research center and developed winglet technology which was published as “A Design Approach and Selected Wind-Tunnel Results at High Subsonic Speeds for Wingtip Mounted Winglets”. According to him, winglet could be described as the small wing-like vertical structures which extend from the wingtip to reduce induced drag in comparison to other wing tip devices or extensions and claimed in his research that the winglet shows 20% reduction in induced drag when compared to tip extension and also improved the lift-to-drag ratio. In 1994, Aviation Partners Inc. (API) developed an advanced design of winglet namely blended winglet. Louis B. Gratzer from Seattle has the patent for blended winglet and intention of the winglet is to reduce the interference drag due to sharp edges as seen in the Whitcomb‟s winglet. Also, Gratzer has the patent for the invention of spiroid-tipped wing in April 7, 1992. Later, “wing grid” concept was developed by La Roche from Switzerland in 1996 and got the patent for his invention. The main purpose of all the above inventions was to decrease the vortex strength at the wingtip. Also, a remarkable work was done by Jamey and Jacob [22], they designed and optimized the Winglet using VLM

methodology (Vortex Lattice Method) also known as Panel Method. The main advantage of this method is that wings are easy to design and it takes less Computational time to calculate Lift and Drag. But the disadvantage is that it solves the problem assuming the flow is inviscid, and the boundary layer is solved separately and both of the results are interpolated to find lift and drag, which raises a question on the validity of results as skin friction drag (which is dependent on viscous modeling) is neglected.

These are the major research work previously undertaken on winglets. Our main aim is to design, analyze and optimize the design using CFD(Computational Fluid Dynamics), which takes viscous flow into account.

Before undertaking this research, a background study was conducted which included an in-depth analysis on aerodynamics and wing design from works of John D. Anderson [3], Daniel P.Raymer [2], and by Mohammad Sadraey [6]. For the design of winglets, we referred Whitcomb‟s existing research on winglets. Our winglet design is majorly based on “Understanding Winglet technology by Fred George [7] and the research by, R. T. Jones and T. A. Lasinski [4].CFD by John D. Anderson [5] and ANSYS User guide [11]. As our main aim was to reduce drag by reducing vortex formation, a study was conducted on turbulent flows and vorticity, which was primarily done from books by S.K Som [10] and Cengel and Cimbala [8] and “Methods for Vortex Identification” by Vivianne Holm´en [9].

IV. Design Process of The Flying Wing

The design process is expounded to enfold all available design aspects. Algorithms were written in MATLAB to simulate the equations to secure the fittest solutions for the defined boundaries. A design space is produced to select the optimum value from the available space.

The whole process followed during the design can be defined as can be shown in following flow chart:

International Journal of Emerging Technology and Advanced Engineering

416 Fig-1: Flow Chart for Design Process

A. Constraint Parameters:

Design parameters were selected after an intensive market research of different UAVs of the same size and weight parameters in the market. Existing COTS airframes like Skywalker X8, Ebee, RVJet were considered while making the table.

From the below parameters defined, size and weight of the aircraft will play a critical in the whole designing process. Also, the maximum payload of the aircraft will be embodied by the gimbal and camera to give live-video feed.

Table-1: Design Parameters

B. Material Selection

Material selection was a crucial point where every available option in the market was tested to simulate real working conditions of the UAV missions (particularly 1. Take-off 2. Flight 3. Land/crash). Loads were applied to create destructive testing conditions and repairable attributes were judged by severity towards each impact.

Table-2: Material Selection

From Table.2, EPP (Expanded Poly-propylene) was chosen as it is most promising for UAV missions of our class.

