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Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.

A98-27974

AIAA 98-1575Moveable Cowl Control for In-creased Hypersonic Performance

Lael vonEggers Rudd, Falcon Rankins,and Darryll J. PinesUniversity of MarylandCollege Park, MD 20742

Inlet Shocks (xo, yo)

Translating Cowl Lip

Desired Shock

AIAA 8th International Space Planes andHypersonics and Technologies Conference

April 27-30,1998 / Norfolk, VAFor permission to copy or repubiish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191


AIAA 98-1575

MOVEABLE COWL CONTROL FOR INCREASEDHYPERSONIC PERFORMANCE

Lael vonEggers Rudd * Falcon Rankins t Dairy 11 J. Pines *Department of Aerospace Engineering

University of Maryland, College Park, MD 20742

Abstract

A novel concept of a moveable cowl is introducedfor improving the performance of integrated hyper-sonic waverider designs. These vehicle designs aretypically computed at one design Mach number.Thus, off-design performance suffers because of flowspillage at the engine inlet. A moveable cowl canbe used to track shock on lip conditions to captureoff-design flow. In this paper the concept of a move-able cowl is discussed to control local and global ef-fects of hypersonic waveriders. Specifically, a simplecaret-wedge configuration is used to study the on/offdesign performance and the pitch control sensitivityof a moveable cowl.

NomenclatureM = Mach numberP0 = Total Pressurer = Cowl lip radiusT = TemperatureT0 - Total Pressurex0 = Initial x-coordinate of cowl lip2/0 = Initial y-coordinate of cowl lip/3 = Shock angle7 = Specific heat ratio6 — Shock stand-off distanceA = Sonic line angle0 = Flow Deflection Angle9e = Sum of previous flow deflection angles<f> = Shock angle for triple point calculationTT = Natural numberfj, = Mach wave angle

subscripts

* Graduate Researcher, Student Member AIAA.tUndergraduate Research Assistant, Student Member

AIAA.* Assistant Professor, Senior Member AIAA.

Copyright ©1998, by the authors. Published by the Amer-ican Institute of Aeronautics and Astronautics, Inc., withpermission.

i, 1 = Initialin = Conditions entering combustormax = Maximum

Introduction

Efficient hypersonic vehicle designs will consist ofan engine integrated to an airframe. Because of thenature of hypersonic vehicle designs, a key elementof the design is performance of the engine duringvarious flight regimes. With so much invested in theengine, it is of extreme interest to be able to en-sure that the engine operates at peak efficiency andmaximizes the performance of the vehicle as a whole.One way to enhance the efficiency of the engine on ahypersonic vehicle is with a moveable or adaptablecowl.

A moveable cowl is usually considered a necessityon hypersonic vehicles to allow shock on Up condi-tions during the acceleration phases of a mission1.Therefore, by allowing the cowl to move with thechange in the shock position, proper mass flow canbe taken into the engine without any flow spillage.Also the lift produced by the inlet is enhanced whenflow spillage is minimized.

In addition to these aerodynamic and propulsionconsiderations, a moveable cowl also provides the op-portunity to prevent over heating of the cowl lip andprovide an alternate method of pitch control for ahypersonic vehicle. Therefore, a moveable cowl canbe looked at in two regimes, local effects, with smallmovements of only millimeters or centimeters, andglobal effects, with movement up to several meters.Local and global effects of the cowl movement canbe summarized as follows:

Local effects:• Avoidance of Type IV shock interactions, which

produce potentially devastating heating rates

• Ability to move cowl to desired location in thepresence of atmospheric uncertainties, thermals,

American Institute of Aeronautics and Astronautics


gusts, etc.Global effects:

• Shock on lip criteria, for mass flow considera-tions during accelerating mission phases

• Pitch control by changing aerodynamic centerof pressure on the cowl and center of gravitylocation

This paper attempts to illustrate the benefits of us-ing a translating cowl for controlling local and globalperformance of hypersonic waveriders.

Shock State Equations

By using the closed-form solution of the 0-/3-Machrelation, state equations can be developed for shockposition and change of position, for a two dimen-sional inlet with an arbitrary number of compressionramps.

