FEASIBLILITY STUDY OF A LASER RAMJET SINGLE-STAGE-TO-ORBIT VEHICLE

41st Aerospace Sciences Meeting and Exhibit 6-9 January 3, Reno, Nevada AIAA 3-497 AIAA 3-497 FEASIBLILITY STUDY OF A LASER RAMJET SINGLE-STAGE-TO-ORBIT VEHICLE Hiroshi KATSURAYAMA, Yasuro HIROOKA, Kimiya KOMURASAKI, and Yoshihiro ARAKAWA ABSTRACT Momentum coupling coefficients, C m, ofa laser ramjet vehicle are calculated by CFD and an engine cycle analysis The flight trajectory ofthe laser ramjet vehicle is calculated by the engine cycle analysis The CFD with the explosion source model can reproduce the experimental data of C m Using this CFD model, C m in a supersonic flight are computed The results show C m and the fraction of laser energy, that is converted to blast wave energy, decreases with the flight altitude due to chemically frozen flow loss C m by the engine cycle analysis is underestamted in comparsion with CFD Since the engine cycle analysis is assumed to be steady state process, the peak pressure in the Humphery cycle is lower than CFD Accordingly, the Humphrey cycle efficiency ofthe engine cycle analysis is degraded This low efficiency ofthe cycle causes the small C m ofthe engine cycle analysis NOMENCLATURE u, v = axial, radial velocity component z,r,θ = cylindrical coordinates A = cross section ofa vehicle γ = specific heat ratio A L = cross section oflaser beam h f = chemical potential energy CAR = capture area ratio ɛ = structure coefficient C d = drag coefficient η d = diffuser efficiency C m = momentum coupling coefficient η B = blast wave efficiency C p = specific heat at constant pressure to the blast wave energy e = total energy per unit volume π d = total pressure ratio E L = total laser energy ρ = density E B = the pressure and kinetic energy τ = viscous stress tensor converted from the laser energy subscripts (Blast wave energy) i = inlet F = thrust s = species g = acceleration ofgravity t = stagnation condition H = flight altitude ofthe vehicle = freestream property h = enthalpy h t+r = sum oftranslational and rotational enthalpy INTRODUCTION j = mass diffusion flux f = fnumber ofoptics There is a strong demand to frequently deliver M = Mach number payloads to a space station at a low cost A pulse m v = vehicle mass laser ramjet vehicle will be able to satisfy this demand: Since energy is provided from a laser base ṁ = mass flow rate P L = laser power on the ground to the vehicle and the atmospheric p = static pressure air can be used as a propellant, the payload ratio is q = heat flux improved drastically In addition, once a laser base R = gas constant is constructed, the cost is only electricity charges V = explosion source volume The pulse laser ramjet vehicle as shown in Fig1 S = maximum cross section ofthe vehicle will be able to achieve SSTO by switching its flight T = static temperature mode Firstly, when the vehicle is launched from t = time the ground, the inlet is closed to prevent the blast U = vehicle speed wave from going upstream beyond the inlet Air is taken and exhausted from the rear side of the Graduate student, Department of Aeronautics and Astronautics, Student Member AIAA mode Secondly, when the vehicle is enough accel- vehicle This flight mode can be called a pulsejet Graduate student, Department of Aeronautics and Astronauticerated that the inflow air becomes free from thermal choking by laser heating, the inlet is open and Associate Professor, Department of Advanced Energy, Member AIAA the flight mode is switched to a ramjet mode Finally, when the vehicle can not breath the enough Professor, Department of Aeronautics and Astronautics, Member AIAA Copyright c 3 by the American Institute of Aeronautics air at high altitude, the flight mode is switched to and Astronautics, Inc All rights reserved a rocket mode 1 Copyright 3 by the American Institute of Aeronautics and Astronautics, Inc All rights reserved

