Engine Inlet Design

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2009

Mike Meller

MAE 422

4/23/2009

Design of an External

Compression, Supersonic, Air-

Breathing Engine Inlet


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Table of Contents1 Shape of Engine Inlet .............................................................................................................................................................. 3

1.1 Introduction ................................................................................................................................................................... 3

1.2 Internal Compression Inlets........................................................................................................................................... 3

1.3 External Compression Inlets .......................................................................................................................................... 4

1.4 Mixed Compression Inlets ............................................................................................................................................. 5

1.5 General Choice of Inlet Shape ....................................................................................................................................... 6

2 Calculation of the Ratio of the Stagnation Pressure Behind the Last Shock to the Stagnation Pressure of the Free Stream

(P0L/P0) .............................................................................................................................................................................................. 7

3 Data and Plots of P0L/P0 vs. Mach Number ........................................................................................................................... 10

3.1 Design 1: Triconic Inlet (1 = 8, 2 = 8, 3 = 9) .......................................................................................................... 10

3.1.1 Data for Design 1 ............................................................................................................................................... 10

3.1.2 Plot for Design 1................................................................................................................................................. 12

3.2 Design 2: Triconic Inlet (1 = 9, 2 = 8, 3 = 8) .......................................................................................................... 13

3.2.1 Data for Design 2 ............................................................................................................................................... 13

3.2.2 Plot for Design 2................................................................................................................................................. 15

3.3 Design 3: Triconic Inlet (1 = 8.33, 2 = 8.33, 3 = 8.33) ........................................................................................... 16

3.3.1 Data for Design 3 ............................................................................................................................................... 16

3.3.2 Plot for Design 3................................................................................................................................................. 18

3.4 Triconic Design Comparison ........................................................................................................................................ 19

3.5 Biconic Comparison 1: (1 = 12.5, 2 = 12.5) ............................................................................................................. 20

3.5.1 Data for Biconic Comparison 1 .......................................................................................................................... 20

3.5.2 Plot for Biconic Comparison 1 ............................................................................................................................ 21

3.6 Biconic Comparison 2: (1 = 14, 2 = 11) ................................................................................................................... 22

3.6.1 Data for Biconic Comparison 2 .......................................................................................................................... 22

3.6.2 Plot for Biconic Comparison 2 ............................................................................................................................ 23

3.7 Plot Comparing both Biconic Designs .......................................................................................................................... 24

3.8 Monoconic Comparison: (1 = 20) .............................................................................................................................. 25

3.8.1 Data for Monoconic Comparison ....................................................................................................................... 25

3.8.2 Plot for Monoconic Comparison ........................................................................................................................ 26

3.9 Comparison Plot of All Previously Discussed Geometries ........................................................................................... 27

4 Discussion of Inlet Design Including the Effects of Viscosity ................................................................................................. 28

5 Discussion of Inlet Design Including the Effects of a Nonzero Angle of Attack ..................................................................... 29

6 Conclusions ........................................................................................................................................................................... 30

7 References ............................................................................................................................................................................ 31


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1 Shape of Engine Inlet1.1 IntroductionThe purpose of this design project is to design the most efficient external compression, supersonic, air-

breathing engine inlet. It is extremely important to have efficient supersonic diffusers like this. The

purpose of the inlet is to decelerate the airspeed to a compatible airspeed for engine operation. Most

gas turbine engines require subsonic flows between about Mach 0.3 to Mach 0.6 at the entrance face of

the engine to operate. The requirement for the model at hand is an engine face upstream Mach of 0.8.

When considering the most aerodynamically efficient system to design, the largest factor we will be

taking into account is the total pressure loss. To have the least amount of pressure loss, it is important

to slow the flow using multiple weak shocks. Using multiple weak shocks will always have a smaller

pressure loss than obtaining the same Mach number using a single (or fewer) shocks, and will therefore

be more efficient. Obviously, there will be complications that will be run into when performing the

design.

One such complication will be the fact that higher supersonic speeds mean a need for more

compression to slow the flow. In external compression inlets, this indicates a need to turn the flow

more, which results in a in an increase in cowl lip angle to align it with the incoming flow at the normal

shock. Unfortunately, an increase in cowl lip angle means a larger inlet frontal angle, which increases

the drag. This is one of the principle reasons purely external compression inlets are not used a great

deal at higher supersonic speeds.

As one might guess, certain methods of compressing the airflow are more efficient in different

conditions. For this reason, there are three general types of supersonic air-breathing engine inlets. The

three types are internal compression, external compression, and mixed compression. Each of these

inlets will discussed more in depth. It is important to note that the focus of this project is on external

compression inlets, however the other methods are briefly observed to help gain a background on the

purposes of their design, and conditions they work best in.

1.2 Internal Compression InletsAs given by the name, internal compression inlets (figure 1.2) perform both the supersonic and subsonic

compression of the air inside the duct. An easy way to think about the internal compression inlet is that

it is a converging-diverging nozzle. The compression is achieved through a series of oblique shock waves,

and then a normal shock just after the throat.

Figure 1.2) Internal compression inlet with reflected oblique shocks and terminal normal shock.


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This is a complex design because it is necessary to have a varying throat area to swallow the shock

past the throat. Additionally, fast reaction bypass doors are also essential past the throat to allow the

proper positioning of the normal shock. This is required because flight and engine conditions are

constantly changing, and in turn, the position of the normal shock will be too unless there is a

mechanism (the fast reaction bypass doors) to properly position the normal shock for best efficiency.

This design is beneficial because it requires a very low cowling angle, therefore it produces less drag.

For this reason, it is better suited for high supersonic Mach numbers, generally greater than Mach 3.5.

1.3 External Compression InletsExternal compression inlets perform the supersonic compression of the airflow before it enters the duct.

These inlets compress the air by either one oblique shock followed by a normal shock, a series of

oblique shocks followed by a normal shock, or just one normal shock.

The simplest of these is obviously compressing the flow by only one normal shock. This is referred to as

a pitot inlet (figure 1.3a), and is the cheapest, lightest, and easiest to design. This method however,

will lose efficiency quickly as you increase the Mach number.

Figure 1.3a) Pitot Inlet with a single normal shock outside of the duct.

The design I will be focusing on, is a series of several oblique shocks followed by a normal shock (figure

1.3b). This is a very reasonable design for Mach numbers below about 2.5. For this Mach range, the

simplicity of this design prevails over the lack of efficiency in total pressure losses. To adjust for

different conditions, namely different Mach numbers, inlet cone positioning is often included in the

design. By moving the cone, the location of the shock system can be changed for different Machnumbers to make the system as efficient as possible. It will be desirable to align the normal shock with

the leading edge of the cowl to avoid spillage, seen in the off-design of figure 1.3b.


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1.5 General Choice of Inlet ShapeAs stated in the title, the type of inlet that is being designed is an external compression inlet. Now,

some basics in the design process of the surface geometry of a supersonic external compression inlet

must be considered. Two very large factors to keep in mind when trying to design the inlet are the

Mach range the aircraft will be operating at, and the terminal shock Mach number necessary for proper

engine function.