Shock Calculation and Position Derivatives

Consider the closed form-solution of the 0-/3-Machrelation derived by Wellmann2:

tan/3 =6 + 9ac d (27o2c + 9a6 - 2)

2(1- 3a&)

I tan - arctan - I

6a (1 - 3a6)(1)

where

a=

c = tan2

d = 4(1 - 3aby(27a?c + 9a& -

-1

(2)

(3)

(4)

(5)

Next the derivative of the 0-/3-Mach relation withrespect to both Mach number and deflection angle,can be determined by differentiating:

„tan 9 = 2 cot 0Mi2 (7 + cos 20) + 2

(6)^ '

Differentiating this expression leads to:

where:

1 - sin2 /?tan/3(Mi2sin2/3-l-

Using the chain rule:

dM = ~d9dMwhere

d8_ _ 1 dydM~ l + y2dM

with y given by eqn. 8 and

dy _ _______4Mi (7 + 1)dM (Mi2 (2 sin2 /3 - (7 + 1)) - 2)2 tan ft

So the total derivative of the shock is given by:

(7)

(8)

(9)

(10)

(11)

State Equations

There are four possible methods for moving thecowl. 1) x-direction only 2) y-direction only 3) xand y-direction (minimum distance to shock) and4) angular rotation. For the present analysis onlymethods 1-3 are used in this paper since they are themost plausible. With this being the case, if one weretrying to match shock on lip criteria, then the statesnecessary for control would be the shock distancefrom the cowl lip and the velocity of the shock withrespect to the lip. Assuming a two-dimensional inletsystem with an arbitrary number of inlet ramps, thestate equations can be developed for each of the threecases considered.

For the x-direction (y fixed) cowl movement, thethe location of the shock can be defined as:

x = tan (13)

where y0, /3S, and Qe refer to the fixed y-location ofthe cowl lip, shock angle, and the total increment ofdeflection angle from multiple ramps, as defined infig. 1. The derivative is given by:

x = —(y0 tan 9t sec2 & D/3) (tan & + tan 0e)

(14)

(tan/3s+tan0c)



where D/3 is given by eqn. 12.For the case where the freedom of movement is

in the y-direction only, the shock location can bedefined as:

(15)

where again fig. 1 shows the definition of these vari-ables. The derivative is given by:

. _ x0 sec2 08D/3 (1 - tan 0, tan 0e)l-tan&tantf,

(o;0tan/3g + x0tanOf) (tan/?atan0e.D/3)1 — tan /3g tan Of

(16)

Finally, for the case where the cowl is allowed totranslate in both the x and y-directions, the distanceto the shock is given by:

d = x0sm/3s (17)

with the derivative given by:

d = x0cos/3sD/3 (18)

Local Effects

Type IV Shock Interaction Avoidance

A Type IV shock interaction occurs when ashock impinges on a bow shock in the subsonicregime3. This can be seen in fig. 2. This typeof interaction leads to very high heating rates,which are undesirable on the shock lip where thestructure is relatively small. Instead it would bemore desirable to reposition the shock such that aType V/VI interaction occurs. This would allowthe lowest heating rates.

Interaction Modeling

A controller can be developed which moves the tipof the cowl to maintain a Type VI shock interaction.This would result in the lowest heating rate appliedto the cowl lip. Refering to fig. 2, let P be Ay abovethe cowl nose and Ax in front of the point T on thecowl. The equation of the impinging shock is3:

= (Ax + r) tan 0 + Ay (19)

where r is the cowl radius and <j> is the shock an-gle. The subsonic region behind the bow shock is

located approximately between rays at angle A fromthe origin where:

A-7 1" -a* — _ "max (20)

Qmax is the maximum wedge angle for theoblique shock. In fact at MOO, one would like the in-tersection of the impinging shock and the bow shock,S, to be above point R.

The exact equation of the bow shock is given by4:

/32y2 = x2 + ax + b (21)

where:

x0 =_ rcosOmax/3 (/32 tan2 <j>s -

- PH COS T)

(22)

(23)

(24)

(25)

r=cowl radius, 8 is the shock stand-off distance givenby:

8 =r (sin 6max - 1) + r cos 0n-££ COS T?)

