Trans. JSASS Space Tech. Japan Vol.1, pp.9-16, 2003 Numerical and Engine Cycle Analyses of a Pulse Laser Ramjet Vehicle By Hiroshi Katsurayama, Kimiya Komurasaki, Ai Momozawa and Yoshihiro Arakawa The University of Tokyo, Tokyo, Japan (Received December 6th, 2002) A preliminary feasibility study of a laser ramjet SSTO has been conducted using engine cycle analysis. Although a large amount of laser energy is lost due to chemically frozen flow at high altitudes, the laser ramjet SSTO was found to be feasible with 100 MW laser power for 100 kg vehicle mass and 1 m2 vehicle cross-section area. Obtained momentum coupling coefficient, Cm, was validated by means of CFD. As a result, the engine cycle analysis was under-estimating Cm. This would be because of the strong unsteady energy input in the actual heating process and the spatially localized pressure on the afterbody. Key Words: Laser Propulsion, Laser Ramjet, SSTO Nomenclature w˙ s : mass rate of production of species s per unit volume A : cross-section area of a vehicle r; θ; z : cylindrical coordinates γ : specific heat ratio AL : cross-section area of laser beam f C:A:R: : capture area ratio ∆es : chemical potential energy of species s at T = 0K Cd : drag coefficient ² : structure coefficient Cm : momentum coupling coefficient ´ : diffuser efficiency Cp : specific heat at constant pressure d s ´B : blast wave efficiency Cv : specific heat at constant volume for species s ¸ : payload ratio s ¼d : total pressure ratio Cv;v : specific heat at constant volume for species s for vibrational energy ½ : density ¿ : viscous stress tensor DCJ : Chapman-Jouguet velocity e : energy per unit mass Subscripts s : species EL : total laser energy t : stagnation condition EB : blast wave energy (the sum of pressure and kinetic energy) 1 : free-stream property f : focusing f number of an afterbody mirror F : thrust 1. Introduction g : acceleration of gravity H : flight altitude of a vehicle h : enthalpy per unit mass There is a strong demand for frequent deliver of pay- j : mass diffusion flux loads to space at low cost. A pulse laser ramjet vehicle M : Mach number could satisfy this demand: The payload ratio would be mv : vehicle mass improved drastically because energy is provided from a m˙ p : air or propellant mass flow rate laser base on the ground to the vehicle and atmospheric PL : laser power air can be used as the propellant. In addition, once a p : static pressure laser base is constructed, the only cost is electricity. q : heat flux The pulse laser ramjet vehicle shown in Fig.1 will be R : gas constant per unit mass able to achieve SSTO by switching its flight mode. Ini- V0 : explosion source volume tially, the air inlet is closed to prevent a blast wave from S : maximum cross-section area of a vehicle going upstream beyond the inlet. Air is taken in and T : static temperature exhausted from the rear side of the vehicle. This flight t : time mode is called “pulsejet mode.” When ram-compression U : vehicle speed becomes available as vehicle velocity increases, the in- u; v : axial, radial velocity components let is opened and the flight mode is switched to “ramjet mode.” Finally, when the vehicle cannot breathe suffi- °c 2003 The Japan Society for Aeronautical and Space Sciences cient air at high altitude, the flight mode is switched to ( 9 ) Trans. JSASS Space Tech. Japan Vol.1 (2003) where X11 ·Z Z ¸ Thrust t+r s s f ½e = ½s Cv (T ) dT ¡ Cv;v (T ) dT ¡ ∆es : Pulse s=1 Laser (3) Blast wave Inflow Inlet The subscript 0 indicates the properties before laser inci- dence and et+r is the sum of translational and rotational Laser plasma s s energy. Cv and Cv;v are taken from Ref. 5). Cm would be a function of EB=EL because only EB contributes to thrust. Therefore, we introduce the blast wave efficiency ´B defined by EB Fig. 1. Pulse laser ramjet vehicle. ´B = : (4) EL “rocket mode.” 3. Engine Cycle Analysis In any flight mode, gas-breakdown occurs by focusing a transmitted laser beam. The front of the produced plasma absorbs the following part of laser beam and ex- 3.1. Analysis method pands in the form of a laser supported detonation (LSD) In the pulsejet mode, thrust was estimated using the 1) 2) wave. This expansion induces a blast wave, and the measured data of Cm as blast wave imparts thrust to a nozzle wall. Myrabo et al. proposed a pulse laser vehicle, named F = CmPL ;Cm = 100N=MW: (5) “Lightcraft,” and