Aircraft Propulsion-2

8/13/2019 Aircraft Propulsion-2

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Unit-1

AIRCRAFT GAS TURBINES

Impulse and reaction blading of gas turbines Velocity triangles and power output Elementary

theory Vortex theory Choice of blade profile, pitch and chord Estimation of stage

performance Limiting factors in gas turbine design- Overall turbine performance Methods ofblade cooling Matching of turbine and compressor Numerical problems.

Axial and radial flow turbines

As with the compressor, there are two basic types of turbineradial flow and axial flow. The

vast majority of gas turbines employ the axial flow turbine.

The radial turbine can handle low mass flows more efficiently than the axial flow machine and

has been widely used in the cryogenic industry as a turbo-expander, and in turbochargers forreciprocating engines. Although for all but the lowest powers the axial flow turbine is normally

the more efficient, when mounted back-to-back with a centrifugal compressor the radial turbine

offers the benefit of a very short and rigid rotor. This configuration is eminently suitable for gas

turbines where compactness is more important than low fuel consumption. Auxiliary power units

for aircraft (APUs), generating sets of up to 3 MW, and mobile power plants are typical

applications.

Impulse and Reaction Turbine

www.Vidyarthiplus.com



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Work can be extracted from a gas at a higher inlet pressure to the lower back pressure by

allowing it to flow through a turbine. In a turbine as the gas passes through, it expands. The work

done by the gas is equivalent to the change of its enthalpy.

It is a well known fact that the turbines operate on the momentum principle. Part of the energy of

the gas during expansion is converted into kinetic energy in the flow nozzles. The gas leavesthese stationary nozzles at a relatively higher velocity. Then it is made to impinge on the blades

over the turbine rotor or wheel. Momentum imparted to the blades turns the wheel. Thus, the two

primary parts of the turbine are,

(i) The stator nozzles, and

(ii) the turbine rotor blades.

Normally a turbine stage is classified as

(i) an impulsion stage, and

(ii) a reaction stage

An impulse stage is characterized by the expansion of the gas which occurs only in the stator

nozzles. The rotor blades act as directional vanes to deflect the direction of the flow. Further,

they convert the kinetic energy of the gas into work by changing the momentum of the gas more

or less at constant pressure.

A reaction stage is one in which expansion of the gas takes place both in the stator and in the

rotor.

The function of the stator is the same as that in the impulse stage, but the function in the

rotor is two fold.

(i) the rotor converts the kinetic energy of the gas into work, and

(ii) contributes a reaction force on the rotor blades.

The reaction force is due to the increase in the velocity of the gas relative to the blades. This

results from the expansion of the gas during its passage through the rotor.

A Single Impulse Stage

Impulse machines are those in which there is no change of static or pressure head of the fluid in

the rotor. The rotor blades cause only energy transfer and there is no energy transformation. The

energy transformation from pressure or static head to kinetic energy or vice versa takes place in

fixed blades only. As can be seen from the below figure that in the rotor blade passage of an

impulse turbine there is no acceleration of the fluid, i.e., there is no energy transformation.




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Hence, the chances are greater for separation due to boundary layer growth on the blade surface.

Due to this, the rotor blade passages of the impulse machine suffer greater losses giving lower

stage efficiencies.

The paddle wheel, Pelton wheel and Curtis stem turbine are some examples of impulse

machines.




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A Single Reaction Stage

The reaction stages are those, in which, changes in static or pressure head occur both in the rotor

and stator blade passages. Here, the energy transformation occurs both in fixed as well as

moving blades. The rotor experiences both energy transfer as well as energy transformation.

Therefore, reaction turbines are considered to be more efficient. This is mainly due to continuous

acceleration of flow with lower losses.

The degree of reactionof a turbomachine stage may be defined as the ratio of the static or

pressure head change occurring in the rotor to the total change across the stage.

Note: Axial-flow turbine with 50% reaction have symmetrical blades in their rotor and stators. It

may be noted that the velocity triangles at the entry and exit of a 50% reaction stage are also

symmetrical.




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Velocity Triangles of a Single Stage Machine

The flow geometry at the entry and exit of a turbomachine stage is described by the velocity

triangles at these stations. The velocity triangles for a turbomachine contain the following three

components.

1. The peripheral / whirl / tangential velocity (u) of a rotor blades2. The absolute velocity (c ) of the fluid and3. The relative velocity (w or v) of the fluid

These velocities are related by the following well-known vector equation.

This simple relation is frequently used and is very useful in drawing the velocity triangles

for turbomachines.




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The notation used here to draw velocity triangles correspond to the x-y coordinates; the

suffix (a or ) identifies components in the axial direction and suffix (t) refers to

tangential direction. Air angles in the absolute system are denoted by alpha (), where as

those in the relative system are represented by beta ().

Since the stage is axial, the change in the mean diameter between its entry and exit can be

neglected. Therefore, the peripheral or tangential velocity (u) remains constant in the velocity

triangles.

It can be proved from the geometry that

ct2 + ct3 = wt2+ wt3

It is often assumed that the axial velocity component remains constant through the stage. For

such condition,

ca= ca1= ca2= ca3




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For constant axial velocity yields a useful relation,

tan 2+ tan 3= tan 2+ tan 3

Expression for Work Output

Though force and torque are exerted on both stationary and moving blades alike, work can only

be done on the moving rotor blades. Thus the rotor blades transfer energy from the fluid to the

shaft. The stage work in an axial turbine (u3= u2= u) can be written as,

W = u2ct2 u3ct3

= u{ct2- (-ct3)}

= u(ct2-ct3)

{Note: Usually this equation will be written with a minus sign between c t2and ct3. Whenever this

is written with a plus sign it is implied that ct3is negative}

This equation can also be expressed in another form,

+=

u

c

u

cuW tt 32

2

The first term

u

ct2 in the bracket depends on the nozzle or fixed angle (2) and the ratio

2c

u= . The contribution of the second term

u

ct3 to the work is generally small. It is also

observed that the kinetic energy of the fluid leaving the stage is greater for larger values of ct3.

The leaving loss from the stage is minimum when c t3 = 0, i.e., when the discharge from the stage

is axial (c3 = ca3). However, this condition gives lesser stage work as can be seen from the above

two equations.




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Blade loading and Flow coefficients

Performance of turbomachines are characterized by various dimensionless parameters. For

example, loading coefficient () and the flow coefficient () have been defined as,

u

c

u

W

a=

=

2

Since the work, W in the above equation is frequently referred to as the blade or stage work, the

coefficient, would also be known as the blade or stage loading coefficient.

For constant axial velocity (ca), it can be shown that

= (tan 2+ tan 3) = (tan 2+ tan 3)

The plots are useful in comparing the performances of various stages of different sizes and

geometries.

Blade and Stage efficiencies

Even though the blade and stage work (outputs) are the same, the blade and the stage efficiencies

need not be equal. This is because the energy inputs to the rotor blades and the stage (fixed bladering plus the rotor) are different. The blade efficiency is also known as the utilization factor ( )

which is an index of the energy utilizing capability of the rotor blades. Thus,

= b

= Rotor blade work / Energy supplied to the rotor blades

= W / Erb

W = u2 ct2+ u3 ct3

( ) ( ) ( )223

3

2

3

2

2

2

3

2

22

1

2

1

2

1wwuucc ++=

The energy supplied to the rotor blades is the absolute kinetic energy in the jet at the entry plus

the kinetic energy change within the rotor blades.




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( ) ( )233

2

2

2

2

3

2

22

1

2

1

2

1uuwwcErb ++=

For axial machines, u = u2= u3

( ) ( )( )22

2

3

2

2

2

2

2

3

2

3

2

2

wwc

wwccb

+

+==

Maximum utilization factor for a single impulse stage.

2

2

32

2

1

)(

c

ccu tt +=

After rearranging the terms, we have

)sin(42

2 ==b

This shows that the utilization factor is a function of the blade-to-gas speed ratio and the nozzle

angle.




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The above Figures show the velocity triangles for one axial flow turbine stage and the

nomenclature employed. The gas enters the row of nozzle blades (These are also known as 'stator

blades' and 'nozzle guide vanes') with a static pressure and temperature, P1, T1and a velocity C1

is expanded to P2,T2and leaves with an increased velocity C2at an angle 2. The rotor blade inlet

angle will be chosen to suit the direction 2of the gas velocity V2relative to the blade at inlet.

