__RESULTS & DISCUSSION:__

__Engine Performance
Analysis: Mixed Flow Turbo-Ramjet __

__Unit thrust:__

The thrust per unit mass flow of a turbo-ramjet in the pure turbojet phase is a strong function of design compressor pressure ratio and design Mach number. The throttle ratio of the engine determines when the turbojet reaches its maximum power requirement condition. After the turbojet reaches this point the temperature of the burner has reached its maximum and the compressor pressure ratio is now further reduced so that the maximum turbine inlet temperature is not exceeded. The Mach number where the turbojet reaches the hook is strongly dependent on the design Mach number, altitude and the throttle ratio setting. With increase in altitude the hook is reached at higher mach numbers as shown for the turbojet operating at 10 km altitude. After the throttle hook is reached, the thrust per unit mass flow falls due to reduction in compressor pressure ratio as shown for the turbojet operating at 5 km.

During the initial part of mixed flow phase the behavior of the turbo-ramjet closely parallels that of an afterburning turbojet. Due to the mixing considerations that were explained earlier, the turbine inlet temperature is reduced causing the compressor pressure ratio to fall. This is compensated by switching on the afterburner which causes a rise in the thrust per unit mass flow. Since the compressor pressure ratio keeps falling after transition the thrust per unit mass flow drops.

The later part of the transition phase is similar in behavior to a ramjet. The thrust per unit mass flow of a ramjet decreases after a particular mach number depending on the value of burner temperature due to the fact that the temperature due to ramming increases very rapidly with mach number which again implies that lesser fuel is added to the air flow and value of velocity at the exit drops relative to velocity at inlet. This however has the effect of increasing propulsive efficiency which will be shown later. The thrust per unit mass flow of a ramjet is higher at high altitudes for the same burner temperature due to the fact that more fuel has to be added to the relatively colder air flow to increase its temperature to the same level as the ramjet operating at lower altitudes. This means that the mass flow at the exit is higher by a greater percentage at higher altitudes which causes increased thrust per unit mass flow.

**
Overall Fuel Air ratio**:

The fuel air ratio of a turbo-ramjet during the turbojet phase is a function of the temperature of the burner. The temperature of the burner increases with increase in Mach number in accordance to the throttle setting and once it reaches its maximum value becomes constant. This means that once this point has been reached then fuel added is lesser since the temperature due to ram compression increases with Mach number and even though the compressor pressure ratio falls after this point the net rise in temperature is higher. This behavior is exhibited by the turbojet operating at 5 km altitude. For the turbojet operating at 10 km the throttle hook has not been reached before transition.

When the transition begins the afterburner is switched on which causes a large jump in overall fuel air ratio of the order of 50% increase. The increase is not as large as one would expect when the afterburner is switched on due to the fact that the temperature of the main burner has been decreased to satisfy mixing conditions. The variation of the fuel air ratio during transition will be explained later in detail.

As mentioned earlier the amount of fuel added to the air flow is more at higher altitudes since the temperature of ambient air decreases with altitude and for the same value of burner exit temperature more fuel has to be added to increase the relatively low temperature air to the required levels.

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Thrust
specific fuel consumption:__

TSFC is defined as mass of fuel burnt per unit thrust produced hence it is a strong function of thrust per unit mass flow and the fuel-air ratio. Though a lesser value of TSFC indicates that it is a more ‘fuel efficient’ engine i.e. for a particular amount of thrust produced the engine consumes lesser fuel in comparison to an engine with higher TSFC, the actual value of thrust may be very low. This is best exhibited by the turbo-ramjet engine during the turbojet phase at very low Mach numbers where the thrust is very low due to low mass flow rate. However, TSFC decreases at high Mach numbers during the ramjet phase due to comparatively large values of thrust produced resulting from a huge rise in mass flow rate and also due to the fact that the fuel air ratio of a ramjet decreases with Mach number due to ramming.

In the transition phase the TSFC increases by large value due to the afterburner operation. As transition progresses the TSFC increases slightly due to comparatively larger drop in thrust per unit mass flow relative to the drop in fuel air ratio drop.

