Balance of Moments for Hypersonic Vehicles

Transcription

1 E s ^^L THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47 St., New York, N.Y T The Society shall not be responsible for statements or opinions advanced in papers or in discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion Is printed only If the paper is published in an ASME Journal. Papers are available from ASME for fifteen months after the meeting. Printed in USA. Copyright 1992 by ASME 92-GT-251 Balance of Moments for Hypersonic Vehicles FRANS G. J. KREMER German Aerospace Research Establishment Institute of Propulsion Technology Linder Hohe, Postfach D-5000 Köln 90, Germany 1 Abstract Ramjet engines propelling hypersonic flight vehicles will be highly integrated into the vehicle, resulting in strong interactions between the vehicle and the engine. An assessment of these interactions in relation to the flight mission is made by simple but adequate modeling of the flight vehicle aerodynamics and the engine performance. Especially moments associated with the propulsion system are of interest. This paper deals with the pitch moments introduced by the ramjet related forces, which are evaluated by one-dimensional engine performance and by modeling of the inlet and nozzle flow. Furthermore, it discusses the balance of moments for the first stage of a two stage transportation system for an ascent trajectory. 2 Nomenclature Symbols A,,, Vehicle wing area CM Aerodynamic moment coefficient CM0Zero incidence moment coefficient CM. dcm /da CM, dcm/dlj CT Thrust coefficient lveh Flight vehicle length M Moment m Vehicle total mass q Dynamic pressure T Thrust Acceleration xs Centre of gravity on roll axis a Angle of attack A Oxidation ratio q Flap angle 0 Flow vector direction Subscripts oo; 1 Undisturbed flow 0 After front shock Of Diffuser inlet 1 Diffuser outlet 2 Combustion chamber inlet 3 Combustion chamber outlet 4, * Nozzle critical point 5 Nozzle exit Presented at the International Gas Turbine and Aeroengine Congress and Exposition Cologne, Germany June 1-4, 1992

2 3 Introduction Worldwide hypersonic airbreathing flight vehicles for transport into orbit are under development (e.g. NASP and Sanger), which will use a ramjet during some part of mission. Here it is assumed, that ramjets supply the required thrust for an ascent trajectory between flight Machnumber 3.5 and 7. The necessity of accumulating sufficient air into the engine has led to a close attachment of the engine to the flight vehicle bottom side. This configuration utilizes the precompression caused by the vehicle nose shock. Furthermore, this concept provides the vehicle's tail for extended expansion of the nozzle flow. The close integration of the engine into the flight vehicle introduces a thrust vector component perpendicular to the roll axis. Therefore, a pitch moment of the ramjet exists. Performance calculations, to obtain the fuel consumption, are based on the balance of forces. Here also the balance of moments is taken into account. This includes aerodynamic moments as well as thrust moments. Both the flight vehicle and the ramjet moments are separately described. To obtain their behavior simple, but adequate calculation models are introduced and explained. Fuel consumption and the engine/vehicle interactions, resulting from the balance of forces and the balance of moments, are looked at. This paper only deals with the pitch moments; roll and yaw moments are not considered, since an east bound flight above the equator is assumed. 4 Aerodynamic Moments 4.1 Aerodynamic Modeling In general the aerodynamic force vector does not pass through the centre of gravity. It therefore introduces an aerodynamic moment. Instead of a time-consuming calculation of the complex three dimensional flow field around the flight vehicle an aerodynamic model is used to evaluate this aerodynamic moment. It describes the behavior of a specific configuration by aerodynamic parameters. For instance, the aerodynamic moment coefficient CM = M/(gA,,,lveh), which depends on Machnumber, angle of attack, Reynoldsnumber and flap angle. Pulling (negative flap angle) or pushing (positive flap angle) the control lever moves the flaps, which are mounted at the vehicle's tail. The aerodynamic model used assumes linearity between the aerodynamic moment coefficient CM and the angle of attack a. For moderate flap angles it also assumes linearity between the aerodynamic moment coefficient and the flap angle Ti: CM = Cm,, + CMQ - a + CM,. 77. (1) Zero incidence aerodynamic moment coefficient CMo and flap angle derivative CM,, only depend on the flight Machnumber; angle of attack derivative CMa also depends on the position of the centre of gravity on the roll axis. It is mentioned, that the aerodynamic model does not include an explicit function between the parameters considered and the Reynoldsnumber. 4.2 Assessment of Aerodynamic Moments A complete set of the aerodynamic moments is not submitted. To illustrate their magnitude the data are discussed for Mach 5 and an angle of attack a = 5 0 Fig. 1 shows the aerodynamic moment coefficient for the above mentioned conditions as a function of the flap angle. The aerodynamic moment coefficient decreases with increasing flap angle. Also the position of the centre of gravity on the roll axis is varied. Displacement of the centre of gravity to the vehicle nose decreases the aerodynamic moment coefficient. Variation of the centre of gravity can RA