Parameters Objective Weightage (Out of 5)

Wingspan <2 meters 5

Cruise Speed 15 m/sec 2

Payload >500 Gram 4

Endurance 30 minutes 4

Stall Speed 10 m/sec 2

GTOW <5 kg 5

Take-Off Distance

Hand-Launched

4

Very Good Good Bad Poor

S.No. Material Weig hted

Strength

/Weight Reparabilit y

1 Carbon

Fiber High

2 Balsa

Wood Low

3 EPO

Foam Low

4 EPP

Foam

Very Low

5 Pink

Foam Low

Material Selection Constraints Parameters

Analysis

Algorithm for Estimation of a,b variables formula

Algorithm for Thrust to Weight (T/W) and Wing

Loading (W/S)

Wing Sizing Algorithm for

Gross Take-Off Weight of

Initial Sizing

Aerodynamic Analysis

Drag/Endurance Calculation

Airfoil Selection

Winglets Incorporatio

Aerodynamic/CFD Analysis Analysis

International Journal of Emerging Technology and Advanced Engineering

417 C. Calculating “a” And “b” Variables for Empty Weight EQ.

Initially, the weight of flying wing is not known exactly, so the GTOW must be estimated which relies on the other aircrafts with a similar configuration and mission available in the market. Thus, historical data is the major source of information for the calculations in this step. Following is the collective data from available flying wings in the market.

Fig-2: Comparison on Weighting Chart

The two main equations that underline calculations in this step are as follows:

( ) (

)

…… (1)

…….(2)

Equation 1 shows the net summation of the GTOW and fuel weight of the aircraft. Also, as our UAV is electrically powered thus,

=0; =

∴ Equation (1) will become,

= - - .….. (3)

The second equation depicts the relationship between the empty weight fraction and GTOW which was scaled to form a linear programming problem in MATLAB.

The different values of weight were grabbed from already available market UAVs. Eqn. (3) and (2) are used to solve for “a” and “b” as there are 2 unknowns and 2 equation that is a system of equation in 2 variables. Different available UAVs give different vales of “a” and “b”. The most optimum design space for the values of “a” and “b” was elected on the basis of mission requirements from the from below plotted graph in MATLAB.

Fig-3: Design Space for „a‟ and „b‟

D. Determining Gross Take-Off Weight:

To find the value of GTOW, MATLAB code was written to find the solution of the two governing equations, i.e. modified Eqn. 1 i.e. Eqn. 3 and Eqn. 2

The estimated weight of the battery and payload was defined from market research and constraint parameters analysis.

A MATLAB program was written and value of GTOW was determined by solving the quadratic equation.

Table-3: Weight Estimation

By analytically solving the quadratic equation in MATLAB, 2 values for GTOW were obtained. Out of the given values obtained one is 485 pounds which is not feasible and impossible value for our requirement, so 8.09 pounds was selected. Thus the GTOW is taken as 8.5 lb. for a safe design. Thus we have tolerance as ((8.5-8.093)*100/8.093) = 5.02 % Tolerance

Table-4: „a‟ and „b‟ Values Weight Estimations(lbs.)

1.5 2.2

Variables Approximation

a 9.412 e-04

International Journal of Emerging Technology and Advanced Engineering

418 E. Thrust to Weight Ratio and Wing Loading

This phase is solely dependent upon the aircraft performance requirements and employs flight mechanics theories. Hence, the technique is an analytical approach.

The aircraft performance requirements deployed to size the aircraft in this step are:

• Stall speed ( )

• Maximum speed ( )

• Maximum rate of climb ( )

• Take-off run ( )

• Ceiling

The equations and graphs have the power loading as the independent variable and wing loading as the dependent variable. The equations used are:

 Stall speed:

 Maximum speed:

(

)

( )

 Take-off Run :

 Rate of Climb

( )

√

√

( )

( )

 Ceiling

(

)

√

√

( )

( )

The code is written on MATLAB for the above defined equations and iterations are run. Out of the graph, optimum values are selected according to constraints defined. Each different point will give changing values of wing and power loading which would eventually change the wing area and power required for it. On running the code the following graph is obtained:

Fig-4: Power Loading vs Wing Loading

The design point which gives the lowest wing loading with the lowest power loading(power loading given the higher priority f0r lowest selection) selected as,

X: Wing loading=W/S=1.69 lb/ft2.

Y: Power loading=W/P=11.78 lb/hp.

International Journal of Emerging Technology and Advanced Engineering

419 Table-5: Reference Area and Power Required

F. Sizing

After defining the wing‟s surface area, the geometry of the wing is defined and parameters like wing sweep and taper ratio are referenced from already justified models as the calculations are judged on the real-life command of the aircraft with the reflection with air.

