Numerical and Engine Cycle Analyses of a Pulse Laser Ramjet Vehicle

Trans. JSASS Space Tech. Japan Vol.1, pp.9-16, 2003

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 η : diffuser efficiency Cp : specific heat at constant pressure d s ηB : blast wave efficiency Cv : specific heat at constant volume for species s λ : payload ratio s πd : total pressure ratio Cv,v : specific heat at constant volume for species s for vibrational energy ρ : density τ : 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) ∞ : 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

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where

X11 ·Z Z ¸ Thrust t+r s s f ρe = ρs 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

ηB deﬁned by

EB Fig. 1. Pulse laser ramjet vehicle. ηB = . (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 ρ u + v EB = ρe (T ) + 2 Volume ¡ ¢# 2 2 Fig. 3. Humphrey cycle with additional isentropic expansion ρ0 u0 + v0 −ρ 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 − ρ U 2SC − m g (15) ρv · ds v dt 2 ∞ d v C.A.R. = RRSinlet and (6) ρv · 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 πd = = 1 + (1 − ηd) M0 and (8) m − pt0 2 v(t=0) 1 − ² Tt1 = Tt0, (9) λ = (16) mv(t=0) where ηd and γ were assumed as 0.97 and 1.4, respectively. 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- = πd . (10) A0 M0 ber diagram, which is calculated under the conditions tabulated in Table 2. The mode is switched from the Here, ρ1, 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 πd = 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 ηBPL ρ3 = ρ2, 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 = ρ3RT3,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. The inlet is closed and hy- drogen propellant is injected between #1 and #2. The 120 120 Cm , km

100 100 N/MW propellant is laser-heated from #2 to #3 and the ﬂow is C H m assumed to choke thermally at #3. Since the energy of m, 80 80 C ﬂow before heating is negligibly small compared to the H laser energy input, the following relations are derived 60 60 from the energy conservation law and the equation of 40 Cm 40 state: H · ¸ 20 20 η P 2 T = B L and (13) 0 0 3 0 2 4 6 8 10 12 14 16 18 20 m˙ p Cp (γ + 1) s Flight Mach number m˙ p RT3 p3 = . (14) Fig. 4. H,Cm vs. M diagram. A3 γ

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ρe and the equation of state are deﬁned as Table 2. Calculation conditions in the engine cycle analysis. ¡ ¢ mv (t = 0), kg PL, MW ηB, %m ˙ p(rocket mode), kg/s X11 ρ u2 + v2 100 500 40 1 ρe = ρ h (T ) − p + , (19) s s 2 Zs=1 s f λ=0.67 λ=0.55 λ=0.30 hs (T ) = Cv (T ) dT + RsT + ∆es and (20) 8000 X11 7000 p = ρsRsT. (21)

=300MW L =113MW s=1 6000 P L =500MW P L P 5000 Here, thermo-chemical properties, transport properties and chemical equilibrium constants are taken from m/s 4000 Rocket U, Ref. 5). Rate coeﬃcients of chemical reactions are taken 3000 from Ref. 8)