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Turbine Inlet Temperature:__

The total temperature of the main burner depends on the value of the design altitude, operating altitude and the throttle ratio setting during the turbojet and ramjet phase. The temperature is also used as the control on pressure in the burner i.e. if the pressure in the burner exceeds design pressure limitations it may be decreased, thus lowering the compressor pressure ratio. After the temperature reaches its maximum possible value as set by material limitations of the turbine, it is held constant. When transition begins the temperature drops to satisfy the mixer constraints and is then held constant since the turbojet is now in the phase of being powered down. The temperature of the burner is not completely decreased as in a real engine the powered down turbojet may be used to run accessories and for cooling purposes. The sudden increase in the temperature is due to the ramjet operation. The ramjet main burner is the afterburner of the turbojet and as there are no moving parts in the afterburner the temperatures at this point may be increased to 2000 K and above thus giving rise to large values of thrust.

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Overall Pressure Ratio (OPR):__

The OPR of a turbojet is constant until it reaches the throttle hook after which since the temperature of the main burner has reached its maximum the OPR has to be reduced in order to satisfy the Turbine inlet temperature limits. During the transition, since the temperature of the burner is reduced and then held constant in order to satisfy mixing conditions the OPR decreases further. In the ramjet phase the turbojet is powered down and hence the OPR is unity.

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Efficiencies:__

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The thermal efficiency of an engine is defined as the power output by the energy input in form of fuel. In an aircraft engine power is defined as thrust*forward velocity. This is the reason why at low mach numbers the value of thermal efficiency of the engine is low. The efficiency of the turbojet is higher than that of the ramjet at the same Mach number due to the presence of the compressor. And it is also clear from the expression for Brayton cycle efficiency that as pressure ratio increases the efficiency of the cycle increases. During transition since the OPR decreases the thermal efficiency also decreases.

The propulsive efficiency increases due to the fact that the increase in the exit velocity of the jet is not as high as rate of increase of the forward velocity of the engine.

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Mass
flow rate:__

The mass flow rate of a turbo-ramjet in the initial turbojet phase increases with increase in flight Mach number. The rate of increase of mass flow is lesser after the engine reaches the throttle hook as the compressor pressure ratio falls after that point.

As transition starts, due to the mixing constraints, the mass flow rate through the compressor drops sharply by around 50%. The bypass ratio initially is very low which means that the mass flow through the ram duct is low. Hence overall mass flow rate is low. As transition progresses towards a bypass ratio of unity the compressor mass flow rate increases due to the effect of ramming and simultaneously the mass flow rate of the ram duct also increases. After this arbitrarily chosen point the turbojet is powered down by cutting its mass flow rate down. In a real engine this decrease in mass flow rate is expected because there is a variable area inlet in front of the turbojet engine which decreases the area in front of the compressor available for the compressor to operate. However at the same time the flow through the ram duct is increasing. But the net effect is a drop in overall mass flow rate. After the transition the mass flow rate increases very rapidly, which is a characteristic of the ramjet engine.

** Note**:

The drop in mass flow rate during the transition can be compensated by increasing the afterburner temperate further thus increasing the thrust per unit mass flow and/or employing other thrust augmentation methods like water injection.

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Uninstalled Thrust:__

The uninstalled thrust of a turbo-ramjet engine is a function of thrust per unit mass flow and mass flow rate. The thrust plot is similar to the plot for mass flow rate. The drop in thrust during transition is due to the drop in mass flow rate. There is a very rapid increase in thrust in the ramjet phase due to the large increase in mass flow rate as mentioned earlier.

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__The variation in transition parameters:__

__Area
ratio of ram duct exit to core duct exit:__

The area ratio increases in proportion to the bypass ratio of the engine. The area of the ram duct exit into the mixer is very less compared to the area of the core flow exit since the mass flow rate through the ram duct is very less when compared to the flow through the core. As the transition progresses the mass flow through the ram duct increases at the cost of the flow through the core. The increase in area ratio, however, is not a pure exponential function before the bypass ratio of unity as both the mass flow rate through the core and the ram duct flow are increasing at the same time. In the analysis of the mixer it is assumed that there is a constant area mixer to simplify the analysis. The loses in total pressure due to mixing and eddy formation when two smaller flow mix into an area that is larger than their sum is calculated by CFD simulation

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Fuel-Air ratio during transition:__

The overall fuel air ratio is sum of fuel air ratio in the main burner divided by a factor of (1+alpha) and the fuel air ratio in the afterburner where alpha is the bypass ratio. The fuel air ratio in the main burner reduces as the temperature is being maintained at a low value and as the temperature due ramming increases at the same time, the net amount of fuel added is lesser. The fuel-air ratio in the afterburner increases due to the fact that the temperature in the mixed stream decreases because of addition of greater proportion of relatively colder mass flow from the ram stream as the transition progresses. Since the temperature of this colder mass flow has to be increased to the afterburner temperature of 2000 K, consequently more fuel has to be added. However as the flight Mach number increases the ramming effect on temperature increases and hence as transition comes to an end the value of fuel air ratio becomes constant and then decreases.