Since these are mere ratios, the overall weight and area will influence the design.

In general, a tailless fixed wing has the following similar geometry characteristics:

 Very low taper ratio  Very low aspect ratio

 High sweep angle at the quarter chord  Winglets to provide directional stability  Negative washout/Tip twist

The UAV which is taken as reference is the Skywalker X8 due to its flying capabilities and its stability-control when compared with the other aircrafts.

For Skywalker X8, these values are extracted for its definition.

Table-6: UAV Skywalker X8Attributes Study

Using the following formulas, Aspect Ratio (AR): Defined as span of wing B, to mean aerodynamic cord C,

Wing area can be defined as span of wing multiply with mean aerodynamic cord.

Wing Area(S):

From, the above two equations aspect ratio can be

mathematically formulated as,

Wingspan= 5.584 ft.

Mean Aerodynamic Chord= 0.9003 ft. Root chord = 1.246 ft.

Tip chord= 0.5548 ft.

To compare the parent UAV, Skywalker X8 and the designed flying wing, the below spreadsheet is defined as,

Fig-5: Design Comparison with Skywalker X8

G. Aerofoil Selection

Airfoil for an aircraft involves the consideration of multiple interrelated parameters and the integration of trade-offs between design requirements. The airfoil selected for the UAV is „s5010‟.

The primary flight requirements and trade-offs that need to be made defined as:

1. A good / ratio. To increase loiter time.

2. Since it does not have a tail and lacks stability in general, a trade-off will have to be done between

performance and excellent stall characteristics. A

gentle transition after the stall angle to enable easy recovery.

a. The aerofoil with the lowest (~0) pitching moment coefficient.

b. Aerofoil with net positive pitching moment. S.no Attributes Equation Estimation

1 Wing area W/(W/S) 8.5/1.69 = 5.029586 ft2 or

0.46726m2

2. Motor Power

W/(W/P) 8.5/11.78= 0.721Hp or 538.285 W

S.no Attributes Values

1. Aspect ratio 5.618

2. Taper ratio 0.4

International Journal of Emerging Technology and Advanced Engineering

420 3. An aerofoil with a proper ideal and design lift

coefficient (same reason as 1st)

Low speed, high lift – (t/c) max=15-18% High speed, low lift- (t/c) max=9-12%

The selection process is purely graphical and deals with the comparison of some shortlisted airfoils on certain graphs like:

Vs. alpha Vs. alpha Vs.

/ Vs. alpha

XFLR5 is the open source software package used to analyze the above graphs.

Taking into consideration of self-stabilizing (reflexed) some of the airfoils shortlisted were:

 E186

 MH-45

 MH-60

 S5020  S5010

The graphs acquired from XFLR5 are used to input in the spreadsheet.

The required ideal lift coefficient and the gross maximum lift coefficient is calculated from following equations:

( )

( )

The stall characteristics are given a score out of 5.

Similarly, the / max and the slope is also compared as given in the design requirements.

On the basis of comparison and trade-offs, the airfoil S5010 which provides excellent stall characteristics and sufficient lift is selected.

Fig-6: Chart for Airfoil Selection.

V. Winglet Design

Winglet is the wing tip extension that is used to reduce the vortex formation at the wingtip. These vortices are caused by pressure differences above and below the wing, causing sideways motion of the air. These vortices cause downwash of the flow stream about the wing tip, causing Induced Drag. The winglets are designed so as to reduce the vortex by the stopping sideways flow, thus reducing the induced drag. There are various winglets that are being used in aircraft industries like blended sharklets, Fenced winglets, Spiroid winglets and raked wing tips.

We chose Sharklets as they are suited for low speed flying aircraft, and are easy to manufacture.

