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CHAPTER 1

INTRODUCTION

1.1 MISSILE

A missile, or guided missile, is a self-propelled guided weapon system, as

opposed to an unguided self-propelled munitions, referred to as just a rocket.

Missiles have four system components: targeting and/or guidance, flight system,

engine, and warhead. The word missile comes from the Latin verb mittere,

meaning "to send". In military usage, munitions projected towards a target are

broadly categorized as follows:

A powered, guided munition that travels through the air or space is known as

a missile (or guided missile.)

A powered, unguided munition is known as a rocket.

Unpowered munitions not fired from a gun are called bombs whether guided or

not; unpowered, guided munitions are known as guided bombs or "smart

bombs".

Munitions that are fired from a gun are known as projectiles whether guided or

not. If explosive they are known more specifically as shells or mortar bombs.

A Powered munitions that travel through water are called torpedoes (an older

usage includes fixed torpedoes, which might today be called mines).

Hand grenades are not usually classed as missiles.

A common further sub-division is to consider ballistic missile to mean a

munitions that follows a ballistic trajectory and cruise missile to describe a

munitions that generates lift.

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1.2 NEED FOR DRAG REDUCTION

Minimization of drag and aerodynamic heating are among the most important

design requirements for hypersonic vehicles. Reducing the aerodynamic drag

enables increasing the range, economizing the fuel usage, simplifying the

propulsion system requirements, and maximizing the ratio of payload to takeoff

gross weight. High levels of aerodynamic heating can cause malfunction or even

damage of the delicate onboard equipment. Excessive heating can cause ablation to

the vehicle surface material, which yields fluctuations in the vehicle performance.

Combined with the presence of high-pressure loads, severe heating can cause a

complete material failure. Employing the conventional thermal protection shields

adds to the weight of the vehicle and the complexity of its design, and

communication blackout caused by the ionized air associated with elevated

temperatures cannot to be solved by the thermal protection shields. Pointed slender

bodies generate lower drag compared with blunt bodies at hypersonic conditions.

They provide a good choice as far as drag reduction is concerned.

However, blunt bodies are found to yield lower heating levels compared with

their pointed counterparts. In fact, blunting the body is viewed as the primary

design option in hypersonic regimes. In some applications, blunting the body nose

becomes a favored design requirement on its own. Consequently, hypersonic

vehicles such as missiles, interplanetary space missions, space planes, and launch

missiles usually have blunt shapes. The design of the reentry vehicles such as

reusable launch vehicles, long-range, and ballistic missiles is rather complicated.

On one hand, it is desired to use a pointed slender geometry to minimize the drag

during the takeoff (ascent) phase. On the other hand, a blunt design is advantageous

during the descent phase to reduce the excessive aero heating levels during reentry

and to generate the desired vehicle deceleration. Obviously, designing a vehicle that

simultaneously satisfies both minimum-drag and aerodynamic heating is not

straight forward and there is a challenging tradeoff between these two vital

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requirements. It is believed that these two requirements can be met by altering the

flow field pattern around the blunt body so as to eliminate the strong detached bow

shock wave.

A variety of techniques have been implemented in this regard. These

techniques include

Spikes and aero disks

Focused gas jet

Laser or microwave beams upstream of the nose stagnation point

Energy deposition using plasma torch

Arc discharge

DC corona discharge

Supersonic projectiles fired ahead of the blunt body

Out of these varieties of techniques, the use of spikes proved to be the

simplest and the most effective technique in reducing both drag and aerodynamic

heating. It is viewed as a compromise of two requirements, namely lower

aerodynamic heating for reentry and lower drag for atmospheric flights. The spike

is simply a slender cylindrical rod mounted at the stagnation point of the blunt body

and projected in the upstream direction. The spike introduces two major

modifications to the flow field upstream of the blunt body. Firstly, it replaces the

strong detached shock wave with a system of weaker oblique shock waves.

Secondly, it acts as a “flow separator”; the spike encourages the separation of the

boundary layer from its surface and the creation of a shear layer. The latter

propagates downstream, reattaches on the blunt body surface, and envelopes a zone

of recirculation in which the flow attains low pressure and velocity values. This

zone screens a considerable portion of the blunt body surface and results in a

significant drop in surface pressure and temperature. Only at the zone of shear layer

reattachment on the blunt body, the local heating rate, and surface pressure attain

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high values. To turn the flow outside the shear layer parallel to the body surface, a

shock wave is created at the reattachment zone: the reattachment shock.

Immediately downstream of the reattachment shock, the flow pressure attains high

local values. The overall effect is a significant reduction in both drag and the

aerodynamic heating as compared with those without the spike. To further enhance

the effectiveness of the spike, a relatively larger tip, called the aero disk, can be

used. An aero disk mounted at the tip of a spike of a fixed length has the role of

providing further reduction in both drag and aerodynamic heating over a wider

range of Mach numbers and incidence angles. It can also compensate the drag

reduction in cases when a shorter spike is necessary for design.

As the angle of attack is increased the effectiveness of the Aero spike

decreases. A favored shock system is not achievable anymore and at angles of

attack > 15°, depending on the specific case, no drag reduction can be gained due to

unfavorable shock system. A movable aero spike that points always into the flow

direction even though the main body has an angle of attack could sustain the

beneficial effect in the region of low and high angles of attack. The point where the

effectiveness is close to zero is shifted to higher α. according to the invention the

aero spike might be pivoted under consideration of the actual flight and flow

conditions of the flying object. In cases where changes of the angle of the upstream

airflow are only expected or relevant in a plane including the longitudinal axis of

the flying object it might be sufficient providing a pivoting axis which is directed

perpendicular to the longitudinal axis and to the aforementioned plane. However, it

is also possible that the link between the aero spike and the flying object is designed

and arranged for providing a three-dimensional degree of freedom of the aero spike

linked at one point at a fixed or movable front surface of the flying object. Such

one-dimensional, two-dimensional or three-dimensional degree of freedom might

be used for aligning the aero spike with the upstream airflow or for adjusting the

angle of the aero spike between the angle of the upstream airflow and the

longitudinal axis of the flying object (in the following “inclination angle”, in the

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literature also denoted with “angle of incidence” or “angle of attack”). Such

embodiment provides the possibility to eliminate or decrease the influence of the

inclination angle on the air stream in the region of the front surface

1.3 TYPES OF MISSILES

Missiles come in types adapted for different purposes:

Surface-to-surface

Air-to-surface missiles (ballistic, cruise, anti-ship, anti-tank, etc.),

Surface-to-air missiles(anti-aircraft and anti-ballistic),

Air-to-air missiles,

Anti-satellite missiles.

All known existing missiles are designed to be propelled during powered

flight by chemical reactions inside a rocket engine, jet engine, or other type of

engine. Non-self-propelled airborne explosive devices are generally referred to

as shells and usually have a shorter range than missiles.

1.4 FORCES ACTING ON MISSILE

The forces acting on a missile in flight consist of aerodynamic, propulsive

(i.e., thrust), and gravitational forces. These forces can be resolved along the

missile’s body-axis system (Xb, Yb, Zb) and fixed to the missile’s center of gravity

(cg). The reference axis system standardized in guided weapons is centered on the

cg and fixed in the body. Thus, any set of axes fixed in a rigid body is a body-fixed

reference frame.

