CHARACTERISTIC FEATURES OF DIAGNOSTICSOF SUPERSONIC HIGH-TEMPERATUREJET PARAMETERS

V. V. Chuprasov,a M. S. Tret’yak,a

and A. F. KlishinbUDC 536.25:536.45

The distribution of the gas temperature over the radius of a supersonic high-temperature free underexpandedjet at different distances from the plasmatron nozzle cut, as well as the distribution of the stagnation pressure,heat flux, and shock layer thickness along the length of a supersonic high-temperature blocked jet, is investi-gated experimentally depending on the sensor diameter. It is shown that in the calculation of the Mach num-ber, static pressure, and thermodynamic enthalpy of the air of the underexpanded jet (near the nozzle cut), itis necessary to account for the thickness of the shock layer formed upstream of the sensor.

Keywords: supersonic high-temperature jet, temperature, stagnation pressure, heat flux, shock layer thickness.

Introduction. Supersonic free underexpanded jets are widely used in engineering and in scientific investiga-tions. However, the distinctive features of the change in their characteristics during interaction with a barrier representan independent problem, since they have been studied inadequately as yet. Partly this is explained by the variety ofthe existing constructions and facilities for obtaining such high-temperature jets that significantly influence their struc-ture and characteristics.

An electric arc gas heater (a plasmatron with a power of about 1.5 MW) was manufactured following a linearscheme: at a nozzle diameter of 15 mm the working gas (air) pressure in the electric arc chamber amounted to10⋅105 N ⁄ m2 at an air flow rate of 100 g ⁄ s [1].

1. Investigation of Thermal and Gas-Dynamical Characteristics of a Plasma Jet. We investigated the in-teraction of a supersonic high-temperature underexpanded jet, issuing from the plasmatron nozzle into the surroundingspace (Fig. 1), with a barrier having the shape of a cylinder with a flat end.

The temperature of the free jet was measured by the method of the optical emission spectroscopy [2]. The in-tensity of plasma radiation from the given jet cross section with a frequency of 50 Hz was recorded with the aid ofa diffraction grating spectrometer onto a video matrix having 576 × 768 pixels. The measurement were made in threejet cross sections at distances from the plasmatron nozzle cut of 5, 10, and 15 mm. The temperature was determinedby the method of relative intensities of the lines of copper (CuI — 510.5 ⁄ 515.3 nm) and iron (FeI — 641.2 ⁄ 643.1nm) without applying the Abel inversion, with the error of temperature determination not exceeding �8%.

It has been established that the maximum gas temperature on the jet axis at the investigated distances fromthe nozzle cut at different instants of time lies in the range 6700–7700 K (Fig. 2). The gas temperature decreases by500–1000 K on moving away (by about 15 mm) from the jet axis over the radius; in this case the temperature profilesobtained for different instants of time of the plasmatron operation can differ by about 1000 K and have different ratesof decrease at the periphery of the plasma jet, indicating the nonstationary character of its efflux, which and is con-firmed by the high-speed video recording with a frequency of 1000 frames per second.

At the assigned regime of plasmatron operation, the Mach disk at the end of the first "roll" of the supersonicunderexpanded jet was formed at a distance of L � 30 mm from the nozzle cut (see Fig. 1).

On blocking the jet with a barrier in the form of a cylindrical sensor (protruding 15 mm from a conical sup-port toward the flow) a substantial rearrangement of the flow structure occurs. Upstream of the barrier a shock layeris formed which mainly determines the gas dynamics of the flow around it and the boundary layer thickness, the mag-

Journal of Engineering Physics and Thermophysics, Vol. 84, No. 5, September, 2011

aA. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Str.,Minsk, 220072, Belarus; email: lof@hmti.ac.by; bFederal State Unitary Enterprise "S. A. Lavochkin Research-Produc-tion Association," 24 Leningradskaya Str., Khimki of Moscow Region, 141400, Russia. Translated from Inzhenerno-Fiz-icheskii Zhurnal, Vol. 84, No. 5, pp. 1040–1045, September–October, 2011. Original article submitted August 25, 2010.

1062-0125/11/8405-1120�2011 Springer Science+Business Media, Inc.1120

nitude of the heat flux to the barrier surface, and so on. Therefore the next cycle of measurements was aimed at thedetermination of the boundary layer thickness depending on the barrier (sensor) diameter and on the given distance tothe nozzle cut. The diameter of sensors d in the experiment was equal to 14, 20, and 30 mm. The shock layer thick-ness l was determined in the vicinity of the stagnation point (on the sensor axis) from the results of processing thevideo pictures of the process of interaction of the high-temperature flow with the end surface of the sensors. The op-erating parameters of the plasmatron, which confirm the assigned regime of its operation, were controlled. Accordingto estimates, the error in the determination of l was not higher than �12%.