2000 Inviscid flux is estimated with the AUSM-DV 9) Ramjet scheme and space accuracy is extended to the 3rd order 1000 by the MUSCL approach with Edwards’s pressure lim- 10) 0 Pulsejet iter. Viscous flux is estimated with a standard central 0 50 100 150 200 250 300 Time, s difference. Time integration is performed with the LU- SGS11) scheme, which is extended to the 3rd order time Fig. 5. Flight velocity vs. time diagram. accuracy by Matsuno’s inner iteration method.12) The calculation is performed with the CFL numbers of 2 ∼ 4. CFD Analysis 20. 4.2. Computational mesh and flight conditions 4.1. Governing equations and numerical scheme Figures 6 shows the computational mesh. The type Axisymmetric Navier-Stokes equations are solved A vehicle has a pulsejet configuration that is almost the 2) with finite rate chemical reactions. The fol- same as the “Label E” Lightcraft. Computed Cm is lowing 11 species of air plasma are considered: compared with the measured data for code validation. + + + + + The type B vehicle is used for the ramjet mode. Cd of N2, O2, NO, N, O, N2 , O2 , NO , N , O and e−. Thermal non-equilibrium effect and radiative en- type B is reduced by half compared to type A. ergy transfer are not considered. Then, the governing Mesh cells are set to be fine between the cowl and the equations are given by: body to correctly capture blast waves. In addition, the mesh is concentrated near the wall to resolve the viscous ∂U ∂F 1 ∂rG ∂F 1 ∂rG H + + = v + v + + S, (17) boundary layer. The outer boundary of the computa- ∂t ∂z r ∂r ∂z r ∂r r tional zone is set far from the vehicle body to reduce the       influence of non-physical reflection waves from the outer ρ ρu ρv boundary. ρu  ρu2 + p   ρuv       2  Mesh convergence was checked with doubly fine cells.  ρv   ρuv   ρv + p   ρe      The result is listed in Table 3, where ∆r is a minimum U =   , F =  (ρe + p) u , G =  (ρe + p) v , min  ρ1   ρ u   ρ v  cell width. Since the difference was only 3 %, 72,000    1   1   .  . . mesh cells were used in this computation. .  .   .  ρ11 ρ11u ρ11v For ramjet flights, combinations of H and M listed in Table 4 were adopted.  0   0   τzz   τzr   τzr   τrr      Table 3. Mesh convergence of Cm at H = 20 km.  uτzz +vτzr +qz  uτzr +vτrr +qr Fv = j  , Gv = j  ,  1z   1r  Cell number ∆rmin, µm Cm, N/MW  .   .  . . 72,000 87.5 66 288,000 43.7 64 j11z j11r

 0   0   0   0   p − τ   0  Table 4. Ramjet ﬂight conditions.  θθ    0   0  H, km M p , atm ρ , kg/m3 H =  0  , S =  w˙  . (18) ∞ ∞    1  20 5 0.055 0.089  .   .  . . 30 8 0.012 0.018 0 w˙ 11

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H. Katsurayama et al.: Numerical and Engine Cycle Analyses of a Pulse Laser Ramjet Vehicle ¥¦¡

Cowl ¥¦ Cowl

¤ rf Plasma

Laser Afterbody LSD front

Afterbody Laser ¡

Forebody Z

Axis of symmetry

§ ¥¦ ¥¦§ ¡¨ Zd rd AL

(a) Type A: Inlet closed, 30◦ slope cowl. ¥¦¡

¥¦ Fig. 7. Model of LSD propagation.

£ wave energy behind the LSD front at each time step.

Physical properties behind the LSD front are calcu- ¢

lated from one-dimensional detonation relations:15) ¡ 2 p1 + ρ1DCJ

p2 = , (22)

§ ¥¨ ¥¨§ ¡© γ2 + 1

2 2 (γ2 + 1) ρ1DCJ ρ2 = , (23) (b) Type B: Inlet open, non-slope cowl. 2 γ2 (p1 + ρ1DCJ)

©¤ T2 = p2/R2/ρ2, (24)

¨¤ X s ρs2 Cv (T2) + Rs

§¤ γ = , (25) 2 ρ Cs (T ) s 2 v 2

¦¤ r

¥¤ γ2p2 v2 = c2 = , (26) £¤ ρ2

¡¢ v1 = DCJ and (27)