It is conventional in aerodynamics to resolve the sum of the normal (or

pressure) forces and the tangential (or viscous shear) forces that act on the surface

due to the fluid motion around a vehicle into three components along axes parallel

and perpendicular to the free-stream direction. These forces are lift (L), drag (D),

and side force (Y). The relation of the lift and the drag forces to the free-stream

velocity is shown in FIGure 2. It should be noted from this FIGure that if an angle

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of attack is generated, the lift vector acting at the center of pressure (cp) has a

destabilizing effect and must be controlled.

1.4.1 LIFT FORCE

Lift–Lift is the component of the resultant aerodynamic force that is

perpendicular (i.e., upward) to the relative wind (direction of flight) or to the

undisturbed free-stream velocity. The aerodynamic lift is produced primarily by the

pressure forces acting on the vehicle surface. Also, the lift force is perpendicular to

the missile’s velocity vector in the vertical plane

1.4.2 DRAG FORCE

Drag–Drag is the component of the resultant aerodynamic force that is

parallel to the relative wind. In other words, it is net aerodynamic force acting in the

same direction as the undisturbed free-stream velocity. The aerodynamic drag is

produced by the pressure forces and by skin friction forces that act on the surface.

The drag force is measured along the velocity vector, but in the opposite direction.

The different types of drag acting on missile surface are skin friction drag,

wave drag, and pressure drag.

FORM DRAG

Form drag or pressure drag arises because of the shape of the object. The

general size and shape of the body are the most important factors in form drag;

bodies with a larger presented cross-section will have a higher drag than thinner

bodies; sleek ("streamlined") objects have lower form drag. Form drag follows

the drag equation, meaning that it increases with the square of velocity, and thus

becomes more important for high-speed aircraft.Form drag depends on the

longitudinal section of the body.

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A prudent choice of body profile is essential for a low drag

coefficient. Streamlines should be continuous, and separation of the boundary

layer with its attendant vortices should be avoided.

SKIN FRICTION DRAG

Skin friction arises from the friction of the fluid against the "skin" of the

object that is moving through it. Skin friction arises from the interaction between

the fluid and the skin of the body, and is directly related to the wetted surface, the

area of the surface of the body that is in contact with the fluid. As with other

components of parasitic drag, skin friction follows the drag equation and rises with

the square of the velocity. Skin friction is caused by viscous drag in the boundary

layer around the object. The boundary layer at the front of the object is usually

laminar and relatively thin, but becomes turbulent and thicker towards the rear. The

position of the transition point depends on the shape of the object.

There are two ways to decrease friction drag: the first is to shape the moving

body so that laminar flow is possible, like an airfoil. The second method is to

decrease the length and cross-section of the moving object as much as practicable.

To do so, a designer can consider the fineness ratio, which is the length of the

aircraft divided by its diameter at the widest point (L/D).

WAVE DRAG

Wave drag is a component of the drag on aircraft, blade tips

and projectiles moving at transonic and supersonic speeds, due to the presence

of shock waves. Wave drag is independent of viscous effects,[1]

and tends to present

itself as a sudden and dramatic increase in drag as the vehicle increases speed. It is

the rise of wave drag that leads to the concept of a sound barrier. Wave drag is best

described as pressure drag due to compressibility effects. It is often caused by the

formation of shock waves around a body, although it exists even if shock waves are

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not present. Shock waves create a considerable amount of drag, which can result in

extreme drag on the body. Although shock waves are typically associated with

supersonic flow, they can form at subsonic aircraft speeds on areas of the body

where local airflow accelerates to sonic speed. The effect is typically seen on

aircraft at transonic speeds (about Mach 0.8), but it is possible to notice the problem

at any speed over that of the critical Mach of that aircraft.

One common solution to the problem of wave drag was to use a swept wing,

which had actually been developed before WWII and used on some German

wartime designs. Sweeping the wing makes it appear thinner and longer in the

direction of the airflow, making a "normal" wing shape closer to that of the von

Kármán ogive, while still remaining useful at lower speeds where curvature and

thickness are important. The wing need not be swept when it is possible to build a

wing that is extremely thin. Several other attempts to reduce wave drag have been

introduced over the years, but have not become common. The supercritical airfoil is

a new wing design that results in reasonable low speed lift like a normal planform,

but has a profile considerably closer to that of the von Kármán ogive. All modern

civil airliners use forms of supercritical aerofoil and have substantial supersonic

flow over the wing upper surface.

1.4.3 SIDE FORCE

Side Force–Side force is the component of force in a direction perpendicular

to both the lift and the drag and is measured in the horizontal plane. The side force

is positive when acting toward the starboard wing, provided that the bank angle

is zero. If the bank angle is zero, if the bank angle is not zero, L and Y will be

rotated by a negative angle about the velocity vector.

1.5 AERO SPIKE

A drag-reducing aerospike is a device used to reduce the forebody

pressure drag of blunt bodies at supersonic speeds. The aerospike creates a

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detached shock ahead of the body. Between the shock and the forebody a zone of

recirculating flow occurs which acts like a more streamlined forebody profile,

reducing the drag. Aerospike consists of a flat circular plate mounted on an

extensible boom which is deployed shortly after the missile breaks through the

surface The use of the aerospike allowed a much blunter nose shape, providing

increased internal volume for payload and propulsion without increasing the drag.

This has the advantage over a structural aerospike that the air density is lower than

that behind a shock wave providing increased drag reduction. Aerospace Sciences

Meeting it was reported that tests were performed at an aerospike-protected missile

dome to Mach 6, obtaining quantitative surface pressure and temperature-rise data

on the feasibility of using aerospikes on hypersonic missiles.

FIG 1.1 Aero spike

1.6 SHOCK WAVE

A shock wave is a type of propagating disturbance. Like an ordinary wave, it

carries energy and can propagate through a medium (solid, liquid, gas or plasma) or

in some cases in the absence of a material medium, through a field such as

the electromagnetic field. Shock waves are characterized by an abrupt, nearly

discontinuous change in the characteristics of the medium. Across a shock there is

always an extremely rapid rise in pressure, temperature and density of the flow. In

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supersonic flows, expansion is achieved through an expansion fan. A shock wave

travels through most media at a higher speed than an ordinary wave. When a shock

wave passes through matter, the total energy is preserved but the energy which can

be extracted as work decreases and the entropy increases. This, for example, creates

additional drag force on aircraft with shocks.

FIG 1.2 Shock wave

1.6.1 NORMAL SHOCK

In elementary fluid mechanics utilizing ideal gasses, a shock wave is treated as a

discontinuity where entropy increases over a nearly infinitesimal region. Since no

fluid flow is discontinuous, a control volume is established around the shock wave,

with the control surfaces that bound this volume parallel to the shock wave (with

one surface on the pre-shock side of the fluid medium and one on the post-shock

side). The two surfaces are separated by a very small depth such that the shock

itself is entirely contained between them. At such control surfaces, momentum,

mass flux, and energy are constant; within combustion detonations can be modeled

as heat introduction across a shock wave. It is assumed the system is adiabatic (no

heat exits or enters the system) and no work is being done. The Rankine–Hugoniot

conditions arise from these considerations.