The observed scenario will have the following general criteria:

The operational Mach range varies from Mach 1 to Mach 3 The Mach number immediately after the terminal normal shock will be approximately Mach 0.8 The maximum angle that the flow can turn before entering the subsonic diffuser is 25 Try to attain the maximum total pressure recovery to be most efficient The aircraft is flying at 45,000 ft The air is assumed to be inviscid and calorically perfect The aircraft is at an angle of attack of zero The flow is assumed to be 2-dimensional

When considering geometries for the inlet, one might think that the having a perfectly curved surface

would be quite beneficial. This would theoretically create a compression fan of infinite oblique shocks,

therefore creating isentropic flow, and creating basically no total pressure loss. In reality, viscous effects

diminish the performance of these isentropic inlets, which can lead to a lower boundary layer health

than the equivalent multiple, straight surfaced geometry. Also, isentropic inlets and their similar

multiple, straight surfaced inlets both have a similar turn angle. This means neither one of these inlets

has an advantage over the other in terms of drag (a larger turn angle results in a larger cowl angle,

which results in a larger drag). Observing this, it was decided that multiple straight faces as opposed toa curved geometry will be sufficient.

Now that it is established that the geometry will be multiple straight faces, there are some other major

factors that still need to be determined. One such factor is the number of oblique shocks before the

terminal shock. Through some research, it was determined that some aircraft use a biconic inlet to

create two oblique shock waves with both waves focused on the lip of the cowl. It is known that the

more oblique shocks that exist, the better the pressure recovery. This is why I am designing the inlet to

have an additional oblique shock. This will make it more efficient. Furthermore, it seems reasonable to

produce something with this triconic geometry since biconic inlets are in existence. Another factor to

consider is the angle of each separate flat surface that creates the triconic geometry. In my calculations,

I will perform several different angle variations to see which configuration is the most efficient.


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After taking all of these factors into account (many more factors are being neglected), a final design has

been settled upon. The design geometry will be a triconic external compression inlet (it will be analyzed

as 2D flow). At different Mach numbers and flying conditions, the point at which the shock waves

intersect will vary. To account for this and reduce the spillover, the center cone will move axially

forward and backward to direct the shocks to line up with the leading edge of the cowl to obtain the

best efficiency. A representation of the general shape of the triconic inlet (2D) is seen in figure 1.5.

Figure 1.5) 2D visual representation of the triconic inlet that will be designed.

2

Calculation of the Ratio of the Stagnation Pressure Behind the LastShock to the Stagnation Pressure of the Free Stream (P0L/P0)

The calculation of the ratio of stagnation pressure behind the last shock to the stagnation pressure of

the free stream (P0L/P0) for the cruising Mach number of 2 can be done by a number of basic relations in

gas dynamics. The scenario being observed is the triconic design 2, with 1 = 9, 2 = 8, 3 = 8. The

process below was used for all the calculations of all the Mach numbers and corresponding stagnation

pressure ratios:

Free stream Mach number: M1 = 2 ; First angle: 1 = 9

Want to find Mach angle, , so must find and first:

= 2 12 3 1 + 12

2 1 + + 12

221/2With the above M1 and 1, this returns: = .

= 2 13 9 1 + 1

22 1 + 1

22 + + 1

442

3 With the above M1, 1, and 1, this returns: =.Now we can find Mach angle, , using the following relation:

= 12 1 + 2 4 + 1

3

3 1 + 12

2

With the above M1, 1, 1, and1, and = 1 for weak shocks (assumed): = .

L

1

43

2


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Now it is possible to find the normal component of M1 before the first oblique shock:

1 = 1In this scenario, = .Using normal shock relations, we can find the normal Mach number, 2, after the fist oblique shock:

2 = 1 + 12

1212 12

In this scenario, = .Next, we will find the Mach number after the first oblique shock:

2 =

2sin1 1

Our second Mach number came out to be = .To calculate the total pressure ration across this first shock, use the following relation:

0201 =12

2 + 1222 + 112

+121

= 1.4

Across this shock wave, =.

Now, we must repeat this process across the subsequent shock waves, where each new is with respect

to the previous one. Following this process, we obtain:

ML = .8355 , which is approximately Mach 0.8, the specified approximate final Mach number.

We also obtain the following total pressure ratios across each of the shock waves:

= . = .

= .Ultimately, we want to obtain the value

001 , the ratio of the total pressure after the last to the total

pressure of the free stream. This is done by multiplying the determined ratios together:

001 =004

04030302

0201 = 1.0000.9917. 9820(.9886) = .


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There is a very important note to make referring to calculations made above, and all the calculations

made in the excel spreadsheets below. There was an error that appeared in the tables for the

calculations of for the first few entries. Due to the geometry of the cone of the inlet, and gas

dynamics, low Mach numbers will experience a detached shock (see figure 2).

This detached shock is treated as a normal shock, and values of 90 are added in to the table wherethey occur. Once a detached shock occurs, values are set to zero for the rest of the surface changes

because the flow is subsonic, and therefore will not experience any more shocks.

Later in the tables the values will be zero early on due to previous normal shocks, then progress up to

90 for the detached shock that will occur as soon as the flow becomes supersonic again for higher initial

Mach numbers. As you progress with higher Mach numbers, the shock will eventually become attached,

and the regular equations will resume their intended functions.

Figure 2)This is an example of a detached shock in supersonic flow, also referred to as a bow shock.
http://upload.wikimedia.org/wikipedia/en/1/13/Bowshockexample.jpg


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3 Data and Plots of P0L/P0 vs. Mach Number3.1 Design 1: Triconic Inlet (1 = 8, 2 = 8, 3 = 9)3.1.1 Data for Design 1

: 1.4

Oblique Shock 1 Oblique Shock 2

1: 8 degrees (Respect to horizontal) 2: 8 degrees (Respect to 1)

M1 1 1 1 Mn1 Mn2 Po2/Po1 M2 2 2 2 Mn2' Mn3 Po3/Po2

1 N/A N/A 90.0000 1.0000 1.0000 1.0000 1.0000 N/A N/A 0.0000 N/A N/A 1.0000

1.1 N/A N/A 90.0000 1.1000 0.9118 0.9989 0.9118 N/A N/A 0.0000 N/A N/A 1.0000

1.2 N/A N/A 90.0000 1.2000 0.8422 0.9928 0.8422 N/A N/A 0.0000 N/A N/A 1.0000

1.3 N/A N/A 90.0000 1.3000 0.7860 0.9794 0.7860 N/A N/A 0.0000 N/A N/A 1.0000

1.4 0.8032 -0.0580 59.3672 1.2046 0.8393 0.9923 1.0744 N/A N/A 90.0000 1.0744 0.9323 0.9995

1.5 1.1156 0.5736 52.5715 1.1912 0.8477 0.9936 1.2079 N/A N/A 90.0000 1.2079 0.8373 0.9920

1.6 1.4383 0.7841 48.0302 1.1896 0.8487 0.9938 1.3195 N/A N/A 90.0000 1.3195 0.7762 0.9758

1.7 1.7760 0.8752 44.5282 1.1921 0.8471 0.9935 1.4232 0.8751 0.1678 57.4217 1.1992 0.8426 0.9929

1.8 2.1308 0.9211 41.6734 1.1968 0.8442 0.9931 1.5225 1.1872 0.6397 51.4222 1.1902 0.8483 0.9937

1.9 2.5036 0.9469 39.2722 1.2027 0.8405 0.9925 1.6191 1.5016 0.8072 47.2971 1.1899 0.8486 0.9937

