Supersonic laser propulsion - OSA Publishing

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Supersonic laser propulsion Yurii Rezunkov1,* and Alexander Schmidt2 1

Institute of Optoelectronic Instrument Engineering, Sosnovyi Bor, Leningrad oblast 188540, Russia 2

Ioffe Physical Technical Institute, Computational Physics Laboratory, Polytekhnicheskaya 26, Saint Petersburg 194021, Russia *Corresponding author: [email protected] Received 2 June 2014; accepted 31 August 2014; posted 12 September 2014 (Doc. ID 213221); published 29 October 2014

To produce supersonic laser propulsion, a new technique based on the interaction of a laser-ablated jet with supersonic gas flow in a nozzle is proposed. It is shown that such parameters of the jet, such as gasplasma pressure and temperature in the ablation region as well as the mass consumption rate of the ablated solid propellant, are characteristic in this respect. The results of numerical simulations of the supersonic laser propulsion are presented for two types of nozzle configuration. The feasibility to achieve the momentum coupling coefficient of Cm ∼ 10−3 N∕W is shown. © 2014 Optical Society of America OCIS codes: (140.3440) Laser-induced breakdown; (240.6670) Surface photochemistry; (220.1770) Concentrators; (350.5400) Plasmas. http://dx.doi.org/10.1364/AO.53.000I55

1. Introduction

The use of laser power to produce thrust has been discussed since the 1970s based on pioneering works by Kantrowitz [1] and Prokhorov [2]. Starting in 2002, the International Symposia on Beamed Energy Propulsion is held regularly [3–6], at which numerous experimental and theoretical investigations on laser propulsion are discussed. Attention is mostly paid to various physical mechanisms of thrust production in a subsonic operation mode when the laser radiation interacts with subsonic gas flow. Thus, such mechanisms of the interaction are considered, i.e., laser breakdown of gases or liquids, laser ablation of solids, and laser detonation of polymers and explosive materials. Various prototypes of laser propulsion engines (LPE) are developed and tested during this period [7], among which LIGHTCRAFT, a vehicle proposed by Dr. Myrabo and other researchers from NASA, should be mentioned above all. The first full-scale 1559-128X/14/310I55-08$15.00/0 © 2014 Optical Society of America

experiments on launching of a small LIGHTCRAFT model to the altitude of 100 m were carried out by using a pulse-periodic CO2 laser in 2002 [8]. Only an insignificant number of the experimental runs were successful when the laser propulsion was sufficiently high. These experiments were mainly carried out at conditions of subsonic flows around the models. Supersonic laser propulsion when the laser radiation interacts with supersonic gas flows has been less considerably investigated. Nevertheless, such mechanisms in laser breakdown of supersonic gas flow under pulsed or repetitively pulsed laser radiation were studied [9–14]. The effect of a resonance conjugation of separate shock waves into a quasistationary shock wave at high-repetition-rate laser radiation in a jet nozzle was manifested in [14,15] as one of perspective operation modes of supersonic laser propulsion. But the experiments carried out by the authors demonstrated essential instability of thrust production in this case. Analysis of the experiments shows that the technique of thrust production imposes mutual constraints on laser characteristics as a function of flow parameters [16]. 1 November 2014 / Vol. 53, No. 31 / APPLIED OPTICS

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In our opinion, production of steady-state supersonic laser propulsion will depend on the process of the laser power deposition in supersonic gas flow [17–19]. Depending on density and pressure of the gas flow and on laser pulse power, duration, and repetition rate, the process is accompanied by such phenomena as fast ionization wave propagating in the gas at velocity 20–100 km/s, laser detonation waves at velocity 3–10 km/s, and radiation waves at velocity 10–40 km/s [20]. Laser breakdown is also accompanied by plasma outflow from the breakdown region at velocity exceeding the inlet flow velocity. In accordance with numerical and experimental data, there are supersonic and subsonic zones behind the breakdown region [18,19]. That is why strict requirements to the laser parameters matching gas flow characteristics must be satisfied to produce laser propulsion. In this paper, we consider a new technique of supersonic laser propulsion, which is produced due to the interaction of a laser-ablated jet with supersonic gas flow in a nozzle. The processes of the interaction and thrust production are examined by numerical analysis, simulating the flow and ablative jet in a parabolic nozzle and a nozzle with off-axis parabola walls. 2. Supersonic Laser Propulsion Features