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Mach
numbers of core and ram duct:__

The Mach numbers of the core and ram streams are determined by the mixing constraints. The Mach number of the core stream is initially high and as the total pressure of the ram stream decreases this value decreases in accordance with the mixing requirement. The Mach number of the ram stream is initially constant up to the point where the total pressure of the ram stream begins to increase beyond the value of total pressure of the core stream due to the increase in flight Mach number.

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Mach
number of the mixed flow stream (M6a):__

The Mach number of the mixed flow stream is determined by the conservation of momentum equation, mass balance and the conservation of energy. As a result the Mach number of the mixed flow shows the characteristics of the Mach number of the core flow initially and then as transition progresses it takes on the characteristics of the ram duct Mach number.

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Pressure ratio across the mixer (π _{m}):__

Π_{m
}is defined as the ratio of total pressure of the mixed stream to the total
pressure of the core flow before the mixer. The pressure ratio of the mixed
stream decreases initially due to mixing and then increases due to the rapid
increase in the total pressure of the ram stream.

__Total
temperature of core and ram stream:__

The total temperature of the core flow is constant as the turbine inlet temperature does not change throughout the transition. The total temperature of the ram stream increases with flight Mach number.

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Temperature ratio across the mixer:__

τ_{m
}is defined as the ratio of total temperatures of the mixed flow to
the total temperature of the core flow. The ratio decreases initially because a
larger amount of colder mass flow is mixing with the core flow. As the
transition progresses the temperature due to ramming increases and this causes a
late rise in total temperature ratio.

__Static
temperature of core and ram streams:__

The core and ram stream temperatures are a function of their total temperatures and Mach numbers. As seen in the graph the temperature of core flow increases as transition progresses and becomes constant. This point corresponds to the point where the Mach number in the core becomes constant. The temperature of the ram stream increases with Mach number but the rate of increase drops slightly because the Mach number of the ram stream exit increases to satisfy mixing considerations.

__Static
pressure of the core and ram streams:__

The static pressure of the core and ram streams are equal to each other during transition in accordance with the Kutta condition. The static pressure increases as transition proceeds due to the increase in total pressure but the rate of increases drops due to the fact that the core stream Mach number becomes constant and the total pressure of the ram stream increases beyond the total pressure of the core.

__Other
parameters of interest:__

__ Unit thrust:__

The thrust per unit mass flow of a turbo-ramjet in the pure turbojet phase is a strong function of design compressor pressure ratio and design Mach number. The throttle ratio of the engine determines when the turbojet reaches its maximum power requirement condition. After the turbojet reaches this point the temperature of the burner has reached its maximum and the compressor pressure ratio is now further reduced so that the maximum turbine inlet temperature is not exceeded. The Mach number where the turbojet reaches the hook is strongly dependent on the design Mach number, altitude and the throttle ratio setting. With increase in altitude the hook is reached at higher mach numbers as shown for the turbojet operating at 10 km altitude. After the throttle hook is reached, the thrust per unit mass flow falls due to reduction in compressor pressure ratio as shown for the turbojet operating at 5 km.

However during transition, compressor pressure ratio falls and also the value of Tt4 is maintained constant with the intent of shutting the turbojet down. Hence the thrust per unit mass flow drops, as the gas does not have as large a temperature drop to increase its velocity with. The larger the temperature drop, the larger is the velocity increase. Once the Ramjet mode is on completely the increase in thrust per unit mass flow is due to the Tt4 increase along with the constant increase in ramming pressure.

The thrust per unit mass flow of a ramjet is higher at high altitudes for the same burner temperature due to the fact that more fuel has to be added to the relatively colder air flow to increase its temperature to the same level as the ramjet operating at lower altitudes.

**
Overall Fuel Air ratio**:

As in the mixed flow Turbo-Ramjet engine, the temperature of the burner increases with increase in Mach number in accordance to the throttle setting and once it reaches its maximum value becomes constant. Once this point has been reached then fuel added per unit mass flow is lesser since the temperature due to ram compression increases with Mach number and even though the compressor pressure ratio falls after this point the net rise in temperature is higher.