2and V2are found by vectorial subtraction of the blade speed U from the absolute velocity C2.

After being deflected, and usually further expanded, in the rotor blade passages, the gas leaves at

P3, T3with relative velocity V3 at angle 3. Vectorial addition of U yields the magnitude and

direction of the gas velocity at exit from the stage, C3and 3. 3is known as the swirl angle.

dimensional effects.




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Vortex theory

It was pointed out earlier that the shape of the velocity triangles must vary from root to tip of the blade

because the blade speed U increases with radius. Another reason is that the whirl component in the flow

at outlet from the nozzles causes the static pressure and temperature to vary across the annulus. With a

uniform pressure at inlet, or at least with a much smaller variation because the whirl component is

smaller, it is clear that the pressure drop across the nozzle will vary giving rise to a corresponding

variation in efflux velocity C2. Twisted blading designed to take account of the changing gas angles is

called vortex blading.

It has been common steam turbine practice, except in low-pressure blading where the blades are

very long, to design on conditions at the mean diameter, keep the blade angles constant from root to tip,

and assume that no additional loss is incurred by the variation in incidence along the blade caused by the

changing gas angles. Comparative tests have been conducted by the earlier researchers on a single-stage

gas turbine of radius ratio 1-37, using in turn blades of constant angle and vortex blading. The results

showed that any improvement in efficiency obtained with vortex blading was within the margin of

experimental error. This contrasts with similar tests on a 6-stage axial compressor, by another researcher,

which showed a distinct improvement from the use of vortex blading. This was, however, not so

much an improvement in efficiency (of about 1-5 per cent) as in the delay of the onset of surging

which of course does not arise in accelerating flow. It appears, therefore, that steam turbine

designers have been correct in not applying vortex theory except when absolutely necessary at

the LP end. They have to consider the additional cost of twisted blades for the very large number

of rows of blading required, and they know that the Rankine cycle is relatively insensitive to

component losses. Conversely, it is not surprising that the gas turbine designer, struggling to

achieve the highest possible component efficiency, has consistently used some form of

vortex blading which it is felt intuitively must give a better performance however small.

Vortex theory has been outlined earlier by Cohen and others where it was shown that if

the elements of fluid are to be in radial equilibrium, an increase in static pressure from

root to tip is necessary whenever there is a whirl component of velocity.Figure 7.8 shows

(see below) why the gas turbine designer cannot talk of impulse or 50 per cent reaction stages.The proportion of the stage pressure or temperature drop which occurs in the rotor must increase

from root to tip. Although Fig. 7.8 refers to a single-stage turbine with axial inlet velocity and no

swirl at outlet, the whirl component at inlet and outlet of a repeating stage will be small

compared with CW2- the reaction will therefore still increase from root to tip, if somewhat less

markedly.




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Choice of blade profile, pitch and chord

The next step is to choose stator and rotor blade shapes which will accept the gas incident upon

the leading edge, and deflect the gas through the required angle with the minimum loss. An

overall blade loss coefficient Y (or A) must account for the following sources of friction loss.

(a) Profile lossassociated with boundary layer growth over the blade profile (including

separation loss under adverse conditions of extreme angles of incidence or high inlet

Mach number).

(b) Annulus lossassociated with boundary layer growth on the inner and outer walls of the

annulus.

(c) Secondary flow lossarising from secondary flows which are always present when a

wall boundary layer is turned through an angle by an adjacent curved surface.

(d) Tip clearance lossnear the rotor blade tip the gas does not follow the intended path,

fails to contribute its quota of work output, and interacts with the outer wall boundary

layer.

The profile loss coefficient Yp is measured directly in cascade tests similar to those described for

compressor blading. Losses (b) and (c) cannot easily be separated, and they are accounted for by

a secondary loss coefficient Ys.




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The tip clearance loss coefficient, which normally arises only for rotor blades, will be denoted by

Yk. Thus the total loss coefficient Y comprises the accurately measured two-dimensional loss Yp,

plus the three-dimensional loss (Ys+Yk) which must be deduced from turbine stage test results.

All that is necessary for our present purpose for finding the choice of blade profile is limited to

the knowledge of the sources of loss.

Figure 7.11 shows a conventional steam turbine blade profile constructed from circular arcs and

straight lines. Gas turbines have until recently used profiles closely resembling this, although

specified by aerofoil terminology.




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Note that the blade profile will be completely determined when (a) the pitch/width ratio (s/w) is

established, and (b) both the camber line angle ' and blade thickness/pitch ratio have been

calculated for various values of x between 0 and 1.




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Turbine Performance

The performance of turbine is limited principally by two factors: compressibility and

stress. Compressibility limits the mass flow that can pass through a given turbine and, stress

limits the wheel speed U. The work per stage depends on the square of the wheel speed.

However, the performance of the engine depends very strongly on the maximum temperature. Of

course, as the maximum temperature increases, the allowable stress level diminishes; hence in

the design of the engine there must be a compromise between maximum temperature and

maximum rotor tip speed U.

For given pressure ratio and adiabatic efficiency, the turbine work per unit mass is proportional

to the inlet stagnation temperature. Since, in addition, the turbine work in a jet or turboshaft

engine is commonly two or three times the useful energy output of the engine, a 1% increase in

turbine inlet temperature can produce a 2% or 3% increase in engine output. This considerable

advantage has supplied the incentive for the adoption of fairly elaborate methods for cooling the

turbine nozzle and rotor blades.

Estimation of stage performance

The last step in the process of arriving at the preliminary design of a turbine stage is to check

that the design is likely to result in values of nozzle loss coefficient and stage efficiency which

were assumed at the outset. If not, the design calculations may be repeated with more probable

values of loss coefficient and efficiency. When satisfactory agreement has been reached, the

final design may be laid out on the drawing board and accurate stressing calculations can be

performed. Before proceeding to describe a method of estimating the design point performanceof a stage, however, the main factors limiting the choice of design, which we have noted during

the course of the worked example, will be summarized. The reason we considered a turbine for a

turbojet engine was simply that we would thereby be working near those limits to keep size and

weight to a minimum. The designer of an industrial gas turbine has a somewhat easier task: he

will be using lower temperatures and stresses to obtain a longer working life, and this means

lower mean blade speeds, more stages, and much less stringentaerodynamic limitations. A power

turbine, not mechanically coupled to the gas generator, is another case where much less difficulty

will be encountered in arriving at a satisfactory solution. The choice of gear ratio between the

power turbine and driven component is normally at the disposal of the turbine designer, and thus

the rotational speed can be varied to suit the turbine, instead of the compressor as we have

assumed here.




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The cooled turbine

Figure 7.29 illustrates the methods of blade cooling that have received serious attention and

research effort. Apart from the use of spray cooling for thrust boosting in turbojet engines, the

liquid systems have not proved to be practicable. There are difficulties associated with




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channelling the liquid to and from the bladeswhether as primary coolant for forced convection

or free convection open thermosyphon systems, or as secondary coolant for closed thermosyphon

systems. It is impossible to eliminate corrosion or the formation of deposits in open systems, and

very difficult to provide adequate secondary surface cooling area at the base of the blades for

closed systems. The only method used successfully in production engines has been internal,

forced convection, air cooling. With 1-5-2 per cent of the air mass flow used for cooling per

blade row, the blade temperature can be reduced by between 200 and 300 C. Using current

alloys, this permits turbine inlet temperatures of more than 1650 to be used. The blades are

either cast, using cores to form the cooling passages, or forged with holes of any desired shape

produced by electrochemical or laser drilling.

Figure 7.30 shows the type of turbine rotor blade introduced in the 1980s. The next step forward

is likely to be achieved by transpiration cooling, where the cooling air is forced through a porous

blade wall. This method is by far the most economical in cooling air, because not only does it

remove heat from the wall more uniformly, but the effusing layer of air insulates the outer

surface from the hot gas stream and so reduces the rate of heat transfer to the blade. Successful

application awaits further development of suitable porous materials and techniques of blade

manufacture. We are here speaking mainly of rotor blade cooling because this presents the most

difficult problem. Nevertheless it should not be forgotten that, with high gas temperatures,

oxidation becomes as significant a limiting factor as creep, and it is therefore equally important

to cool even relatively unstressed components such as nozzle blades and annulus walls.