(/32 tan </>«-/? (/32 tan2 </>s - l) * + tan 77) - tan 77

(26)

Os is the flow deflection which would give a sonicdownstream Mach number, 0S is the shock anglewhich would give a sonic downstream Mach numberand T) is given by:

2AR is given by:

J

(27)

(28)

which is the familiar Area-Mach number relation-ship, and PR=total pressure ratio across an obliqueshock with angle:

(29)

The location of point Q (see fig. 2), transition fromType IV to Type V interaction, is determined byusing the sonic line and letting:

y = —i tan A (30)



Substituting this value for y into eqn. 21 one obtainsa quadratic equation in X given by:

(/32 tan2 A - l) x2 - ax - b = 0 (31)

whose solution must lie in the following range:

-S < XQ < 0 (32)

The point R, corresponding to the transition fromType V to Type VI, is solved by taking the derivativeof eqn. 21 with respect to x, obtaining:

where:dy—dx

(33)

(34)

where <J>B is the shock angle obtained from numeri-cally iterating the triple point shock problem, shownin fig. 3. Squaring both sides of eqn. 33 and substi-tuting in eqn. 21 one obtains another quadratic in xgiven by:

whose solution must again lie in the following range:

-8 < XR < 0 (36)

Finally, the location of the impinging shock is de-termined by letting:

y = x tan 0 + h (37)

Putting this value into eqn. 21, one obtains,

(/32 tan2 0 - 1) x2 + (2fcj/32 tan 0 - a) x+ (/32fc? - 6) = 0

which is solved for x$ where:

-S < xs < 0

(38)

(39)

Therefore, a controller can be made which keeps thepoint xs greater than XR throughout the mission.

Global Effects

Vehicle Model for Global Effects

In order to understand the global effects of amoveable cowl, on vehicle performance, a generichypersonic caret-wedge waverider with scramjetpropulsion code has been developed. The code usesa simple geometry with inviscid quasi-1-D flow.Fig. 4 shows the geometry of a vehicle generatedby this code. Below is a basic description of theequations used in modeling the vehicle.

Caret- Wing/Wedge Configuration

The caret-wedge waverider is generated by a 2-Dforebody producing a 2-D oblique shock, which isattached to the caret-wings. The top of the wedge isa flat surface. If the vehicle is at an angle of attack,either an oblique shock or Prandtl-Meyer expansionis formed on the top of the wedge and wing sections.

Met

Because of the 2-D nature of the caret-wedge wa-verider the inlet consists of an arbitrary number ofinlet ramps each producing a 2-D shock, given byeqn. 1, which is attached to the caret-wings. Theflow after the final ramp is then turned back tofreestream by a final shock which is also modeledby eqn. 1. Fig. 5 shows the shock structure of theinlet.

Combustor

Since the purpose of this study is to understandthe effect of cowl movement on a hypersonic vehi-cle, the combustor has been modeled by a simplequasi-1-D method instead of by detailed a detailedmodel of the molecular reaction effects. The temper-ature profile along the x-direction of a typical scram-jet engine has been assumed. The combustor hasbeen chosen as a constant area combustor. Influencecoefficients given by Shapiro6 have then been usedto determine the thermodynamic variables through-out the combustor. The length of the combustorhas been assumed to be 3 meters long, a resonableapproximation for an actual vehicle.

The temperature profile is approximated by thefollowing equation:

T(x) = Ti (40)



The influence coefficients for a constant area com-bustor are given by:

dM2 (1 + jM2) (1 +If2"" 1-M2

dT0 = (1 - M2)T0 (1-

dT0 (41)

T

dP0 jM2 dT0

Pa ~ 2 T0

Differentiating eqn. 40:

and

— =dx

dT_~T

3250 -

dT dxdxT(x)

(43)

(44)

(45)

So that, the iteration scheme uses the influence coef-ficients from above at each increment of the combus-tor, and then the corresponding Mach number andtotal pressure are solved recursively:

M?

oi+l_ p . i— ^01 T

(46)

(47)

With this recursion, all other thermodynamic prop-erties can be obtained.

Nozzle

Fig. 6 shows the geometry of the nozzle. A flatplate has been used with two expansion waves at thecorner and bottom of the cowl lip. The method ofcharacteristics6 has been used to determine the forceson the nozzle surface. A typical nozzle would havea very complicated flow pattern due to the plumeshock generated from the expansion fan at the endof the cowl lip7. However for purpose of analysis, thiscan be neglected as long as the last characteristic linedoes not intersect with the nozzle surface7.

Shock on Lip

To illustrate the typical movements of shocklocations, two missions have been studied, anacceleration to design Mach number, and a cruise

mission with atmospheric disturbances. A forebody,similar to fig. 1, with deflection angle of 6 deg andthree inlet ramps of 5, 4, and 3 degrees respectivelyhave been used. The length of the inlet has beenassumed to be 30m long.