2 2.8951 0.9624 37.2101 1.2095 0.8363 0.9919 1.7137 1.8238 0.8833 44.1031 1.1927 0.8468 0.9935

2.1 3.3055 0.9723 35.4125 1.2169 0.8319 0.9911 1.8069 2.1558 0.9234 41.4959 1.1972 0.8439 0.99312.2 3.7352 0.9790 33.8269 1.2247 0.8272 0.9902 1.8987 2.4988 0.9466 39.3003 1.2026 0.8405 0.9925

2.3 4.1843 0.9836 32.4154 1.2329 0.8224 0.9892 1.9896 2.8533 0.9611 37.4121 1.2087 0.8368 0.9919

2.4 4.6528 0.9869 31.1489 1.2414 0.8175 0.9882 2.0795 3.2196 0.9706 35.7630 1.2153 0.8328 0.9912

2.5 5.1409 0.9894 30.0053 1.2502 0.8125 0.9870 2.1685 3.5978 0.9772 34.3058 1.2222 0.8287 0.9905

2.6 5.6487 0.9912 28.9666 1.2592 0.8075 0.9858 2.2568 3.9879 0.9818 33.0058 1.2293 0.8245 0.9897

2.7 6.1761 0.9926 28.0186 1.2683 0.8025 0.9845 2.3444 4.3898 0.9852 31.8369 1.2367 0.8202 0.9888

2.8 6.7232 0.9938 27.1496 1.2777 0.7975 0.9830 2.4313 4.8033 0.9878 30.7791 1.2441 0.8159 0.9878

2.9 7.2901 0.9946 26.3499 1.2872 0.7926 0.9815 2.5175 5.2284 0.9897 29.8164 1.2518 0.8117 0.9868

3 7.8767 0.9954 25.6114 1.2968 0.7876 0.9799 2.6031 5.6647 0.9913 28.9359 1.2595 0.8074 0.9858


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Oblique Shock 3 Terminal Normal Shock

3: 9 degrees (Respect to 2)

M3 3 3 3 Mn3' Mn4 Po4/Po3 M4 ML PoL/Po4 PoL/Po1

1.0000 N/A N/A 0.0000 N/A N/A 1.0000 1.0000 1.0000 1.0000 1.0000

0.9118 N/A N/A 0.0000 N/A N/A 1.0000 0.9118 0.9118 1.0000 0.9989

0.8422 N/A N/A 0.0000 N/A N/A 1.0000 0.8422 0.8422 1.0000 0.9928

0.7860 N/A N/A 0.0000 N/A N/A 1.0000 0.7860 0.7860 1.0000 0.9794

0.9323 N/A N/A 0.0000 N/A N/A 1.0000 0.9415 0.9415 1.0000 0.9919

0.8373 N/A N/A 0.0000 N/A N/A 1.0000 0.8455 0.8455 1.0000 0.9857

0.7762 N/A N/A 0.0000 N/A N/A 1.0000 0.7839 0.7839 1.0000 0.9697

1.1094 N/A N/A 90.0000 1.1094 0.9045 0.9986 0.9045 0.9134 0.9992 0.9843

1.2341 N/A N/A 90.0000 1.2341 0.8217 0.9891 0.8217 0.8298 0.9987 0.9748

1.3398 N/A N/A 90.0000 1.3398 0.7665 0.9719 0.7665 0.7740 0.9984 0.9570

1.4370 0.9182 0.2720 53.1764 1.1503 0.8748 0.9967 1.2334 0.8221 0.9892 0.9715

1.5292 1.2086 0.6566 47.7153 1.1313 0.8883 0.9977 1.3901 0.7439 0.9606 0.9433

1.6179 1.4976 0.8058 43.9212 1.1223 0.8949 0.9981 1.5253 0.6923 0.9216 0.9040

1.7039 1.7897 0.8776 40.9941 1.1178 0.8982 0.9983 1.6495 0.6541 0.8762 0.8583

1.7878 2.0867 0.9169 38.6173 1.1158 0.8997 0.9984 1.7665 0.6242 0.8274 0.8092

1.8699 2.3895 0.9405 36.6258 1.1156 0.8999 0.9984 1.8783 0.5999 0.7773 0.7587

1.9504 2.6987 0.9556 34.9204 1.1165 0.8992 0.9984 1.9860 0.5798 0.7274 0.7085

2.0296 3.0144 0.9658 33.4365 1.1183 0.8978 0.9983 2.0903 0.5627 0.6787 0.65952.1074 3.3366 0.9729 32.1292 1.1208 0.8960 0.9982 2.1918 0.5482 0.6319 0.6125

2.1840 3.6652 0.9781 30.9658 1.1237 0.8938 0.9981 2.2907 0.5355 0.5874 0.5678

2.2595 4.0002 0.9819 29.9219 1.1271 0.8913 0.9979 2.3874 0.5245 0.5455 0.5258


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3.1.2 Plot for Design 1

Figure 3.1.2) The above plot shows the efficiency of a supersonic, external compression, triconic inlet for

the conditions of 1 = 2 = 8, and 3 = 9.

The above plot, figure 3.1.2, is the inlet efficiency for the triconic inlet with 1= 2= 8, and 3 = 9. Theidea behind these chosen angles was to see the effect of keeping the change in angle between each of

the three flat sections similar, but experimenting with a larger angle at the last oblique shock. The next

relationship that is going to be observed is if the angles are flipped begin with 9, and have the last two

angles be 8. It is visible in the graph that with each new oblique shock that occurs, the efficiency

briefly goes up again, but never quite to the same height as the previous peak because of losses. Once

the terminal normal shock occurs (around Mach 2), it is clear that the total pressure recovery decreases

steadily at a much sharper rate (and consistently) than within the oblique shock range. At Mach 3, the

efficiency drops all the way down to 0.5258.

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1 1.5 2 2.5 3

P0L

/P0

Mach Number

Inlet Efficiency: P0L/P0 vs. M

Triconic Design 1

8,8,9


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3.2 Design 2: Triconic Inlet (1 = 9, 2 = 8, 3 = 8)3.2.1 Data for Design 2

: 1.4


1: 9 degrees (Respect to horizontal) 2: 8 degrees (Respect to 1)


1.0 N/A N/A 90.0000 1.0000 1.0000 1.0000 1.0000 N/A N/A 0.0000 N/A N/A 1.00001.1 N/A N/A 90.0000 1.1000 0.9118 0.9989 0.9118 N/A N/A 0.0000 N/A N/A 1.0000

1.2 N/A N/A 90.0000 1.2000 0.8422 0.9928 0.8422 N/A N/A 0.0000 N/A N/A 1.0000

1.3 N/A N/A 90.0000 1.3000 0.7860 0.9794 0.7860 N/A N/A 0.0000 N/A N/A 1.0000

1.4 0.7553 -0.6432 63.1866 1.2495 0.8129 0.9871 1.0025 N/A N/A 90.0000 1.0025 0.9975 1.0000

1.5 1.0765 0.3881 54.4699 1.2207 0.8296 0.9907 1.1637 N/A N/A 90.0000 1.1637 0.8657 0.9958

1.6 1.4037 0.7008 49.5111 1.2169 0.8319 0.9911 1.2806 N/A N/A 90.0000 1.2806 0.7960 0.9826

1.7 1.7440 0.8302 45.8105 1.2190 0.8306 0.9908 1.3863 0.7107 -0.9531 68.7743 1.2922 0.7899 0.9807