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Figure 7.31 (a) illustrates the principal features of nozzle blade cooling. The air is introduced

in such a way as to provide jet impingement cooling of the inside surface of the very hot leading

edge. The spent air leaves through slots or holes in the blade surface (to provide some film

cooling) or in the trailing edge.

FIG. 7.31 (a) Turbine nozzle cooling [(b) courtesy Rolls-Royce]




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Figure 7.35: Shows a typical temperature distribution at the mid-span of

a blade designed to operate with Tg= 1500 and T= 320 .

It may be noted that the final design calculation for a cooled blade will involve an estimation ofthe two-dimensional temperature distribution over the blade cross-section at several values of

l/L. Finite difference methods are used to solve the differential equations, and conduction within

the blade is taken into account. Figure 7.35 shows a typical temperature distribution at the mid-

span of a blade designed to operate with Tg= 1500 and = 320 . It emphasizes one of the

main problems of blade cooling, i.e. that of obtaining adequate cooling at the trailing edge.

Finally, an estimation will be made of the thermal stresses incurred with due allowance for

redistribution of stress by creep: with cooled blades the thermal stresses can dominate the gas

bending stresses and be comparable with the centrifugal tensile stresses.

Finally, mention must be made of an alternative approach to the high- temperature turbinetheuse of ceramic materials which obviates the need for elaborate cooling passages. Much effort has

been expended on the development of silicon nitride and silicon carbide materials for small

turbine rotors (both axial and radial) in which it would be difficult to incorporate cooling

passages. Adequate reliability and life are difficult to achieve, but demonstrator engines have

been ran for short periods. Ceramic rotor blades are being investigated for use in stationary gas

turbines for powers up to about 5 MW, and experimental trials are expected in the late 1990s.

The use of ceramic turbines in production engines, however, remains an elusive goal three

decades after optimistic forecasts about their introduction.

Blade Cooling

Blade cooling is the most effective way of maintaining high operating temperatures making use

of the available material. Blade cooling may be classified based on the cooling site as external

cooling and internal cooling. Another classification based on the cooling medium is liquid

cooling and air cooling.




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External Cooling

The external surface of the gas turbine blade is cooled by making use of compressed air from the

compressor.

Other methods of external cooling are film cooling and transpiration cooling.

Internal Cooling

Internal cooling of blades is achieved by passing air or liquid through internal cooling passages

from hub towards the blade tip. The cooling of the blades is achieved by conduction and

convection.

Hollow blades can also be manufactured with a core and internal cooling passage. Based on the

cooling medium employed, blade cooling may be classified into liquid cooling and air cooling.

Requirements for Efficient Blade CoolingIn a conventional cooled blade, cooling is obtained due to convection by passing cooling air

through internal passages within the blade. The success in obtaining the large reduction in metal

temperature at the expense of a small quantity of cooling flow is governed by the skill in

devising and machining the cooling passages. Because the internal cooling relies on the cooling

air scrubbing against the cooling surface, the internal surface area must be large and the velocity

of the cooling air must be high. This implies that the cross-sectional flow area of the passage

must be small.

The design of the blade internal geometry for cooling is more complex because of the various

aerodynamic, heat transfer, stress and mechanical design criteria that must be satisfied. The most

successful designs have incorporated radial passages through which cooling air passes, escaping

at the tip.

The radial flow turbine

In a radial flow turbine, gas flow with a high tangential velocity is directed inwards and leaves

the rotor with as small a whirl velocity as practicable near the axis of rotation. The result is that

the turbine looks very similar to the centrifugal compressor, but with a ring of nozzle vanesreplacing the diffuser vanes as in Fig. 7.37. Also, as shown there would normally be a diffuser at

the outlet to reduce the exhaust velocity to a negligible value.




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Turbine and Compressor Matching

The problem of matching turbine and compressor performance has great importance for jet

engines, which must operate under conditions involving large variations in thrust, inlet pressure,

and temperature, and flight Mach number. Matching the components of turbofan and turboprop

engines involves similar considerations and procedures.

Essentially the matching problem is simple, though the computation can be length. The

steady-state engine performance at each speed is determined by two conditions: continuity of

flow and a power balance. The turbine mass flow must be the sum of the compressor mass flow

and the fuel flow, minus compressor bleed flow. Also the power output of the turbine must be

equal to that demanded by the compressor.

In principle, the matching computations could proceed as follows:

1. Select operating speed2.

Assume turbine inlet temperature

3. Assume compressor pressure ratio4. Calculate compressor work per unit mass5. Calculate turbine pressure ratio required to produce this work6. Check to see if compressor mass flow plus fuel flow equals turbine mass flow; if not,

assume a new value of compressor pressure ratio and repeat steps 4, 5, and 6 until

continuity is satisfied.

7. Now calculate the pressure ratio across the jet nozzle from the pressure ratios across thediffuser, compressor, combustor, and turbine.

8. Calculate the area of jet nozzle outlet necessary to pass the turbine mass flow calculatedin step 6 with pressure ratio calculated in step 7 and the stagnation temperature

calculated. If the calculated area does not equal the actual exit area, assume a new value

of turbine inlet temperature (step-2) and repeat the entire procedure.




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The designer will try to match turbine and compressor so that the compressor is operating

near its peak efficiency through the entire range of operation, as shown in the below

figure, where the operating line (i.e., the locus of stead-state matching condition) runs

through the centers of the islands defined by the constant-efficiency lines.




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Problems

In a single-stage impulse turbine the nozzle discharges the fluid on to the blades at an angle of

650 to the axial direction and the fluid leaves the blades with an absolute velocity of 300 m/s at

an angle of 30

0

to the axial direction. If the blades have equal inlet and outlet angles and there isno axial thrust, estimate the blade angle, power produced per kg/s of the fluid and blade

efficiency.

Solution:

Since the axial thrust is zero,

Ca3 = Ca2 = Ca

w3 = w2




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ca3 = ca2 = ca = ca3 x cos 3

= 300 x cos 30 = 259.8 m/s

c2= ca2/cos 2= 259.8/cos 65 = 614.7 m/s

u = ct2 wt2 = wt3 - ct3

c2 sin 2- ca2tan 2 = ca3tan 3 c3 sin 3

Since ca2 = ca3 = ca and 2 = 3 =

2catan = c2 sin 2 + c3 sin 3

tan = (614.7 x sin 65 + 300 x sin 30) / 2 x 259.8

= 1.3609

= 53.70

2 = 3= 53.70

u = c2 sin 2- ca2tan 2

= 614.7 x sin 65 259.8 x tan 53.7

= 203.43 m/s

ct2 = c2 sin 2

= 614.7 x sin 65

= 557.1 m/s

ct3 = c3 sin 3




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= 300 x sin 30

= 150 m/s

WT = 203.43 x (557.1 + 150) x 10-3

= 144 kJ/kg

= u/c2 = 203.43 / 614.7 = 0.33

Blade efficiency = 4 (sin 2 - 2)

= 4 x (0.33 x sin 65 0.332) = 0.761

= 76.1 %




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Aircraft Engine Performance Parameters

Uninstalled thrust of a jet engine (single inlet and single exhaust) is given by

Uninstalled thrust of a jet engine (single inlet and single exhaust) is given by

It is most desirable to expand the exhaust gas to the ambient pressure, which gives




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In this case, the uninstalled thrust equation becomes,

The installed thrust T is equal to the uninstalled thrust F minus the inlet drag D inletand minus

nozzle drag Dnozzle , or

T = F Dinlet- Dnozzle

Problem:

An advanced fighter engine operating at Mach 0.8 and 10 km altitude has the following

unistalled performance data and uses a fuel with low heating value 42,800 kJ/kg:

Uninstalled thrust = 50 kN

Mass flow rate of air = 45 kg/sec

Mass flow rate of fuel = 2.65 kg/sec

Determine the specific thrust, thrust specific fuel consumption, exit velocity, thermal efficiency,

propulsive efficiency, and overall efficiency (assume exit pressure equal to ambient pressure).

Find the installed thrust when the total drag is equal to 10% of the uninstalled thrust.