Parameters affecting winglet Design: Sweep angle, Cant Angle, taper ratio, Span length (height). Experimentation indicated that the winglet's trailing edge should be positioned near the wing's trailing edge for maximum effectiveness [7]. Whitcomb found the elliptical load distribution could be preserved if the winglet had approximately a 0.3 taper ratio and a side force loading about the same as the wing loading [1]. Giving the winglet a slight cant angle or dihedral also improves its aerodynamics. Whitcomb [1] found that this reduced the interference at the junction of the winglet and wingtip at transonic speeds and that it pushed the tip vortex outboard, thus further reducing nearby vortex intensity. The optimum cant angle for Whitcomb's experiment was 15 degrees.

Usually, height of winglet was taken around 10-20%. We took 11.1% as suggested by the NASA reports [1].

Specifications:

 Air foil: S5010 (same as that of wing)

 Tip chord of the wing (winglet root chord): 0.155 m

 Height of winglet: 0.085m

 Taper Ratio: .3 (Standard value for winglets on most commercial aircrafts)

International Journal of Emerging Technology and Advanced Engineering

421 VI. CFD Analysis of Body without Winglet

The CFD analysis of the wing was done on 5 angles of attacks: 0, 2, 4, 6, 8 degrees. The software used is ANSYS and the code is Fluent.

A. Geometry:

The CAD geometry was made in DS Solidworks. It was then imported in ANSYS Design Modular in

“.step” file. First, as the flying wing Body is symmetrical, therefore it was divided into half which helped in restraining the elements to half thereby reducing simulation run time. The enclosure was then made of dimension 3m*1m*1m. Then using the Boolean tool the wing body was subtracted from the enclosure.

This process was done separately for each angle of attack.

Fig-7: Cad Model of Wing without Winglets

B. Meshing:

The Meshing was done in ICEM. Initially, the Named Selections where created which included an inlet, outlet, wing face, wing end, ambient wall etc. Then meshing attributes like minimum element sizing, maximum face sizing, inflation layers were edited to suit our case. To ensure low skewness elements, prism elements are extruded from the wing surface in the first step. After this, the rest of the domain is populated by the generic tetrahedral elements. The triangle height on surfaces must vary gradually to ensure good prism characteristics. Subsequent prism layers should show a constant geometric rate of increase in their height. A good transition at the interface between the prismatic layers and the tetrahedral region is a must to ensure a mesh satisfying the numerical requirements in terms of cell-size deviation. Thus, it is imperative to find the right balance of growth rate, first aspect ratio and total number of layers to avert numerical diffusion.

The choice of the turbulence model used depends on the importance given to near wall effects or how the flow behaves near the wall. For this, it is it is important to know about the concept of wall .

If our aim is to resolve the effects close to the wall i.e., in the viscous sub layer then the size of the mesh size should be small and dense enough near the wall so that nearly all the effects are captured efficiently. However, in some cases, when the wall effects can be ignored, a semi-empirical formula may be incorporated to bridge between the viscosity affected region and fully turbulent region. Hence, the mesh needn‟t be dense or small near the wall i.e., coarse mesh would work.

Based on the characteristic scales of our geometry the Reynolds number is determined for our model such that:

= =

= 3.7797

5

Where ρ and μ are the fluid density and viscosity respectively, U is the free stream velocity, and L is the characteristic length (e.g. pipe diameter, body length, Chord length etc.)

The definition of the y+ value is such that:

Fig-8: The boundary layer developed over flat plate (Çengel, Cimbala[8])

The known values are plugged into the above equation to estimate (First cell height).

International Journal of Emerging Technology and Advanced Engineering

422 The k-ε models, the LES, and the RMS model are primarily used for core turbulent flows (i.e., regions far from walls). However, the Spalart-Allmaras and k-w models are distinct in the sense that they can be applied throughout the boundary layer, provided that the mesh resolution is sufficient close to the wall.