1.8 2.1003 0.8940 42.8385 1.2239 0.8277 0.9903 1.4864 1.0325 0.3140 58.4433 1.2666 0.8035 0.9847

1.9 2.4741 0.9291 40.3601 1.2304 0.8238 0.9895 1.5830 1.3474 0.6664 53.5635 1.2736 0.7997 0.9837

2.0 2.8661 0.9501 38.2440 1.2380 0.8194 0.9886 1.6773 1.6656 0.8088 49.9729 1.2844 0.7940 0.9820

2.1 3.2767 0.9634 36.4068 1.2464 0.8147 0.9875 1.7699 1.9911 0.8788 47.0962 1.2964 0.7878 0.9800

2.2 3.7064 0.9723 34.7915 1.2553 0.8097 0.9863 1.8609 2.3259 0.9176 44.6935 1.3088 0.7815 0.9778

2.3 4.1552 0.9784 33.3571 1.2647 0.8045 0.9850 1.9508 2.6707 0.9410 42.6347 1.3213 0.7754 0.9755

2.4 4.6234 0.9828 32.0728 1.2744 0.7993 0.9836 2.0395 3.0261 0.9560 40.8395 1.3337 0.7694 0.9731

2.5 5.1111 0.9860 30.9151 1.2844 0.7940 0.9820 2.1273 3.3922 0.9662 39.2537 1.3461 0.7636 0.9706

2.6 5.6183 0.9885 29.8654 1.2947 0.7887 0.9803 2.2143 3.7692 0.9733 37.8388 1.3583 0.7579 0.9679

2.7 6.1450 0.9903 28.9086 1.3052 0.7833 0.9785 2.3004 4.1569 0.9784 36.5661 1.3704 0.7525 0.9652

2.8 6.6913 0.9918 28.0327 1.3159 0.7780 0.9765 2.3857 4.5552 0.9823 35.4135 1.3824 0.7472 0.9625

2.9 7.2574 0.9930 27.2277 1.3268 0.7727 0.9744 2.4703 4.9641 0.9852 34.3638 1.3943 0.7421 0.9596

3.0 7.8431 0.9939 26.4850 1.3379 0.7674 0.9722 2.5541 5.3832 0.9874 33.4030 1.4061 0.7371 0.9567


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3: 8 degrees (Respect to 2)


1.0000 N/A N/A 0.0000 N/A N/A 1.0000 1.0000 1.0000 1.0000 1.0000

0.9118 N/A N/A 0.0000 N/A N/A 1.0000 0.9118 0.9118 1.0000 0.9989

0.8422 N/A N/A 0.0000 N/A N/A 1.0000 0.8422 0.8422 1.0000 0.9928

0.7860 N/A N/A 0.0000 N/A N/A 1.0000 0.7860 0.7860 1.0000 0.9794

0.9975 N/A N/A 0.0000 N/A N/A 1.0000 0.9975 0.9975 1.0000 0.9871

0.8657 N/A N/A 0.0000 N/A N/A 1.0000 0.8657 0.8657 1.0000 0.9865

0.7960 N/A N/A 0.0000 N/A N/A 1.0000 0.7960 0.7960 1.0000 0.9738

0.9142 N/A N/A 0.0000 N/A N/A 1.0000 0.9142 0.9142 1.0000 0.9717

1.0576 N/A N/A 90.0000 1.0576 0.9465 0.9998 0.9465 0.9465 1.0000 0.9750

1.1397 N/A N/A 90.0000 1.1397 0.8823 0.9973 0.8823 0.8823 1.0000 0.9707

1.2109 N/A N/A 90.0000 1.2109 0.8355 0.9917 0.8355 0.8355 1.0000 0.9627

1.2768 N/A N/A 90.0000 1.2768 0.7980 0.9832 0.7980 0.7980 1.0000 0.9515

1.3395 N/A N/A 90.0000 1.3395 0.7667 0.9719 0.7667 0.7667 1.0000 0.9374

1.3998 0.7548 -0.6462 65.8667 1.2775 0.7976 0.9831 0.9525 1.0507 1.0002 0.9448

1.4584 0.9429 0.1183 60.2732 1.2665 0.8035 0.9847 1.0300 0.9712 1.0000 0.9424

1.5155 1.1266 0.4596 56.7824 1.2679 0.8028 0.9845 1.0840 0.9245 0.9993 0.9377

1.5714 1.3088 0.6395 54.0720 1.2724 0.8003 0.9839 1.1304 0.8889 0.9977 0.9314

1.6261 1.4910 0.7448 51.8228 1.2783 0.7972 0.9830 1.1729 0.8596 0.9951 0.92381.6797 1.6738 0.8112 49.8919 1.2847 0.7938 0.9819 1.2126 0.8344 0.9915 0.9151

1.7324 1.8577 0.8555 48.1990 1.2915 0.7903 0.9808 1.2505 0.8124 0.9870 0.9052

1.7842 2.0429 0.8863 46.6929 1.2983 0.7868 0.9797 1.2868 0.7927 0.9816 0.8944


15/31


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3.3 Design 3: Triconic Inlet (1 = 8.33, 2 = 8.33, 3 = 8.33)3.3.1 Data for Design 3

: 1.4


1: 8.3333 degrees (Respect to horizontal) 2: 8.3333 degrees (Respect to 1)


1.0 N/A N/A 90.0000 1.0000 1.0000 1.0000 1.0000 N/A N/A 0.0000 N/A N/A 1.00001.1 N/A N/A 90.0000 1.1000 0.9118 0.9989 0.9118 N/A N/A 0.0000 N/A N/A 1.0000

1.2 N/A N/A 90.0000 1.2000 0.8422 0.9928 0.8422 N/A N/A 0.0000 N/A N/A 1.0000

1.3 N/A N/A 90.0000 1.3000 0.7860 0.9794 0.7860 N/A N/A 0.0000 N/A N/A 1.0000

1.4 0.7882 -0.2226 60.4246 1.2176 0.8314 0.9910 1.0538 N/A N/A 90.0000 1.0538 0.9498 0.9998

1.5 1.1033 0.5188 53.1780 1.2008 0.8417 0.9927 1.1936 N/A N/A 90.0000 1.1936 0.8462 0.9934

1.6 1.4273 0.7589 48.5120 1.1986 0.8431 0.9929 1.3067 N/A N/A 90.0000 1.3067 0.7826 0.9782

1.7 1.7659 0.8614 44.9482 1.2010 0.8416 0.9927 1.4110 0.8227 -0.0840 59.3527 1.2139 0.8337 0.9914

1.8 2.1211 0.9128 42.0562 1.2057 0.8386 0.9922 1.5105 1.1368 0.5565 52.6099 1.2002 0.8421 0.9928

1.9 2.4942 0.9414 39.6304 1.2119 0.8349 0.9916 1.6071 1.4510 0.7692 48.2281 1.1986 0.8430 0.9929

2.0 2.8858 0.9586 37.5509 1.2189 0.8306 0.9908 1.7017 1.7716 0.8626 44.8956 1.2011 0.8415 0.9927