Thrust Inflow Inlet Blast wave Pulse Laser shock wave Diffuser Isentropic expansion Isentropic expansion Ram compression 1 3 4 Laser plasma Isometric heating Fig Ramjet engine cycle analyses Fig1 Pulse laser ramjet vehicle Air-breakdown occurs by focusing a transmitted pulse laser beam by the nozzle wall The front ofproduced plasma absorbs the following part of laser pulse and expands in the form of Laser Supported Detonation wave (LSD) 1) This expansion induces a blast wave The blast wave imparts the thrust to the nozzle wall Myrabo et al proposed a pulse laser vehicle, named Lightcraft, and conducted flight tests with a scaled model ) Their latest model, with additional solid ablative propellants, recorded the launch altitude of11-meters 3) Wang et al 4) computed the flow field in the Lightcraft resting on the ground The objective ofthis paper is to analytically examine the feasibility of the laser ramjet SSTO vehicle The launch trajectory is calculated by an engine cycle Analysis Since there is not adequate investigation about the supersonic flight so far, and an experiment is difficult under the supersonic flight, the momentum coupling coefficient is computed by CFD Finally, C m deduced by the engine cycle analysis is compared with C m by CFD MOMENTUM COUPLING AND BLAST WAVE EFFICIENCY In the laser propulsion, the momentum coupling coefficient C m is an performance indicator C m is the ratio ofcumulative impulse to one pulse laser energy and defined as, t C m = Fdt (1) E L The absorbed laser energy is converted into the blast wave energy E B, chemical potential energy and radiation energy Since only energy, E B,is converted to the thrust, C m would be function of E B /E L We introduce the blast wave efficiency η B defined by η B = E B () E L Pressure 1 Isometric heating Ram compression 3 Isentropic expansion 4 Volume Fig3 Humphrey cycle (with additional isentropic expansion 1 ) The flight trajectory is calculated using this η B in a engine cycle analysis In order to validate this analysis, the thrust is also computed by CFD ENGINE CYCLE ANALYSIS Analysis Method Pulsejet mode In a pulsejet mode, thrust is estimated using the experimental data of C m C m is assumed constant F = C m P L (3) Ramjet mode In a ramjet mode, thrust is calculated by an engine cycle analysis assuming Humphrey cycle 5) as indicated in Figs and 3 The area ratio is listed in Table 1 A is defined as, S CAR = inlet ρv ds S ρv ds, (4) A = CAR S (5) From Point to Point 1, air is ram-compressed The total pressure ratio and total temperature are the followings, π d = p t1 p t = ( 1+(1 η d ) γ 1 M ) γ γ 1 (6), T t1 = T t (7)

Table 1 Aera ratios S A /S A 1 /S A /S = A 3 /S A 4 /S 1m 6 38 75 1 5 4 η d and γ are assumed as 97 and 14, respectively Then, M 1 is calculated by solving the following equation by Newton-Rapson method ( +(γ 1) M 1 ) γ+1 (γ 1) M 1 = π d A 1 A ( +(γ 1) M ) γ+1 (γ 1) M (8) Density, temperature and pressure at Point 1 are calculated by M 1, p t1 and T t1 From Point 1 to Point, air is isentropically expanded to prevent thermal choking by laser heating at the throat The physical properties at location are calculated by the Eqs (6) (8) with π d =1 From Point to Point 3, the air is isometrically heated The physical properties at location 3 are calculated by mass conservation law and energy conservation law ρ 3 = ρ, u 3 = u,t 3 = T + η BP L C p ṁ, p 3 = ρ RT,M 3 = u 3 / γrt 3 (9) where Eq(11) is used as η B (ρ ) Finally, air is again isentropically expanded from Point 3 to Point 4, and the thrust is calculated as the following, F = ṁ (u 4 u )+A 4 (p 4 p ) (1) Rocket mode As the vehicle reaches high altitudes in the ramjet mode, the mass flow rate decreases due to the low air density In this calculation, the flight mode is switched from the ramjet mode to the rocket mode when the thermal choking occurs in the ramjet mode In the rocket mode, Point 1 