Chapter 1
Introduction
HISTORY
The history of aeronautics stated with the Wright Brothers’ first airplane flight on 17 December 1903. Robert H. Goddard was the first person to launch first liquid fueled rocket on 16 March 1926. Manned orbital spacecraft like Mercury, Vostok, and Gemini of 1960 travelled at Mach 25; Apollo spacecraft that returned men from the moon in 1969 travelled at Mach 36 are the first recorded hypersonic flight in the history of man.
Wernher von Braun was a German, later American, space architect and aerospace engineer. He credited with inventing the Saturn V for the United State and the V-2 rocket for Nazi Germany. The V-2 was the first object which was manufactured to achieve hypersonic flight. The V-2 rocket reached a maximum speed of Mach 5 in February 1949. In April 1961, during the world’s first piloted orbital flight the first human, Major Yuri Gagarin, a Russian travelled at hypersonic speed.
The concept of first hypersonic aircraft to travel at higher Mach numbers was conceived by Robert Carman and Hubert Drake of NACA (now NASA) in 1953 [1]. They gave a design of hypersonic booster/orbiter combination, where each aircraft has a sharp nose, slender fuselage, low aspect ratio, and thin straight wings. These features were adopted in the F – 104 that is designed for Mach 25. Seven years later, the X – 20 Dynasoar that used a sharply swept delta wing with a blunt, rounded leading edge, and a thick fuselage. This project was cancelled in 1963 without the production of vehicle.
In November 2004 the X – 43 made a record in aeronautical history by achieving sustained flight at Mach 10 for a period of about 10s. The experimental hypersonic aircraft which is an unmanned is the X-43 powered by scramjet engine with multiple planned scale variations intended to test the hypersonic flight involving several aspects. The NASA’s Hyper X-program is a part of the experiment. The X-43 is the fastest aircraft with a record of speed nearly at Mach 9.6. RLV-TD is the first unmanned test vehicle developed for the Reusable Launch Vehicle Technology Demonstration Programme by the Indian Space Research Organisation (ISRO).
NASA started a new 10 – years initiative called New Aviation Horizons, or NAH, to build a series of five large scale experimental aircrafts called X – planes. The motive of this project is to build aircraft with the features like clean energy (or transition to low carbon propulsions), travel at high speeds, high safety assurance, and low noise (sonic thump).
MOTIVATION
In this era of rapid advancement in technologies, every country has its own contribution to the development of aircraft and missiles. These aircraft and missiles are capable of traveling at a speed which is more than five times the speed of sound. These capabilities increase the military power of a country. Globalization has increased the need for everyone to travel across the globe in less time possible. So this raised a need for the development of civilian aircraft that can travel at high speed and are safe.
The total number of passenger trips is estimated to raise from 3.3 billion trips in 2014 to 7 billion trips in 2034. This requires over 36,000 new aircraft requirement over the 20 – years period [2].
The complexity in the design of geometry and selection of materials for the manufacturing of such aircraft is limited. So the research and development in this area play a major role in the development of better and safe aircraft with increased efficiencies. This project will provide a new design of hypersonic aircraft. It is important to industry practice as hypersonic aircraft over land will enable a revolution in transportation.
PROBLEM STATEMENT
Shockwave generally increases the drag force on the aircraft causing decreasing the efficiency of the flight and high skin temperatures. Sonic booms are caused by shockwaves in a case of supersonic and hypersonic aircraft. These sonic booms travel long distances and make aircraft visible to radar. The existing hypersonic aircraft have been rebuked for their limitations in modelling geometry, including the inability to use the shockwaves for the lift and avoidance of sonic boom. Briefly, there a need arises for a better understanding the limitations in designing of better aircraft geometry that uses shockwaves for lift and avoids sonic boom. In particular, the following research points need to be addressed:
The typical methods to reduce sonic boom.
Utilize a shockwave to produce thrust.
Unify different techniques to provide a high lift-to-drag ratio.
1.4 AIM AND OBJECTIVES
This thesis is aimed to design the hypersonic aircraft geometry. The aircraft geometry used here can be defined as the shape of aircraft that overcome the problems stated or minimize the effects of stated problems.