Taking into account the established assumptions, in a system where the

downstream properties are becoming subsonic: the upstream and downstream flow

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properties of the fluid are considered isentropic. Since the total amount of energy

within the system is constant, the stagnation enthalpy remains constant over both

regions. Though, entropy is increasing this must be accounted for by a drop in

stagnation pressure of the downstream fluid.

1.6.2 OBLIQUE SHOCK

When analyzing shock waves in a flow field, which are still attached to the

body, the shock wave which is deviating at some arbitrary angle from the flow

direction is termed oblique shock. These shocks require a component vector

analysis of the flow; doing so allows for the treatment of the flow in an orthogonal

direction to the oblique shock as a normal shock.

1.6.3 BOW SHOCK

When an oblique shock is likely to form at an angle which cannot remain on

the surface, a nonlinear phenomenon arises where the shock wave will form a

continuous pattern around the body. These are termed bow shocks. In these cases,

the 1D flow model is not valid and a complex analysis is needed to predict the

pressure forces which are exerted on the surface.

1.6.4 DETACHED SHOCK

These shocks are curved, and form a small distance in front of the body.

Directly in front of the body, they stand at 90 degrees to the oncoming flow, and

then curve around the body. Detached shocks allow the same type of analytic

calculations as for the attached shock, for the flow near the shock. They are a topic

of continuing interest, because the rules governing the shock's distance ahead of the

blunt body are complicated, and are a function of the body's shape. Additionally,

the shock standoff distance varies drastically with the temperature for a non-ideal

gas, causing large differences in the heat transfer to the thermal protection system

of the vehicle. See the extended discussion on this topic at Atmospheric reentry.

These follow the "strong-shock" solutions of the analytic equations, meaning that

for some oblique shocks very close to the deflection angle limit, the downstream

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Mach number is subsonic. See also bow shock or oblique shock. Such a shock

occurs when the maximum deflection angle is exceeded. A detached shock is

commonly seen on blunt bodies, but may also be seen on sharp bodies at low Mach

numbers.

1.6.5 ATTACHED SHOCK

These shocks appear as attached to the tip of sharp bodies moving at

supersonic speeds. Examples: Supersonic wedges and cones with small apex angles.

The attached shock wave is a classic structure in aerodynamics because, for a

perfect gas and inviscid flow field, an analytic solution is available, such that the

pressure ratio, temperature ratio, angle of the wedge and the downstream Mach

number can all be calculated knowing the upstream Mach number and the shock

angle. Smaller shock angles are associated with higher upstream Mach numbers,

and the special case where the shock wave is at 90° to the oncoming flow (Normal

shock), is associated with a Mach number of one. These follow the "weak-shock"

solutions of the analytic equations.

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CHAPTER 2

LITERATURE SURVEY

2.1 EXPERIMENTAL RESULTS ON THE FEASIBILITY OF AN

AEROSPIKE FOR HYPERSONIC MISSILES (Lawrence D. Huebner, Anthony

M. Mitchell, Ellis J. Boudreaux)

A series of wind tunnel tests have been performed on an aerospike-protected

missile dome at a Mach number of 6 to obtain quantitative surface pressure and

temperature-rise data, as well as qualitative flow visualization data. These data were

used to determine aerospike concept feasibility and will also provide a database to

be used for calibration of computational fluid dynamics codes. Data were obtained

on the hemispherical missile dome with and without an aerospike that protrudes

ahead of the dome along the axisymmetric center line. Data were obtained on two

models (one pressure, one temperature) in the NASA Langley 20-Inch Mach 6

Tunnel at a free-stream Reynolds number of 8.0x106/ft and angles of attack from 0

to 40 degrees. Surface pressure and temperature-rise results indicate that the

aerospike is effective for very low angles of attack (<5 degrees) at Mach 6. Above 5

degrees, impingement of the aerospike bow shock and the flow separation shock

from the recirculation region created by the aerospike causes pressure and

temperature increases on the windward side of the dome which exceed values

observed in the same region with the aerospike removed. Flow characterization

obtained via oil-flow and schlieren photographs provides some insight into the

quantitative surface data results, including vortical flow and shock-wave

impingement.

2.2 FLOW FIELD ANALYSIS OVER AERO-DISC ATTACHED TO

BLUNT-NOSED BODY AT MACH 6 (R. C. Mehta, R. Kalimuthu, E.

Rathakrishnan)

Aero- spike attached to a blunt body significantly alters its flow field and

influences aerodynamic drag at high speeds. The dynamic pressure in the

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recirculation area is highly reduced and this leads to the decrease in the

aerodynamic drag. Consequently, the geometry of the aero-spike has to be

simulated in order to obtain a large conical recirculation region in front of the blunt

body to get beneficial drag reduction. Axisymmetric compressible Navier-Stokes

equations are solved using a finite volume discretization in conjunction with a

multistage Runge-Kutta time stepping scheme. The effect of the various types of

aerospike configurations on the reduction of aerodynamic drag is evaluated

numerically at Mach 6 at a zero angle of attack. The computed density contours

agree well with the schlieren pictures. Additional modification to the tip of the

spike to get the different type of flow field such as formation of shock wave,

separation area and reattachment point are examined, including a conical spike, flat

disk spike and hemispherical disk spike attached to the blunt body. Shock polar is

obtained using the velocity vector plot. The bow shock distance ahead of the

hemispherical and flat-disc is compared with the analytical solution and good

agreement found between them. The influence of the shock wave generated from

the spike, interacting with the reattachment shock is used to understand the cause of

drag reduction.

2.3 MISSILE FOR THE SUPERSONIC RANGE WITH A POROUS FRONT

PIECE

The missile has an aero-spike that extends from a front face surface, where

the aero-spike has a front body i.e. aero-disk, formed with a porous material, whose

open pores form flow channels. The front body has a front surface that is oriented

transverse to a longitudinal axis of the missile. A deflecting unit is provided

downstream of the channels for outwardly deflecting air flowing through the

channels. The aero-spike is formed with a bar, which bears the front body and is

supported by a carrier body and a retaining element.

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2.4 RECENT ADVANCES IN THE AEROTHERMODYNAMICS OF

SPIKED HYPERSONIC VEHICLES (M.Y.M. Ahmed, N. Qin)

Among a variety of design requirements, reducing the drag and aeroheating

on hypersonic vehicles is the most crucial one. Unfortunately, these two objectives

are often conflicting. On one hand, sharp slender forebodies design reduces the drag

and ensures longer ranges and more economic flights. However, they are more

vulnerable to aerodynamic heating. On the other hand, blunt forebodies produce

more drag; however, they are preferred as far as aeroheating is concerned. In

addition, in the context of hypersonic vehicles, blunt geometries are preferred over

slender ones for practical implications such as higher volumetric efficiency, better

accommodation of crew or on-board equipment.

In principle, a blunt vehicle flying at hypersonic speeds generates a strong

bow shock wave ahead of its nose, which is responsible for the high drag and

aeroheating levels. There have been a number of efforts devoted towards reducing

both the drag and the aeroheating by modifying the flowfield ahead of the vehicle's

nose. Of these techniques, using spikes is the simplest and the most reliable

technique. A spike is simply a slender rod attached to the stagnation point of the

vehicle's nose. The spike replaces the strong bow shock with a system of weaker

shocks along with creating a zone of recirculating flow ahead of the forebody thus

reducing both drag and aeroheating.