Solution:




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Fs = 50/45 = 1.1111kN/(kg/sec)

= 1111.1 m/s

TSFC = 2.65 / 50

= 0.053 (kg/sec)/kN

= 53 mg/N-sec

V0 = Moao

= 239. 6 m/sec

Using the above equation exit velocity,

Veis obtained as 1275.6 m/s




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Power output of the engine = 37.475 x 106W

Power input to the engine through fuel = 113.42 x 106W

Propulsive power or Thrust Power = 50,000 x 239.6

Thermal efficiency = 37.475 x 106/ 113.42 x 106

= 33.04 %

Propulsive Efficiency = 50,000 x 239.6 / 37,475 x 106

= 31.97 %

Overall efficiency = 50,000 x 239.6 / 113.42 x 106

= 10.56 %

For additional numerical problems please refer the following books

1. Mathur, M., and Sharma, R.P., Gas Turbines and Jet and Rocket Propulsion,Standard Publishers, New Delhi, 1988.

2. Ganesan, V., Gas Turbines, Tata McGraw-Hill Publishing Company Limited,New Delhi. Second Edn. 2003.

Additional reading

1. Hill, P.G. & Peterson, C.R. Mechanics & Thermodynamics of Propulsion Addison Wesley Longman INC, 1999.

2. Cohen, H., Rogers, G.F.C. and Saravanamuttoo, H.I.H., Gas Turbine Theory, LongmanCo., ELBS Ed., 1989.




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Unit-2

RAMJET PROPULSION

Operating principle Sub critical, critical and supercritical operation Combustion in ramjet

engine Ramjet performance Sample ramjet design calculations Introduction to scramjet

Preliminary concepts in supersonic combustion Integral ramrocket- Numerical problems.

Ramjets

Ramjets can be thought of as propulsive devices evolved out of turbojets. Ramjets operates well only at high speeds, typically between M = 2.0 and 4.0. The combustion mode being not very different from that of an afterburner, the specificfuel consumption is comparable to that of afterburner. The ramjet, unlike turbojet and turbofan does not produce any thrust at zero speed. Ramjets are mostly contemplated for use in military applications.




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SCRAM JET ENGINES

A scram jet engine is an engine that is much lighter than a conventional jet engine, canpropel an object at speeds of over 5000 miles per hour and has no moving parts.

If you could get it to work, the trip from London to Sydney would only take two hours! This technology would also be very useful to launch small satellites. The engine runs on oxygen, which it gets from the atmosphere, and a small amount of

hydrogen.

The engine would save a fantastic amount on the cost of fuel. This technology has been around since the 1950s but the problem is the motor will only

become efficient at five times the speed of sound or Mach 5.

Because of this the plane would need two engines, an engine capable of getting it toMach 5 and a Scram Jet.

A ramjet engine

A scramjet engine




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A ramjet has no moving parts and achieves compression of intake air by the forwardspeed of the air vehicle.

Air entering the intake of a supersonic aircraft is slowed by aerodynamic diffusioncreated by the inlet and diffuser to velocities comparable to those in a turbojet augmenter.

The expansion of hot gases after fuel injection and combustion accelerates the exhaust airto a velocity higher than that at the inlet and creates positive push.

Scramjet is an acronym for Supersonic Combustion Ramjet. The scramjet differs from the ramjet is that combustion takes place at supersonic air

velocities through the engine.

It is mechanically simple, but vastly more complex aerodynamically than a jet engine. Hydrogen is normally the fuel used. A scramjet (supersonic combustion ramjet) is a variation of a ramjet with the key

difference being that the flow in the combustor is supersonic.

At higher speeds it is necessary to combust supersonically to maximize the efficiency ofthe combustion process.

Projections for the top speed of a scramjet engine (without additional oxidizer input) varybetween Mach 12 and Mach 24 (orbital velocity), but the X-30 research gave Mach 17

due to combustion rate issues.

By way of contrast, the fastest conventional air-breathing, manned vehicles, such as theU.S. Air Force SR-71, achieve slightly more than Mach 3.2 and rockets achieved Mach

30+ during Apollo.

Like a ramjet, a scramjet essentially consists of a constricted tube through whichinlet air is compressed by the high speed of the vehicle, fuel is combusted, and then

the exhaust jet leaves at higher speed than the inlet air.

Also like a ramjet, there are few or no moving parts. In particular there is no high speedturbine as in a turbofan or turbojet engine that can be a major point of failure.

A scramjet requires supersonic airflow through the engine, thus, similar to a ramjet,scramjets have a minimum functional speed. This speed is uncertain due to the low

number of working scramjets, relative youth of the field, and the largely classified nature

of research using complete scramjet engines.

However it is likely to be at least Mach 5 for a pure scramjet, with higher Mach numbers7-9 more likely. Thus scramjets require acceleration to hypersonic speed via other means.

A hybrid ramjet/scramjet would have a lower minimum functional Mach number, andsome sources indicate the NASA X-43A research vehicle is a hybrid design.

Recent tests of prototypes have used a booster rocket to obtain the necessary velocity. Air breathing engines should have significantly better specific impulse while within

the atmosphere than rocket engines.

However scramjets have weight and complexity issues that must be considered. Whilevery short suborbital scramjets test flights have been successfully performed, perhaps




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significantly no flown scramjet has ever been successfully designed to survive a flight

test.

The viability of scramjet vehicles is hotly contested in aerospace and space vehiclecircles, in part because many of the parameters which would eventually define the

efficiency of such a vehicle remain uncertain.

This has led to grandiose claims from both sides, which have been intensified by the largeamount of funding involved in any hypersonic testing. Some notable aerospace gurus

such as Henry Spencer and Jim Oberg have gone so far as calling orbital scramjets 'the

hardest way to reach orbit', or even 'scramjets' due to the extreme technical challenges

involved.

Major, well funded projects, like the X-30 were cancelled before producing any workinghardware.

The scramjet is a proposed solution to both of these problems, by modifications of theramjet design. The main change is that the blockage inside the engine is reduced, so that

the air isn't slowed down as much. This means that the air is cooler, so that the fuel canburn properly. Unfortunately the higher speed of the air means that the fuel has to mix

and burn in a very short time, which is difficult to achieve.

To keep the combustion of the fuel going at the same rate, the pressure and temperaturein the engine need to be kept constant. Unfortunately, the blockages which were removed

from the ramjet were useful to control the air in the engine, and so the scramjet is forced

to fly at a particular speed for each altitude. This is called a "constant dynamic pressure

path" because the wind that the scramjet feels in its face is constant, making the scramjet

fly faster at higher altitude and slower at lower altitude.

The inside of a very simple scramjet would look like two kitchen funnels attached bytheir small ends. The first funnel is the intake, and the air is pushed through, becomingcompressed and hot. In the small section, where the two funnels join, fuel is added, and

the combustion makes the gas become even hotter and more compressed. Finally, the

second funnel is a nozzle, like the nozzle of a rocket, and thrust is produced.

Note that most artists' impressions of scramjet-powered vehicle designs depict waveriderswhere the underside of the vehicle forms the intake and nozzle of the engine. This means

that the intake and nozzle of the engine are asymmetric and contribute directly to the lift

of the aircraft. A waverider is the required form for a hypersonic lifting body

A scramjet is a type of engine which is designed to operate at the high speeds normallyassociated with rocket propulsion.

It differs from a classic rocket by using air collected from the atmosphere to burn its fuel,as opposed to an oxidizer carried with the vehicle.

Normal jet engines and ramjet engines also use air collected from the atmosphere in thisway.

The problem is that collecting air from the atmosphere causes drag, which increasesquickly as the speed increases.




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Also, at high speed, the air collected becomes so hot that the fuel no longer burnsproperly.

Theory

All scramjet engines have fuel injectors, a combustion chamber, a thrust nozzle and aninlet, which compresses the incoming air.

Sometimes engines also include a region which acts as a flame holder, although the highstagnation temperatures mean that an area of focused waves may be used, rather than a

discrete engine part as seen in turbine engines.

Other engines use pyrophoric fuel additives, such as silane, to avoid such issues. An isolator between the inlet and combustion chamber is often included to improve the

homogeneity of the flow in the combustor and to extend the operating range of the

engine.

A scramjet is reminiscent of a ramjet.

In a typical ramjet, the supersonic inflow of the engine is decelerated at the inlet tosubsonic speeds and then reaccelerated through a nozzle to supersonic speeds to produce

thrust. This deceleration, which is produced by a normal shock, creates a total pressure

loss which limits the upper operating point of a ramjet engine.

For a scramjet, the kinetic energy of the freestream air entering the scramjet engine islarge compared to the energy released by the reaction of the oxygen content of the air

with a fuel (say hydrogen).