The project has the following objectives:
- To provide a model to reduce the intensity of sonic boom
- To develop a model that uses the shockwaves in addition to thrust
- To create a turbulent flow near engine inlet for better mixing of air and fuel
1.5 THESIS OUTLINE
Chapter 1 includes the history, motivation, problem statement, aims and objectives of the project. Chapter 2 gives the theoretical background of the project which describes basic terms and procedures involved. Chapter 3 gives the information about the modelling equations that govern the mathematical analysis of the project. Chapter 4 gives the methodology of design and analysis of aircraft used in the project. Chapter 5 deals with the both numerical and graphical results. Chapter 6 provides the conclusions and scope of future work.
Chapter 2
Literature review
2.1 PREVIOUS RESEARCH
Various researchers contributed their part in the field of subsonic, supersonic, and hypersonic aircraft.
John M Morgensten in his work on low sonic boom shock control [3] provided a control device to reduce the effect of shock waves produced at the supersonic speed. The control device consists of retractable control surface located at the nose of the aircraft. This control surface can be moved between an extended position and a retracted position. The control surface when extended increases the air pressure at the nose thereby decreasing slope of shock wave and pressure amplitude as the wave travels towards the ground.
Donald C. Howe, Preston A. Henne, Jimmy L. Hancock, and Robert R. Wolz in their work on controlling and reducing sonic boom [4] provided air spike technology to reduce the intensity of sonic boom. The air spikes can have one or more cross – sections. These cross – sections project forward from the fuselage leading end or rearward from the trailing end of fuselage of the aircraft. The varying cross – sections on the aircraft reduces the coalescence of shock waves created during the supersonic flight. The air spike causes the asymmetric pressure distribution reducing the ground – directed pressure contour which has lesser magnitude than the pressure contour in other directions.
Gecheng Zha, Hongsik Im, and Daniel Espinal in their work toward zero sonic boom and high efficiency supersonic flight [5] showed that it is possible to remove or achieve very low sonic boom using a supersonic blended wing body or bi – directional flying wing configuration. This uses an isentropic compression surface to reduce the sonic boom.
Randall T. Voland, Charles R. McClinton, Lawrence D. Huebner [6] in their paper gave the detailed development of technologies of X – 43A hypersonic aircraft.
Laurie A. Marshall, Catherine Bahm, and Griffin P. Corpening [7] discussed the results of the final flight of the NASA X – 43A project. They discussed the results for two planned flights, one at Mach 7 and other at Mach 10.
Scott A. Berry, Robert J. Nowak, and Thomas J. Horvath [8] in their work provided the methods to control the boundary layer for hypersonic airbreathing vehicles. They worked on both active and passive methods for control of hypersonic boundary layers on airbreathing configurations.
Scott Berry, Kamran Daryabeigi, Kathryn Wurster, and Robert Bittner [9] gave details of boundary layer transition on X – 43A for both Mach 7 and Mach 10 flight conditions.
2.2 THEORETICAL BACKGROUND
To help guide the aircraft design this chapter will go through some principles which are fundamental in the airfoil, aircraft parts, motion of aircraft, aerodynamic efficiencies, and basic CFD procedure.
2.2.1 Airfoil
Figure 1: Airfoil section
The general airfoil section and terminology are shown in figure 1. The terms involved are explained below:
Chord: The straight line joining the trailing edge and the leading edge is the chord of an airfoil.
Angle of attack (α): The airfoil chord makes an angle with the freestream velocity vector. This angle is known as the angle of attack, denoted by α.
Lift: Lift is the resultant normal force to the upstream velocity. Lift is denoted by L.
Drag: The resultant force in the direction of upstream velocity is the Drag. It is denoted by D.
Aspect ratio: Ratio of wingspan to its mean chord is called the aspect ratio.
2.2.2 Aircraft Motion
There are three basic movements of aircraft. They are yaw, pitch and roll. These terms are explained in detail as follows:
Yaw: Yaw is the twisting or oscillation of aircraft along the perpendicular axis of the aircraft.
Pitch: Pitch is the twisting or oscillation of aircraft along the lateral axis of the aircraft.
Roll: Roll is the twisting or oscillation of aircraft along the longitudinal axis of the aircraft.
These are shown in the figure 2. The direction vectors shown in the figure 2 gives the clear understanding of the yaw, pitch, and roll.