Since their introduction to the high-speed vehicles domain in the late 1940s,

spikes have been extensively studied using both experimental facilities and

numerical simulation techniques. The present paper is devoted to surveying these

studies and illustrating the contributions of the authors in this field. The paper also

raises some of the areas in the field that need further investigations.

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2.5 SUPERSONIC GUIDED MISSILE HAS FORWARD-DIRECTED

ARRAY OF ROTATING AERO-SPIKES SYNCHRONIZED WITH

INTERNAL RADAR OR INFRARED DETECTOR

A supersonic guided missile has a nose cone with a number of forward-

directed aero-spikes over an e.g. an infrared detector or radar antenna. The aero-

spike array can be rotated around the missile longitudinal axis. The aero-spikes can

describe more than one concentric circle. Their rotation is induced by the oncoming

airflow. The antenna is fixed. The rotation of the aero-spikes is synchronized with

the radar aerial information capture operation.

2.6 WAVE DRAG REDUCTION CONCEPT FOR BLUNT BODIES AT

HIGH ANGLES OF ATTACK

The present investigation is an attempt to improve the aerodynamic

effectiveness of aero-spike located at the nose of supersonic blunt bodies flying at a

wide range of angles of attack (AOA). For this purpose, the use of pivoting spikes,

which can maintain their favorable alignment relative to the incoming flow

independent from the body’s orientation, is proposed. The proof-of-concept

experiments for the pivoting spikes have been conducted in the Ludwieg Tube

Facility at DLR Göttingen at Mach 2, 3 and 5 for angles of attack from 0 to 30

degrees. The model tested is a cylindrical body with a hemispherical nose.

Additionally to the body equipped with a pivoting spike the reference body without

a spike and the body with a conventional fixed spike were investigated. The results

containing shadowgraph visualizations, direct force measurements and infrared heat

flux measurements show the clear advantages of the pivoting spikes.

2.7 WAVE DRAG REDUCTION DUE TO A SELF ALIGNING AERODISK

(Christian Schnepf, Erich Schülein,Oliver Wysocki)

One of the most important aerodynamic design goals was and is the reduction

of aerodynamic drag. No matter whether a flight object is flying with subsonic or

supersonic speed, the drag is limiting flight speed and range. A different approach

in aerodynamic design for different flow regimes arises from the different sources

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of drag. In supersonic flight the wave drag plays the most important role. As a result

a favored round and rather blunt nose in subsonic and transonic flight has a large

drawback in supersonic flight, due to the occurring bow shock. Considering only

aerodynamics, sharp and pointed nose are most beneficial in supersonic flight. But

the available space in a cone or a wedge shaped nose is limited. Therefore it is not

practicable for the integration of avionic or a seeker.

A well known concept of reducing the wave drag while keeping a blunt nose

in supersonic flight is the Aero-spike concept. A thin rod mounted on the tip of a

blunt body is the simplest design of an Aerospike and the beneficial effect on the

drag is investigated since decades. Slight variations of the initial design include

cones, spheres or disks that are additionally mounted on the tip of the rod. In the

ideal case the boundary layer on the rod separates along the whole rod surface due

to the pressure rise over the initial bow shock. The separated boundary layer forms

a shear layer that reattaches under a certain angle on the blunt nose. As a result the

outer flow is deflected and an oblique shock is formed. The shear surface itself also

deflects the oncoming flow like an actual conical body would do and the initial bow

shock is transformed to a weaker conical shock. The conical shock units further

downstream with the reattachment shock. With this simple method a drag reduction

of more than 50 percent can be achieved in comparison with a blunt body. But this

high reduction rates are only possible for very low angles of attack α. As the angle

of attack is increased the effectiveness of the Aerospike is decreases. A favored

shock system is not achievable anymore and at angles of attack > 15°, depending on

the specific case, no drag reduction can be gained due to unfavorable shock A

movable Aerospike that points always into the flow direction even though the main

body has an angle of attack could sustain the beneficial effect in the region of low

and high angles of attack. The point where the effectiveness is close to zero is

shifted to higher α. This paper deals with such an Aerospike, in fact it is just a disk

that is mounted to a frame. On the other end of the frame small wings are attached.

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The aerodynamic forces acting on the wings induce a pitching moment about the

hinge and align the disk with the oncoming flow.

The dynamics and performance of the self-aligning disk concept will be

numerically investigated on generic missile geometry and compared with available

experimental data. Since the Aero disk should be aligned with the oncoming flow

due to aerodynamic forces a 6 DOF flight mechanic tool is coupled with the flow

solver to calculate the pitching motion parameter of the aero disk. A pitching

motion of the disk relative to the missile is realized by the chimera technique.

In the angle of attack of the aero disk α2 is plotted vs. the angle of attack of

the missile. In this test case the missile undergoes a sinusoidal pitching maneuver

with a frequency of f = 5 Hz and angles of attack between α = 0° and α =20° at M =

1.4. The numerical simulation yields to small declination of the disk to the

oncoming flow for high angles of attack. But neglecting this small declination the

self-aligning aero disk shows a good performance. At high angle of attack and also

at high pitching rates the aero disk is aligned to the oncoming flow and a wave drag

reduction is sustained.

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CHAPTER 3

METHODOLOGY

3.1 INTRODUCTION

There are basically three approaches of solving a fluid mechanics problem.

Experimental

Theoretical

Computational

3.1.1 EXPERIMENT

Problem of matching flow conditions n the experimental setup.

Time of experiment due to large amount of energy utilization by the setup.

Large Perturbation on flow due to external atmosphere.

3.1.2 THEORETICAL

The constraints imposed on the theoretical approach are difficulty in solving

large systems of partial differential equations (PDE’s) with more than 2-3

dependant variables.

3.1.3 COMPUTATIONAL

A numerical simulation of the problem is free of the above mentioned

constraints.

3.2 COMPUTATIONAL FLUID DYNAMICS

Computational fluid dynamics is the analysis of systems involving fluid flow,

heat transfer and associated phenomenon such as chemical reactions by means of

computer simulation. The technique is very powerful and spans a wide range of

industrial and non-industrial application areas. Some examples are aerodynamics of

aircraft and vehicles, hydrodynamics of ships, combustion, turbo machinery,

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electrical and electronic engineering, chemical process engineering, external and

internal environmental of buildings’, marine engineering, environmental

engineering, hydrology and oceanography, metrological, biomedical engineering

etc, from the 1960s onwards. The aerospace industry has integrated CFD technique

into design, R&D and manufacture of aircraft and jet engines. Most recently the

method has been applied to the design of internal combustion engines, combustion

chamber of gas turbines and furnaces. Furthermore motor vehicles manufactures

now routinely predict drag forces, under-bonnet airflow and the in-car environment

with CFD. Increasingly CFD is becoming a vital component in the design of

industrial products and processes.

The ultimate aim of development in the CFD field s to provide a capability

comparable to other CAE (computer aided engineering) tools such that as stress

analysis codes. The main reason why CFD has lagged behind s the tremendous

complexity of underlying behavior, which produce a description of the fluid flow is

at the same economical and sufficiently complete.

The availability of affordable high performance computing hardware and the

introduction of user friendly interfere has lead to a recent upsurge of interest and

CFD s poised to make an entry into the under industrial community in the 1990s.

Clearly the investment cost of a CFD capability is not small but the total expense is

not normally great as that of high quality experimental based approaches to fluid

design.