" #

11 Z T

¦¤ £¤ £ ¦ ¨

¨ X 2

h = Cs (T ) dT + R T + ∆ef (28) ¤ 2 v s 2 s s=1 0 (c) Overall mesh (72,000 cells) 1 ¡ 2 2¢ PL/AL Fig. 6. Computational mesh. = h1 + DCJ − v2 + , (29) 2 ρ1DCJ where subscripts 1 and 2 denote the states in front of and behind the LSD, respectively. Cs are taken from Ref. 5). 4.3. Explosion source model v 13) The velocities refer to the coordinate relative to the LSD An explosion source model was employed instead of wave. Since the laser beam is focused cylindrically, the solving complex propagation processes of the LSD wave: cross-section area of the laser beam is An explosion source was modeled as a pressurized vol- rf − rd ume centered at a laser focus. A blast wave is driven AL = 2πrd . (30) by the burst of this source. The focus is located at the f middle on the inner cowl surface. Since the LSD pro- Here, rf and rd are the positions of the focus and the 1) 2) cess is considered to be isometric heating, density in detonation wave front, respectively. f = rf /zd is 3.6. the source is invariant during the heating process. The The history of PL was taken from Ref. 16). h2 and γ2 are gas in the source is assumed to be in chemical equilib- calculated by solving iteratively Eqs. (21) ∼ (26) with rium, and the chemical composition is calculated by the the chemical equilibrium calculation. Then, the location method of Ref. 14). of the LSD wave is calculated by

In order to estimate the source volume and ηB, LSD drd wave propagation was analytically calculated. Figure = −DCJ. (31) 7 shows the calculation model: The LSD wave is the dt plane wave which propagates in the laser channel, and At p = 1 atm, the LSD wave is not sustained at the the shape of the LSD front is a line. The physical proper- laser intensity below approximately 1MW/cm2.17, 18) In ties on the LSD front are uniform. In addtion, the physi- the present computation, the laser absorption is assumed cal properties in the region ionized by the LSD wave are terminated when the laser intensity on the LSD wave de- invariant. EB is calculated by accumulating the blast cays to this threshold. Figure 8 shows the histories of

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laser intensity, fractional laser absorption and ηB. Re- sulting fractional absorption and ηB were 60 % and 27 %, respectively. Table 5 shows the source volume deter- mined using this ηB.

The blast wave is driven at t0 = 0 µs by the burst of the source volume. Fractional absorption is simply assumed invariant for any atmospheric density because the LSD threshold is unknown in reduced atmospheric (a) At t = 45 µs densities. (pmax = 6.71 atm, pmin = 0.77 atm, dp = 0.30 atm) 4.4. Computed results of the pulsejet mode Figure 9 shows the pressure contours. After the burst of the explosion source, the shock wave reaches the afterbody at t = 45 µs and sweeps the afterbody. It leaves the afterbody tail at t = 190 µs. The thrust history is shown in Fig.10. Positive thrust is kept until t = 125 µs and then negative thrust continues until t = 1000 µs. At t > 1000 µs, thrust is almost zero.

Since computed Cm agreed well with the experimental data listed in Table 6, this computational code with (b) At t = 100 µs several physical models was found reproducing experi- (pmax = 3.86 atm, pmin = 0.52 atm, dp = 0.17 atm) mental data. 4.5. Computed results of the ramjet mode Figure 11 shows the pressure contours in the ramjet mode. The shock wave sweeps the afterbody without being spat out from the inlet. Figure 12 shows the thrust histories. The thrust at H = 30 km is smaller than that at H = 20 km due to the small mass ﬂow rate and low

ηB. Computed Cm is listed in Table 7.

100 70 (b) At t = 190 µs 2

Laser intensity on the LSD wave 60 (pmax = 3.54 atm, pmin = 0.75 atm, dp = 0.14 atm)

Fig. 9. Pressure contours after an explosion with EL = 400J, 50 10 H = 0 km and M = 0.

Fractional laser absorption 40 ¨§¢¤¢¤¢

¦ ¢¤¢ ¥

1 Energy fraction, % LSD threshold Total

20 ¦§¢¤¢¤¢

ηB ¢¤¢ 10 ¡

Laser intensity on the LSD wave, MW/cm ¥

0.1 0 ¡£¢¤¢¤¢ 0 1 2 3 4 5 6 7 8 9

Time, µs Thrust, N

¢¤¢ ¥

Fig. 8. Histories of EB and laser intensity at H = 0 km.