Figure 2: Aircraft Motion
Pitch is the up-down motion of the nose of the aircraft. To descend or climb an aircraft, the aircraft’s pitch is changed by the pilot. The side-to-side rotation of the aircraft is the roll, during which time one wing is lowered while the other is raised. Yaw is the right – to – left motion of the nose of the aircraft.
2.2.3 Basic Aircraft Parts
The basic parts of any aircraft (most aircraft) are shown in figure 3. The parts shown in the figure 3 are common to most aircraft. In case of supersonic and hypersonic aircraft, the aircraft has many other parts which are not shown in the figure 3.
Figure 3: Basic Aircraft Parts
The details and functioning of parts shown in the figure 3 are explained as follows:
Ailerons: At the rear of the wing ailerons are located one on each side. Ailerons work opposite to each other, that is when one is lowered, the other is raised. Ailerons reduce the lift on the one side of the wing while increasing the lift on one wing other. By doing this, they turn the aircraft by rolling the aircraft sideways. The method of steering a fixed-wing aircraft is provided by ailerons. Ailerons change the roll of the aircraft.
Elevator: The elevator helps the aircraft to elevate. At the tail of the aircraft the elevator is located and it directs the nose of the aircraft either downwards or upwards in order to make the airplane descend and ascend. Elevator changes the pitch of the aircraft.
Empennage: The entire tail section of the aircraft, including the elevator, both the vertical and horizontal stabilizers, and the rudder is called the empennage. As a combined unit, it helping guide the aircraft like the feather on the arrow.
Flap: Flaps are used to produce high lift or high drag. By changing the curvature of the wing, or camber the lifting ability of the wing at slower speeds will be improved. When fully extended they also create more drag. This makes an aircraft lose altitude (or descend) faster, in the process without gaining airspeed. The main different types of flaps are plain, split, slotted and fowler.
Fuselage: The portion of the airplane used to fuse or literally join the other parts together is the fuselage. It is the body of the aircraft that holds the cargo and passengers inside.
Fin or Vertical Stabilizer: The vertical stabilizer stabilizes the right – left motion of the aircraft. Most aircraft use a single stabilizer, while some use multiple stabilizers.
Horizontal Stabilizer: The horizontal stabilizer is an upside-down wing, used to provide a downward force (push) on the tail. Airplanes usually are nose-heavy; to compensate this a downward force is required to keep the nose level with the rest of the aircraft. The angle of stabilizer can be controlled by some aircraft and thereby control the level of downward force during the flight, while others are fixed in place.
Pylon: A structure on the wing of an aircraft used for carrying a weapon, engine, fuel tank, or other load.
Rudder: The rudder is located on the tail of the aircraft attached to the vertical stabilizer. It helps to steer the nose of the aircraft right and left this motion is known as yaw. Its main purpose is to ensuring that the aircraft’s tail follows the nose, rather than sliding out to the side, by counteracting certain types of drag, or friction.
Slat: A slat is found on jet-powered aircraft which is a high lift device. On the leading edge of the wing, Slats are mounted and they are similar to the flaps. They also assist in increasing the lift and drag by changing the curvature of the wing, or the camber.
Spoiler: The spoiler disrupts, or spoils, the flow of air across the upper surface of the wing. They are used to completely destroy the lifting ability of the wing upon landing, ensuring that the entire weight of the airplane rests firmly on the wheels, making the brakes more effective and shortening the length of runway needed to stop the aircraft.
2.2.4 Waverider
A waverider is an aircraft design that uses shock waves that are generated during supersonic and hypersonic flight to improve lift – to – drag ratio using a phenomenon known as compression lift. Waverider design can be used only for the hypersonic aircraft. Terence Nonweiler [10] of Queen’s University was the first person to describe the concept of waverider in 1951. He used delta wing configuration in his aircraft design and testing. The different types of waverider configurations are: Caret wing waveriders, Cone flow waveriders, Viscous optimized waverider, and Hypersonic sail waveriders. Hypersonic aircraft while re – entry generates lift only from the underside of fuselage. Waveriders have sharp leading edges and sharp nose. Due to this, shock – surface is attached to the underside of the aircraft. The air gets locked between the fuselage and the shock waves and can escape only from the rear of the fuselage. This phenomenon is the called compression lift.
2.2.5 Aerodynamic Efficiencies
Specific parameters like drag coefficient, lift coefficient, pressure, and velocity variation effects aerodynamic efficiency. The dimensionless forms of lift and drag are given by lift coefficient and drag coefficient respectively.