Thus the heat released from combustion at Mach 25 is around 10% of the total enthalpyof the working fluid.

Depending on the fuel, the kinetic energy of the air and the potential combustion heatrelease will be equal at around Mach 8.

Thus the design of a scramjet engine is as much about minimizing drag as maximizingthrust.

This high speed makes the control of the flow within the combustion chamber moredifficult. Since the flow is supersonic, no upstream influence propagates within the

freestream of the combustion chamber.

Thus throttling of the entrance to the thrust nozzle is not a usable control technique. In effect, a block of gas entering the combustion chamber must mix with fuel and have

sufficient time for initiation and reaction, all the while travelling supersonically through

the combustion chamber, before the burned gas is expanded through the thrust nozzle.

This places stringent requirements on the pressure and temperature of the flow, andrequires that the fuel injection and mixing be extremely efficient.

Usable dynamic pressures lie in the range 20 to 200 kPa (0.2-2 bar), where

whereqis the dynamic pressure of the gas




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(rho) is the density of the gas

vis the velocity of the gas

Fuel injection and management is also potentially complex. One possibility would be that the fuel is pressurized to 100 bar by a turbo pump, heated

by the fuselage, sent through the turbine and accelerated to higher speeds than the air by a

nozzle.

The air and fuel stream are crossed in a comb like structure, which generates a largeinterface.

Turbulence due to the higher speed of the fuel lead to additional mixing. Complex fuelslike kerosine need a long engine to complete combustion.

The minimum Mach number at which a scramjet can operate is limited by the fact thatthe compressed flow must be hot enough to burn the fuel, and of high enough pressure

that the reaction is finished before the air moves out the back of the engine.

Additionally, in order to be called a scramjet, the compressed flow must still besupersonic after combustion.

Here two limits must be observed: Firstly, since when a supersonic flow is compressed it slows down, the level of

compression must be low enough (or the initial speed high enough) not to slow down the

gas below Mach 1.

If the gas within a scramjet goes below Mach 1 the engine will "choke", transitioning tosubsonic flow in the combustion chamber.

This effect is well known amongst experimenters on scramjets since the waves caused bychoking are easily observable.

Additionally, the sudden increase in pressure and temperature in the engine can lead to anacceleration of the combustion, leading to the combustion chamber exploding.

Secondly, the heating of the gas by combustion causes the speed of sound in the gasto increase (and the Mach number to decrease) even though the gas is still traveling

at the same speed. Forcing the speed of air flow in the combustion chamber under

Mach 1 in this way is called "thermal choking".

It is clear that a pure scramjet can operate at Mach numbers of 6-8, but in the lowerlimit, it depends on the definition of a scramjet.

Certainly there are designs where a ramjet transforms into a scramjet over the Mach 3-6range (Dual-mode scramjets). In this range however, the engine is still receiving

significant thrust from subsonic combustion of "ramjet" type.

The high cost of flight testing and the unavailability of ground facilities have hinderedscramjet development.

A large amount of the experimental work on scramjets has been undertaken in cryogenicfacilities, direct-connect tests, or burners, each of which simulates one aspect of the

engine operation.




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Further, vitiated facilities, storage heated facilities, arc facilities and the various types ofshock tunnels each have limitations which have prevented perfect simulation of scramjet

operation.

The HyShot flight test showed the relevance of the 1:1 simulation of conditions in the T4and HEG shock tunnels, despite having cold models and a short test time.

The NASA-CIAM tests provided similar verification for CIAM's C-16 V/K facility andthe Hyper-X project is expected to provide similar verification for the Langley AHSTF ,

CHSTF and 8 ft HTT.

Computational fluid dynamics has only recently reached a position to make reasonablecomputations in solving scramjet operation problems.

Boundary layer modeling, turbulent mixing, two-phase flow, flow separation, and real-gas aerothermodynamics continue to be problems on the cutting edge of CFD.

Additionally, the modeling of kinetic-limited combustion with very fast-reacting speciessuch as hydrogen makes severe demands on computing resources.

Reaction schemes are numerically stiff, having typical times as low as 10-19 seconds,requiring reduced reaction schemes.

Much of scramjet experimentation remains classified. Several groups including the USNavy with the SCRAM engine between 1968-1974, and the Hyper-X program with the

X-43A have claimed successful demonstrations of scramjet technology. Since these

results have not been published openly, they remain unverified and a final design method

of scramjet engines still does not exist.

The final application of a scramjet engine is likely to be in conjunction with engineswhich can operate outside the scramjet's operating range.

Dual-mode scramjets combine subsonic combustion with supersonic combustion foroperation at lower speeds, and rocket-based combined cycle (RBCC) engines supplementa traditional rocket's propulsion with a scramjet, allowing for additional oxidizer to be

added to the scramjet flow.

RBCCs offer a possibility to extend a scramjet's operating range to higher speeds orlower intake dynamic pressures than would otherwise be possible.

Advantages and disadvantages of scramjets

Special cooling and materials

Unlike a rocket that quickly passes mostly vertically through the atmosphere or a turbojetor ramjet that flies at much lower speeds, a hypersonic airbreathing vehicle optimally

flies a "depressed trajectory", staying within the atmosphere at hypersonic speeds.

Because scramjets have only mediocre thrust-to-weight ratios, acceleration would belimited. Therefore time in the atmosphere at hypersonic speed would be considerable,

possibly 15-30 minutes.




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Similar to a reentering space vehicle, heat insulation from atmospheric friction would bea formidable task. The time in the atmosphere would be greater than that for a typical

space capsule, but less than that of the space shuttle.

Therefore studies often plan on "active cooling", where coolant circulating throughout thevehicle skin prevents it from disintegrating from the fiery atmospheric friction.

Active cooling could require more weight and complexity. There is also safety concernsince it's an active system.

Often, however, the coolant is the fuel itself, much in the same way that modern rocketsuse their own fuel and oxidizer as coolant for their engines.

Both scramjets and conventional rockets are at risk in the event of a cooling failure. Half an engine

The typical waverider scramjet concept involves, effectively, only half an engine. Theshockwave of the vehicle itself compresses the inlet gasses, forming the first half of theengine. Likewise, only fuel (the light component) needs tankage, pumps, etc. This greatly

reduces craft mass and construction effort, but the resultant engine is still very much

heavier than an equivalent rocket or conventional turbojet engine of similar thrust.

Simplicity of design

Scramjets have few to no moving parts. Most of their body consists of continuoussurfaces. With simple fuel pumps, reduced total components, and the reentry system

being the craft itself, scramjet development tends to be more of a materials and modelling

problem than anything else.

Additional propulsion requirements

A scramjet cannot produce efficient thrust unless boosted to high speed, around Mach 5,depending on design, although, as mentioned earlier, it could act as a ramjet at low

speeds. A horizontal take-off aircraft would need conventional turbofan or rocket engines

to take off, sufficiently large to move a heavy craft. Also needed would be fuel for those

engines, plus all engine associated mounting structure and control systems. Turbofan

engines are heavy and cannot easily exceed about Mach 2-3, so another propulsion

method would be needed to reach scramjet operating speed. That could be ramjets or

rockets. Those would also need their own separate fuel supply, structure, and systems.

Many proposals instead call for a first stage of droppable solid rocket boosters, which

greatly simplifies the design.




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Pulsejet is a constant volume combustion device which is quite efficient only at low speeds and

uses unsteady combustion for its operation. Once the system is started, it works by taking in air

and fuel and combustion them during a part of the cycle and exhausting it during the next part of

the cycle. In order to promote and sustain the operation, a flapper device of metal or plastic, in

recent times, is used in front end.

Super sonic diffuser may be divided into two separate parts: the supersonic inlet and the

subsonic diffuser. Although this division is a convenient one, it must be remembered that the

phenomena in the supersonic and subsonic parts of the diffuser can, and often do, interact.

It should be remembered that the higher the Mach number, the greater will be our percentage

loss in pressure across a normal shock. Thus, at very high mach numbers, there is an appreciable

difference between (1) isentropic compression through out and (2) compression with a normal

shock.

The limitations imposed by the losses associated with a normal shock at higher Mach numbers

stimulated the development of a modified simple inlet design which incorporates a spike or

wedge in the nose section of the diffuser.

The modified design utilizes the spike or wedge to produce an oblique shock at the nose

section, and, the mach number after an oblique shock are greater than one. Consequently, in

addition to the oblique shock, we have a normal shock near the minimum area section. The




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compression after the normal shock is of the standard subsonic diffuser type; that is, an increase

in area decreases the velocity.