Laser propulsion is based on two processes: (1) bulk laser breakdown of gas propellant or (2) laser ablation of solids under the action of a high peak power laser pulse. To increase laser intensity in a breakdown area, two types of optical beam concentrators are used, namely, axial and off-axial paraboloid [8–13]. As a rule, the concentrators also operate as jet nozzles. The efficiency of laser propulsion production can be determined through the momentum coupling coefficient Cm , which is the ratio of produced thrust T to the laser power P, namely, Cm  T∕P. Usually, Cm varies from a few dynes to 100 dynes per Watt. Recent investigations on supersonic laser propulsion demonstrate low efficiency of thrust production if axial paraboloid is used as a beam concentrator and nozzle [7]. At that, the coupling coefficient decreases with increasing of incoming flow Mach number (down to 10 dyne/W). One of the important causes of the propulsion performance degradation was increasing of the air drag with increasing flow Mach number. At the same time, the design of LIGHTCRAFT is developed to satisfy the conditions of supersonic flight of the vehicle in the upper atmosphere [8]. It includes a concentric slit nozzle formed by the (1) engine cowl, (2) off-axis parabolic afterbody, and (3) forebody, which form the incoming flow at the nozzle inlet (see Fig. 1). The shape of the forebody and position of the engine cowl are to transform incoming supersonic flow into a subsonic one and to increase the gas pressure inside the nozzle formed by the cowl and parabolic afterbody. In this case, laser propulsion I56

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Fig. 1. Schematic of LIGHTCRAFT vehicle [8].

is produced due to the interaction of laser detonation waves with the nozzle walls. But the numerical analysis made in [13] shows that high-power shock waves generated in a breakdown region move upstream against subsonic flow and periodically shut down the flow in the slit channel, which results in pulsation of a thrust generation and in decrease of the laser propulsion efficiency. These shock waves are finally blown downstream and become pressure waves. The estimated momentum coupling coefficient in the case of focusing a laser beam on the cowl is fairly constant at about 15 dyne/ W. It is worth mentioning that the coupling coefficient is found to be sensitive to the beam focus location. Similar effects were observed in large-scale experiments with the LIGHTCRAFT prototype, presented in [21]. These experiments were carried out using supersonic shock tube and TEA CO2 laser with a pulse energy up to 1 kJ that corresponds to a gigawatt peak power of the laser pulse. In the experiments, the LIGHTCRAFT model diameter was 25 cm. The static gas pressure of the flow inside the shock tube was varied to simulate flight of the vehicle at an altitude of 30 km. Moreover, such parameters of the flow, as Reynolds and Mach numbers, were adequate to the flight conditions. Temperature, heat transfer, and rarefaction conditions are also to be taken into account to satisfy the conditions of Prandtl and Knudsen number similarity. The experiments demonstrated the efficiency of thrust production as Cm  6 − 30 dyne∕W in dependence of laser pulse energy in this case. Schlieren photos of the flow in the model jet nozzle showed formation of shock waves at a leading edge of the nozzle and generation of a set of shocks close to the central body of the model. These waves resulted in decreasing the momentum coupling coefficient of laser propulsion at high energy laser pulses. To obtain optimal supersonic mode of the LIGHTCRAFT operation, the condition of precise pressure recovery of gas flow in the slit inlet in dependence of the incoming flow Mach number is determined [22]. The forebody surface is shaped in such a way that a bow shock wave arising in supersonic flow directs incoming flow into the slit nozzle without additional pressure losses and shocks (Fig. 2). This arrangement provides rather uniform flow in the slit channel in spite of structural complexity of the vehicle and incoming flow. But in pulsed mode

Fig. 2. Supersonic version of the LIGHTCRAFT design [22].