Coefficient of lift: The relation between the lift generated and fluid density around a body is given by the coefficient of lift or lift coefficient. It is given by
C_L = L/(1/2 ρv^2 A)
where C_L is the coefficient of lift, ρ is the density of a fluid, L is the lift force, v is the upstream velocity, and A is the surface area.
Coefficient of drag: The relation between the drag generated and fluid density around a body is given by the coefficient of drag or drag coefficient. It is given by
C_D = D/(1/2 ρv^2 A)
where C_D is the coefficient of drag, ρ is the density of a fluid, D is the drag force, v is the upstream velocity, and A is the surface area.
2.2.6 Basic Design Tools
The general design tools for parametric modelling can be explained as follows:
Sketch Entities: Sketch entities contains the tools for creating sketches in any plane. The main tools in sketch entities are lines commands, circles commands, rectangles commands, arcs commands and ellipse commands. The objectives of these tools are creating sketches.
Sketch relations: Sketch relations are the tools used for creating geometric relations. To capture the design intent these relations are used. Vertical, horizontal, dashed line, parallel, perpendicular, coincident and tangent are the sketch relations.
Cut and Boss features: Cut and boss tools are used for creating basic features to the design. Extrudes tools, revolves tools, sweeps tools, loft tools are the tools present in cut and boss tools. The objectives of these tools are to create extrude features, revolve features, sweep feature and loft features to the model.
Dimensions: Dimension for the design are given by using dimensions’ tools. Standard dimensions and smart dimensions are the two tools used for applying and editing dimensions of the sketch or the model.
By using these tools, the sketch of the model can be created and the basic sketch can be converted to the geometry of the desired model.
2.2.7 Basic CFD procedure
Computational fluid dynamics or simply CFD is the art of replacing partial differential equations that govern fluid flows by a set of algebraic equations and solving them by using digital computers to obtain solutions. The following steps are used in CFD analysis:
Pre–processing:
Defining geometry: The solid models built are used as geometry for the analysis of fluid flow over them.
Meshing: The model is meshed by defining mesh size and shape.
Boundary conditions: The fluid velocity and pressure at the inlet are the necessary boundary conditions. These are defined as initial conditions.
Define the goals of the project.
After defining the goals, the solution methods are set for simulation.
Post-processing:
Solution: The solution obtained will have magnitude and vector values of the defined goals.
Visualization: The expected results are velocity and pressure contours, and vector plots for different iterations.
Chapter 3
MATHEMATICAL MODEL
This chapter gives the numeric and various formulations that govern the fluid flow and are used in CFD analysis. The N-S describes how the density, pressure, and velocity are related to a moving fluid. The Navier – Strokes (N-S) equations which are formulations of momentum, mass, and energy conservation laws are used by the CFD software to solve the fluid flow problem. The two-equation turbulence model [11,12], k-ε, turbulent kinetic energy (k) – turbulent energy dissipation rate (ε) is used in predicting turbulence.
3.1 GOVERNING EQUATIONS
The governing equations which are mass, momentum, and energy conservation laws are given as follows:
A. Conservation of mass (Continuity equation):
The conservation of mass principle states that in the absence of mass sources and sinks, a region will conserve its mass on a local level. It is given as:
∂ρ/∂t+ ∇.[ ρ(v ) ⃗ ]=0
Where ν is the velocity and ρ is the density of the fluid.
B. Conservation of momentum:
The conservation of momentum principle states that in the absence of any external force acting on a body, the body retains its total momentum (product of its mass and velocity). It is given as:
ρ [ (∂ν ⃗)/∂t+( ν ⃗.∇) ν ⃗ ]=f
where f is the external force per unit volume acting on the material volume.
C. Conservation of energy:
It is governed by the first law of thermodynamics which states that energy can be neither created nor destroyed during a process; it can change from one form into another. It is given as:
∂/∂t (ρⅇ)+ ∇ .[ ρν ⃗ⅇ ]= – ∇ .( ∑_j▒〖h_i J_j 〗 )+ S_h
where ⅇ is the total energy of the system.