Fig-9: Mesh Sizing

In our case, where the low-Reynolds-number effects are dominant throughout the flow domain, the placement of the first node in our near-wall inflation mesh becomes very important. The wall function approach would have been inadequate and thus, invalid. But, if the case involves high-Reynolds-number flows where the viscosity-affected near-wall region does not need to be resolved, the wall function approach is more suitable as it saves computational resources. It is desirable to resolve the boundary layer all the way to the wall using a finer mesh for an accurate prediction of the separation point and flow separation.(Example- In case of determining the drag or lift forces experienced by wings) The wall Y+, apart from being dependent on the first layer thickness, also depends upon the local fluid velocity. That aspect cannot be neglected. And that is why, it is important that the Y+ values are checked regularly as part of the post-processing procedure so as to ensure that it lies in the valid range for our flow physics and turbulence model selection. Consequently, for a y+ value approximately equal to 1 with 10-15 cells within the boundary layer thickness renders any wall models useless as we are already resolving the flow all the way to the wall. A y+ value between 30 and 300 would work sufficiently if we want to work on a coarse mesh with wall functions to capture the velocity profile close to wall. In the laminar sub-layer region or Y+ < 5 inertial forces are less dominating and the flow is primarily laminar, this is known as the low-Re region. Low-Re turbulent models such the SST model as mentioned earlier aim to resolve this area and thus require an appropriate mesh refinement to be efficacious. This is paramount for flows with a changing pressure gradient and where we expect to see flow separation.

After grasping the concept of wall Y+, inflation layer was generated at wing face and wing end separately. In all the 5 AOA cases, it was found that grid independence was reached around 2.1 million cells approximately. The specification of meshing attributes were the same for all 5 AOA and are as follows:

Fig-10: Inflation Settings

The elements in the mesh were of Generic tetrahedral structure.

AOA Elements Nodes

0⁰ 2,725,678 4,677,429

4⁰ 2,567,772 4,785,634

8⁰ 2,215,345 4,213,457

Table-7: Mesh Stats for the given 3 AOA‟s

Fig.-11: Mesh Preview without Winglet

C. Solution:

The Simulation was then performed using FLUENT code. In boundary condition, the velocity was kept 15m/s and outlet gauge pressure was set as 0 Pa.

International Journal of Emerging Technology and Advanced Engineering

423 Standard wall function such as ε-based models work on Y+ >30 which implies that our boundary layer mesh lies completely within the log-law region of the boundary layer and we can work with coarse mesh. But in practice, this may be difficult to achieve because of the varying geometrical and velocity scales associated with the model.

Scalable wall function offers a novel alternative. This wall function displaces the mesh to a Y+ ~ 11.225 for any level of refinement and this assists in avoiding the erroneous modelling of the laminar sub-layer and buffer region.

Performance on meshes of intermediate resolution can also be improved if we use Enhanced wall treatment for ε-based models on refined low-Re grids. However the use of non-equilibrium (enhanced) wall treatment for low-Re modelling of the turbulent boundary layer is generally not recommended and a suitable ω-based formulation, such as the SST model gives reliable results.

The use of a low-Re model is recommended advisable if our aim is to maximize the accuracy of the predicted boundary layer velocity profile or thermal profile, or if the developing boundary layer will tend to separate (due to a varying pressure gradient and not because of discontinuities in the geometry). Low-Re models are also required for drag calculations or determining pressure-drop accurately. The quality of the numerical results obtained will depend on the overall resolution of the boundary layer as discussed before. Thus, the low-Re SST model is the most suitable choice since the use of the k-omega formulation for the boundary layer region helps in resolving up till the viscous sub-layer and no extra wall functions are introduced. In the free-stream, the SST model switches to a k-epsilon formulation which is better suited to free shear flows.

Turbulence model used was SST turbulence model. The standard model in ANSYS FLUENT is based on the Wilcox model [25]. This Wilcox Model subsumes modifications for low-Reynolds-number effects, compressibility, and shear flow spreading [24]. The Wilcox model estimates free shear flow spreading rates that are in close agreement with measurements for far wakes, mixing layers, and plane, radial, and round jets, and is applicable to both wall-bounded flows and free shear flows [25].

The Shear-Stress Transport (SST) model was originally developed by Menter, to effectively blend the robust and accurate formulation of the model in the near-wall region with the free-stream independence of the model in the far field. To achieve this, the model is converted into a formulation. The SST model is basically a blend of the standard k-w and the transformed k-e model. The

SST model is similar to the standard model, but includes the following refinements [11]:

 This blending function is incorporated/multiplied into the k-e and k-w equations and is so designed that

near the wall, the standard k-w model is active while as we move away from the surface, the effect of

fades away and the k-e model becomes

prominent.