is closed and H fuel is injected between Point 1 and Point The fuel is laser-heated from Point to Point3 and the flow is assumed to choke thermally at Point 3 Since the energy offlow before laser-heating is negligibly small as compared with the input laser energy, the flowing relation is derived from the energy conservation law and the state equation, T 3 = η [ ] BP L, (11) ṁ p C p (γ +1) p 3 = ṁp RT 3 A 3 γ (1) From Point 3 to Point 4, the isentropic expansion is assumed, and the thrust is calculated by Eq(18) Cd 3 1 4 6 8 1 Mach number Fig4 C d used for the trajectory calculation The vehicle mass changes according to the injected fuel mass, m v (t) =m v () t ṁ p dt (13) Launch trajectory and payload ratio The vertical launch trajectory is calculated by solving the following motion equation by the 4th order Runge-Kutta scheme du m v dt = F 1 ρ U SC d m v g (14) Herein, the flight condition is decided automatically by tracing the trajectory The trajectory is calculated till the time, t e, when the vehicle accelerates to the first cosmic velocity, 791 km/s The payload ratio is estimated from the following, m p = te t r ṁ p dt, (15) Payload ratio = m v () mp 1 ɛ m v () (16) where t r is the time when the rocket mode starts Although ɛ must be about 5 to achieve SSTO by SCRamjet engine, 6) the structure weight of laser ramjet vehicle can be reduced due to the simple structure In this calculation, ɛ is assumed to be 1 SSTO Trajectory by Engine Cycle Analysis Figure 5 show the Mach number vs altitude diagram which is calculated under conditions tabulated in Table The mode switch from the pulsejet to the ramjet occurs at M = and H = 7 km C m ofthe ramjet mode has the maximum value, N/MW, at the point and then gradually decreases with the flight altitude owing to the decrease ofmass flow rate 3

H, km 18 16 14 1 1 8 6 4 Pulsejet Cm Ramjet Cm H 4 6 8 1 1 14 16 18 Flight Mach number Fig5 H, C m Vs M diagram U, m/s 8 7 6 5 4 3 1 Rocket Cm 18 16 14 1 1 5 1 15 5 3 Time, s Pulsejet Ramjet PL=5MW PL=3MW Rocket PL=113MW 8 6 4 Cm, N/MW PR=67 PR=55 PR=3 Fig6 Flight velocity Vs time diagram The mode switch from the ramjet to the rocket occurs at M =87 and H = 36 km where C m of the ramjet is 49 N/NW In the rocket mode, C m is almost constant value, 3 N/MW Figure 6 shows payload ratios for P L = 113, 3 and 5MW, where the parameters except P L is the same as Table Table Calculation conditions in engine cycle analysis m v (t =) 1 kg P L 5 MW η B 4 % C m (pulsejet) 1 N/MW ṁ p 1 kg/s η d 97 ɛ 1 CFD ANALYSIS Governing Equations Axisymmetric Navier-Stokes equations are solved Chemical reactions are treated as finite rate reactions The following 11 species ofair plasma are considered: N, O, NO, N, O, N +, O+, NO+, N +, O + and e The effects ofthermal non-equilibrium and radiative energy transfer are not considered Then, the governing equations are given by U t + F z + 1 rg r r = F v z + 1 rg v + H r r r + S (17) ρ ρu ρv ρu ρu ρv + p ρuv U = e ρuv ρv + p ρ 1, F = (e + p) u, G = (e + p) v, ρ 1 u ρ 1 v ρ 11 ρ 11 u ρ 11 v τ zz τ zr τ zr τ F v = uτ zz +vτ zr +q rr z j 1z, G v = uτ zr +vτ rr +q r j 1r, j 11z j 11r p τ θθ H =, S = ω 1 (18) ω 11 E and the equation ofstate are defined as E = ρ s h s (T ) p + ρ ( u + v ), (19) 11 p = ρ s R s T () 11 h s and the transport properties are taken from Ref (7) In the air chemical reaction model, the forward rates of Ref (8) are used The backward rates are calculated by the principle ofdetailed balance The chemical equilibrium constants are also taken from Ref (8) Numerical Scheme Inviscid flux is estimated with the AUSM-DV scheme 9) and space accuracy is extended to 3rdorder by the MUSCL approach with Edwards s pressure limiter 1) Viscous flux is estimated with a standard central difference Time integration is performed with the LU-SGS 11) scheme which is extended to 3rd-order time accuracy by Matsuno s inner iteration method 1) The calculation is performed with the CFL number of 4