3.2 STANDARD k-ε MODEL
The k-ε model with the turbulent viscosity μ_t and thermal diffusivity k_t is formulated as
μ_t=ρC_μ k^2/ε
k_t=(c_p μ_t)/(Pr_t )
where ε is the turbulence kinetic energy dissipation rate per unit mass due to viscous stresses are given by
ε=1/2 μ/ρ { ∇ν ⃗’+(∇ν ⃗’)^T } ∶ { ∇ν ⃗^’+(∇ν ⃗’)^T }
The turbulent energy dissipation rate ε and the turbulent kinetic energy k are computed using
∂/∂t (ρk)+∇⋅(ρν ⃗k)=∇⋅(μ_(e_(ff,k) ) ∇k)+ P_k-ρε
∂/∂t (ρε)+∇⋅(ρν ⃗ε)=∇⋅(μ_(e_(ff,ε) ) ∇ε)+ C_(ε_1 ) ε/k P_k-C_(ε_2 ) ρ ε^2/k
where
μ_(e_(ff,k) )= μ+μ_t/σ_k
μ_(e_(ff,ε) )= μ+μ_t/σ_ε
with the turbulent Prandtl number (Pr_t) and other model constants assigned the following values:
C_(ε_1 )=1.44,
C_(ε_2 )=1.92,
C_μ=0.09,
σ_k=1.0,
σ_ε=1.3,
Pr_t=0.9
Chapter 4
Methodology
This chapter gives the details about the design and CFD analysis of the aircraft. The geometry of aircraft is created using Solidworks and CFD analysis is carried out using Solidworks Flow Simulation. The detailed methodology is given as follows:
DESIGN OF GEOMETRY
Full-scale models of Northrop B-2 and Lockheed F-22 are designed according to the technical data and blueprints from their respective companies. The design of geometry has the following steps:
Open Solidworks and choose the command File > New > Part.
Select the system of units as MMGS and choose the sketch plane.
Select the front plane from the Sketch tab and insert the front view of blueprint using Sketch Picture. Similarly, select the top plane and right planes and insert top view and right view of blueprint respectively.
Make sure that the views imported exactly intersect at their mating points. Also, see that there are no interferences and gaps between the intersecting points.
From the Features tab select Reference geometry > Plane. With front plane as First Reference create planes at the section marks along the right view of the blueprint.
Set the transparency of each plane to the required level.
Now select the planes created one – by – one. Draw splines on each plane by selecting sketch plane and using Spline from the Sketch tab. These splines should exactly coincide with the surface of the aircraft i.e., the spline shape and the surface shape should match exactly. Use Sketch Relations whenever required. Repeat the same procedure for each plane at the section marks.
Using 3D Sketch from the sketch tab draw splines in between the previously created splines. Using top view of the blueprint make sure these splines exactly coincide with the surface of the aircraft.
From the Surfaces tab select Lofted Surface. Selecting splines created on the planes parallel to the front plane as Profiles and the 3D splines as Guide Curves execute the Lofted Surface command. This generates the outer surface of the aircraft.
Use Fillet from the Surfaces tab and select the edges of the surfaces generated. Define Fillet radius and execute the command. This gives the smooth curved edges by eliminating sharp edges.
Using Cut With Surface from the Surfaces tab, cut the intersecting bodies or parts.
Mirror the entire geometry created about the plane of symmetry. This gives the entire aircraft model.
Thus the models of Northrop B-2 and Lockheed F-22 are created using Solidworks. The standard third angle projections are as shown in figure 4 and figure 5.
Figure 4: Standard views of Northrop B-2
Northrop B-2 is a subsonic aircraft with a maximum speed of Mach 0.8. It was a nuclear warhead carrier that was used by United States air force. It can reach a top speed of 1250 km/h. It is a flying wing; it has no fuselage or tail. The standard views are shown in figure 4. Figure 4 give the detailed front view, side views, top view, and bottom view of the Northrop B – 2.
The Lockheed F-22 is a supersonic aircraft which reach a top speed of 2,410 km/h, Mach 1.95. It is an all-weather aircraft that is still in use by US air force. F-22 uses delta wing clipped at the end. The standard views are shown in figure 5.
Figure 5: Standard views of Lockheed F-22
In the figure 5 we can see the third angle projections of Lockheed F – 22 showing top view, bottom view, front view, and side views.
The hypersonic aircraft uses WaveRider design. The hypersonic aircraft is designed using Solidworks. The design procedure is given below:
The design process starts with command File > New > Part.