It might be asked why a diffuser which has two shock waves, namely, an oblique and a normal

shock, would give better results than a simple inlet which has only one normal shock. The reason

for this is that the losses across a series of weak shock are less than the losses across one orseveral strong shocks. This means that the losses across the normal shock which follows the

oblique shock are considerably less than the losses across a normal shock in the free stream.

Increasing the number of oblique shocks before the normal shock reduces the losses through

the shock system. It must be noted that the complexity of the inlet also increases as the number

shocks increases. In addition to the number of shocks, the pressure losses are also function of the

shock arrangement. It may be noted that the maximum total pressure recovery occurs when the

total pressure recovery is the same across each of oblique shocks, and very nearly equal to that

across the final normal shock.

The three basic modes operation frequently referred to are subcritical operation, critical

operation, and supercritical operation. All these three inlets are operated at the design Mach

number, MD, which by definition, means that the conical shock or conical shock extended will

intersect the cowl lip.

At the subcritical operation, the normal shock is external and subsonic velocities exit atthe cowl.

For this condition mass-flow ratio based on capture area is less than one; spillageexists; the inlet is not swallowing air at maximum capacity; pressure recovery is low

since some of the air goes through a single, near normal shock; inlet drag is high

because of the intense shock; operation is generally unstable and conducive to acondition called buzz (normal shock moves in and out of the inlet at relatively high

frequencies). An important instability that occurs during the subcritical operation of

most supersonic inlets. This phenomenon, known as buzz, consists of a rapidoscillation of the inlet shock and flow pattern; the resultant internal disturbance is very

detrimental to engine performance. In a ramjet, for instance, the onset of buzz usually

extinguishes combustion. Although the pulses of the shock system are similar, the

interval between pulses is not constant; hence buzz cannot be considered a periodic

phenomenon. Although it is not thoroughly understood, buzz has been shown to be afunction of conditions only at , and immediately downstream of, the inlet.

In general subcritical operation is unsatisfactory and should be avoided. As the flow resistance downstream of the diffuser is increased, the mass-flow ratio can

be reduced to its limit value of 0 at which point no flow exits.

For critical operation, both maximum mass flow and ram recovery are attained for thedesign Mach number; thus condition represents the optimum performance condition. It

has the disadvantage, however, of being, marginally unstable in actual applications




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because small changes in angles of attack or yaw or boundary layer separation can

induce the critical mode of operation across the threshold into the subcritical regime.Consequently, for actual operation it is usually better to operate the inlet in a more

stable condition, the supercritical regime.

The three basic modes operation frequently referred to aircraft inlets are subcritical operation,

critical operation, and supercritical operation, which are shown schematically for a typical case

in the above figure. With entirely diverging internal flow such as this, the normal shock position

is determined by a downstream flow restriction rather than by the inlet geometry. Hence

operating mode is sensitive to variations in exhaust-nozzle area and fuel flow rate. Subcritical

operation entails spilling of flow and a normal shock upstream of the inlet. Low and high

subcritical operations differ only in the extent of spilling. Supercritical operation occurs at the

same mass flow as critical operation, but with increased losses, since the normal shock occurs at

a higher Mach number. All these three inlets are operated at the design Mach number, MD, which

by definition, means that the conical shock or conical shock extended will intersect the cowl lip.




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The ramjet has the virtue of maximum simplicity, with no need for turbomachinery, and

maximum tolerance to high-temperature operation and minimum mass-per-unit thrust at suitable

flight Mach numbers. The ramjet also has its limitations. As well as being generally incapable of

steady operation at subsonic Mach numbers, it has an upper Mach number limit. For the

conventional ramjet (in which the supersonic inlet air is slowed to subsonic speeds to provide

stable combustion prior to the nozzle expansion), there is a limiting Mach number of about 6,

above which the temperature of the air entering the combustor is so high that combustion cannot

be completed. Most of the chemical energy of combustion is nonusefully transformed intodissociation reactions that on expansion do not provide the exhaust velocity needed for

satisfactory ramjet performance. To avoid this problem, substantial research has been, and is still

being, focused on the supersonic combustion ramjet (SCRAMJET). The difference between this

and the conventional ramjet is that combustion is to take place in a supersonic stream. Fuel must

be injected into the supersonic stream (without causing disruptive shock waves) and must mix

and burn in a millisecond or so. Conventional fuels do not ignite quickly enough, and gaseous

hydrogen seems the most likely candidate. Design of the fuel injector is a formidable challenge;

so is the problem of cooling a vehicle designed to operate at Mach numbers of 4 or higher.

Hydrogen could conceivably serve for structural cooling as well as for engine fuel.

It will be clear from this discussion that future designs for supersonic (or even hypersonic)

aircraft must cope with the design challenges of a whole range of flight Mach numbers.




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Supersonic Combustion

The losses associated with subsonic ramjet combustion can be substantial. If ramjets are to be

applied to hypersonic flight, additional problems arise because of extremely high temperature at

the entrance to the combustion chamber. This not only makes vehicle cooling very difficult, but

it leads to severe combustion loss due to dissociation.

Figure shows the air temperature reached after adiabatic deceleration from a high-altitude

ambient temperature of 220 K and from flight Mach number M to a chamber pressure of either 1

or 10 atm. For hypersonic flight (e.g. for M > 8) the temperature of the air in the chamber is quite

dependent on the pressure: The higher the pressure, the less dissociation and the higher the

temperature of the mixture. The temperature of the combustion products is likewise pressure

dependent.

Figure shows, for a combustion pressure of 10 atm and a flight Mach number of 10, there

is no temperature rise due to combustion; all of the combustion energy is absorbed bydissociation. One sees from the above Figure, the strange result that, at sufficiently high Mach

number, the temperature of the combustion products can be lower than that of the incoming air.

Consideration of the speed with which the fuel and air can be converted into dissociation

products may show that there is sufficient residence time in the combustion chamber to approach

equilibrium composition. But during the subsequent expansion in the nozzle, one cannot take

equilibrium composition for granted. It is quite possible that the expansion will be too rapid for

the composition to readjust, after each step of temperature and pressure reduction, to a new

equilibrium composition. If the expansion extremely rapid, the mixture may be effectively

frozen with the initial (high-temperature) composition. This would mean that little of the

combustion energy of the fuel (for the M = 10 case) would be available for acceleration of the

combustion products to produce thrust. The chemical kinetics of the recombination processes in

the nozzle would, in general, have a strong effect on the thrust and the propulsion efficiency of

the engine.

Some researchers have proposed the concept of the supersonic combustion as a way to avoid

this dissociation loss as well as the stagnation pressure losses associated with deceleration in

supersonic-to-subsonic inlets. With supersonic combustion, fluid temperatures are relatively low,

and this decreases the dissociation loss because dissociation depends on static rather than

stagnation temperature. Wall heat transfer, in contrast, depends essentially on stagnation

temperature, so the wall-cooling problem is not removed by employing supersonic combustion.

The stagnation pressure loss due to supersonic heating depends on the extent to which the fluid is

being accelerated while combustion is taking place.

The use of supersonic combustion requires fuel to be injected into, and mixed with, a

supersonic stream without excessive shock losses.




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The main advantages of the ramjet engine are;

1. High temperature can be employed2. In the absence of rotating machinery its construction is very simple and cheap3. It can operate effectively at high supersonic Mach numbers4. It is not very sensitive to the quality of fuel5. It provides high thrust per unit weight and frontal area




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Ramjet engines Main disadvantages are;

1. It requires a launching device at supersonic speed2. It is unsuitable for subsonic flight3. It has low thermal efficiency and high TSFC4. Its maximum operating altitude is limited

Ideal Efficiency

Various process occurring in the ramjet engine can be represented by an open circuit Brayton

cycle. This cycle is considered here with the following assumptions:

1. Steady one-dimensional flow2. Isentropic compression and expansion, s = 0, P0 = 03. Perfect gas4. Constant pressure heat addition in the combustion chamber, P2 = P35. Very low Mach number in the combustion chamber.