of the laser propulsion, the flow becomes nonuniform due to a shock wave generated in the breakdown region. The shock wave propagates into the channel and chocks inlet during a time interval needed for the pressure in the vehicle nozzle to arise. The choking of the slit channel results also in pulsation of the thrust. The brief analysis of laser propulsion in the supersonic mode of operation shows that the conditions of steady-state interaction of a laser pulse with a supersonic flow are to be created by excluding generation of strong shock waves choking an inlet of a supersonic nozzle. Moreover, it is necessary to determine the conditions of optimal laser power release in supersonic flow to obtain high efficiency of thrust production. Let us consider the processes of laser pulse interaction with a supersonic flow in more detail to specify the conditions. 3. Processes of Laser Pulse Interaction with Supersonic Gas Flows

We have previously noted that the interaction of the laser pulse with the gas is followed by complex gas dynamic effects, in particular, generation of a quasi-stationary shock wave [14]. These phenomena strongly complicate thrust production in LPEs. To analyze these effects, let us consider numerical and experimental studies of the problem. Numerical simulations of laser power deposition in supersonic flows discovered physical details of the shock wave and thermal gas wake generation downstream of the breakdown region. The peculiarity properties of the processes considerably depend on pulse repetition rate (PRR). High-intensive gas jets directed out of a center of the breakdown region at the initial point of time of the interaction are observed [18]. The jet flow velocity significantly exceeds the incoming flow velocity. A shock wave is generated thereafter, which has a characteristic shape for a bow shock generated in front of a solid body streamlined by a supersonic flow. Moreover, the generation of the assembled shock wave in front of the breakdown region and thermal gas wake downstream of the region is dependent on PRR. Results obtained in [18] demonstrate that the thermal wake consists of individual plasma zones weakly coupled with each other at low PRR. But when the repetition rate exceeds 40–50 kHz at flow and Mach number equals to 2, the thermal wakes becomes a simply connected continuous zone. Lateral size of the wake weakly changes downstream. But the structure of the wake remains visibly vortex.

As shown in [18], the Mach number of gas flow behind a breakdown center depends on the modes of laser pulse interaction with a gas, which are (a) spherical energy explosion and (b) laser-sustained detonation waves. In case (a), it is assumed that the laser power deposition happens instantly and the explosion model of the deposition can be applied for calculations. Analysis of gas dynamic effects carried out in the framework of the explosion model shows that gas speed of sound remains constant if the isobaric condition of the flow in the region is fulfilled. It will be realized if the Mach number in the central part of the flow is equal to 0.2M ∞ , where M ∞ is the Mach number of incoming flow. The result indicates the fact that the flow behind the energy release point is subsonic at M ∞ < 5 and supersonic at M ∞ > 5. In the case (b), the flow velocity and Mach number of plasma jet (M 0 ) are determined as for the gas in rest. M 0 is varied from 1.0 to 1.5, and the Mach number is independent of the velocity of the incoming flow. This means that the flow right behind the breakdown region is significantly subsonic because of increase of the gas enthalpy and, thus, gas speed of sound due to absorption of the laser power. These data indicate that the strong strict correlations between gas flow parameters and laser pulse characteristics, determining modes of laser pulse/ supersonic flow interaction are required to efficiently input the laser power into the gas volume and to integrate a number of low-intensity shock waves into a high-intensity wave [14]. For example, the experimental study of laser propulsion demonstrated instability of thrust production under the action of laser radiation generated at a high repetition rate because of this reason. In the following sections, we consider laser ablation of solid propellant in a supersonic flow as the mechanism providing steady-state production of the supersonic laser propulsion. 4. Laser-Ablated Jet in a Supersonic Gas Flow

Laser ablation of solids was considered as a technique to produce thrust by Kantrowitz in 1972 for the first time [1]. As such, volatile solids are efficient to produce laser propulsion of a low thrust rate. But to obtain maximal specific thrust, which is determined as a ratio of the thrust to propellant mass consumption, poor evaporated solids should be used [2]. We assume that the laser-ablated jet will allow additional acceleration of supersonic flow in a jet nozzle if the ablation will be induced closely by the nozzle walls. The assumption is based on the effects produced by a gas jet on a supersonic flow close to a solid body [23,24]. In accordance with the laser ablation theory [25], the momentum coupling coefficient Cm created by the ablation jet can be defined as the ratio of specific recoil impulse vE of the jet and laser radiation flux Φ if we consider a repetitively pulsed laser. In the case of applying a CW laser, this is the ratio of evaporated gas pressure pa and laser radiation intensity I. 1 November 2014 / Vol. 53, No. 31 / APPLIED OPTICS