Select the system of units as MMGS and choose the sketch plane.
First draw the outline of the aircraft using Point, Line, Spline, 3 Point Arc, and Rectangle commands from the Sketch toolbar.
Trim away the unnecessary lines or curves using Trim Entities from the Sketch toolbar.
Then join different surfaces using Extruded Boss, Swept Bose, and Lofted Bose commands from the Features tab.
Now using Solidworks Surfaces, create the surface for the designed geometry.
Create the engine inlet and outlet bore using Extruded Cut Form Features toolbar.
Use Fillet from the Surfaces tab and select the edges of the surfaces generated. Define Fillet radius and execute the command. This gives the smooth curved edges by eliminating sharp edges.
Using Cut With Surface from the Surfaces tab, cut the intersecting bodies or parts.
The hypersonic aircraft designed is shown in figure 6 with its standard views in third angle projection. Figure 6 shows the top view, bottom view, front view, and side views of the hypersonic aircraft.
Figure 6: Standard views of Hypersonic aircraft
From the figure 6, it can be seen that the hypersonic aircraft has fuselage which is slender at one end and becomes blunt at the other end. The fuselage itself acts as the streamlined body. Due to this, shock – surface is attached to the underside of the aircraft. The air gets locked between the fuselage and the shock waves and can escape only from the rear of the fuselage. This provides the compression lift on the aircraft in addition to the lift produced due to buoyancy.
CFD SIMULATION
Finite volume methods (FVM) of computational fluid dynamics (CFD) with the help of cartesian based meshes are used in determining parameters like drag coefficient, lift coefficient, pressure, and velocity variation. The structured cartesian immersed – body mesh with rectangular cells (cuboids) are used. The geometry of aircraft is created using Solidworks and CFD analysis is carried out using Solidworks Flow Simulation. The CFD analysis has the following steps:
CFD Pre-processing
The process of importing geometry and executing CFD analysis is described in the following steps:
Import the geometry under study using command Open > File.
Start the simulation process by clicking SOLIDWORKS Flow Simulation from SOLIDWORKS Add – Ins.
Now the General Settings Navigator window shows up in the Solidworks workspace.
From the Navigator choose the Analysis type > External.
Also, select Exclude internal space and Exclude cavities without flow conditions in the Analysis type.
Also, choose Reference axis. Tick the Gravity and Time – dependent (if required) in the Analysis type from the Navigator.
Next, select the air as the Project Fluid from the Fluids in the Navigator.
Also, select Flow Characteristic > Flow type > Laminar and Turbulent.
From the Navigator select Wall conditions. Select Default wall thermal condition > Adiabatic wall and Roughness = 100 micrometer.
From the Initial and ambient conditions tab in the Navigator define the flow conditions.
Once the general settings are defined, set the goals, iterations, physical time and goal convergence options in the Calculation control options.
Finally, run the simulation.
By following these steps the pre-processing step is completed.
4.2.2 Grid Generation
The grids for models are created using structured cartesian immersed – body mesh which consists of fluid cells, solid cells, and partial cells. The fluid cells and solid cells contain fluid and solid respectively. The partial cells contain both fluid and solid. Each cell is in the shape of a cuboid. The respective count of cells for different aircraft are listed in Table 1.
Table 1: Analysis Mesh
Model Fluid cells Solid cells Partial cells Total cells
Northrop B-2 197777 9230 6948 207007
Lockheed F-22 227896 842 826 228738
Hypersonic aircraft 465556 330825 208208 796381
Table 1 has four rows and five columns. The rows and columns of the Table 1 represent the aircraft model and number of mesh cells used in the meshing of different aircraft respectively. The size of computational domain for different aircraft is listed in Table 2.
Table 2: Size of computational domain
Model Northrop B-2 Lockheed F-22 Hypersonic aircraft
X min -15.000 m -16.500 m -2.000 m
X max 15.000 m 16.500 m 2.000 m
Y min -8.000 m -12.000 m -10.000 m
Y max 8.000 m 12.000 m 10.000 m
Z min -35.000 m -8.000 m -4.000 m
Z max 35.000 m 8.000 m 4.000 m
Table 2 gives the size of the computational domain for different aircraft. The dimensions of the computational domain are shown in meters. The negative value represents the value of the dimension in respective negative axes.