¢ Afterbody

Cowl

¢¤¢

Table 5. Explosion source.

¡£¢¤¢¤¢

¢ ¡£¢¤¢ ¡ ¢¤¢§¢ 3 ¡ H, km EL,J ηB (t0), % V0, cm Time, µs 0 400 26.8 17.4 300 18.8 44.4 Fig. 10. Thrust history in the pulsejet mode (Type A). 20 400 17.2 51.3 500 16.1 55.6 300 12.8 94.6 4.6. Effect of chemically frozen flow loss 30 400 12.8 94.6 500 13.2 111.5 Figure 13 shows the histories of ηB. tse is the time when the blast wave finishes sweeping the afterbody.

( 14 ) H. Katsurayama et al.: Numerical and Engine Cycle Analyses of a Pulse Laser Ramjet Vehicle

2000 Table 6. Cm at H = 0km. Vehicle name C , N/MW m EL=500J Label E (Ref. 2)) 100 1500 Type A (present) 107 EL=500J 1000 EL=400J

EL=400J Thrust, N 500

EL=300J 0 H=30km, M=8

H=20km, M=5 EL=300J -500 1 10 100 (a) At t = 12 µs. Time, µs −2 (pmax = 2.27 atm, pmin = 2.1 × 10 atm, dp = 0.11 atm) Fig. 12. Thrust histories in the ramjet mode (Type B).

M=0 35 H=0km, (b) At t = 20 µs. 30 −2 (pmax = 4.63atm, pmin = 2.1 × 10 atm, dp = 25 0.23 atm) M=5 ,%

B =20km,

η H 20

M=8 15 H=30km,

tse 10

0 1 10 100 (c) At t = 38 µs. Time, µs −2 (pmax = 4.27 atm, pmin = 2.0 × 10 atm, dp = 0.21 atm) Fig. 13. History of ηB in the case of EL = 400 J. Fig. 11. Pressure contours after an explosion with EL = 400 J, H = 20 km and M = 5.

Table 8. Time average of ηB from t0 to tse. Table 7. Computed Cm in the ramjet mode. H, km MEL,J ηB, % H, km M m˙ p, kg/s EL,J Cm, N/MW 0 0 400 38.5 300 66.9 300 26.6 20 5 1.4 400 66.0 20 5 400 25.6 500 64.0 500 24.5 300 40.3 300 16.2 30 8 0.6 400 41.0 30 8 400 16.0 500 41.0 500 15.8

At H = 0km, ηB is increased due to energy recovery from the chemical potential (recombination reactions). sweeping the afterbody before the recovery of ηB be- At t > 10µs, the recovery rate is decreased and chemical comes maximum, and a large amount of chemical energy potential energy is frozen. is lost. Table 8 shows the time average ηB from t0 to tse.

At H = 20 km and 30 km, the blast wave ﬁnishes The dependency of ηB on EL was found to be weak.