Substantial reduction of lead times and cost of new design

Ability to study systems where controlled experiments are difficult or impossible

to perform) e.g. very large systems). Practically unlimited level of details of

results.

Ability to study the system under conditions at and beyond their normal

performance limits (e.g. safety studies and accidents scenarios).

21

In contrast CFD codes can produce extremely large volumes of results at

virtually no added expense and it is very cheap to perform parametric studies,

for instance to optimize equipment performance.

3.3 FUNDAMENTAL PRINCIPLES OF CFD

The physical aspects of any fluid flow are governed by three fundamental

principles:

Conservation of mass

Conservation of momentum

Conservation of energy

These fundamental principle can be expressed in terms of mathematical

equations, which n there general form or either integral equation or partial

differential equation. CFD is the art of replacing the integral or partial derivatives

(as the case may be) n these equations with discretized algebraic forms, which n

turn are solved to obtain number for the flow field values at discrete points ‘n’ time

and or space.

By discretizing the governing system of PDE’s in to finite difference

equations and solving them numerically the solution to fluid flow problems much

faster and with accurate results, can be obtained. Numerical techniques can be

classified based on the discretization methods applied to the governing methods

applied to the governing PDE’s.

Finite different method

Finite volume method

In the finite difference method, the continuous problem domains discredited

so that the dependent variables exist only at discrete points. Finite differences are

used to arrive at an algebraic representation of the governing PEDs. In the finite

volume method; a control volume of the flow domain is identifier. The control

22

volume remains fixed in the space as the flow passes through it. The conservation

form of governing PDEs is then applied to this control volume. The distinctive

nature of the finite volume approach is that a balance of some physical property is

made on the region in the neighborhood of the grid point.

Computational simulations, combined with experimental testing, afford a

cost-effective means of geometrical modifications reevaluating numerous

geometrical modifications required for developing flight vehicles. Such evaluations

are performed to ensure that the final design will meet requires\d performance

characteristics. Flow solutions computed with CFD codes presents detailed flow

information, which might be too expensive and some cases impossible to obtain in

wind tunnel. Aircraft industry relies heavily on computational methods in design of

new aircraft or in modification of existing one.

In aeronautical applications, the computational; analysis of the aerodynamic

performance off the aircraft requires a multi-step process. First, a geometric

description of the configuration is obtained in discritized form; second, a grid is

generated around the object, which provides a set of points on which the flow field

solution is calculated by solving the appropriate governing equations of fluid

dynamics. Enormous amounts of the flow field solution data for pressure,

temperature and velocity variables are then processed to obtain the aerodynamic

quantities of interest, namely, the lift, drag and moment coefficients and other

parameters required to assess the aircraft’s performance.

3.4 STAGES OF CFD

The main stages in a CFD study are:

3.4.1 PRE-PROCESSING

Problem formulation (governing equation and boundary conditions)

construction of a computational mesh).

23

3.4.2 SOLVING

Numerical solution of the governing equations.

3.4.3 POST PROCESSING:

Plotting and analysis of results.

This is seldom a one-way process- the sequence may be repeated several

times with different meshes to establish the desired accuracy, or with different

values of a parameters to examine sensitivity to that variable.

3.5 FLUENT

FLUENT is a computational fluid dynamics (CFD) software package to

simulate fluid flow problems. It uses the file-volume method and finite difference

method (2D) to solve the governing equations for a fluid. It provides the capability

to use different physical models such as incompressible, invisid or viscous, laminar

or turbulent, etc, geometry and grid generation is done using GAMBIT which is the

preprocessor bundled with FLUENT.

3.6 GAMBIT

GAMBIT is a software package to help analysis and designers build and

mesh models for computational fluid dynamics and other scientific applications.

GAMBIT receives user input by means of its graphical user interface (GUI). The

gambit GUI makes the basic steps of building, meshing and assigning zone types to

a model simple and intuitive, yet it is versatile enough to accommodate a wide

range of modeling application.

24

CHAPTER 4

PRE-PROCESSING IN GAMBIT

4.1 IMPORTNG CATIA FILE

The geometry of the missile is created in CATIA V5.The dimension of the

missile is taken from the journal “EXPERMENTALI NVESTIGATION ON

SPKED BODY IN HYPERSONIC FLOW”. The geometry is saved in step format

to be imported in GAMBIT.

FIG 4.1 GEOMETRY OF MISSILE

The geometry of the missile is imported by,

File>import> step, then Browse to select the desired step file and click

accept. The step file will be imported.

FIG 4.2 GEOMETRY IMPORTED FROM CATIA

25

4.2 CREATING THE FLOW DOMAIN

The flow domain is created by creating vertices and joining them

appropriately to form edges. The flow domain is a semicircle which has a radius of

15 times the diameter of the missile.

The edges are created by joining the vertices. Click the edge creation

command and select the respective vertices to make the edges. To create the arc,

select the arc creation command. Specify the center and end points of the arc and

click accept. The 1st half of the flow domain is created.

The other half is created by copying the edges. Click the move/copy edges

command. Select the check box ‘copy’ and type as ‘reflect’. Define the axis of

reflection as negative Y axis. Then click ok. The full flow domain is created.

FIG 4.3 FLOW DOMAIN CREATION

4.3 FACE CREATION

The edges can be joined together to form faces (which are planar surface in

2D). Two faces are created.

26

4.3.1 CHANGING THE VERTEX TYPE

Select change vertex type command from face mesh. Select the face and the

vertices whose type has to be changed. The vertices shown in the FIGure are

changed to side for the ease of boundary layer meshing. Select the check box

“boundary layer only”.

FIG 4.4 VERTEX TYPE CHANGE

4.3.2 EDGE MESHING

The edge mesh command is selected. The interval count for each edge is

specified to mesh the edge.

4.3.3 BOUNDARY LAYER MESHING

Boundary layers define the spacing of mesh node rows in regions

immediately adjacent to edges and/or faces. They are used primarily to control

mesh density and, thereby, to control the amount of information available from the

computational model in specific regions of interest.

27

To define a boundary layer, you must specify the following information:

Boundary-layer algorithm

Height of the first row of mesh elements

Growth factor—which specifies the height of each succeeding row of

elements

Total number of rows—which defines the depth of the boundary layer

Edge or face to which the boundary layer is attached

Face or volume that defines the direction of the boundary layer

The following are the parameters to be specified for the creating the boundary layer.

First length 0.005

Growth factor 1.2

Number of rows 31

The edges that need boundary layer are selected (the surface of the missile).Click

apply to create the boundary layer.

FIG 4.5 BOUNDARY LAYER FORMATION

28

4.4 MESHING THE MODEL

The mesh sub pad contains command buttons that allow performing mesh

operations involving boundary layers, edges, faces, volumes and groups.

4.5 FACE MESHING COMMANDS

4.5.1 SPECIFYING THE FACES

Gambit allows specifying any face for a face meshing operation; however,

the shape and topological characteristics of the face, as well as the vertex type

associated with the face, determines the type(s) of mesh schemes(s) that can be

applied to the face.

4.5.2 SPECIFYING THE MESHING SCHEME

To specify the face meshing, it is required to specify two parameters.

Elements

Type

The element parameter defines the shape(s) of the element that are used to mesh the

face. The type parameter defines the pattern of mesh elements on the face.