The structured cartesian immersed – body mesh is shown in figure 7. In figure 7 the squares outside the curved line represent the fluid cells. The gap shows the solid surface and the cells with small dashed lines represent the partial cell (cells that contain both solid cells and fluid cells).
Figure 7: Structured cartesian immersed – body mesh
The mesh for the different aircraft are shown in the figures 8 – 10.
Figure 8: Lockheed F-22 basic mesh
Figure 8 shows the basic mesh of the Lockheed F – 22. Basic meshing of any geometry represents the meshing of the complete computational domain. To make it clear in the pictorial representation, the meshing of the computational domain is shown as thin layers. The meshing of the solid geometries is shown in the figures 9 and figure10.
Figure 9.a: Northrop B-2 mesh isometric view 1
Figure 9.b: Northrop B-2 mesh isometric view 2
Figure 10.a: Hypersonic Aircraft mesh isometric view 1
Figure 10.b: Hypersonic Aircraft mesh isometric view 2
Figure 9.a and figure 9.b gives the meshing of the Northrop B – 2. The meshing of aircraft is shown in the isometric view. To show the meshing of the geometry of the aircraft, the meshing of the computational domain which shows the fluid cells is hidden. Figure 10.a and figure 10.b gives the meshing of the hypersonic aircraft. The meshing of aircraft is shown in the isometric view. To show the meshing of the geometry of the aircraft, the meshing of the computational domain which shows the fluid cells is hidden. From the figures 8 – 10, it can be seen that the type of element of meshing used here is a cuboid.
4.2.3 Flow Conditions
The flow conditions including different boundary and initial conditions for different aircraft are shown in Table 3.
Table 3: Flow conditions
Parameters Northrop B-2 Lockheed F-22 Hypersonic aircraft
Solver Pressure based steady state Pressure based steady state Pressure based transient
Turbulence model k-ε k-ε k-ε
Velocity (m/s) 281 669.444 Table from time (Table 4)
Angle of attack (degree) 0° 0° Table from time
(Table 4)
Initial pressure (Pa) 101325 101325 Table from time
(Table 4)
Initial temperature(K) 293.20 293.20 Table from time
(Table 4)
Turbulent energy,k (J/kg) 1 1 1
Turbulent dissipation,ε (W/kg) 1 1 1
Table 3 shows the different flow conditions used in the CFD analysis of the aircraft. The parameters used to describe the flow conditions are shown the Table 3. It also gives the values of the flow parameters.
The conditions for hypersonic aircraft are time dependent. A transient state study for 5 seconds is used to analyze the hypersonic aircraft. The CFD analysis starts from 0th second and ends at 5th second. The dependency of various input parameters at their corresponding time step is tabulated in Table 4.
Table 4: Flow conditions of Hypersonic aircraft
Time (s) 0 1 2 3 4 5
Altitude (m) 12000 12000 15000 18000 22000 30000
Velocity (m/s) 343 1715 1715 1715 1715 1715
Angle of attack (degree) 0 5 10 15 20 25
Initial pressure (Pa) 19330.4 19330.4 12044.6 7504.84 3999.79 1171.87
Initial temperature (K) 216.650 216.650 216.650 216.650 218.650 226.650
Table 4 shows how the altitude (m), velocity (m/s), angle of attack (degree), initial pressure (Pa), and initial temperature (K) vary from 0th second to 5th second.
Chapter 5
RESULTS AND POST-PROCESSING
This chapter gives the results of the simulation and the visualization of the results. The steps involved in obtaining results and creating graphics of the results are explained in the following sections. The post-processing i.e., the visualization of the results is done only for the Hypersonic aircraft.
5.1 GOALS REPORT
The CFD simulation of different aircraft gives the numerical values of the goals defined. These results for different aircraft are shown in Table 5.
Table 5: Goals report table
Parameters Northrop B-2 Lockheed F-22 Hypersonic aircraft
Lift coefficient (No units) 0.0109101 0.0034572 0.0288081
Drag coefficient (No units) 0.0055856 0.0090064 0.0031610
Lift Force (N) 847707.743 87776.237 1.309e+008
Drag Force (N) 434000.549 228665.206 1.437e+007
Skin temperature (K) 380.910 500.81 2425.80
The CFD analysis gives us the lift and drag coefficient along with lift, drag forces, and aircraft skin temperatures. The values of different parameters are plotted as graphs as follows:
A. Northrop B-2:
This aircraft is a subsonic fighter jet. The vector plots for different iterations are given below.