Acceleration Mission

For this study an acceleration of 0.5g's has beenassumed for the vehicle. The design Mach numberis 10, and it is assumed that the scramjet engine willturn on at Mach 6. Since scramjets are particularlysensitive to massflow conditions, only the scram-jet portion of the mission acceleration is considered.The x-coordinate and y-coordinate movements of theshock locations versus Mach number can be seenin figs. 7 and 8 respectively, and x-coordinate andy-coordinate movements of the shock locations ver-sus time can be seen in figs. 9 and 10 respectively.

It can be seen that for an acceleration mission onlyone shock will be able to be tracked to the cowl lip.This will most likely be the fourth shock for engineconsiderations, and it also has the smallest changesin translation. It is clear that the bandwidth is smallthen to track the fourth shock on this particualr mis-sion.

Cruise Mission

In reality, the atmosphere is not deterministic andthe standard atmosphere is just an approximationwhich neglects thermals, gusts, etc. that may be en-countered in actual flight. This section looks at theeffects of these on the movement of the inlet shocks.A thermal is assumed to occur randomly once ev-ery 20 km, being randomly 0.1-2 km long, with arandom temperature distribution of plus or minus10 degrees. A wind gust has also been assumed tooccur randomly once every 20 km (not necessarilyat the same thermal location), being randomly 0.1-2km long, with a velocity distribution of plus or mi-nus 15 m/s. The cruise mission was given a rangeof 500 km. Figs. 11 and 12 show the change in lo-cation of the shocks over range for this particularmission. Figs. 13 and 14 show the change in loca-tion of the shocks over time. As shown small ran-dom disturbances in the atmosphere can produce sig-nificant changes in shock location, primarily in thex-direction. These shock movements can have pro-nounced effects on the vehicle dynamics (describedbelow). For this type of mission a faster cowl con-troller would be needed but would not be required tomove as great a distance as the acceleration mission



cowl.It should be noted that if the cowl were to move to

these particualr distances, the vehicle's moment andother aerodynamic forces would change which couldproduce changes in the shock angles of the forebody.Therefore, the dynamics of the cowl must be takeninto account to get a realistic understanding of theproblem. This is taken up in the next section.

Pitch Control Capability

The authors would like to thank Dr. Mike Framefor providing the method used in the shock interac-tion section. The first and second authors would alsolike to thank the University of Maryland, AerospaceEngineering Department, for providing support forthis research. The second author would like to thankthe Summer Scholars and ASPIRE programs for pro-viding financial support.

References

A vehicle was generated from the above designcode. Fig. 4 shows the geometry. With this vehicleon design, the cowl was allowed to translate in thepositive and negative x-direction. For the case con-sidered, the vehicle is assumed to be on-design and inlevel flight at zero degree angle of attack. Since thepurpose of this section is to show that pitch can beaffected by cowl movement, no constraint was placedon the vehicle being trimmed. The forces on thecowl lip were calculated by assuming an expansionfan on the bottom of the lip when moved in the neg-ative x-direction and atmospheric pressure on thefront when moved in the positive x-direction, shownschematically in fig. 15. Fig. 16 shows the momentproduced on the vehicle when the cowl is translatedalong the x-direction. As can be seen, the nega-tive movement of the cowl does produce a substan-tial change in vehicle moment. However, the move-ment in the positive x-direction does not produceany change in moment. This is true only under thecurrent assumptions of the cowl being massless andat zero angle of attack. This case would correspondto an uncontrollabilty of the dynamics with positivecowl movement. The above example demonstartesthe potential for vehicle control via cowl movement.Further analysis is necessary however to dynamicallyfly a vehicle while allowing movement of the cowl.

Summary and Conclusions

1 Takashima, N., Lewis, M. J., and Lockwood,M. K., "Waverider Configuration Developmentfor the Dual Fuel Vehicle," AIAA 7th Interna-tional Space Planes and Hypersonic Systems andTechnologies Conference, November 1996.

2 vonEggers Rudd, L. and Lewis, M. J., "Compar-ison of Shock Calculation Methods," to appear inJournal of Aircraft, July-August 1998.

3 Frame, M. J., "Analytical Solutions of Hyper-sonic Type IV Shock Interactions," PhD Thesis,University of Maryland, College Park, 1998.