When the transition begins the afterburner is switched on which causes a large jump in overall fuel air ratio of the order of 50% increase. The increase is larger than in case of the mixed flow Turbo-Ramjet as mixing conditions do not have to be satisfied.

__Thrust
specific fuel consumption:__

TSFC during the turbojet phase rises as the thrust per unit mass flow decreases initially with fuel air ratio increasing at the same time. TSFC decreases at high Mach numbers during the ramjet phase due to comparatively large values of thrust produced resulting from a huge rise in mass flow rate and also due to the fact that the fuel air ratio of a ramjet decreases with Mach number due to ramming.

In the transition phase the TSFC increases by large value due to the sudden rise in fuel air ratio as explained earlier. As transition progresses the TSFC increases slightly due to comparatively larger drop in thrust per unit mass flow relative to the drop in fuel air ratio drop.

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Temperature:__

As in the mixed flow Turbo-Ramjet, after the temperature reaches its maximum possible value as set by material limitations of the turbine, it is held constant. But unlike the mixed flow Turbo-Ramjet mixing conditions do not have to be satisfied, hence the Tt4 is not reduced but is then held constant since the turbojet is now in the phase of being powered down. Later though, the sudden increase in the temperature is due to the ramjet operation. The ramjet main burner is separate from that of the turbojet and as there are no moving/rotating parts to be encountered, the temperatures at this point may be increased to 2000 K and above thus giving rise to large values of thrust.

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Overall Pressure Ratio (OPR):__

The OPR of a turbojet is constant until it reaches the throttle hook after which since the temperature of the main burner has reached its maximum the OPR has to be reduced in order to satisfy the Turbine inlet temperature limits. During the transition, since the temperature of the burner is reduced and then held constant in order to satisfy mixing conditions the OPR decreases further. In the ramjet phase the turbojet is powered down and hence is represented mathematically as having an OPR equal to unity.

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Efficiencies:__

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1.
Thermal __

The thermal efficiency of an engine is defined as the power output by the energy input in form of fuel. In an aircraft engine power is defined as thrust*forward velocity. This is the reason why at low mach numbers the value of thermal efficiency of the engine is low. The efficiency of the turbojet is higher than that of the ramjet at the same Mach number due to the presence of the compressor. And it is also clear from the expression for Brayton cycle efficiency that as pressure ratio increases the efficiency of the cycle increases. During transition since the OPR decreases the thermal efficiency also decreases.

__2.
Propulsive__

The propulsive efficiency increases due to the fact that the increase in the exit velocity of the jet is not as high as rate of increase of the forward velocity of the engine.

__Mass
flow rate:__

The mass flow trend initially is the same as in the mixed flow Turbo-Ramjet , which is not surprising as the initially the engine operates as a simple turbojet. However, as transition starts, and there being no mixing constraints, the mass flow rate does not drop. In fact as Tt4 is not reduced, overall mass flow rate continues to rise. As transition progresses towards a bypass ratio of unity the compressor mass flow rate increases due to the effect of ramming and simultaneously the mass flow rate of the ram duct also increases. As explained previously, after this arbitrarily chosen point the turbojet is powered down by cutting its mass flow rate down, which leads to an overall decrease in m0. After the transition the mass flow rate increases very rapidly, which is a characteristic of the ramjet engine.

** Note**:

The drop in mass flow rate during the transition can be compensated by increasing the afterburner temperate further thus increasing the thrust per unit mass flow and/or employing other thrust augmentation methods like water injection.

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Uninstalled Thrust:__

The uninstalled thrust of a turbo-ramjet engine is a function of thrust per unit mass flow and mass flow rate. The thrust plot is similar to the plot for mass flow rate. The drop in thrust during transition is due to the drop in mass flow rate. There is a very rapid increase in thrust in the ramjet phase due to the large increase in mass flow rate as mentioned earlier.

__Exit
Velocities:__

Exit velocities together with the mass flow provide the exit gross thrust or momentum which propels the vehicle forward. Hence V9 keeps increasing as more and more thrust is generated, the initial rate of increase is explained by the fact that Tt4 is also increased by way of adding more fuel per unit mass slow through the engine. Hence predictably it levels off during transition as Tt4 is maintained constant. The Ramjet stream has a low velocity initially as ramming pressure is low, and hence forth rises with corresponding rise in thrust as well.