4.5.3 EDGE MESH INTERVALS

If you grade or mesh the edges of a face prior to creating a mapped mesh,

you must specify the edge mesh intervals such that the numbers of mesh intervals

on opposing sides of the logical rectangle are equal. For meshing purposes, a single

side of the logical rectangle consists of all edges that exist between any two End

type vertices.

4.5.4 SPECIFYING SPACING

The interval length ratio, R, is a function of both the edge length, L, and the

number of intervals, n. gambit provides three different ways to specify the number

if intervals on an edge.

29

Interval count

Interval size

Shortest edge (%)

INTERVAL COUNT

When the interval count option is selected on the input, the actual number of

mesh intervals to be placed on the edge is to be given. Gambit grades or meshes the

edge with enough nodes to result in the specified number of intervals. That is

m=n+1

Where m is the number of mesh nodes on the edge, including the end points

and n is the interval count.

INTERVAL SIZE

When the interval size option is selected, you must input an interval length.

Gambit uses the interval length to determine the total number of intervals on the

edge according to the following equation:

n=L/d

Where n is the number of internals on the edge, lays the edge length and d is

the interval size (user input). If n is non integer, gambit rounds to the nearest whole

number of the intervals on the edge.

4.6 QUAD: MAP MESHING SCHEME

When you apply the Quad: Map meshing scheme to a face, GAMBIT meshes

the face using a regular grid of quadrilateral face mesh elements, The Quad: Map

meshing scheme is applicable primarily to faces that are bounded by four or more

edges, however not all such faces are suitable for mapping. To be “mappable,” a

face must not violate restrictions related to the following parameters:

Vertex types

30

Edge mesh intervals

The vertex-type and edge mesh interval restrictions for the Quad: Map meshing

Scheme is as follows.

4.6.1 VERTEX TYPES

To be map able, a face must represent a logical rectangle. (For the exception

to this criterion, see NOTE (1), below.) To represent a logical rectangle, a face must

include four End type vertices, and all other vertices associated with the face must

be designated as Side type vertices.

FIG 4.6 MAP MESSING OF GEOMETRY

4.7 SPECIFYING BOUNDARY TYPES IN GAMBIT

SPECIFY THE ZONE TYPE

Zone types define the physical and operational characteristics of the model at

its boundaries and within specific regions of the domain.

Boundary types

Continuum types

31

Boundary type specifications define the characteristics of the model and its

external and internal boundaries. Continuum type specifications definer the

characteristics of the model within specified regions of its domain.

FIG 4.7 BOUNDARY CONDTIONS

4.8 EXPORTING THE MESH

After creating the boundary entities it is exported to the mesh that is 2D mesh

in fluent.

32

CHAPTER 5

POST-PROCESSING IN FLUENT

5.1 SETUP PROBLEM IN FLUENT

The flow over the missile is simple 2D problem. In addition the overall

problem geometry, grid and boundary locations and types have already been

defined in gambit. We can import the mesh file with all its information in fluent.

5.1.1 READING MESH FILES

Mesh files are created using GAMBIT. From FLUENT's point of view, a

mesh file is a subset of a case file. The mesh file contains the coordinates of all the

nodes, connectivity information that tells how the nodes are connected to one

another to form faces and cells, and the zone types and numbers of all the faces.

The mesh file does not contain any information on boundary conditions, flow

parameters, or solution parameters.

To import a mesh file select,

File > Read > Mesh

5.2 CHANGING THE SCALE OF MESH

The mesh is created in unit mm. The mesh is scaled to convert the units into

meter. Select Mesh > Scale.

5.3 CHECKING THE MESH

The information about the mesh file can be viewed by selecting

Mesh > Check

FLUENT will display the details of the mesh file on the screen.

33

5.4 DEFINING THE SOLVER:

The problem considered here is high speed compressible flow so we choose

density based solver.

5.4.1 DENSITY-BASED SOLVER

The density-based solver in FLUENT solves the governing equations of

continuity, momentum, and (where appropriate) energy and species transport

simultaneously as a set, or vector, of equations. Governing equations for additional

scalars will be solved sequentially (i.e., segregated from one another and from the

coupled set). Two algorithms are available for solving the coupled set of equations,

the coupled-explicit formulation and the coupled-implicit formulation, Select

Models > Solver

Solver -Density based

Formulation -Explicit

Space -2D

Time -Steady

Velocity formulation -Absolute

Gradient option -Green Gauss cell based

Porous formulation -Superficial velocity,

Select Define > Models > Energy equation

Enable the energy equation because the problem involves compressible flow.

5.4.2 DEFINING THE TYPE OF MATERIAL

The material used here is fluid (air). To specify the material type select

Define > Materials

34

The selection of density in FLUENT is very important. Set the density

relationship based on your flow regime. For compressible flows, the ideal gas law is

the appropriate density relationship.

To set the operating condition select Define > Operating conditions

Operating pressure= 0Pa

5.4.3 SETTING THE BOUNDARY CONDITIONS

Boundary conditions specify the flow and thermal variables on the

boundaries of your physical model. They are, therefore, a critical component of

your FLUENT simulations and it is important that they are specified appropriately.

Select Define > Boundary conditions

In the boundary conditions panel the zones and types are displayed. Select

the zone that you wish to modify. Select the zone, the zone type and click the set

button.

5.4.4 PRESSURE FAR-FIELD BOUNDARY CONDITIONS

Pressure far-field conditions are used in FLUENT to model a free-stream

condition at infinity, with free-stream Mach number and static conditions being

specified. The pressure far-field boundary condition is often called a characteristic

boundary condition, since it uses characteristic information (Riemann invariants) to

determine the flow variables at the boundaries. This boundary condition is

applicable only when the density is calculated using the ideal-gas law.

The inputs to pressure far field are

Gauge pressure 21.95Pa

Mach number 6

Temperature 247.021

The fluid is air. Set the motion type as stationary.

35

5.4.5 PRESSURE OUTLET BOUNDARY CONDITIONS

Pressure outlet boundary conditions require the specification of a static

(gauge) pressure at the outlet boundary. The value of the specified static pressure is

used only while the flow is subsonic. Should the flow become locally supersonic,

the specified pressure will no longer be used; pressure will be extrapolated from the

flow in the interior. All other flow quantities are extrapolated from the interior. A

set of “backflow” conditions are also specified should the flow reverse direction at

the pressure outlet boundary during the solution process. Convergence difficulties

will be minimized if you specify realistic values for the backflow quantities.

5.4.6 WALL BOUNDARY CONDITIONS

Wall boundary conditions are used to bound fluid and solid regions. In

viscous flows, the no-slip boundary condition is enforced at walls by default, but

you can specify a tangential velocity component in terms of the translational or

rotational motion of the wall boundary, or model a “slip" wall by specifying shear.

(You can also model a slip wall with zero shears using the symmetry boundary

type, but using a symmetry boundary will apply symmetry conditions for all

equations). The shear stress and heat transfer between the fluid walls are computed

based on the flow details in the local flow field.

For our problem we specify “no slip” boundary condition and the wall is stationary.

5.5 SOLVING THE PROBLEM

The input for the problem are specified, next we should describe the convergence

criteria.

Solve > Controls > Solution

The equations are flow and modified turbulent viscosity. The Courant number b

default is 1 and modified turbulent viscosity is 0.8 Then click ok.