2.1 3.2963 0.9696 35.7404 1.2266 0.8261 0.9900 1.7946 2.1013 0.9107 42.2003 1.2054 0.8388 0.9923

2.2 3.7260 0.9769 34.1453 1.2348 0.8213 0.9890 1.8862 2.4415 0.9383 39.9434 1.2110 0.8354 0.9917

2.3 4.1750 0.9820 32.7263 1.2434 0.8163 0.9879 1.9766 2.7927 0.9552 38.0101 1.2172 0.8317 0.9910

2.4 4.6435 0.9856 31.4540 1.2524 0.8113 0.9867 2.0662 3.1553 0.9663 36.3266 1.2240 0.8276 0.9903

2.5 5.1314 0.9883 30.3057 1.2615 0.8062 0.9855 2.1548 3.5294 0.9739 34.8423 1.2311 0.8235 0.9895

2.6 5.6390 0.9904 29.2634 1.2709 0.8011 0.9841 2.2426 3.9151 0.9793 33.5205 1.2385 0.8192 0.9886

2.7 6.1662 0.9919 28.3125 1.2806 0.7960 0.9826 2.3297 4.3122 0.9832 32.3340 1.2461 0.8149 0.9876

2.8 6.7131 0.9931 27.4413 1.2903 0.7909 0.9810 2.4161 4.7206 0.9861 31.2615 1.2538 0.8105 0.9865

2.9 7.2796 0.9941 26.6398 1.3003 0.7858 0.9793 2.5018 5.1402 0.9884 30.2864 1.2617 0.8062 0.9854

3.0 7.8660 0.9949 25.8999 1.3104 0.7807 0.9775 2.5868 5.5708 0.9901 29.3956 1.2697 0.8018 0.9843


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3: 8.3333 degrees (Respect to 2)


1.0000 N/A N/A 0.0000 N/A N/A 1.0000 1.0000 1.0000 1.0000 1.0000

0.9118 N/A N/A 0.0000 N/A N/A 1.0000 0.9118 0.9118 1.0000 0.9989

0.8422 N/A N/A 0.0000 N/A N/A 1.0000 0.8422 0.8422 1.0000 0.9928

0.7860 N/A N/A 0.0000 N/A N/A 1.0000 0.7860 0.7860 1.0000 0.9794

0.9498 N/A N/A 0.0000 N/A N/A 1.0000 0.9498 0.9498 1.0000 0.9908

0.8462 N/A N/A 0.0000 N/A N/A 1.0000 0.8462 0.8462 1.0000 0.9862

0.7826 N/A N/A 0.0000 N/A N/A 1.0000 0.7826 0.7826 1.0000 0.9713

1.0724 N/A N/A 90.0000 1.0724 0.9340 0.9996 0.9340 0.9340 1.0000 0.9837

1.2062 N/A N/A 90.0000 1.2062 0.8383 0.9922 0.8383 0.8383 1.0000 0.9774

1.3144 N/A N/A 90.0000 1.3144 0.7787 0.9768 0.7787 0.7787 1.0000 0.9618

1.4127 0.8279 -0.0647 59.1991 1.2134 0.8339 0.9914 1.0751 0.9317 0.9995 0.9747

1.5052 1.1198 0.5379 52.8944 1.2004 0.8419 0.9928 1.1998 0.8423 0.9928 0.9682

1.5939 1.4072 0.7497 48.7581 1.1985 0.8431 0.9929 1.3002 0.7859 0.9793 0.9538

1.6797 1.6960 0.8463 45.6067 1.2003 0.8420 0.9928 1.3903 0.7438 0.9606 0.9337

1.7633 1.9886 0.8975 43.0556 1.2038 0.8398 0.9924 1.4744 0.7104 0.9377 0.9093

1.8449 2.2864 0.9275 40.9177 1.2084 0.8370 0.9920 1.5542 0.6827 0.9117 0.88181.9249 2.5899 0.9464 39.0844 1.2136 0.8339 0.9914 1.6308 0.6594 0.8835 0.8521

2.0033 2.8993 0.9590 37.4863 1.2192 0.8305 0.9908 1.7048 0.6393 0.8537 0.8208

2.0805 3.2147 0.9678 36.0755 1.2251 0.8270 0.9902 1.7765 0.6218 0.8230 0.7887

2.1564 3.5362 0.9740 34.8176 1.2312 0.8234 0.9894 1.8463 0.6065 0.7919 0.7562

2.2311 3.8635 0.9787 33.6868 1.2375 0.8197 0.9887 1.9144 0.5928 0.7607 0.7236


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3.3.2 Plot for Design 3

Figure 3.3.2) The above plot shows the efficiency of a supersonic, external compression, triconic inlet for

the conditions of 1= 2= 3 = 8.33.

The above plot, figure 3.3.2, is the inlet efficiency for the triconic inlet with 1= 2= 3 = 8.33. The idea

behind these chosen angles was to see the effect of keeping the change in angle between each of the

three flat sections identical, since it was assumed that close to uniform compression would be most

efficient. This graph is definitely the smoothest when it comes to transitioning, but it is not as efficient.

Once the terminal normal shock occurs (around Mach 2), it is clear that the total pressure recovery

decreases steadily at a much sharper rate (and consistently) than within the oblique shock range also.

The final efficiency at Mach 3 was 0.7236 for this orientation.

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

1.0500

1.0 1.5 2.0 2.5 3.0

P0L

/P0

Mach Number


Triconic Design 3

8.33,8.33,8.33


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3.4 Triconic Design Comparison

Figure 3.4) The above plot shows the efficiency comparison of the three previously discussed supersonic,

external compression, triconic inlets.

Comparing all 3 of the triconic designs in figure 3.4, some important trends are noticed. At our cruising

Mach of 2, Design 3, 1= 2= 3 = 8.33, is the most efficient. However when observing the whole range

of free stream Mach values from 1 to 3, Design 2, 1= 9 and 2 = 3 = 8, is very obviously the most

efficient. At Mach 3, it ends with an efficiency of 0.8944 when compared to designs 1 and 3, who end

with efficiencies of 0.5258 and 0.7236 respectively.

When weighing the benefits of each design, it is decided that Design 2, 1= 9 and 2 = 3 = 8, is the

best out of these three. Even though at cruising Mach 2 its efficiency is slightly less than Design 3, the

broader range that Design 2 is more efficient for is far more beneficial.