 To account for the turbulent shear stress transport, a modified definition of turbulent viscosity is used.

The turbulence kinetic energy, and the specific dissipation rate, are obtained from the following transport equations:

And,

SST model produces good results, certainly much better when dealing with partially separated flows.

Solver used was “Pressure-Based” and the Pressure-Velocity coupling algorithm used was “Coupled”. The pressure-based solver allows you to solve your flow problem in either a segregated or coupled manner. Using the coupled approach offers some advantages over the non-coupled or segregated approach. The coupled scheme obtains a robust and efficient single phase implementation for steady-state flows, with superior performance compared to the segregated solution schemes.

The coupled algorithm solves the momentum and pressure-based continuity equations together. The pressure-pressure-based coupled algorithm obtains a more robust and efficient single phase implementation for steady-state flows.

The first half of total iteration ran on 1st order upwind scheme to stabilize the continuity, the second of iteration ran on 2nd order upwind Scheme so as to achieve a higher order of accuracy.

The convergence criteria was kept to none.

D. Post Processing/Contours:

International Journal of Emerging Technology and Advanced Engineering

424 Table-8 :Lift & Drag values for different AOA‟s

Other than examining lift and drag, vortex formation on the wing ends was also studied. ANSYS CFD Post Processing has following methods to define, identify and visualize vortices:

1. Helicity

2. Lambda 2 criterion 3. Q-Criterion 4. Swirl strength

Helicity is referred to as the dot product of vorticity and velocity vector.

The rest 3 methods are based on Velocity based tensor: The velocity gradient tensor D can be written as Dij = ∂ui/ ∂xj .

As this is a second order tensor it can be broken into a symmetric and a skew-symmetric part

Dij = Sij + Ωij

Where Sij = 1/2(∂ui/ ∂xj + ∂uj/ ∂xi) And Ωij = 1/2(∂ui/ ∂xj − ∂uj /∂xi).

Sij is known as the rate-of-strain tensor, and Ωij is the vorticity tensor [9]. The characteristic equation for ∇u is given by λ3 _{+ Pλ}2 _{+ Qλ + R = 0 [9] ,}

Where P, Q, and R are the three invariants of the velocity gradient tensor [9]. Decomposition into symmetric and anti-symmetric parts these invariants can be expressed as follows. P = −tr(D)

Q =1/2(tr(D)2 −tr(D2)) = 1/2||Ω||2 −||S||2 R= −det(D)

The Q-Criterion methodology defines a vortex as a “connected fluid region with a positive second invariant of ∇u” i.e. Q > 0 [9]. In this a secondary condition on the pressure is added, requiring it to be lower than ambient pressure in the vortex [9]. Looking at the definition of the second invariant we can see that Q represents the local balance between shear strain rate and vorticity magnitude, defining vortices as areas where the vorticity magnitude is greater than the magnitude of rate-of-strain.

The λ2-criterion looks for a pressure minimum but removes the effects of unsteady straining and viscosity by discarding these terms. On evaluating the gradient of the Navier-Stokes equations, we get:

aij = − 1/ρ(pij + νui,jkk )

Where aij is the acceleration gradient and pij is symmetric part. Decomposing the acceleration gradient into symmetric and anti-symmetric parts we get the vorticity transport equation as the anti-symmetric part and the symmetric part:

DSij /Dt − νSij,kk + ΩikΩkj + SikSkj = − ρ/pij

The first two terms on the left-hand side represent unsteady irrotational straining and viscous effects respectively [9]. Therefore, only S2 + Ω2 is considered to determine if there is a local pressure minimum that entails a vortex [9]. A vortex is defined as “a connected region with two negative eigenvalues of S2 + Ω2” [9]. Since S2 + Ω2 is symmetric it has real eigenvalues only, and by ordering the eigenvalues λ1 ≤ λ2 ≤ λ3 the definition becomes equivalent to requiring that λ2 < 0 [9]. Generally visualized as isosurfaces for different values of −λ2

. In planar flows, the three conditions that were described above are equivalent.