P2 P02 P03

T2 T02 T03

Compression and expansion process here are thermodynamically different from turbo jetengine. These process here experience only energy transformation; there is no energy

transfer such as compressor and turbine work within the engine. Thrust work is obtained

from the energy supplied in the fuel during process 2-3. Heat is rejected during process 4-

1 outside the engine. However, the ideal efficiency of the ramjet engine is still given by

Equation,

( )

/1

11

11

==

rt

i

Here, the temperature ratio, with the above assumption is given by

2

1

01

1

02

1

2

2

11 iM

T

T

T

T

T

Tt

+====




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Substituting the value of t from the above Equation to the previous equation we get,

2

1

2

1

2

12

11

2

1

211

11

M

M

Mi

+

=

+

=

)(1

1

21

11

2

1

Mf

M

i =

+

=

Though the actual thermal efficiency of the ramjet engine will be much lower than the

value given by the above equation it demonstrates an important characteristic i.e., the

efficiency increases with the flight Mach number and has a high value (76.19 % at M 1=

4) at higher operating Mach numbers.

Other performance parameters and efficiencies defined for air-breathing engines are also

applicable for the ram jet engine.




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The thermal efficiency or the Air standard Efficiency of the ideal cycle 1-2s-3-4s is given by,

= work / heat supplied

= 1 Qr/Qs

= 1 (T4s T1)/(T3-T2s)

The pressure ratio in the compressor and turbine is same,

i.e., r = P2/P1= P3/P4

Therefore the corresponding temperature ratios are given by,

/)1(

4

3

/)1(

1

2/)1(

4

3

1

2

=

====

P

P

P

Pr

T

T

T

Tt

s

s

( )

/1

11

11

==

rtAS

. A ramjet engine operates at M = 1.5 at an altitude of 6500 m. The diameter of theinlet diffuser at entry is 50 cm and the stagnation temperature at the nozzle entry is 1600

K. The calorific value of the fuel used is 40 MJ/kg. The properties of the combustion

gases are same as those of air (= 1.4, R = 287 J/kg K). The velocity of air at the diffuser

exit is negligible.

Calculate (a) the efficiency of the ideal cycle (b) flight speed (c) air flow rate (d) diffuser

pressure ratio (e) fuel-air ratio (f) nozzle pressure ratio (g) nozzle jet Mach number (h)propulsive efficiency (i) and thrust. Assue the following values; D = 0.90, B= 0.98, j

= 0.96, stagnation pressure loss in the combustion chamber = 0.02P02.




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At Z = 6500 m the properties of air are

T1 = 245.90 K, p1 = 0.440 bar, a1 = 414.5 m/s

= 0.624 kg/m3

(a)Ideal cycle efficiency

1

1

21

1

2

1M

i

+

=

= 0.310 Ans.

(b)M1= u/a1U = M1a1 = 1.5 x 314.5 = 471.75 m/s

Flight speed = 1698.3 kmph Ans.

( C) Area of cross section of the diffuser inlet

A1= d2/4 = 0.52/4 = 0.1963 m2




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11uAma =

= 0.624 X 471.48 X 0.1963

Air flow rate = 57.752 kg/s Ans.

(d)For negligible velocity at the diffuser exit,P02= P2

2

1

/)1(

1

2

2

1

1

M

P

P

D

=

D= 0.9, M1= 1.5

P2/P1= 3.2875 Ans.

P2= 3.2875 x 0.44 = 1.446

(e) 45.1211 21

1

01=+= M

TT

= 1.45 x 245.9 = 356.55 K

ffBpa QmTTCm

= )( 0203

fBp

a

fQTTC

m

mf /)( 0203 ==

f = 1.005 (1600-356.55)/0.98 x 40000




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Propulsive efficiency = 0.6693 Ans

(i)

umCmF

skgmmm

skgxm

a

fa

f

=

=+=+=

==

4

/593.59841.1752.57

/841.103188.0752.57

= (59.593 x 937.185 57.752 x 471.75) 10-3

Thrust = 28.614 kN Ans

Ram rocket

Air-augmented rockets (also known as rocket-ejector, ramrocket, ductedrocket, integral rocket/ramjets, or ejector ramjets) use the supersonic exhaust of some kind of

rocket engine to further compress air collected by ram effect during flight to use as additional

working mass, leading to greater effective thrust for any given amount of fuel than either the

rocket or a ramjet alone.

They represent a hybrid class of rocket/ramjet engines, similar to a ramjet, but able to give useful

thrust from zero speed, and are also able in some cases to operate outside the atmosphere, with

fuel efficiency not worse than both a comparable ramjet or rocket at every point.

Operation

A normal chemical rocket engine carries oxidizer and a fuel, sometimes pre-mixed, as in a solid

rocket, which are then burned. The heat generated greatly increases the temperature of the

mixture, which is then exhausted through a nozzle where it expands and cools. The exhaust is

directed rearward through the nozzle, thereby producing a thrust forward. In this conventionaldesign, the fuel/oxidizer mixture is both the working mass and energy source that accelerates it.

One method of increasing the overall performance of the system is to collect either the fuel or the

oxidizer during flight. Fuel is hard to come by in the atmosphere, but oxidizer in the form ofgaseous oxygen makes up 20% of the air and there are a number of designs that take advantage

of this fact. These sorts of systems have been explored in the LACE (liquid air cycle engine)

concept.




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Another idea is to collect the working mass instead. With an air-augmented rocket, an otherwise

conventional rocket engine is mounted in the center of a long tube, open at the front. As therocket moves through the atmosphere the air enters the front of the tube, where it is compressed

via the ram effect. As it travels down the tube it is further compressed and mixed with the fuel-

rich exhaust from the rocket engine, which heats the air much as a combustor would in a ramjet.

In this way a fairly small rocket can be used to accelerate a much larger working mass thannormally, leading to significantly higher thrust within the atmosphere.

A liquid air cycle engine (LACE) is a spacecraft propulsion engine that attempts to gain

efficiency by gathering part of its oxidizer from the atmosphere. In a LOX/LH2 bipropellant

rocket the liquid oxygen needed for combustion is the majority of the weight of the spacecraft onlift-off, so if some of this can be collected from the air on the way, it might dramatically lower

the take-off weight of the spacecraft.

Principle of operation

LACE works by compressing and then quickly liquefying the air. Compression is achievedthrough the ram-air effect in an intake similar to that found on a high-speed aircraft like

Concorde, where intake ramps create shock waves that compress the air. The LACE design thenblows the compressed air over a heat exchanger, in which the liquid hydrogen fuel is flowing.

This rapidly cools the air, and the various constituents quickly liquefy. By careful mechanical

arrangement the liquid oxygen can be removed from the other parts of the air, notably water,nitrogen and carbon dioxide, at which point it can be fed into the engine as normal. The

hydrogen is so much lighter than oxygen that the now-warm hydrogen is often dumped

overboard instead of being re-used as fuel, at a net gain.

One issue with the LACE system is that in order to appreciably reduce the mass of the oxygen

carried at launch, a LACE vehicle needs to spend more time in the lower atmosphere where itcan collect enough oxygen to supply the engines. This leads to greatly increased vehicle heating

and drag, which offset somewhat the savings in oxidizer weight, but this in turn is offset by

higher Isp (Specific impulse) permitting a lifting trajectory which greatly reduces gravity losses.More significantly the LACE system is far heavier than a rocket engine, and the performance of

launch vehicles of all types is particularly affected by dry mass, rather than any oxidizer mass

which would be burnt off over the course of the flight.

Additional Reading:

1. Hill, P.G. & Peterson, C.R. Mechanics & Thermodynamics of Propulsion Addison WesleyLongman INC, 1999.

2. Cohen, H., Rogers, G.F.C. and Saravanamuttoo, H.I.H., Gas Turbine Theory, Longman Co.,ELBS Ed., 1989.

3. Gorden, C.V., Aero thermodynamics of Gas Turbine and Rocket Propulsion, AIAA EducationSeries, New York, 1989.

4. Mathur, M., and Sharma, R.P., Gas Turbines and Jet and Rocket Propulsion, StandardPublishers, New Delhi, 1988.




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Unit-3

FUNDAMENTALS OF ROCKET PROPULSION

Operating principle Specific impulse of a rocket internal ballistics- Rocket nozzle

classification Rocket performance considerations Numerical Problems.

Rockets Special Features and Applications

Historical Reference The basic principles of all propulsive devices lie with the laws of motion due to Newton

(17th

Century AD). These laws are phenomenological and therefore one can expect that

even before Newton there may have existed many devices working on the principles of

reaction.