0.5

0.6

0.7

0.8

0.9

1

1.1

1 1.5 2 2.5 3

P0L

/P0

Mach Number

Triconic Design Comparison

Efficiency P0L/P0 vs. M

8, 8, 9

9, 8, 8

All 8.33


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3.5 Biconic Comparison 1: (1 = 12.5, 2 = 12.5)3.5.1 Data for Biconic Comparison 1: 1.4

1: 12.5 degrees 2: 12.5 degrees (Respect to 1)

M1 1 1 1 Mn1 Mn2 P o2 /Po1 M2 2 2 2 Mn2' Mn3 Po3/ Po2 M3 ML P oL/Po3P oL/P o1

1.0 N/A N/A 90.0000 1.0000 1.0000 1.0000 1.0000 N/A N/A 0.0000 N/A N/A 1.0000 1.0000 1.0000 1.0000 1.0000

1.1 N/A N/A 90.0000 1.1000 0.9118 0.9989 0.9118 N/A N/A 0.0000 N/A N/A 1.0000 0.9118 0.9118 1.0000 0.9989

1.2 N/A N/A 90.0000 1.2000 0.8422 0.9928 0.8422 N/A N/A 0.0000 N/A N/A 1.0000 0.8422 0.8422 1.0000 0.9928

1.3 N/A N/A 90.0000 1.3000 0.7860 0.9794 0.7860 N/A N/A 0.0000 N/A N/A 1.0000 0.7860 0.7860 1.0000 0.9794

1.4 N/A N/A 90.0000 1.4000 0.7397 0.9582 0.7397 N/A N/A 0.0000 N/A N/A 1.0000 0.7397 0.7397 1.0000 0.9582

1.5 N/A N/A 90.0000 1.5000 0.7011 0.9298 0.7011 N/A N/A 0.0000 N/A N/A 1.0000 0.7011 0.7011 1.0000 0.9298

1.6 1.2352 0.0824 56.0215 1.3268 0.7727 0.9745 1.1221 N/A N/A 90.0000 1.1221 0.8950 0.9981 0.8950 0.8950 1.0000 0.9726

1.7 1.5914 0.5339 50.9979 1.3211 0.7755 0.9755 1.2457 N/A N/A 90.0000 1.2457 0.8150 0.9876 0.8150 0.8150 1.0000 0.9635

1.8 1.9570 0.7267 47.3919 1.3248 0.7737 0.9748 1.3525 N/A N/A 90.0000 1.3525 0.7606 0.9692 0.7606 0.7606 1.0000 0.9448

1.9 2.3363 0.8243 44.5353 1.3326 0.7699 0.9733 1.4515 N/A N/A 90.0000 1.4515 0.7190 0.9444 0.7190 0.7190 1.0000 0.9192

2.0 2.7314 0.8795 42.1688 1.3426 0.7652 0.9713 1.5459 1.0432 -0.4601 60.2641 1.3423 0.7653 0.9713 1.0337 0.9678 1.0000 0.9434

2.1 3.1436 0.9133 40.1554 1.3542 0.7598 0.9688 1.6370 1.3663 0.3014 53.9103 1.3228 0.7746 0.9752 1.1711 0.8607 0.9953 0.9403

2.2 3.5735 0.9351 38.4113 1.3669 0.7541 0.9661 1.7257 1.6842 0.5981 49.9761 1.3215 0.7753 0.9755 1.2742 0.7994 0.9836 0.9269

2.3 4.0217 0.9500 36.8800 1.3803 0.7481 0.9630 1.8124 2.0033 0.7424 47.0034 1.3256 0.7733 0.9747 1.3651 0.7549 0.9664 0.90712.4 4.4886 0.9604 35.5217 1.3944 0.7421 0.9596 1.8975 2.3266 0.8225 44.6004 1.3323 0.7700 0.9734 1.4491 0.7199 0.9451 0.8827

2.5 4.9742 0.9680 34.3067 1.4091 0.7359 0.9559 1.9811 2.6554 0.8711 42.5862 1.3406 0.7661 0.9717 1.5283 0.6913 0.9206 0.8551

2.6 5.4788 0.9737 33.2124 1.4241 0.7298 0.9520 2.0634 2.9905 0.9027 40.8582 1.3498 0.7618 0.9698 1.6039 0.6673 0.8937 0.8251

2.7 6.0026 0.9780 32.2208 1.4396 0.7236 0.9478 2.1444 3.3324 0.9241 39.3512 1.3597 0.7573 0.9676 1.6767 0.6467 0.8653 0.7936

2.8 6.5456 0.9813 31.3179 1.4554 0.7175 0.9433 2.2244 3.6810 0.9393 38.0205 1.3701 0.7527 0.9653 1.7470 0.6288 0.8359 0.7611

2.9 7.1079 0.9840 30.4919 1.4715 0.7114 0.9386 2.3032 4.0364 0.9504 36.8340 1.3808 0.7480 0.9629 1.8152 0.6131 0.8059 0.7283

3.0 7.6895 0.9861 29.7335 1.4879 0.7054 0.9336 2.3810 4.3986 0.9587 35.7676 1.3917 0.7432 0.9602 1.8815 0.5993 0.7759 0.6955

Oblique Shock 1 Oblique Shock 2 Terminal Normal Shock


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3.5.2 Plot for Biconic Comparison 1

Figure 3.5.2) The above plot shows the efficiency of a supersonic, external compression, biconic inlet for

the conditions of 1= 2 = 12.5.

The above plot, figure 3.5.2, is the inlet efficiency for the biconic inlet with 1= 2 12.5. The purpose of

the above and following plots were to see how much less efficient a more efficient biconic inlet was

than a triconic inlet. The chosen angles were to see the effect of keeping the change in angle between

each of the three flat sections identical, since it was assumed that close to uniform compression would

be most efficient. Once the terminal normal shock occurs (just prior to Mach 2), it is clear that the total

pressure recovery decreases steadily at a much sharper rate (and consistently) than within the oblique

shock range also. The final efficiency at Mach 3 was 0.6955 for this orientation.

0.6000

0.6500

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

1.0500

1.0 1.5 2.0 2.5 3.0

P0L

/P0

Mach Number


Biconic Comparison 1

12.5,12.5


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3.6 Biconic Comparison 2: (1 = 14, 2 = 11)3.6.1 Data for Biconic Comparison 2: 1.4

1: 14 degrees 2: 11 degrees (Respect to 1)

M1 1 1 1 Mn1 Mn2 P o2/P o1 M2 2 2 2 Mn2' Mn3 Po3/Po2 M3 ML PoL/ Po3PoL/ Po1

1.0 N/A N/A 90.0000 1.0000 1.0000 1.0000 1.0000 N/A N/A 0.0000 N/A N/A 1.0000 1.0000 1.0000 1.0000 1.0000

1.1 N/A N/A 90.0000 1.1000 0.9118 0.9989 0.9118 N/A N/A 0.0000 N/A N/A 1.0000 0.9118 0.9118 1.0000 0.9989

1.2 N/A N/A 90.0000 1.2000 0.8422 0.9928 0.8422 N/A N/A 0.0000 N/A N/A 1.0000 0.8422 0.8422 1.0000 0.9928

1.3 N/A N/A 90.0000 1.3000 0.7860 0.9794 0.7860 N/A N/A 0.0000 N/A N/A 1.0000 0.7860 0.7860 1.0000 0.9794

1.4 N/A N/A 90.0000 1.4000 0.7397 0.9582 0.7397 N/A N/A 0.0000 N/A N/A 1.0000 0.7397 0.7397 1.0000 0.9582

1.5 N/A N/A 90.0000 1.5000 0.7011 0.9298 0.7011 N/A N/A 0.0000 N/A N/A 1.0000 0.7011 0.7011 1.0000 0.9298

1.6 1.1337 -0.5551 60.5370 1.3931 0.7426 0.9599 1.0232 N/A N/A 90.0000 1.0232 0.9775 1.0000 0.9775 0.9775 1.0000 0.9599

1.7 1.5024 0.2754 53.7707 1.3713 0.7521 0.9650 1.1757 N/A N/A 90.0000 1.1757 0.8577 0.9949 0.8577 0.8577 1.0000 0.9601

1.8 1.8749 0.5936 49.6611 1.3720 0.7518 0.9649 1.2896 N/A N/A 90.0000 1.2896 0.7913 0.9811 0.7913 0.7913 1.0000 0.9467

1.9 2.2583 0.7456 46.5498 1.3793 0.7486 0.9632 1.3913 N/A N/A 90.0000 1.3913 0.7434 0.9603 0.7434 0.7434 1.0000 0.9250

2.0 2.6558 0.8285 44.0286 1.3900 0.7439 0.9606 1.4866 N/A N/A 90.0000 1.4866 0.7059 0.9340 0.7059 0.7059 1.0000 0.8972

2.1 3.0692 0.8780 41.9119 1.4028 0.7385 0.9575 1.5777 1.0506 -0.9211 69.1105 1.4740 0.7105 0.9378 0.8662 1.1629 1.0042 0.9017