3 tail-heavy M = 5; a = 5 0 M = 5; a = / ^ nose-heavy ^M ----a_ ' -- n -z Flap angle [degr] If 3.^z xs/lveh > Flap angle [degr] Figure 1: Aerodynamic moment coefficient as a function of the flap angle and variation of position of centre of gravity. be achieved by displacement of the fuel mass During unpowered flight at Mach 5 and at an angle of attack a = 5 0, the aerodynamic moments are balanced by setting the flap angle at 11. The centre of gravity is assumed at 0.65 * l veh (Fig. 1). To nose up (negative flap angle) decreases the lift/drag ratio, as shown in Fig. 2. The lift/drag ratio should always be maximized for having a minimum fuel requirement [1]. According to Fig. 2 this is achieved by setting the flap angle close to zero. Fig. 1 shows, that any displacement of the centre of gravity towards the vehicle's tail increases the flap angle (if balance of moments has to be kept). Increasing the flap angle increases the lift/drag ratio. There are two ways of obtaining balance of moments. First is by pulling (or pushing) the control lever, so influence the vehicle aerodynamics. Second is to displace the centre of gravity. A combination of both methods also is possible. Figure 2: Lift/drag ratio as a function of the flap angle. 5 Ramjet Induced Moments 5.1 Ramjet Modeling Above the vehicle's aerodynamic moments are discussed. The ramjet thrust vector also contributes to the pitch moment, especially since the engine nozzle will not be symn. ' -ical. To evaluate the engine moment a calculation model of the ramjet performance was established to calculate all thermodynamic data in characteristic cross sections (Fig. 3). The undisturbed flow is deflected and compressed by the front shock of the vehicle (oo 0). The boundary layer ahead of the engine intake causes a displacement and a momentum loss. Total pressure loss within the diffuser (0 -^ 1) is accounted for by using a kinetic efficiency number. Friction and fuel-air-mixing causes further pressure loss(1 * 2). In the combustion chamber (2 -^ 3) the fuel (H2 ) is burnt; dissociation occurs, because of the high temperatures (up to 3000 K). Part of the dissiocation enthalpy is regained within the convergent part of the nozzle (3 * 4). The critical area of the nozzle is variable and adjusted to pass the incoming mass flow. Finally the flow 3

4 MT zai ^7^r r^^^j 7 _ /, BALL /Zl. ET UR I F eo _ ^,,, T // tail-heavy 1 y q = 50 kpa; a = 50 A CO0 0' 1 G H nose-heavy Flight Alachnumber Figure 3: Ramjet model with cross sections 00 --> 5 and control volume ABCDEFGHIJ. expanses in the divergent part of the nozzle (4 + 5), where the chemical equilibrium is assumed to be frozen. An asymmetrical nozzle is chosen, since the tail base of the vehicle will be used for additional expansion. To obtain the flow angle 0 5, a Mach line is assumed at the oblique nozzle exit (HI in Fig. 3). Knowing the flow thermodynamics the momentum theory is used to obtain the thrust related moment. Note, that especially for highly integrated hypersonic engine/vehicle configurations the choice of the control volume rises a particular problem [2] [3] [4]. In this paper the control volume has been chosen according to Fig. 3 (boundary ABCDEFGHIJA). 5.2 Assessment of Ramjet Induced Moments This section discusses the influence of flight Machnumber, oxidation ratio and angle of attack on the engine moment. Fig. 4 shows the engine moment coefficient as a function of the flight Machnumber and variation of the oxidation ratio. The oxidation ratio is the reciprocal value of the fuel ratio. The engine moment coefficient can act Figure 4: Engine moment coefficient as a function of flight Machnumber and variation of the oxidation ratio. nose-heavy (for increased oxidation ratio) or tail-heavy (for decreased oxidation ratio); for oxidation ratio A = 1.7 the engine moment coefficient equals to about zero. The engine moment coefficient decreases with decreasing oxidation ratio. Burning more fuel increases the pressure at the oblique nozzle exit. This causes an increased nose-heaviness (negative pitch moment). The absolute value of the engine moment coefficient decreases with increasing flight Machnumber. Fig. 5 shows the influence of the angle of attack on the engine moment coefficient. For oxidation ratios above 1.5 the engine coefficient moment increases with increasing angle of attack. For low oxidation ratio an angle of attack is found having a minimum engine moment coefficient. Understanding of this behavior requires looking at the nozzle exit flow, which predominantly determines the engine moment. Increasing the angle of attack increases the engine mass flow. The nozzle exit pressure increases, resulting in an increased nose-heavy 4