1 6 4 5 1 z, cm 15 (a) Type A : 3 slope cowl (inlet is closed) 1 4 3 ηb 1 LSD threshold rgy ne ee st Bla v wa Energy fraction [%] 6 5 Ab so rb ed r, cm 8 nsity ve a r inte Lase e LSD w on th 1 en er gy Laser intensity on the LSD wave [MW/cm ] 1 1 1 4 1 6 Time [µs] 8 1 Fig8 Histories of E B and laser intensity at H = km 1 r, cm 8 6 set far from the vehicle body to reduce the influence of non-physical reflection waves from the outer boundary The mesh convergence of Cm at H = km is checked with doubly divided cells 4 5 1 z, cm 15 Table 3 Mesh convergence of Cm at H = km (b) Type B : non-slope cowl (inlet is open) Cell number 7, 88, 7 6 Cm, N/M W 17 14 r, cm 5 Since the difference is only 3 %, the 7, cells are used in this computation For a supersonic flight, the following conditions is chosen from the calculated trajectory 4 3 1-6 -4 - z, cm 4 6 8 Table 4 Supersonic flight condition H, km (c) Overall mesh (7, cells) Fig7 Computational mesh M 5 p, atm 55 ρ, kg/m 3 89 Explosion Source Model A explosion source model13) is employed instead of solving complex propagation processes of LSD wave: The explosion source is modeled as a pressurized volume centered at the laser focus The blast wave is driven by burst of this source The focus is located at the middle on the inner cowl surface Since LSD processes can be considered as isometric heating,1) the density in the source is assumed to be invariant during the heating process The source is assumed to be in chemical equilibrium The chemical composition is calculated by the method in Ref (14) Computational Mesh and Flight Condition Figures 7 (a) (c) show computational meshes Type A vehicle is used in the pulsejet mode This is almost the same as the Label E Lightcraft) The computed Cm is compared with the experimental C m data to validate this computation Type B vehicle with a non-slope cowl is used in the ramjet mode since Cd of Type B is half of Type A The mesh cells are set to be fine between the cowl and body to correctly capture a blast wave In addition, the mesh is concentrated near the wall to resolve the viscous boundary layer The mesh width in the vicinity of the wall is y = 8µm The outer boundary of the computational zone is One Dimensional LSD Analysis In order to model the explosion source, 1-D LSD propagation process is calculated From three con5

servation equations and C-J condition, the the following relations are derived 15) p = p 1 + ρ 1 DCJ, (1) γ +1 ρ = (γ +1)ρ 1 DCJ γ (p 1 + ρ 1 DCJ ), () T = p /R /ρ, (3) γ p v = c =, (4) ρ v 1 = D CJ, (5) h = h 1 + 1 ( DCJ v P L /A L ) +, ρ 1 D CJ (6) where the subscripts 1 and denote the states in front of and behind the LSD wave, respectively The velocities refer the coordinate relative to the LSD wave Since the laser beam is focused cylindrically as shown in Fig7, A L =π (r f r d ) tan 1 (f) Here, r f and r d are the radius ofthe focus and the detonation wave front, respectively f is 36 ) The history of P L is taken from the Ref (16) The Eqs (3) (8) are iteratively solved with chemical equilibrium calculation Then, the location oflsd is calculated by dr d dt = D CJ (7) In an atmospheric pressure, CO laser intensity below 1MW can not sustain LSD wave 17) In the present computation, the laser absorption is assumed to finish when laser intensity on the LSD wave decays to this threshold E B is defined as the sum ofkinetic energy at t = t l when P L /A L =1MW/cm, tl [ E B = h t+r h t+r 1 + 1 (D CJ v ) ]ρ 1 D CJ A L dt (8) Figure 8 shows the history ofthe laser intensity, and absorbed laser energy and blast wave energy When laser intensity on the LSD wave decays to LSD threshold, 6 % oflaser energy is absorbed by plasma and 6 % oflaser energy is converted to blast wave energy Table 5 shows the source volume decided by this η B The blast wave is driven at t =µs by burst ofthis