To initialize the solving process select,

36

Solve > Initialize > Initialize

Select the zone as Far field, the initial values will be computed. Without initializing

the problem the iterating process cannot be carried out.

The criteria for convergence have to be specified to find the end result of our

problem. Select

Solve > Monitors > Residual

Click the print option to display the values of residual during iteration. Click the

convergence criteria for continuity equation, energy equation, momentum equation

and nut. Select

Solve > Monitors > Force

Click the print option and force as Drag, the zone is wall

The X component and y component is specified according to the angle of attack

requirements.

To check the convergence we monitor the pressure at the outlet. Select

Solve > Monitors > Surface

Select the check boxes print and plot. Then click define.

Specify the following

Report type -area weighted average

Report of -total pressure

Surface -outlet

The surface monitor will plot the total pressure at the outlet of the flow domain and

display the same on the screen.

To carry out the iteration at the user specified input, select

37

Report > Reference values

Specify the zone far field as specified in the initialization.

The final step is to begin the iteration process. Select

Solve > Iterate

Specify the number of iterations and reporting intervals. Click iterate and the

calculation begins. When the convergence criteria are met the message is displayed

as “solution is converged”.

After the solution is converged the contour plot, velocity vector and the XY plot are

taken.

Select Display > Contours, to take the contour plot

Display > Vectors, to get the vector plot.

Plot > XY plot, to get the solution XY plots for various parameters.

5.6 SAVING THE FILE

To save the results of iteration select

File > Write > Case and data.

The post processing operation in Fluent is thus complete.

38

CHAPTER 6

ANALYSIS OF MISSILE WITHOUT AEROSPIKE

FIG.6.1 CONTOUR OF ATATIC PRESSURE (MISSILE WITHOUT

AEROSPIKE)

FIG.6.2 CONTOUR OF STATIC TEMPERATURE (MISSILE WITHOUT

AEROSPIKE)

39

CHAPTER 7

CONTOUR OF STATIC PRESSURE

7.1FIXED SPIKE (l/d=1) 7.2 MOVABLE SPIKE (l/d=1)

FIG.A STATIC PRESSURE FIG.A STATIC PRESSURE

CONTOUR AT 5 DEG AOA CONTOUR AT 5 DEG AOA

FIG.B STATIC PRESSURE FIG.B STATIC PRESSURE

CONTOUR AT 10 DEG AOA CONTOUR FOR AT 10 DEG AOA

FIG.C STATIC PRESSURE FIG.C STATIC PRESSURE

CONTOUR AT 15 DEG AOA CONTOUR AT 15 DEG AOA

40

7.3 FIXED SPIKE (l/d=1.5) 7.4 MOVABLE SPIKE (l/d=1.5)

FIG.A STATIC PRESSURE FIG.A STATIC PRESSURE

CONTOUR AT 5 DEG AOA CONTOUR FOR AT 5 DEG AOA

FIG.B STATIC PRESSURE FIG.B STATIC PRESSURE

CONTOUR AT 10 DEG AOA CONTOUR AT 10 DEG AOA

FIG.C STATIC PRESSURE FIG.C STATIC PRESSURE

CONTOUR AT 15 DEG AOA CONTOUR AT 15 DEG AOA

41

7.5 FIXED SPIKE (l/d=2) 7.6 MOVABLE SPIKE (l/d=2)

FIG.A STATIC PRESSURE FIG.A STATIC PRESSURE

CONTOUR AT 5 DEG AOA CONTOUR AT 5 DEG AOA

FIG.B STATIC PRESSURE FIG.B STATIC PRESSURE

CONTOUR AT 10 DEG AOA CONTOUR AT 10 DEG AOA

FIG.C STATIC PRESSURE FIG.C STATIC PRESSURE

CONTOUR AT 15 DEG AOA CONTOUR AT 15 DEG AOA

42

CHAPTER 8

CONTOURS OF STATIC TEMPERATURE

8.1 FIXED AEROSPIKE(l/d=1) 8.2 MOVABLE AEROSPIKE(l/d=1)

FIG.A STATIC TEMPERATURE FIG.A STATIC TEMPERATURE

CONTOUR AT 5 DEG AOA CONTOUR AT 5 DEG AOA

FIG.B STATIC TEMPERATURE FIG.B STATIC TEMPERATURE

CONTOUR AT 10 DEG AOA CONTOUR AT 10 DEG AOA

FIG.C STATIC TEMPERATURE FIG.C STATIC TEMPERATURE

CONTOUR AT 15 DEG AOA CONTOUR AT 15 DEG AOA

43

8.3 FIXED AEROSPIKE(l/d=1) 8.4 MOVABLE AEROSPIKE(l/d=1)

FIG .A STATIC.TEMPERATURE FIG .A STATIC TEMPERATURE

CONTOUR AT 5 DEG AOA CONTOUR AT 5 DEG AOA

FIG.B STATIC TEMPERATURE FIG.B STATIC TEMPERATURE

CONTOUR AT 5 DEG AOA CONTOUR AT 5 DEG AOA

FIG.C STATIC TEMPERATURE FIG.C STATIC TEMPERATURE

CONTOUR AT 15 DEG AOA CONTOUR AT 15 DEG AOA

44

8.5 FIXED AEROSPIKE(l/d=1) 8.6 MOVABLE AEROSPIKE(l/d=1)

FIG.A STATIC TEMPERATURE FIG.A STATIC TEMPERATURE

CONTOUR AT 5 DEG AOA CONTOUR AT 5 DEG AOA

FIG.B STATIC TEMPERATURE FIG.B STATIC TEMPERATURE

CONTOUR AT 10 DEG AOA CONTOUR AT 10 DEG AOA

FIG.C STATIC TEMPERATURE FIG.C STATIC TEMPERATURE

CONTOUR AT 15 DEG AOA CONTOUR AT 15 DEG AOA

45

CHAPTER 9

COEFFICIENT OF LIFT Vs ANGLE OF ATTACK

FIG.9.1 Cl Vs α FOR FIXED AEROSPIKE

FIG.9.2 CL Vs α FOR MOVABLE AEROSPIKE

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

5 10 15

CL

angle of attack

CL Vs α for fixed aerospike

l/d=1

l/d=2

l/d=1.5

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

5 10 15

CL

α

CLVs α for movable aerospike

l/d=1

l/d=1.5

l/d=2

46

FIG.9.3 CL Vs α FOR l/d=2

FIG.9.4 CL Vs α FOR l/d=1.5

FIG.9.5 CL Vs α FOR l/d=1

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

5 10 15

CL

α

CL Vs α

l/d=2(fixed)

l/d=2(movable)

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

5 10 15

CL

α

CL Vs α

l/d=1.5(fixed)

l/d=1.5(movable)

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

5 10 15

CL

α

CL Vs α

l/d=1(fixed)

l/d=1(movable)