5 tail-heavy.0010 M^ = 5; q = 50 kpa _.0010 nose-heavy Angle of attack [degr] A ^'M sz Fuel mass [ton] Figure 5: Engine moment coefficient as a function of angle of attack and variation of the oxidation ratio. moment. The calculation also shows, that increasing the angle of attack decreases the exit flow angle 0 5 (Fig. 3). This causes the increasing tail-heavy moment, which is reinforced by the increased mass flow. 6 Balance of Moments The aerodynamic moments and engine moments are discussed separately. At flight conditions balance of all forces and balance of all moments is required. For the following considerations an ascent trajectory with dynamic pressure q = 50 kpa and constant acceleration v = 1 m/s 2 is assumed. During a flight mission balance of moments at each flight point is required: this means the aerodynamic moment has to counterbalance the engine moment. Moments of inertia only have to be regarded, when performing quick manoeuvres. For instance during the pull-up-manoeuvre before releasing the second stage. These are not considered within this paper. There are two ways to achieve balance of moments: setting the flap angle or displacing the centre of gravity. Fig. 6 shows the possi- Figure 6: Position of the centre of gravity on roll axis (in reference to vehicle length) as a function of remaining fuel mass. ble displacement of the centre of gravity, when pumping the unused fuel to the front or to the back end of the tank. A tank volume of 5 m width, 4.5 m height and 56.5 in is assumed; take-off mass is assumed 340 tons, including 90 tons fuel. For the tank geometry chosen a maximum displacement of the centre of gravity is possible at 41.5 tons of remaining hydrogen fuel. This results in the relative small value of * l veh Fuel consumption to reach Mach 3.5 is assumed 20 tons. Three different cases were calculated. The first case (1) represents the conventional, but unrealistic situation, which considers only the balance of forces. The flap angle equals to zero and the centre of gravity equals 0.65 * l veh. For this case the ascension between Mach 3.5 and 7 requires 27.4 tons of hydrogen fuel. The second case (2) includes balance of moments, aerodynamically achieved by actuation of the control lever. (The centre of gravity keeps at place). Fig. 7 shows the flap angle 5

6 1 q = 50 kpa; v = 1 m/s 2 e.0 q = 50 kpa; v = 1 m/s 2 10 t5 (3) (2) 45.5 v rs (2) (3) (1) -20 Flight Alachnumber 40 Flight afachnumber Figure 7: Flap angle as a function of flight Machnumber with (3) and without (2) displacement of the centre of gravity. Figure 8: Angle of attack as a function of flight Machnumber with (2,3) and without (1) balance of moments and with (3) and without (2) displacement of the centre of gravity. as a function of flight Machnumber. The control lever is pulled (negative flap angle 17) for all flight conditions. However for increasing flight Machnumber the absolute flap angle decreases. The consumption adds up to 36.5 tons of hydrogen, an increase of almost 10 tons compared to the first case. This shows the importance of regarding balance of moments for performance calculations of hypersonic flight vehicles, since otherwise too optimistic fuel consumption values are determined. For the last case (3) also balance of moments is calculated. Here additional fuel displacement (according to Fig. 6) is applied. Fig. 7 shows, that the flap angle is less, although still pulling of the control lever is required at all flight conditions. The fuel consumption between Mach 3.5 and 7 now adds up to 30 tons. That is an 18% reduction compared to the second case, where no displacement of the centre of gravity was applied. The figures show, that even a small fuel mass displacement has a significant influence on the fuel consumption. 7 Engine/Vehicle Interaction Understanding the above impact of the displacement of centre of gravity requires a closer view into the engine/vehicle interactions. These interactions have special importance for hypersonic flight configurations, since the angle of attack influences both the aerodynamic and the engine forces and moments. Balance of moments is usually achieved by setting the flap angle. As mentioned before changing the flap angle has an impact on the lift/drag ratio. Changing the flap angle also influences the lift coefficient. This requires another angle of attack, if balance of forces has to be maintained. Fig. 8 quantifies the angle of attack. If only balance of forces and no balance of moments is calculated the angle of attack increases from 4.3 at Mach 3.5 to 5.1 at Mach 7. Taking balance of moments into account the angle of attack increases at Mach 3.5 about 1 (if applying only flap angle balancing, case 2). The increase of the angle of 6