Rockets working directly on the principle of reaction are perhaps the simplest of thepropulsive engines.

The reciprocating engines and gas turbine engines are relatively more complex. The Chinese are credited with the invention of rockets probably in 12-14thcentury AD. Indians used the rockets as effective weapons in late 18 th century against British and in

19thcentury, the rockets became a part of the warfare in Europe. But it was only in the

early part of the present century that man has recognized the full potential of rocket

owing to the interests in space travel/satellite technology and like.

Tsiolkovsky (USSR 1903) Goddard (USA, 1912) and Oberth (1921) are the pioneers ofmodern rocketry.

The liquid propellant rocket owe their genesis to these people. The German V-2 rockets (25 tons, 65 sec, LOX-Alchol) and the post-second World war

progress in rocketry are too familiar to all.

Principle

All the conventional propulsion systems work by causing a change of momentum in a working

fluid in a direction opposite to the intended motion. Rockets fall under the category of direct

acting engines since the energy liberated by the chemical process is directly used to obtain

thrust. Being non-air breathing devices the basic component of a rocket are

(i) Combustion chamber where exothermic processes produces gases at high temperatureand pressure, and

(ii)Nozzle, which accelerate the fluid to high velocities and discharge them into surroundingatmosphere thereby deriving the desired force or thrust.




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Some Special Features

The non-air breathing nature of rockets makes them very distinct among the propulsive devices.

(a)The reaction system does not depend on the surrounding atmosphere. There are novelocity limitations and altitude ceiling.

(b)Since it has to carry its own oxidizer required for combustion reaction, the specificpropellant consumption is very high. Rockets consume approximately 15kg/kg-hr of

propellant compared to about 1 kg/kg-hr of fuel by turbojet engine.

(c)High pressure operation is possible and hence the ratio of energy liberation per unitvolume (and also unit weight of hardware) is very high.

(d)Main part of the rockets contains no moving element. Hence there is no constraint oninternal aerodynamics and the reliability is high. This also implies quick response times,

which makes them ideal control components.

With the above features, it is clear that the rockets are the most suitable power plants for

(i)

High altitude and space applications where atmospheric oxygen is not available,eg. Launch vehicles and satellite control rockets.

(ii) All applications where high thrust are required for short duration: missiles, boosters,JATO etc.

Rockets in Space Applications

There are a variety of rockets when it comes to launching and satellite control. Many of these are

non-chemical in nature but are restricted to extremely low thrust levels.

Sl

No Type

Order of

Magnitude ofThrust (N) F/W OperationalTime

Isp

(sec) Applications

1

Solar sail

(not a rocket in

fact)

10-5

10-4

Years Satellite Altitude

control

2

Electric Prop.

(Electro thermal,

Electro Static,

Electro

Magnetic)

10-6 - 10-2 10-5-10-3 Years 150 - 6000

Satellite control,

stabilization, orbit

maneuver

3Stored cold gas

(N2, NH3etc.)10-2 - 10-1 ~ 10-3 Years 50 - 100 -do-

4 Nuclear Rocket upto 105 20-30 Minute tohours 800 Interplanetary andspace travel

5

Chemical Rocket

(Solid, Liquid

and Hybrid)

upto 107 upto 80Seconds to

minutes@150-450

Launch vehicles,

Missiles, Control

rockets, Sounding

rockets, JATO etc

@ shuttle main engine operate for about 8 min at a time but over 7 hrs cumulatively.




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Classification of Chemical Rockets

Depending on the context, the chemical rockets are classified in many ways as follows:

(a)Type of propellant: Solid, Liquid (mono propellant / bipropellant and hybrid rockets)(b)Application: Launch vehicle, ABMs, JATOs, ICBM, IRBM, SAM etc.(c)Size of Unit (and thrust level sometimes): 10 ton, 100 kg etc.(d)Type of subsystem: Turbopump fed, clustering, grain type etc.

Specific Impulse

The specific impulse of a rocket,Isp, is the ratio of the thrust to the flow rate of the weight ejected,that is

where Fis thrust, is the rate of mass flow, and gis the acceleration of gravity at ground

level.

Specific impulse is expressed in seconds. When the thrust and the flow rate remain constantthroughout the burning of the propellant, the specific impulse is the time for which the rocket

engine provides a thrust equal to the weight of the propellant consumed.

For a given engine, the specific impulse has different values on the ground and in the vacuum ofspace because the ambient pressure is involved in the expression for the thrust. It is therefore

important to state whether specific impulse is the value at sea level or in a vacuum.

There are a number of losses within a rocket engine, the main ones being related to theinefficiency of the chemical reaction (combustion) process, losses due to the nozzle, and losses

due to the pumps.

Overall, the losses affect the efficiency of the specific impulse. This is the ratio of the realspecific impulse (at sea level, or in a vacuum) and the theoretical specific impulse obtained with

an ideal nozzle from gases coming from a complete chemical reaction. Calculated values of

specific impulse are several percent higher than those attained in practice.

From Equation (2.8) we can substitute C for Fin Equation (2.23), thus obtaining

Equation (2.24) is very useful when solving Equations (2.18) through (2.21). It is rare we aregiven the value of Cdirectly, however rocket engine specific impulse is a commonly given

parameter.




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Internal Ballistics

The parameters that govern the burning rate and mass discharge rate of rocket motors are called

internal ballistic properties; they include

r propellant burning rate (velocity of consumption), m/sec or mm/sec or in/sec.

K ratio of burning surface to throat area, Ab/At

p temperature sensitivity of burning rate, expressed as percent change of burning

rate per degree change in propellant temperature at a particular value of chamber

pressure.

K- temperature sensitivity of pressure expressed as percent change of chamber

pressure per degree change in propellant temperature at a particular value of K,

and the influences caused by pressure, propellant ingredients, gas velocity, or acceleration.

The subsequent solid propellant rocket parameters are performance parameters; they include

thrust, ideal exhaust velocity, specific impulse, propellant mass fraction, flame temperature,

temperature limits and duration.

Propellant Burning Rate

The rocket motors operation and design depend on the combustion characteristics of the

propellant, its burning rate, burning surface, and grain geometry. The branch of applied science

describing these is known as internal ballistics.

Solid propellant burns normal to its surface. The (average) burning rate, r, is defined as theregression of the burning surface per unit time. For a given propellant, the burning rate is mainly

dependent on the pressure, p, and the initial temperature, Ti, of the propellant. Burning rate is

also a function of propellant composition. For composite propellants it can be increased by

changing the propellant characteristics:

1. Add a burning rate catalyst, often called burning rate modifier (0.1 to 3.0% of propellant)or increase percentage of existing catalyst.

2. Decrease the oxidizer particle size.3. Increase oxidizer percentage4. Increase the heat of combustion of the binder and/or the plasticizer5. Imbed wires or metal staples in the propellant




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Apart from the propellant formulation and propellant manufacturing process, burning ratein a

full-scale motor can be increased by the following

1. Combustion chamber pressure2. Initial temperature of the solid propellant prior to start3. Combustion gas temperature4. Velocity of the gas flow parallel to the burning surface5. Motor motion ( acceleration and spin-induced grain stress)

Burning rate data are usually obtained in three ways namely, from testing by:

1. Standard strand burners, often called Crawford burners2. Small-scale ballistic evaluation motors3. Full-scale motors with good instrumentation

A strand burner is a small pressure vessal (usually with windows) in which a thin strand

or bar of propellant is ignited at one end and burned to the other end. The strand can be

inhibited with an external coating so that it will burn only on the exposed cross-sectionalsurface; chamber pressure is simulated by pressurizing the container with inert gas. The

burning rate can be measured by electric signals from embedded wires, by ultrasonic

waves, or by optical means. The burning rate measured on strand burners is usually lower

than that obtained from actual rocket motor firing (by 4 to 12%) because it does not truly

simulate the hot chamber environment of an actual rocket motor. Also small ballistic

evaluation motors usually have a slightly lower burning rate than full-scale large motors,

because of scaling factors.

During development of a new or modified solid propellant, it is tested extensively or

characterized. This includes the testing of the burn rate (in several different ways) underdifferent temperatures, pressures, impurities, and conditions. It also requires

measurements of physical, chemical, and manufacturing properties, ignitability, aging,

sensitivity to various energy inputs or stimuli (e.g., shock, friction, fires), moister

absorption, c

Aircraft Propulsion-2

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