4 Moeckel, W. E., "Approximate Method for Pre-dicting Form and Location of Detached ShockWaves Ahead of Plane or Axially SymmetricBodies," NACA TN D-1921, July 1949.

5 Shapiro, A. H., "The Dynamics and Thermody-namics of Compressible Fluid Flow," New York:John Wiley & Sons, 1953.

6 Anderson, J. D., "Modern Compressible Flowwith Historical Perspective," New York: Mc-Graw Hill, Inc., 1990.

7 Tarpley, C., "The Optimization ofEngine-Integrated Hypersonic Waveriderswith Steady State Flight and Static Mar-gin Constraints," PhD Thesis, University ofMaryland, College Park, 1995.

A novel concept for controlling shock on lip crite-ria has been presented. Preliminary analytical andsimulation results indicate that it is possible to movethe cowl lip to control local and global effects. Fur-ther research is required to couple the dynamics ofthe cowl with the vehicle.

Acknowledgements



Inlet Shocks v

Translating Cowl Lip

Figure 1: Inlet Shock Structure

Bow Shock

ImpingingShock

P'

y=x tan((p)+k|

Figure 4: Typical Vehicle Generated From DesignCode

Figure 2: Cowl Lip Shock Structure

TopSurfm

Matm

Shear Layer:„..--- P4=P264 94=ei + 82

Bow Shock

Figure 3: Triple Point Shock Structure for TypeV/VL Transition Point

Figure 5: Vehicle Inlet Model


Nozzb Surfaca

CombiKtortoNozzbExpansion Fan

OOC

CO•5

I

-0.25

-0.5

. -0.75

-1

-1.25

-1.5

-1.75

Cowl Expansion Fan 7 8Mach Number

10

Figure 6: Vehicle Nozzle Model Figure 8: Acceleration Y-location of Shock Move-ments vs. Mach Number

x o

SL0)oE

Iin•5I

X 0,Mach Number 100

Time (sec)200

Figure 7: Acceleration X-location of Shock Move- Figure 9: Acceleration X-location of Shock Move-ments vs. Mach Number ments vs. Time


? ° "

= -0.25- J^-^^^

1 ^P^« -0.5 ̂ ^3 ^^S /i

!-X^ /S ' /

\ "• /f /

-1.25 - /a> /

1 '" - /1-175-/

T1 / , , , , !*" 0 100

0.06

0.04

S 0.02S

^^^ 1 '/ */ g-0.02

/ 1

' -0.04

——— Shock 1--- Shock2•--- Shocks

. • • • - • • • Shock4

ll 1'I 1 1

I 11f

_0.06 ————————————————————————————————————————————————————————————————0 50 100 150 200 250 300 350 400 450 500

Range (km)

Figure 12: Cruise Y-location of Shock Movementsvs. Range

iyr\n

Time (sec)nt .

Figure 10: Accelerationments vs. Time

0.3 •

02 -

1.O-

I °'1

1 . ,1

I 'l '

•s|-0.2.

^

-0.3 •

* 0 50 100 150 200

fY-location of Shock Move- | 0.1 •

££. o -or

8-0.1 •SBS|-0.2 •

X

-0.3 •

-0.4L

——— Shock 1

ll 1l| 1 r

-—— Shock 1

Shock2• — • Shocks

Shock4

1Jl

I1

20 40 60 80 100 120 140 160Time (sec)

_ _ _ Shock 2- - - - - shocks Figure 13: Cruise X-location of Shock Movements' —————— ̂ vs. 1'ime

0.06

^T+'V t-A

3 0.02SS8-i •S-0.02

250 300 350 400 450 500 1Range (km) j?

>-0.04

Figure 11: Cruise X-location of Shock Movementsvs. Range

-nnR

——— Shock 1--- Shock2

— _ . Qhrv*k ^• — • — •• onocK o- • - - • • - • - Shock*

ll I' I

I|1

1

'0 20 40 60 80 100 120 140

Time (sec)

Figure 14: Cruise Y-location of Shock Movementsvs. Time


Inlet Shocks

Pexp-Ax translation

Inlet Shocks

Patm

Patm+Ax translation

Figure 15: Shock Structure on X-Direction CowlTranslation

2.97E+06

— 2.96E+06

C 2.95E+06

E 2.94E+06£

2.93E+06

2.92E+06

2.91 E+06

-0.5 0Cowl Extension (m)

0.5

Figure 16: Vehicle Moment vs. X-Direction CowlLocation

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