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4) Wang, T-S., Chen, Y-S., Myrabo, L.N. and Mead, F.B.Jr.: Table 9. Comparison of Cm between CFD and Engine Cycle Advanced Performance Modeling of Experimental Laser Analysis (ECA). Lightcraft, J. Propul. Power, 18 (2002), pp.1129-1138. 5) Gupta, R.N., Yos, J.M., Thompson R.A. and Lee, K.P.: A Cm (CFD), Cm (ECA), H, km MEL,J Review of Reaction Rates and Thermodynamic and Trans- N/MW N/MW port Properties for an 11-Species Air Model for Chemical and 300 66.9 60.7 Thermal Nonequilibrium Calculations to 30,000 K, NASA RP 20 5 400 66.0 58.4 1232, 1990. 500 64.0 55.9 6) Bussing, T.R.A. and Pappas, G.: An Introduction to Pulse Detonation Engines, AIAA Paper 94-0263, 1994. 300 40.3 22.9 7) Shiramizu, M., NAL TM 598, 1989 (in Japanese). 30 8 400 41.0 22.7 8) Park, C.: Review of Chemical-Kinetic Problems of Future 500 41.0 22.4 Flight NASA Missions, I: Earth Entries, J. Thermophys. Heat Transfer, 7 (1993), pp.385-398. 9) Wada, Y. and Liou, M.S. : A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities, NASA 5. Comparison between Engine Cycle Analysis TM-106452, 1994. 10) Edwards, J.R. : A Low-Diffusion Flux-Splitting Scheme and CFD for Navier-Stokes Calculations, Comput. Fluids, 26 (1997), pp.635-659. 11) Jameson, A. and Yoon, S.: Lower-Upper Implicit Schemes In order to validate the engine cycle analysis, Cm with Multiple Grids for the Euler Equations, AIAA J., 25 was re-calculated with the same flight conditions, ve- (1987), pp.929-935. 12) Matsuno, K. : Actual Numerical Accuracy of an Iterative hicle cross-section area and ηB as the CFD conditions. Scheme for Solving Evolution Equations with Application to The result is shown in Table 9. Engine cycle analy- Boundary-Layer Flow, Trans. J. Soc. Aeronaut. Space. Sci., sis was under-estimating Cm. This would be partly be- 38 (1996), pp.311-322. cause of strong unsteady energy input during the cycle: 13) Ritzel, D.V. and Matthews, K.: An Adjustable Explosion- Although shock heating has been taken into account, source Model for CFD Blast Calculations, Proc. of 21st In- ternational Symposium on Shock Waves, 1997, pp.97-102. actual heating is very localized and the peak pressure is 14) Botton, B., Abeele, D.V., Carbonaro, M. and Degrez G.: about 10 ∼ 13 times higher than that deduced by en- Thermodynamic and Transport Properties for Inductive gine cycle analysis. Accordingly, the Humphrey cycle Plasma Modeling, J. Thermophys. Heat Transfer, 13 (1999), efficiency of the engine cycle is under-estimated. pp.343-350. 15) Landau, L.D. and Lifshitz, E.M.: Fluid Mechanics, 2nd ed., Another possible reason would be the pressure local- Butterworth-Heinemann, Oxford, 1987, Ch.14. ization on the afterbody: Since shock waves are reflected 16) Messitt, D.G., Myrabo, L.N. and Mead, F.B.Jr.: Laser Initi- and focused on the afterbody, pressure is strongly local- ated Blast Wave for Launch Vehicle Propulsion, AIAA Paper 2000-3848, 2000. ized there. This 3-D effect would contribute to large Cm 17) Pirri, A.N., Root, R.G. and Wu, P.K.S.: Plasma Energy in CFD. Transfer to Metal Surfaces Irradiated by Pulsed Lasers, By incorporating these effects to cycle analysis, the AIAA J., 16 (1978), pp.1296-1304. feasibility of a laser ramjet SSTO would be enhanced. 18) Mori, K. Komurasaki, K. and Arakawa, Y.: Influence of the Focusing f Number on the Heating Regime Transition in Laser Absorption Waves, J. Appl. Phys., 92 (2002), pp.5663- 6. Summary 5667.

A preliminary feasibility study of the laser ramjet SSTO has been conducted using engine cycle analysis. The results show that the laser ramjet SSTO is feasible 2 with PL ≥ 100MW for 100 kg vehicle mass and 1 m vehicle cross-section area. The obtained Cm is 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 process and spatially localized pressure on the afterbody.

References

1) Raizer, Y.P.: Laser-Induced Discharge Phenomena, Consul- tants Bureau, New York and London, 1977, Ch.6. 2) Myrabo, L.N., Messitt, D.G. and Mead, F.B.Jr.: Ground and Flight Tests of a Laser Propelled Vehicle, AIAA Paper 98-1001, 1998. 3) Myrabo, L.N.: World Record Flights of Beam-Riding Rocket Lightcraft: Demonstration of “Disruptive” Propulsion Tech- nology, AIAA Paper 01-3798, 2001.

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