Q-criterion is widely a used method for vortex determination method and was also suggested when asked on various CFD Forums. It provides insight into the vorticity aligned with the fluid stream.

Following contours were observed for the 3 AOAs out of 5:

Fig-12: for 0⁰ AOA, without Winglets

Fig-13: for 4⁰ AOA, without Winglets

AOA Lift Drag

0⁰ 4.383N 0.508N

2⁰ 8.56N 0.645N

4⁰ 11.19N 0.748N

6⁰ 16.02N 0.992N

International Journal of Emerging Technology and Advanced Engineering

425 Fig.-14: for 8⁰ AOA, without Winglets

Q-criterion values for body with winglets for 0.0004 level:

Table-9: Q-Criterion Values for the 5 AOA‟s

Hence, we see, as the AOA increases, Vortex formation increases dramatically, thus increasing the drag.

VII. CFD Analysis of Body with Winglets

A. Geometry:

Same steps were followed as on body without winglets. The CAD geometry was made in SolidWorks. It was then imported in ANSYS in “.step” file. First, as the flying wing Body is symmetrical therefore it was divided into half then Enclosure was made of dimension 2m*1m*1m. Then using the Boolean tool the wing body was subtracted from the enclosure. This process was done separately for each angle of attack.

Fig-15: CAD Model with Winglet

B. Meshing:

The Meshing was done in ICEM. First Named Selections where created which included an inlet, outlet, wing face, winglet end, ambient surroundings etc. Then general face sizing was done. After that inflation was given at wing face and winglet end separately. In all the 5 AOA cases it was found that grid independence was reached around 4.2 million cells approximately. The specification of meshing attributes were the same for all 5 AOA and are as follows:

Fig-16: Mesh Sizing

Fig-17: Inflation Settings

The elements in the mesh were the generic tetrahedral structure.

AOA Elements Nodes

0⁰ 4,243,789 8,815,647

4⁰ 4,726,504 9,115,945

8⁰ 4,587,697 8,678,765

Table-10: Mesh Stats

AOA Q-Criterion values

0⁰ 11.12 s-2

2⁰ 14.93 s-2

4⁰ 16.88 s-2

6⁰ 17.23 s-2

International Journal of Emerging Technology and Advanced Engineering

426 Fig-18: Mesh Preview, Wing with Winglet

C. Solution

The Simulation was then performed using the FLUENT code. In boundary condition, the velocity was kept 15m/s and outlet gauge pressure was set as 0 Pa. The same turbulence model SST k-w model was used. Solver used was Pressure-Based and the Pressure-Velocity coupling algorithm used was “Coupled”.

The first half of total iteration ran on 1st Order Upwind scheme, the second of iteration ran on 2nd order Upwind Scheme so as to achieve a higher order of accuracy.

The convergence criteria was again kept to none.

D. Post processing/Contours:

In this case too we examined the vortex formation and following were the results:

AO Lift Drag

0⁰ 4.86N 0.523N

2⁰ 8.95N 0.638N

4⁰ 12.57N 0.727N

6⁰ 16.13N 0.956N

8⁰ 20.64N 1.22N

Table-11: Value of Lift and Drag at few AOA‟s

Fig-19: at 0⁰ AOA

Fig-20: at 4⁰ AOA

Fig-21: at 8⁰ AOA

Q-criterion values for body with winglets for 0.0004 level:

AOA Q-criterion Values

0⁰ 11.41 s-2

2⁰ 12.34 s-2

4⁰ 13.78 s-2

6⁰ 14.67 s-2

8⁰ 16.18 s-2

Table-12: Value of lift and drag at various AOA

VIII. Comparison of Results

Comparing both we can clearly see that with incorporation of winglet there was a slight increase in Drag at 0 AOA (2.95%) as compared to the model without winglets at same AOA. After further analyzing this anomaly we came to the

conclusion that this is because at 0 AOA, viscous component are more prevalent than the pressure component of the drag.

But as the AOA increases the pressure component becomes more prevalent i.e. the vortex formation effect has a greater effect on the aerodynamics of the wing.