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Let us define these parameters to calculate numerically the interaction of the ablation jet with supersonic flow. In the approximation of a quasistationary evaporation of solid material under the laser radiation, the evaporated mass rate can be determined as [25] _  ρa ca ; m

(1)

where ρa is the vapor mass density, and ca is the adiabatic speed of sound in the vapor flow. The vapor pressure pa also can be determined by following _ a ∕M a ; pa  1  γM 2a mv

(2)

where M a is the Mach number of the vapor jet, γ is the adiabatic exponent (usually γ  1.1 if the temperature of the vapor gas exceeds 104 K), and va is gas velocity in the ablation jet. The vapor pressure created closely by the solid surface depends on modes of the laser radiation interaction with plasma generated by the laser power in this region. We assume also that the plasma temperature near the solid surface is limited in a value by the effect of cut  off frequency depending on the electron number of the plasma and on radiation wavelength [20]. It is also assumed that the plasma temperature depends on whether the radiation is pulsed or continuous. To determine the ablation parameters, the ablation energy Q of laser radiation to ablate each gram of the solid target is usually defined as Q  Ei ∕Δm;

(3)

where Ei is the laser pulse energy, and Δm is the ablated mass. At the pulsed mode of laser ablation, the ablated mass can be determined as follows: Δm  Iτi ∕Q ;

(4)

where τi is laser pulse duration. Total evaporated mass consumption can be determined as m  P∕Q  Ei f ∕Q ;

2 ρ 3 6 ρu 7 6 7 W6 7; 4 ρv 5 2 6 6 6 G6 6 4

ρE 0 τxi τyi τij vj  q

2

3

ρV

6 ρVu  pi 6 F6 4 ρVv  pj 3

7 7 7; 5

ρVE  pV

7 7 7 7: 7 5

Here, conventional notation is used. The system of the governing equations is completed by the equations of a gas state, namely, p  pρ; T;

E  eρ; P 

ρV 2 ; 2

(7)

where eρ; p is the internal gas energy. These equations were used for solving the model problem in which the interaction of a 2D or axisymmetric supersonic flow at the surface of a plate or a cylinder with a transverse supersonic jet imitating an ablation torch was analyzed. We also considered the solution of the problem of a supersonic flow of a gas through the standard axisymmetric parabolic nozzle as well as the nozzle with a wall formed by off-axis parabola, taking into account the interaction of the flow with transverse jets. In the numerical solution of the initial equations, their discretization and explicit linearization in the computational mesh are carried out. To improve the stability of the computational algorithm, a transition from the conservative to main variables was performed in the term containing the time derivative. The main difficulty in the numerical solution of the problem is associated with computation of convective fluxes at the faces of the control volume. For this purpose, the counterflow scheme with separation of flows is used [26]. This scheme makes it possible to obtain explicit expressions for convective fluxes

(5)

where f is PRR. The interaction of a laser ablative jet with supersonic gas flow is studied using a model of semiinfinite gas flow. The mathematical model of the interaction is based on Navier–Stokes equations, which can be written in a vector form as ∂ ∂t

Z

Z V

WdV 

S

F − GdS  0:

(6)

In these equations, vectors W; F, and G have the following forms: I58

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Fig. 3. Pressure distribution in the case of transverse jet injection into supersonic flow.

Table 1.