source volume Table 5 Explosion source H, km E L,J η B (t ), % V,cm 3 4 6 174 3 188 444 4 17 513 5 161 556 where the absorption fraction of laser energy is assumed to be constant, 6 %, because the LSD threshold is unknown in reduced atmospheric density Thrust, N Thrust [N] 8 7 6 5 4 3 1-1 4 6 8 1 1 14 Time, µs 3 5 15 1 5-5 inlet Fig9 Thrust history cowl total body -1 5 1 15 Time [µs] Fig1 Each thrust received by body, cowl and closed inlet Computed Results at H =km A blast wave is driven at H = km by the explosion source in Table 5 The history ofaxial thrust is shown in Fig9 After the positive thrust maintains till 15 µs, the negative thrust continues till 9 µs After 15 µs, the thrust almost is equal to zero Figure 1 shows the thrust received by the body, cowl and closed inlet till µs After the explosion source bursts at t, the shock wave expands suddenly and decays Therefore, the thrust received by the cowl decreases fast The thrust received by the closed inlet and the afterbody decreases slower than that of the cowl Figures 11 (a) (c) shows the propagation processes ofthe shock wave The shock wave starts to sweep on the afterbody at t 1 =45µs The shock wave propagates beyond the middle ofthe after- 6

(a) At t 1 =45µs (p max =671atm, p min =77atm, dp=3atm) (a) At t =1µs (p max =7atm, p min =1 1 atm,dp= 11atm) (b) At t = 1µs (p max =386atm, p min =5atm, dp=17atm) (b) At t =µs (p max =463atm, p min =1 1 atm,dp= 3atm) (b) At t 3 = 19µs (p max =354atm, p min =75atm, dp=14atm) Fig11 Pressure contours in H = km body at t = 1µs Then, the shock wave leaves the afterbody tail at t 3 = 19µs The computed C m agrees with the experimental data, as listed in Table 6 Consequently, this computational code with this physical modeling is found to reproduce the experimental data Table 6 Comparison of C m at H = km Vehicle name C m, N/MW Label E (Ref ()) 1 Type A (present) 17 Computed Results at H= km Figures 1 (a) (b) show pressure contours after an explosion with E L = 4J at H = km and (c) At t =38µs (p max =47atm, p min = 1 atm,dp= 1atm) Fig1 Pressure contours after an explosion with E L = 4J at H = km and M =5 M = 5 The blast wave sweeps the afterbody from the inlet from t =1µsto38µs, without being spat out from the inlet Figure 13 shows the thrust histories The blast wave speed of H = km case is faster than that of H = km case due to small ambient pressure and high speed inflow The computed C m, ṁ and CAR are listed in: Table 7 The computed C m at H = km E L,J C m, N/MW 3 679 4 648 5 618 Because η B decreases with E L, C m also decreases with E L Variation of η B after Explosion The time-variation of η B is investigated E B is 7

Thrust [N] 16 14 1 1 8 6 4 - EL=5J EL=4J EL=3J H=km η, % B 45 4 35 3 5 15 1 H= km, EL=4J H= km, EL=4J -4 5-6 1 3 4 5 6 7 8 9 1 Time [µs] Fig13 Thrust histories of H = km 4 6 8 1 1 14 16 Time, µs Fig15 History of η B in the case of E L = 4J integrated overall the computational zone such as, [ p p E B = (9) γ 1 + ρ ( u + v ) ( )] ρ u + v dv The subscript indicates the values before the explosion Figure 15 shows the time variation of η B from the just exploded time to the time when the blast wave finishes to sweep the afterbody At H = km, η B recovers due to the energy conversion from the chemical potential from t =µs tot = 1µs After t = 1µs, the recovery rate decreases and the chemical potential energy is frozen At H = km, the blast wave finishes to sweep the afterbody before the recovery of η B is completed Consequently, large chemical energy is frozen Since the chemically frozen loss increases with the atmospheric density, C m decreases with the flight altitude DISCUSSION In order to validate the engine cycle analysis, C m ofthe engine cycle analysis are compared with C m ofcfd The engine cycle analysis is conducted with the same flight conditions and vehicle cross sections as CFD η B ofthe engine cycle analysis