International Journal of Emerging Technology and Advanced Engineering

427 We can see that there is slight decrease in Drag reduction of

UAV as angle of attack increases to 8⁰ because when seen overall the drag tends to increase when as AOA increases. We understand it well from equation of drag force:

Therefore there is a net decrease in drag reduction at 8⁰. With incorporation of winglets, it was observed that vortex formation was reduced due to blocking of sideways flow arising due to pressure difference. Also, it was found that the new reduced vortex of low intensity was being formed at winglet end, as shown in contours, of the wing with winglet‟s post processing, pushing the vortex formation away from the planform area. Both of these above statements imply that by the incorporation of winglets we can reduce the influence of vortex formation, which reduce the downwash, decreasing the induced drag.

Fig-22 Comparison of Drag Forces for Wing, with Winglet and without Winglet

IX. Acknowledgements

The success of the completion of this project is strongly attributed to Dr. B.B. Arora under whose guidance the project has been taken. His knowledge and constant motivation went a long way which shaped the outcome in a beautiful manner. We would also like to thank our families and peers who acted as pillars of support throughout the project‟s completion.

X. References

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[2] Daniel P. Raymer, “Aircraft Design: A Conceptual Approach” (AIAA Education Series) American Institute of Aeronautics and Astronautics, 1989 - Technology & Engineering - 729 pages.

[3] John D. Anderson, “Fundamentals of Aerodynamics”, Boston: McGraw-Hill, 2001, Pages-892.

[4] R. T. Jones, T. A. Lasinski, “Effect of Winglets on the Induced Drag of Ideal Wing Shapes", NASA TM-81230, 1980.

[5] John D. Anderson, “CFD”, McGraw-Hill Education, 01-Feb-1995 - Science - 547 pages.

[6] Mohammad H. Sadraey, “Aircraft Design: A Systems Engineering Approach”, John Wiley & Sons, 28Nov2012 Technology & Engineering pages-778.

[7] Fred George, “Understanding Winglet Technology”, pp. 1-7. [8] Yunus A. Çengel, John M. Cimbala, “Fluid

Mechanics: Fundamentals and Applications”, 2006, pages-994.

[9] Vivianne Holm´en, “Methods for Vortex Identification”, November 21st 2012.

[10]S. K. Som, G. Biswas, “Introduction to Fluid Mechanics and Fluid Machines”, 3rd

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[11]ANSYS FLUENT USER‟S GUIDE.

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[15]Laurent Dumas, “Optimization and Computational Fluid Dynamics”, pp. 191-215, Springer Berlin Heidelberg Germany, 2008.

International Journal of Emerging Technology and Advanced Engineering

428 [17]Chainani. A, Perera. N, “CFD Investigation of Airflow on a

Model Radio Control Race Car”, WCE 2008 Vol. II, July 2 - 4, 2008, London, U.K

[18]Yeung W. W. H., Parkinson G.V., “Analysis and Modeling of Pressure Recovery for Separated Reattaching Flows”, ASME Journal of Fluids Engineering, Vol. 126, No. 3, pp. 355–361, 2004

[19]Wolf-Heinrich Hucho, “Aerodynamics of Road Vehicles”, SAE International, 1998.

[20]Joseph Katz, “Race Car Aerodynamics: Designing for Speed”, 1995.

[21]Shabir Grover, "Analysis on Drag Reduction of Bluff Body using Dimples", International Journal of Advanced Production and Industrial Engineering IJAPIE, Sp.Issue, pp. 4-11, 2017.

[22]Jacob Weierman, Jamey D. Jacob, “Winglet design and Optimization for UAVs” , AIAA-2010-4224

[23]Sesha Prakash and Unmanned Aerial Systems Technology Sector, Lockheed Martin Corporation, United States of America.

[24]Junjanna G.C, Dr. N Kulasekharan, Dr. H.R Purushotham, “Performance Improvement Of A Louver-Finned Automobile Radiator Using Conjugate Thermal CFD Analysis”, International Journal of Engineering Research & Technology (IJERT), ISSN: 2278-0181 - Vol. 1 Issue 8, October – 2012.

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