Laser-Ablated Jet Parameters at Pulsed Mode of Ablation 

I

Ti

Q

Ei

f

VE

P

_ m

W cm−2

K

J g−1

J cm−2

Hz

m s−1

W

g s−1

5.2E  7 2.0E  8 8.4E  8

1.74E  4 3.42E  4 7.00E  4

1.3E  4 2.5E  5 5.0E  4

0.52 2.00 8.40

5E  3 7E  3 1E  4

6.0E  6 1.5E  5 3.2E  3

1E  6 1E  5 1E  4

77 4 0.2

5.2E  7 2.0E  8 8.4E  8

1.74E  4 3.42E  4 7.00E  4

1.3E  4 2.5E  5 5.0E  4

0.52 2.00 8.40

5E  3 7E  3 1E  4

6.0E  6 1.5E  5 3.2E  3

1E  4 1E  5 1E  5

77 6 6.4

(a)

(b)

at the faces of computational meshes without solving the Riemann problem. To determine the local time step, the CFL criterion is used; in this case, the eigenvalues of the preconditioned system of equations are used as local velocity scales. The interaction of a laser ablation jet with a supersonic flow was first tested using the model of a selfinfinite gas stream flowing close by an infinite plate. The ablation parameters were chosen as follows: ablation jet velocity is 2800 m/s at ablated mass flow _  0.077 kg∕s). The incoming gas flow velocrate, m ity V  590 m∕s, which corresponds to Mach number M 0  1.9 at altitude, H  30 km. The laser-ablated jet has some specific physical features, which differs it from the conventional gas jet. These ablation features should be taken into attention at a numerical simulation of the ablative jet-flow interaction. First of all, the ablative jet is always perpendicular to the solid surface independently of the laser beam incident angle. Second, the velocity and ablative mass rate depend on the laser radiation power flux, absorption efficiency of the laser power by solids, its evaporation temperature, and so on [27]. Figure 3 illustrates the results of simulation of the jet-flow interaction. As one can see from the figure, a detached shock wave is created at a small distance in front of the ablation region, and the shock wave front has a curved structure, which is perpendicular to a solid surface. Behind the wave, the flow velocity decreases up to a subsonic magnitude, but the velocity reaches a supersonic character right downstream from the ablation point. Moreover, the flow velocity behind the ablation area is significantly higher than the incoming flow velocity, and the flow additional acceleration is assumed to be used to produce thrust.

of a propellant. Both subsonic and supersonic modes of laser propulsion have been studied with the parabolic design during past decades. The second is an off-axis parabolic nozzle used in the LIGHTCRAFT model to focus a laser beam on a shroud surface and to produce a thrust in subsonic and supersonic modes. It is also required to determine laser characteristics providing laser ablation of various solid materials. As it is known [27], high-radiation intensity has to be achieved if continuous ablation of the solid propellant is applied. Because of this reason, CW laser power of megawatt class has to be applied to maintain the ablative evaporation of the propellant. In contrast, the high intensity of laser power easily can be provided if pulsed mode of the laser ablation is applied. We assume also a quasi-continuous laserablated jet will be created if PRR will be sufficiently high. Then we expect high-power solid state and gas lasers with a short laser pulse to be applied as a laser power source in considering the problem. In Table 1, the ablation and laser parameters determined by using the initial ablation data published in [25] are listed for various power of laser and ablation intensity of a propellant. The temperature of laser-ablated vapor is determined as an equilibrium temperature of the plasma produced at a given pulse laser intensity.

5. Laser-Ablation Propulsion in Supersonic Flows

To simulate the laser propulsion production at a supersonic mode, two designs of laser beam concentrators are chosen. The first is a parabolic beam concentrator, which was closely studied in various experiments on laser propulsion. It is assumed the parabolic has a mirrored inner surface focusing laser beam in a focus region to initiate a laser breakdown

Fig. 4. Radial pressure profiles at the nozzle exit for different mass flow rates in the ablative jet. 1 November 2014 / Vol. 53, No. 31 / APPLIED OPTICS

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Table 2.