Graph 1: Lift coefficient
Graph 2: Drag coefficient
Graph 3: Lift force
Graph 4: Drag force
B. Lockheed F-22:
F-22 is a supersonic aircraft that travels at speeds more than the speed of sound. The vector plots for different iterations are given below.
Graph 5: Lift coefficient
Graph 6: Drag coefficient
Graph 7: Lift force
Graph 8: Drag force
C. Hypersonic aircraft:
Hypersonic aircraft is tested at Mach 5 starting from Mach 1 at 0th second to Mach 5 at 5th second. The vector plots for hypersonic aircraft are plotted against physical time. The physical time can be interpreted as in Table 4.
Graph 9: Lift coefficient
Graph 10: Drag coefficient
Graph 11: Lift force
Graph 12: Drag force
5.2 POST- PROCESSING OF HYPERSONIC AIRCRAFT
The hypersonic aircraft is analyzed by using Solidworks Flow Simulation for 0, 5, 10, 15, 20, 25 angles of attack measured in degrees at altitudes of 12000 m, 15000 m, 18000 m, 22000 m, and 30000 m with a constant speed of Mach 5. In addition to vector plots, streamlines, contours, and surface plots are obtained. The velocity and pressure contours are shown for 5, 10, 15, 20, 25 angles of attack measured in degrees. The post-processing of results is given below:
Figure 11: Pressure contour at 5° angles of attack
Figure 12: Pressure contour at 10° angles of attack
Figure 13: Pressure contour at 15° angles of attack
Figure 14: Pressure contour at 20° angles of attack
Figure 15: Pressure contour at 25° angles of attack
Figure 16: Velocity contour at 5° angles of attack
Figure 17: Velocity contour at 10° angles of attack
Figure 18: Velocity contour at 15° angles of attack
Figure 19: Velocity contour at 20° angles of attack
Figure 20: Velocity contour at 25° angles of attack
Figure 21: Pressure Cut plot
Figure 22: Velocity Cut plot
Figure 23: Arrow plot
Figure 24: Streamlines
Figure 25: Pressure Isolines
Figure 26: Velocity Isolines
Figure 27: Surface pressure distribution
Figure 28: Surface pressure distribution
Figure 11 to figure 15 shows the pressure contours of the hypersonic aircraft for different angle of attack. Figure 16 to figure 20 gives the velocity contours of the hypersonic aircraft for different angle of attack. The angle of attack varies as 5, 10, 15, 20, and 25 degrees in the pressure contour and velocity contour plots. The pressure cut plot of the hypersonic aircraft is shown the figure 21. Figure 22 gives the velocity cut plot of the hypersonic aircraft. Figure 23 gives the arrow plot which shows the directions of fluid particles over the entire computational domain. The streamlines are shown in the figure 24. Pressure isolines and velocity isolines are shown in figure 25 and figure 26 respectively. The surface pressure distribution is shown in figure 27 and figure 28.
Chapter 6
CONCLUSIONS
The outline of this thesis is to provide a geometry for hypersonic aircraft using waverider design. This project helped to design guidelines for hypersonic aircraft design and ultimately lead to test the aircraft using commercially available CFD software. These guidelines lead to design and testing of aircraft.
6.1 CONCLUSION
The aerodynamic coefficients are calculated using Solidworks Flow Simulation solver using a real fluid model with air as working fluid. From the tables 5, it can be seen as the speed of aircraft increases from subsonic to hypersonic the aerodynamic drag of the aircraft increases rapidly. This aerodynamic drag increases the skin temperatures of the aircraft. Also, it can be noted that the waverider concept in the design of hypersonic aircraft uses the phenomenon of compression lift to produce additional lift to the aircraft.
6.2 FUTURE WORK
The intent of this paper is to show how to design a waverider hypersonic aircraft and perform analysis using CFD software. The aircraft model is not tested and should be tested using experimental methods. Also, the aircraft results shown in this thesis are for fluids treated as in continuum. In reality, the aircraft should also be analyzed and tested for fluids that are not in continuum using Rarified Gas Dynamics.
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