2.2 3.4996 0.9095 40.0948 1.4169 0.7327 0.9539 1.6657 1.3762 0.0837 61.8952 1.4693 0.7122 0.9392 0.9600 1.0423 1.0001 0.89602.3 3.9476 0.9306 38.5102 1.4321 0.7266 0.9498 1.7514 1.6927 0.4707 58.1870 1.4883 0.7053 0.9335 1.0119 0.9883 1.0000 0.8866

2.4 4.4139 0.9453 37.1119 1.4481 0.7203 0.9454 1.8350 2.0077 0.6586 55.3916 1.5103 0.6975 0.9265 1.0548 0.9489 0.9998 0.8757

2.5 4.8986 0.9560 35.8664 1.4647 0.7140 0.9406 1.9169 2.3245 0.7632 53.1096 1.5331 0.6897 0.9189 1.0933 0.9170 0.9991 0.8636

2.6 5.4019 0.9638 34.7485 1.4819 0.7076 0.9354 1.9973 2.6449 0.8269 51.1739 1.5560 0.6822 0.9111 1.1289 0.8900 0.9978 0.8504

2.7 5.9242 0.9698 33.7388 1.4996 0.7012 0.9299 2.0763 2.9696 0.8683 49.4935 1.5787 0.6750 0.9030 1.1625 0.8665 0.9959 0.8363

2.8 6.4654 0.9744 32.8218 1.5177 0.6949 0.9241 2.1539 3.2992 0.8966 48.0117 1.6010 0.6681 0.8948 1.1945 0.8456 0.9933 0.8214

2.9 7.0257 0.9780 31.9851 1.5361 0.6887 0.9179 2.2304 3.6338 0.9168 46.6898 1.6229 0.6617 0.8865 1.2251 0.8270 0.9902 0.8058

3.0 7.6051 0.9809 31.2184 1.5549 0.6825 0.9115 2.3056 3.9735 0.9316 45.5002 1.6445 0.6555 0.8782 1.2545 0.8101 0.9864 0.7896

Oblique Shock 1 Oblique Shock 2 Terminal Normal Shock


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3.6.2 Plot for Biconic Comparison 2

Figure 3.6.2) The above plot shows the efficiency of a supersonic, external compression, biconic inlet for

the conditions of 1= 14 , and 2 = 11.

The above plot, figure 3.6.2, is the inlet efficiency for the biconic inlet with 1= 14 , and 2 = 11. The

chosen angles were to see the effect of keeping the change in angle between each of the three flat

sections similar, but having an initial larger angle. This is because this orientation was more efficient for

triconic inlets. The final efficiency at Mach 3 was 0.7896 for this orientation.

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

1.0500

1.0 1.5 2.0 2.5 3.0

P0L

/P0

Mach Number


Biconic Comparison 2

14,11


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3.7 Plot Comparing both Biconic Designs

Figure 3.7) The above plot shows the efficiency of a supersonic, external compression, triconic inlet for

the conditions of 1= 2= 8, and 3 = 9.

Comparing these two biconic designs in figure 3.7, some important trends are noticed. At our cruising

Mach of 2, Comparison 1, 1= 2 12.5, is the most efficient. However when observing the whole range

of free stream Mach values from 1 to 3, Comparison 2, 1 = 14 and 2 = 11, is slightly more efficient. At

Mach 3, it ends with an efficiency of 0.7896, when compared to Comparison 1 with an efficiency of

0.6955.

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1 1.5 2 2.5 3

P0L

/P0

Mach Number

Biconic Comparison


12.5, 12.5

14 ,11


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3.8 Monoconic Comparison: (1 = 20)3.8.1 Data for Monoconic Comparison: 1.4

1: 20 degrees (Respect to horizontal)

M1 1 1 1 Mn1 Mn2 Po2/Po1 M2 ML PoL/Po2 PoL/Po1

1.0 N/A N/A 90.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.1 N/A N/A 90.0000 1.1000 0.9118 0.9989 0.9118 0.9118 1.0000 0.9989

1.2 N/A N/A 90.0000 1.2000 0.8422 0.9928 0.8422 0.8422 1.0000 0.9928

1.3 N/A N/A 90.0000 1.3000 0.7860 0.9794 0.7860 0.7860 1.0000 0.9794

1.4 N/A N/A 90.0000 1.4000 0.7397 0.9582 0.7397 0.7397 1.0000 0.9582

1.5 N/A N/A 90.0000 1.5000 0.7011 0.9298 0.7011 0.7011 1.0000 0.9298

1.6 N/A N/A 90.0000 1.6000 0.6684 0.8952 0.6684 0.6684 1.0000 0.8952

1.7 N/A N/A 90.0000 1.7000 0.6405 0.8557 0.6405 0.6405 1.0000 0.8557

1.8 N/A N/A 90.0000 1.8000 0.6165 0.8127 0.6165 0.6165 1.0000 0.8127

1.9 N/A N/A 90.0000 1.9000 0.5956 0.7674 0.5956 0.5956 1.0000 0.7674

2.0 2.2025 0.2372 53.4229 1.6061 0.6666 0.8929 1.2102 0.8359 0.9918 0.8856

2.1 2.6310 0.5077 50.3645 1.6172 0.6633 0.8887 1.3122 0.7798 0.9772 0.8684

2.2 3.0693 0.6580 47.9755 1.6343 0.6584 0.8821 1.4035 0.7382 0.9573 0.8445

2.3 3.5205 0.7495 46.0071 1.6547 0.6527 0.8741 1.4885 0.7052 0.9334 0.8159

2.4 3.9863 0.8091 44.3362 1.6773 0.6465 0.8650 1.5689 0.6780 0.9066 0.7842

2.5 4.4679 0.8498 42.8902 1.7015 0.6402 0.8551 1.6458 0.6551 0.8776 0.7505

2.6 4.9659 0.8788 41.6213 1.7269 0.6337 0.8444 1.7199 0.6355 0.8474 0.7156

2.7 5.4810 0.9001 40.4960 1.7534 0.6273 0.8331 1.7915 0.6184 0.8164 0.6802

2.8 6.0136 0.9161 39.4898 1.7806 0.6209 0.8212 1.8610 0.6034 0.7852 0.64492.9 6.5639 0.9285 38.5839 1.8086 0.6146 0.8089 1.9285 0.5902 0.7542 0.6100

3.0 7.1323 0.9383 37.7636 1.8372 0.6084 0.7960 1.9941 0.5784 0.7236 0.5760



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3.8.2 Plot for Monoconic Comparison

Figure 3.8.2) The above plot shows the efficiency of a supersonic, external compression, monoconic

inlet for the conditions of 1 = 20.