Laser-Ablated Jet Parameters at Pulsed Mode of Parabolic Nozzle Operation

τi S

Ei J cm−2

f Hz

_ m m s−1

_ m m s−1

_ m m s−1

1.0E − 8 1.0E − 7 1.0E − 6

0.52 5.2 52

6E  4 6E  3 6E  2

0.77 0.77 0.77 P  1E  4W

7.7 7.7 7.7 P  1E  5W

77 77 77 P  1E  6W

As one can see from the table, there is a correlation of the laser output power with the modes of laser operation. In the following analysis, we considered two extreme cases, which include the first rows of Tables 1(a) and 1(b). The data were used for calculation of thrust production in the LIGHTCRAFT vehicle model. Figure 4 demonstrates radial pressure profiles in nozzle outlet (model exit diameter is 0.5 m). It is seen that the effect of the ablative jet manifests itself not only in addition to the nozzle flow momentum, but, mainly, in change of the flow structure so that the pressure is redistributed and significantly increases in the vicinity of the nozzle wall, providing rise of the thrust. In the case of the parabolic nozzle, we considered a simpler model of the supersonic laser propulsion because the beam focus occupies less area in the center of the parabolic. Table 2 summarizes laser and ablation parameters for the case when plasma temperature is 104 K and initial jet velocity is 5 × 103 m∕s at the specific ablation energy of Q  1.3 × 104 J∕g. Laser output power and laser pulse duration are chosen as variable parameters. Results of simulations of interaction of the supersonic flow with the laser ablative jet in a parabolic nozzle (nozzle exit diameter is 10 cm) are shown in Figs. 5 and 6. Figure 5 presents distribution of the flow Mach number nozzle axial cross section. A stationary shock wave, generated by interaction of the incoming flow

Fig. 5. Pressure distribution in the parabolic nozzle with ablative central rod. Upper: without ablative jet. Lower: with ablative jet. I60

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Fig. 6. Mach number distribution in the parabolic nozzle with ablative central rod. Upper: without ablative jet. Lower: with ablative jet.

with the ablative jet, results in change in the gas dynamic structure of the flow. In the presence of the jet, the pressure increases in the vicinity of the nozzle wall. The shock wave influences Mach number distribution; its maximum value decreases slightly and shifts to the nozzle axis (see Fig. 6). Radial profiles of pressure and velocity at the nozzle exit are shown in Fig. 7. It is seen that, in the case with the ablative jet, the domain of pressure rise extends closer to the nozzle axis, and the pressure is higher than that in the case without the

Fig. 7. Radial pressure and velocity profiles at nozzle exit cross section. Curves marked by symbols correspond to the case of ablative jet presence.

Fig. 8. Diagram of the nozzle. 1, 2, and 3 denote the engine cowl, off-axis parabolic afterbody concentrator, and conical forebody, respectively.

jet. Interaction of the ablative jet and the incoming flow results in the shock wave (see Fig. 5) and, therefore, in decrease of the velocity in the vicinity of the nozzle axis. Computations show that interaction of the ablative jet with the incoming flow results in increase of axial component of the pressure force, acting on the nozzle wall. For the case under study, this “additional force” is equal to 310 N. We also considered a supersonic nozzle with the off-axis paraboloid. A diagram of this supersonic nozzle is presented in Fig. 8. Such a nozzle operates in a mode regime close to “scramjet.” For the case presented below the incoming flow Mach number, M 0  5, gas parameters correspond to atmosphere at altitude 30 km (P0 > 1192 Pa, T 0 > 226 K); the “ablative” jet velocity is U j et > 2000 m∕s, temperature T j et > 2800 K, and the jet mass flow rate. 70 g/s. Figure 9(b) demonstrates that the ablative jet significantly changes the flow structure. Characteristic rarefaction zone downstream of the critical cross section disappears; the shock wave, appearing in the vicinity of the critical cross section due to interaction of the incoming flow with the ablative jet, results in rise of the pressure in the divergent part of the nozzle, near the afterbody, and, therefore, in rise of the thrust. A complex set of shock waves generated in interaction of the supersonic flows is clearly seen in Fig. 10. The flow is characterized by considerable acceleration in the vicinity of the engine cowl. In this case, thrust, calculated as axial component of the pressure force acting on the nozzle walls, is equal to 1340 N.

Fig. 9. Pressure distribution in the supersonic nozzle with offaxis paraboloid: (a) without ablative jet and (b) with ablative jet.