7 f6 Z.014 ^ q = 50 kpa; v = 1 m/s 2 Flight Afacknumber (2).3 `i t q = 50 kpa; v = 1 m/s N (2) Flight Alachnumber Figure 9: Thrust coefficient as a function of flight Machnumber with (2,3) and without (1) balance of moments and with (3) and without (2) displacement of the centre of gravity. Figure 10: Oxidation ratio as a function of flight Machnumber with (2,3) and without (1) balance of moments and with (3) and without (2) displacement of the centre of gravity. attack is less, if applying additionally displacement of the centre of gravity (case 3). Changing the angle of attack, combined with the change of flap angle has a dramatic impact on the thrust requirement. This is mainly due to the increased aerodynamic drag (lift/drag ratio decreases, Fig. 2). Fig. 9 shows the thrust coefficient CT = T/(qA) as a function of flight Machnumber. At Mach 3.5 thrust requirement changes from (case 1) to (case 2). This is a 30% increase. A substantial reduction in thrust requirement is gained by applying additional displacement of the centre of gravity (case 3 compared to case 2). Changing the angle of attack also influences the ramjet flow, causing an increased engine thrust. This however can not compensate the increased flight mechanic thrust requirement, so decreasing the oxidation ratio is inevitable. Fig. 10 quantifies this decrease, showing the oxidation ratio as a function of the flight Machnumber. At Mach 3.5 the oxidation ratio decreases from 1.75 to nearly stochiometric (case 2, balance of moments by flap angle setting). The fuel flow increases, which adds up to the total consumption. Again applying additional displacement of the center of gravity shows a beneficial influence (case 3). As described above the angle of attack and the oxidation ratio are important parameters influencing the engine moment coefficient. Fig. 11 shows the engine moment coefficient as a function of flight Machnumber. If only balance of forces is calculated (case 1) the engine moment coefficient decreases with increasing flight Machnumber. Due to the engine/vehicle interactions the nose-heavy engine moment coefficient increases dramatically (case 2). Having an increased nose-heavy engine moment, balance of moments requires an equal increased tail-heavy aerodynamic moment. This means pulling the control lever additionally, so the flap angle decreases even more. This closes the circle of engine/vehicle interactions. 7

8 q = 50 kpa; v = 1 m/s nose-heavy Figure 11: Engine moment coefficient as a function of flight Machnumber with (2,3) and without (1) balance of moments and with (3) and without (2) displacement of the centre of gravity. Fig. 11 demonstrates the importance of this interactions (case 3). Applying additional displacement of the centre of gravity reduces the nose-heavy engine moment significantly, especially at low flight Machnumbers. In conclusion even a small displacement of the centre of gravity, achieved by the displacement of the remaining fuel, reduces above described interactions significantly. This has an important beneficial effect on the fuel consumption. 8 Summary Flight machnumber (1) (3) (2) The importance of including balance of moments for performance calculations of hypersonic flight vehicles using ramjets is shown. A specific hypersonic airbreathing engine/vehicle- configuration was assumed. Models for the determination of the flight vehicle aerodynamic, and the ramjet related forces and moments have been presented. Balance of moments, which included aerodynamic and engine moments, was calculated for an ascent trajectory between Mach 3.5 and 7. Compared to a performance calculation only based on balance of forces, a significant increase in fuel consumption is noticed. Two ways of achieving balance of moments were applied; first aerodynamically by setting the flap angle, second by additional displacement of the centre of gravity. It is shown, that even the small displacement of the centre of gravity of * 11e h has a benecifial effect on fuel consumption of 18%. This was explained, when looking at the engine/vehicle interactions: balancing aerodynamically evokes an increased nose-heavy engine moment. This requires additional pulling of the control lever. An important benecifial effect on the fuel consumption is attained by pumping hydrogen fuel to the back side of the fuel tank. 9 References [1] Kremer, F.G.J.: Trajectory optimization considerations for ramjet engines. Hypersonic Combined Cycle Propulsion, AGARD-CP-479, Madrid [2] Lehrach, R.P.C.: Thrust/Drag accounting for aerospace plane vehicles. AIAA , San Diego, June [3] Herrmann, 0.; Rick, H.: Kraftebilanz and Bestimmungs des Nettoschubs bei Antriebssystemen von Raumtransporter - Hyperschallf lugzeugen. Hamburg 1989, DGLR [4] Numbers, K:Hypersonic propulsion system force accounting. ISABE , Nottingham,