are taken from the time-average value of CFD between the just exploded time and the time when the blast wave finishes to sweep the afterbody Table 8 η B ofthe engine cycle analysis E L,J η B, % 3 66 4 59 5 49 Cm, N/MW 7 6 5 4 3 1 CFD Engine cycle analysis 3 4 5 EL, J Fig17 Comparison of C m between CFD and the engine cycle analysis Fig17 shows C m ofcfd and the engine cycle analysis C m ofthe engine cycle analysis are underestimated Since the engine cycle analysis is assumed to be steady state process, the peak pressure at Point 3 shown in Fig3 is lower than CFD Accordingly, the Humphrey cycle efficiency is degraded This low efficiency ofthe cycle causes the small C m of the engine cycle analysis In order correctly to estimate C m by the engine cycle analysis, the unsteady effect should be incorporated to the cycle SUMMARY The flight trajectory ofthe laser ramjet vehicle is calculated by the engine cycle analysis 8

The CFD with the explosion source model can reproduce the experimental data of C m Using this CFD model, C m in the supersonic flight is computed The results show C m and η B decrease with the flight altitude due to chemically frozen flow loss C m by the engine cycle analysis is underestimated in comparison with CFD Since the engine cycle analysis is assumed to be steady state process, the peak pressure in the Humphrey cycle is lower than CFD Accordingly, the Humphrey cycle efficiency ofthe engine cycle analysis is degraded This low efficiency ofthe cycle causes the small C m ofthe engine cycle analysis REFERENCES 1) Raizer, YP: Laser-Induced Discharge Phenomena, Consultants Bureau, New York and London, 1977, Ch6 ) Myrabo, LN, Messitt, DG, and Mead, FBJr: Ground and Flight Tests ofa Laser Propelled Vehicle, AIAA Paper 98-11, 1998 3) Myrabo, LN: World Record Flights ofbeam- Riding Rocket Lightcraft: Demonstration of Disruptive Propulsion Technology Flight Tests ofa Laser Propelled Vehicle, AIAA Paper 1-3798, 1 4) Wang, TS, Mead, FBJr, Larson, CW: Advanced Performance Modeling of Experimental Laser Lightcrafts, AIAA Paper 1-3664, 1 5) Bussing, TRA, and Pappas, G: An Introduction to Pulse Detonation Engines, AIAA Paper 94-63, 1994 1) Edwards, JR : A Low-Diffusion Flux- Splitting Scheme for Navier-Stokes Calculations, Computers & Fluids, 6 (1997), pp635-659 11) Jameson A, and Yoon, S Lower-Upper Implicit Schemes with Multiple Grids for the Euler Equations, AIAA Journal,5 (1987), pp99-935 1) Matsuno, K : Actual Numerical Accuracy ofan Iterative Scheme for Solving Evolution Equations with Application to Boundary- Layer Flow, Trans Japan Soc Aero Space Sci, 38 (1996), pp311-3 13) Ritzel, DV, and Matthews, K: An adjustable explosion-source model for CFD blast calculations, Proc of 1st International Symposium on Shock Waves, pp97-1,1997 14) Botton, B, Abeele, DV, Carbonaro, M, and Degrez G: Thermodynamic and Transport Properties for Inductive Plasma Modeling, J Thermophys Heat Transfer, 13 (1999), pp343-35 15) Landau, LD and Lifshitz, EM: Fluid Mechanics, nd ed, Butterworth-Heinemann, Oxford, 1987, Ch14 16) Messitt, DG, Myrabo, LN and Mead, FBJr: Laser Initiated Blast Wave for Launch Vehicle Propulsion, AIAA -3848, 17) Pirri, AN, Root, RG, and Wu, PK: Plasma Energy Transfer to Metal Surfaces Irradiated by Pulsed Lasers, AIAA J, 16 (1978), pp196-134 6) Shiramizu, M, Techincal Memorandum of National Aerospace Laboratory ofjapan No598, 1989 7) Gupta, RN, Yos, JM, Thompson RA and Lee, KP: A Review ofreaction Rates and Thermodynamic and Transport Properties for an 11-Species Air Model for Chemical and Thermal Nonequilibrium Calculations to 3, K, NASA RP 13, 199 8) Park, C: Review ofchemical-kinetic Problems offuture Flight NASA Missions, I: Earth Entries, Calculations to 3, K, J Thermophys Heat Transfer, 7 (1993), pp385-398 9) Wada, Y, and Liou, MS : A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities, NASA TM-1645, 1994 9