Fig. 10. Mach number distribution in the supersonic nozzle with off-axis paraboloid: (a) without ablative jet and (b) with ablative jet.

Our analysis shows a limited case of laser propulsion production, which depends on the ablation mass rate for the given conditions of the LIGHTCRAFT ve_ exceeds hicle modeling flight in the atmosphere. If m 164 g/s, the flow becomes unstable along with thrust production, which looks like surging of the LIGHTCRAFT nozzle. Figure 11 presents typical variation in time of the pressure coefficient for the nozzle walls _ > 225 g∕s. Oscillating behavior of the presat m sure coefficient is a result of nonstationary processes accompanying interaction of the incoming flow and the ablative jet. To estimate the efficiency of thrust production as a result of the jet-flow interaction in the nozzle, we assume to use a conventional definition of laser propulsion momentum coupling coefficient Cm . In this case, the coefficient can be determined as a ration of the thrust increase under laser-ablated jet in respect to initial thrust produced by a nozzle to laser power applied, that is Cm  Δ

T : P

(8)

The thrust increase is determined through integration of the gas pressure distribution over the

Fig. 11. Time variation of the pressure coefficient at the ablative _ > 225 g∕s. jet mass flow rate, m 1 November 2014 / Vol. 53, No. 31 / APPLIED OPTICS

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inner surface of nozzle. For the limited case presented, the coupling coefficient reaches 10−3 N∕W (100 dyne/W), and the efficiency can be considered as the perspective one to produce the supersonic laser propulsion by using the tested technique. 6. Conclusion

We analyzed the main effects of laser propulsion at a supersonic mode of its production. It is shown that the laser technique has been used at the present time to produce thrust that has a principal physical limitation caused by (1) instability of supersonic gas flow response on pulse breakdown of the gas propellant and (2) initiation of strong shock waves choking an inlet of a supersonic nozzle of the tested vehicles. To exclude the effects, we proposed to use a laserablated jet generated close to the nozzle inner walls as a new technique of supersonic laser propulsion. In this case, the thrust augmentation is the result of reconfiguration of supersonic flow through the nozzle due to interaction of the jet with the flow. Numerical analysis of various examples of the supersonic laser propulsion demonstrates the operation stability of thrust production if the ablated mass rate does not exceed a limited value. If so, then a surging mode of the thrust production is observed. But to reach that surge, a powerful laser must be applied. The momentum coupling coefficient of Cm  10−3 N∕W can be obtained in this case and indicates the effectiveness of applying the laser ablation propulsion in supersonic flows. In our opinion, the technique of the laser-ablated jet interaction with supersonic flows also can be used to increase thrust production by hypersonic ramjet engines because the technique does not require forced stagnation of the flow. References 1. A. Kantrowitz, “Propulsion to orbit by ground-based lasers,” Astronaut. Aeronaut. 10, 74–76 (1972). 2. F. V. Bunkin and A. M. Prokhorov, “The use of laser power to produce a thrust,” Sov. Phys. Usp. 119, 425–446 (1976). 3. A. V. Pakhomov, ed., “Beamed energy propulsion,” in International Symposium on Beamed Energy Propulsion AIP Conference Proceedings, 2002, Vol. 664, paper 723. 4. K. Komurasaki, ed., “Beamed energy propulsion,” in International Symposium on Beamed Energy Propulsion AIP Conference Proceedings, 2003, Vol. 702, paper 560. 5. C. Phipps, ed., “Beamed energy propulsion,” in International Symposium on Beamed Energy Propulsion AIP Conference Proceedings, 2009, Vol. 1230, paper 498. 6. H. A. Eckel, ed., “Beamed energy propulsion,” in International Symposium on Beamed Energy Propulsion AIP Conference Proceedings, 2011, Vol. 1402, paper 412. 7. Y. A. Rezunkov, “Laser propulsion, the overview of recent investigations,” J. Opt. Technol. 74, 18–39 (2007). 8. L. N. Myrabo and J. S. Lewis, LIGHTCRAFT, Flight Handbook (Apogee Books, 2009).

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