conducted flight tests with a scaled model.2) Their latest model, with additional solid ab- In the ramjet mode, thrust was calculated by an en- lative propellants, recorded the launch altitude of 71 gine cycle analysis method assuming the Humphrey cy- meters.3) Wang et al. computed the flow field in the cle6) as indicated in Figs.2 and 3. Area ratios at Points Lightcraft in the pulsejet mode.4) The objectives of this paper are to analytically exam- ine the performance of a laser ramjet vehicle in super- Inlet Air sonic flights and to study the feasibility of SSTO launch Shock wave Nozzle Exhaust by the vehicle. A simple engine cycle analysis is con- Isentropic ducted along with a CFD simulation. Isentropic expansion expansion 1 2 3 4 2. Momentum Coupling Coefficient and Blast 0 Ram compression Wave Efficiency Isometric heating In pulse laser propulsion, the momentum coupling co- Fig. 2. Laser ramjet engine cycle. efficient Cm is commonly used as a performance indi- cator. Cm is the ratio of cumulative impulse to pulsed Isometric heating laser energy and defined as 3 R t 0 F dt Isentropic expansion Cm = : (1) EL 1 Ram compression Laser energy absorbed in a gas is distributed into blast Pressure 2 wave energy EB, chemical potential energy and radiation energy. EB is defined as " ¡ ¢ 0 4 Z 2 2 t+r ½ u + v EB = ½e (T ) + 2 Volume ¡ ¢# 2 2 Fig. 3. Humphrey cycle with additional isentropic expansion ½0 u0 + v0 ¡½ et+r (T ) ¡ dV; (2) #1 ! #2. 0 0 2 ( 10 ) H. Katsurayama et al.: Numerical and Engine Cycle Analyses of a Pulse Laser Ramjet Vehicle From #3 to #4, isentropic expansion was assumed, and Table 1. Area ratios. thrust was calculated by Eq.(12). SA =S A =S A =S = A =S A =S 0 1 2 3 4 Vertical launch trajectories are calculated by solving 1m2 0.6 0.38 0.75 1 the following equation of motion by the 4th order Runge- Kutta scheme: #0 » #4 in Fig.2 are listed in Table 1. A0 is defined as dU 1 RR m = F ¡ ½ U 2SC ¡ m g (15) ½v ¢ ds v dt 2 1 d v C:A:R: = RRSinlet and (6) ½v ¢ ds S Herein, flight conditions were decided by tracing the tra- A0 = C:A:R: £ S: (7) jectory. Cd is the function of M in Ref. 7). The payload ratio was estimated when the vehicle reached the first From Point #0 to #1, air is ram-compressed. The total cosmic velocity, 7.91 km/s: pressure ratio and total temperature are: Z · ¸ γ ¡ γ¡1 pt1 γ ¡ 1 2 m˙ pdt ¼d = = 1 + (1 ¡ ´d) M0 and (8) m ¡ pt0 2 v(t=0) 1 ¡ ² Tt1 = Tt0; (9) ¸ = (16) mv(t=0) where ´d and γ were assumed as 0.97 and 1.4, respec- tively. Then, M1 was calculated by solving the following Although ² is about 0.25 to achieve SSTO using a equation by the Newton-Rapson method: SCRamjet engine,7) the structure weight of the laser £ ¤ γ+1 ramjet vehicle can be reduced due to its simple struc- 2 + (γ ¡ 1) M 2 2(γ¡1) 1 ture. In this calculation, ² is assumed as 0.1. M1 £ ¤ γ+1 3.2. Computed trajectory and payload ratio 2 + (γ ¡ 1) M 2 2(γ¡1) A1 0 Figure 4 shows the altitude and Cm vs. Mach num- = ¼d : (10) A0 M0 ber diagram, which is calculated under the conditions tabulated in Table 2. The mode is switched from the Here, ½1, T1 and p1 were calculated using M1, pt1 and pulsejet to the ramjet at M = 2:0 and H = 7 km. C of Tt1. From #1 to #2, the air is isentropically expanded. m Physical properties at #2 were calculated by Eqs. (8)» the ramjet mode has the maximum value of 185 N/MW and then gradually decreases with the altitude due to (10) with ¼d = 1. From #2 to #3, the air is isometrically heated. Physical properties at #3 were calculated as the decrease in air mass flow rate. The mode is switched from the ramjet to the rocket at M = 8:7 and H = 36 ´BPL ½3 = ½2; u3 = u2;T3 = T2 + and km. In the rocket mode, Cm is 30 N/MW independent Cpm˙ p p of M and H. Figure 5 shows the payload ratios for p3 = ½3RT3;M3 = u3= γRT3: (11) PL = 113; 300 and 500 MW. This indicates that the laser ramjet SSTO is feasible with PL & 100MW for Finally, the air was again isentropically expanded from 100 kg vehicle mass and 1 m2 vehicle cross-section area. #3 to #4, and thrust was calculated as the following: F =m ˙ p (u4 ¡ u0) + A4 (p4 ¡ p0) : (12) 200 Pulsejet 200 As the vehicle reaches high altitudes, the mass flow Ramjet Rocket rate taken from the inlet decreases due to the decrease 180 180 in air density. In this calculation, the flight mode is 160 160 switched to the rocket mode just before thermal choking 140 140 occurs in the ramjet mode.