This monoconic plot was also done strictly for comparison purposes to the triconic design. Monoconic

designs are pretty limited in attempting to have a better total pressure recovery and efficiency. It is

included to show with calculations why it is less efficient than triconic designs, and by what margin. An

angle of 20 was chosen over the maximum allowed 25 because this allowed more of the shocks to beattached over the range of Mach numbers, and it also produced a better efficiency.

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

1.0 1.5 2.0 2.5 3.0

P0L

/P0

Mach Number


Monoconic Comparison

20


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3.9 Comparison Plot of All Previously Discussed Geometries

Figure 3.9) The above plot shows the comparison of the efficiencies of all the previously discussed

supersonic, external compression, inlets.

The above plot, figure 3.9, serves as a very important comparison of all the above plots. It allows us todirectly compare monoconic, biconic, and most importantly triconic inlet designs at various angle

configurations. We can clearly see that in general, the more oblique shocks you have decelerating and

compressing the flow, the more efficient it becomes.

The overall design that was chosen is Design 2, the triconic inlet with 1= 9 and 2= 3 = 8.

This is because for almost the entire Mach range from 1 to 3, it is clearly the most efficient due to its

much higher total pressure recovery and final efficiency at Mach 3 of 0.8944. Additionally, the Mach

number after the terminal shock was 0.7927 extremely close to the desired Mach of 0.8 for entrance

into the engine.

0.5

0.6

0.7

0.8

0.9

1

1.1

1 1.5 2 2.5 3

P0L

/P0

vs.M

Mach Number

Comparison of All Three Designs


Tri: 8 ,8 ,9

Tri: 9 ,8 ,8

Tri: All 8.33

Bi: Both 12.5

Bi: 14, 11

Mono: 20


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4 Discussion of Inlet Design Including the Effects of ViscosityViscosity and boundary layer control are extremely large factors in the design of supersonic inlets.

Throughout the above design, these effects were considered negligible, and the focus was on varying

geometry and seeing the resulting total pressure recoveries.

Boundary layers will basically build up on any exposed surfaces to the flow. Since the pressure increasesas you progress with the flow along the external compression geometry, the boundary layer is prone to

separation especially if the pressure gradient is very large. And since there are shocks occurring on the

geometry, the pressure gradient will be of considerable size, which almost ensures that boundary layer

separation will occur.

For a boundary layer to separate in 2-dimensional flow, there are a few main changes in flow that occur.

The large pressure gradient will outweigh the shear forces that transfer momentum to the wall. In this

scenario, the fluid near the wall will first become stagnant, and actually reverse at some point. You can

see this happening in figure 4.1. When boundary layer separation occurs, there will be a large reduction

in the uniformity of flow to the engine which can create potential problems.

Figure 4.1) Flow at a 2-dimensional separation point in flow due to viscous effects.

It is necessary to prevent boundary layer separation so as to avoid the non-uniform flow that is

associated with it. Some physical design elements must then be considered to achieve this. Most likely,

the best fix for this problem is to suck out the boundary layer just prior to where shocks occur. This

essentially eliminates the existence of the boundary layer before a large pressure gradient (the shocks),

therefore eliminating the possibility of the boundary layer detaching. This is known as bleeding the

airflow. Bleeding the airflow can be done a few ways. Two very common methods involve a slot, or

many pores to suck out the boundary layer (figure 4.2).

Figure 4.2) Different mechanisms for bleeding the boundary layer.


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5 Discussion of Inlet Design Including the Effects of a Nonzero Angle ofAttack

The entire design process above dealt with the inlets at an angle of attack of zero. Now, we must briefly

consider the effects of a nonzero angle of attack. From these effects, the inlet design must be improved

in order to be most efficient for not only a angle of attack of zero, but also various nonzero angles ofattack.

As expected, there will be a greater loss in total pressure if there is an angle of attack when the inlet is

designed for an angle of attack of zero. This is clearly evident in figure 5, where there are some basic

relationships displayed corresponding to the total pressure loss, the incidence angle (angle of attack),

different inlet Mach numbers, and blade design.

The y-axis of the plots in figure 5, is the total-pressure-loss coefficient, which is determined by the

equation:1 = (1 2 )/(1 1). Observing an inlet Mach of 0.8, our engine requirement, youcan see the least total pressure loss occurs in an incidence range hovering around 0. As you increase or

decrease the incidence, the total pressure loss will increase significantly.

One option for minimizing this loss could be a variable angle inlet. A complex program would be

necessary to take into account your Mach number, angle of attack, altitude, current rate of change in

altitude, and many other factors. The program would observe these inputs, and output to a mechanism

to change the angle the inlet sits on the aircraft to maximize the efficiency of the inlet geometry. This

sounds good in theory, however it would be extremely complicated to design, and very expensive. The

losses would most likely outweigh the gains. This is why the internal components are considered more

heavily to help with this.

In reality, the design process to take into account the angle of attack would shift to the compressor rotor

blades within. In the overall design process before, this was obviously beyond the scope of the project.

However, if we were to consider the compressor blades, observing figure 5 once again, I would choose

the double-circular arc blade. This is because for our operational Mach number at the engine inlet, 0.8,

there are the least losses in total pressure for larger angles of attack.

Figure 5)


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6 ConclusionsAfter performing some elements of the design process of a supersonic, external compression, air-

breathing aircraft engine, I have realized there are many things to take into account when considering

geometries for such an inlet. I initially decided I wanted a triconic design due the existence of biconic

inlets, and some gas dynamic relations. It is known that the more oblique shocks that occur, the more

aerodynamically efficient the system is due to the better total pressure recovery.

I varied the angles a great deal in the Excel spreadsheets used to calculate all the necessary values, and

settled on a triconic configuration of 1= 9 and 2= 3 = 8. This is because for almost the entire Mach

range from 1 to 3, it is evidently the most efficient due to its much higher total pressure recovery and

final efficiency at Mach 3 of 0.8944.

The sections that focused on viscous effects and angle of attack effects are present to show that there

are so many different conditions that can adversely affect our efficiency. The engineer needs to be

aware that there are countless factors to consider, have patience, and design preventative measures to

avoid these undesired scenarios to obtain the greatest degree of efficiency.


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7 ReferencesAnderson, John. Modern Compressible Flow. New York: OPEN UNIVERSITY PRES, 2004.

"File:Bowshockexample.jpg -." Wikipedia, the free encyclopedia. 24 Apr. 2009

.

"Isentropic compression inlet for supersonic aircraft invention." Freshpatents.com: Patent Applications

Updated Each Week, RSS, Keyword Monitoring. 14 Apr. 2009

.

Kerrebrock, Jack L. Aircraft engines and gas turbines. Cambridge, Mass: MIT P, 1977.

Kerrebrock, Jack L. Aircraft engines and gas turbines. Cambridge, Mass: MIT P, 1992.

Mattingly, Jack D., William H. Heiser, and Daniel H. Daley. Aircraft engine design. Washington, D.C:

American Institute of Aeronautics and Astronautics, 1987.

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