47

CHAPTER 10

COEFFICIENT OF DRAG Vs ANGLE OF ATTACK

FIG 10.1 Cd Vs α FOR FIXED AEROSPIKE

FIG.10.2 Cd VS Α FOR MOVABLE AEROSPIKE

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

4.00E-02

4.50E-02

5 10 15

Cd

angle of attack

Cd Vs α for fixed aerospike

l/d=1

l/d=2

l/d=1.5

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

5 10 15

Cd

α

Cd Vs α for movable aerospike

l/d=1

l/d=1.5

l/d=2

48

FIG 10.3 Cd Vs α FOR l/d=2

FIG.10.4 Cd Vs α FOR l/d=1.5

FIG.10.5 Cd VS Α FOR L/D=1

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5 10 15

Cd

α

Cd Vs α

l/d=2(fixed)

l/d=2(movable)

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

5 10 15

Cd

α

Cd Vs α

l/d=1.5(fixed)

l/d=1.5(movable)

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

5 10 15

Cd

α

Cd Vs α

l/d=1(fixed)

l/d=1(movable)

49

CHAPTER 11

STATIC PRESSURE DISTRIBUTION OVER THE MISSILE

11.1.FIXED AEROSPIKE

FIG.A STATIC PRESSURE DISTRIBUTION L/D=1

FIG.B STATIC PRESSURE DISTRIBUTION L/D=1.5

FIG.C STATIC PRESSURE DISTRIBUTION L/D=2

50

11.2 MOVABLE AEROSPIKE

FIG.A STATIC PRESSURE DISTRIBUTION L/D=1

FIG.B STATIC PRESSURE DISTRIBUTION L/D=1.5

FIG.C STATIC PRESSURE DISTRIBUTION L/D=2

51

CHAPTER 12

STATIC TEMPERATURE DISTRIBUTION OVER THE MISSILE

12.1 FIXED AEROSPIKE

FIG.a STATIC TEMPERATURE DISTRIBUTION l/d=1

FIG.b STATIC TEMPERATURE DISTRIBUTION l/d=1.5

FIG.c STATIC TEMPERATURE DISTRIBUTION l/d=2

52

12.2 MOVEABLE AEROSPIKE

FIG.a STATIC TEMPERATURE DISTRIBUTION l/d=1

FIG.b STATIC TEMPERATURE DISTRIBUTION l/d=1.5

FIG.c STATIC TEMPERATURE DISTRIBUTION l/d=2

53

FIG.12.3 FLOW RECIRCULATION AT THE NOSE CONE

TABLE.1 CL AND CD FOR MISSILE WITH FIXED AERO SPIKE (l/d=1)

Angle of attack coefficient of lift coefficient of drag

5 1.26E-02 2.81E-02

10 2.59E-02 3.30E-02

15 4.00E-02 4.19E-02

TABLE.2 CL AND CD FOR MISSILE WITH FIXED AERO SPIKE (l/d=1.5)

Angle of attack coefficient of lift coefficient of drag

5 1.34E-02 2.59E-02

10 2.79E-02 3.07E-02

15 4.39E-02 3.97E-02

54

TABLE.3 CL AND CD FOR MISSILE WITH FIXED AERO SPIKE (l/d=2)

Angle of attack coefficient of lift coefficient of drag

5 1.41E-02 2.47E-02

10 3.07E-02 3.02E-02

15 4.78E-02 3.66E-02

TABLE.4 CL AND CD FOR MISSILE WITH MOVABLE AERO SPIKE (l/d=1)

Angle of attack coefficient of lift coefficient of drag

5 6.84E-03 2.70E-02

10 1.45E-02 2.88E-02

15 2.36E-02 3.18E-02

TABLE.5 CL AND CD FOR MISSILE WITH MOVABLE AERO SPIKE (l/d=1.5)

Angle of attack coefficient of lift coefficient of drag

5 5.84E-03 2.46E-02

10 1.23E-02 2.59E-02

15 2.01E-02 2.84E-02

TABLE.6 CL AND CD FOR MISSILE WITH MOVABLE AERO SPIKE (l/d=2)

Angle of attack coefficient of lift coefficient of drag

5 5.42E-03 2.32E-02

10 1.14E-02 2.43E-02

15 1.83E-02 2.66E-02

55

CHAPTER 13

DISCUSSION FOR RESULTS

The analysis has been carried out for missile without aero spike, missile with

aero spike of l/d ratios 1, 1.5 and 2 at angles of attack 5˚, 10˚ and 15˚ respectively.

From the contour plot we can the formation of bow shockwave at the nose of

the missile. The pressure and temperature downstream the bow shock is very high.

The shockwave at the tip of the nose cone is locally a normal shock. The flow

properties change drastically downstream the normal shock. The blunt nosecone

produces very high drag force due to these reasons.

The use of aero spike has made the strong bow shock into weaker expansion

waves. The pressure and temperature at the tip of the nose is very high due to the

local normal shock. The nosecone is well protected from very high temperature due

to the presence of aero spike. The flow properties downstream the oblique shock is

not altered to a great extent. The recirculation region at the point of attachment of

the aero spike to the nosecone reduces the drag produced.

The flow recirculation along the length of the aerospike pushes the

shockwave away from the missile. The surface of the missile and the oblique

shockwave forms a diverging passage for the air flow. Supersonic flow will be

accelerated in a diverging passage.

In case of the movable aerospike, the air flow recirculation is more on the

windward side of the missile. Hence the pressure, temperature is reduced and the

drag produced is less when compared to the fixed aerospike.

The CL Vs α graph shows that, the coefficient of drag increases with angle of

attack. The coefficient of drag is also reduced.

56

CHAPTER 14

CONCLUSION

The CFD analysis for different cases such as for missile without spike,

missile with aero spike of l/d ratios 1, 1.5 and 2 at angles of attack 5˚, 10˚ and 15˚

have been carried out. The coefficient of lift and coefficient of drag has been found

for each case. From the results, it is proved that the use of movable aero spike that

aligns itself with the direction of flow produces less drag force than the missile with

fixed spike and the missile without spike. The length to diameter ratio which gives

the maximum drag reduction is l/d=2. When this critical length of the spike is

increased it will lead to adverse effects.

FUTURE ENHANCEMENT

Further study on this project can be made for angles of attack greater than

15˚. The mechanism to deflect the spike to align it with the flow direction can be

developed. The pitching moment of the missile having aero spike must be

calculated in order to optimize the missile. Modifications can be made to the disc

shape of the aero spike which will give the least drag penalty.

57

CHAPTER 15

REFERENCES

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65-74.

3. FUJITA, M. and KUBOTA, H. Numerical simulation of flow field over a

spiked-nose, Computational Fluid Dynamics J, 1992, 1, (2), pp 187195.

4. GUENTHER, R.A. and REDING, J.P. Fluctuating pressure environment of a

drag reduction spike, J Spacecraft and Rockets, 1977, 44, (12), pp 705-710.

cylinder at a Mach number of 6.8, NASA TN D-118, December Fluid

Mechanics, 1960, 8, (4), pp 584-592.

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7. MAULL, D.J. Hypersonic flow over axially symmetric spiked bodies, J

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9. MEHTA, R.C. Heat transfer study of high speed flow over a spiked blunt

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6.80, AIAA paper 2000-0344, January 2000.

58

11. MILICEV, S.S., PAVLOVIC, M.D., RISTIC, S. and VITIC, A. On the

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hypersonic flow, AIAA paper 2001-1828, April 2001.

13. REDING, J.P., GUENTHER, R.A. and RICHTER, B.J. Unsteady

aerodynamic considerations in the design of a drag-reduction spike, J

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investigation of supersonic flows around a spiked blunt body, AIAA paper

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