The distance from the plasmatron nozzle cut to the barrier x varied in the range 15–40 mm. Since in the caseof a free jet the sensor is immersed in a subsonic flow behind the Mach disk (x � 1.3L), the distance from the barrierto the Mach disk was measured. In the presence of a barrier in the jet, the Mach disk was displaced toward the nozzlerelative its position in the free jet. It turned out that in the investigated range of sensor diameter d and in the consid-ered range of distances x the dependence of the magnitude of the Mach disk displacement δ along the jet axis on thesensor diameter (Fig. 3) is close to a linear one: δ � 0.185d.

Experimental data on the change in the thickness of the shock layer l formed in a supersonic jet ahead ofthe barrier as functions of the sensor diameter d and of the distance x are presented in Fig. 4. As the distance fromthe nozzle increases, the shock layer thickness grows due (as will be shown below) to the considerable decrease in thestagnation pressure along the jet and correspondingly to the decrease in the gas density in the shock layer. The gasstagnation temperature in the shock layer decreases insignificantly (within 5%) with increase in the distance from thenozzle cut from 15 to 30 mm, even though the thermodynamic temperature in the free jet at this distance decreasesby about 20%.

Fig. 2. Temperature distribution over the jet radius at different distances fromthe plasmatron nozzle cut: 1) x = 5 mm; 2) 10; 3) 15 (two curves 1 and twocurves 2 were plotted at different instants of time).

Fig. 3. Dependence of the magnitude of displacement of the Mach disk rela-tive to its position in a free jet on the sensor diameter.

Fig. 1. General view of the free high-temperature jet issuing from the plasma-tron nozzle.

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Figure 4 presents also the results of calculations of the shock layer thickness l by means of the formula [3]

l = x − L [1 − A exp (− Bx ⁄ L)] , (1)

obtained at the ratio of the diameters of the sensor and nozzle d ⁄ dnoz = 2.5 and the values of the coefficients A =1.58 and B = 2.06. Our experimental results considerably exceed the data calculated from Eq. (1). This is due to thefact that in our experiments the gas density in the shock layer (stagnation pressure and temperature) differ from thedata of [3].

It follows from the experimental data of Fig. 4 that the shock layer thickness increases also with the sensordiameter, but in the relative coordinates l ⁄ d the experimental data obtained in the form of the dimensionless shocklayer thickness depend practically only on the distance (Fig. 5). Straight line 1 represents the dependence of the rela-tive shock layer thickness on flow past the flat end of the cylinder calculated by means of the formula applied for afree supersonic flow around bodies:

l

d = 1.6

⎛⎜⎝

K − 1

K + 1

⎞⎟⎠ +

0.27

(M − 1)0.65 . (2)

In calculations for the adiabatic coefficient the value K = 1.18 was adopted that, with an accuracy of up to 5%, aver-ages the values of coefficients in the range of pressures and temperatures of air in a plasma jet (p = (0.3–5)⋅105

N ⁄ m2, T = 6500–9000 K).According to estimates, about 15% below line 1 lie the results of calculations from the formula given in [4]:

ld

= 0.515 √⎯⎯ε1 − ε

,

and from the formula of [5] which yields the values close to those given by the previous formula:

ld

= (0.5 + 0.3ε) √⎯⎯ε ,

where ε is calculated from

ε = K − 1K + 1

+ 2

(K + 1) M2 .

Fig. 4. Dependence of the shock layer thickness on the sensor diameter and onthe distance from the barrier to the nozzle cut: 1) calculation by Eq. (1); 2) d= 14 mm; 3) 20; 4) 30.

Fig. 5. Dependence of the relative shock layer thickness on the distance fromthe barrier to the nozzle cut: 1) calculation by Eq. (2); 2) calculation by Eq. (3);3) d = 14 mm; 4) 20; 5) 30.

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Based on the experimental data presented in Fig. 5, a generalized linear dependence of the relative shocklayer thickness on the distance x between the barrier and the nozzle cut was obtained

l

d = 0.44

⎛⎜⎝

x

L −

dnoz

2L⎞⎟⎠ + 0.054 , (3)

which is valid in the investigated range of the values (0.2 < (x ⁄ L) − (dnoz ⁄ 2L) < 0.8 of the plasmatron jet parameters.

It was established in this case that the well-known techniques [4, 5] for calculating the thickness of the shock layer,formed in a free supersonic flow upstream of a cylindrical body with a flat end, lead to results differing fundamentallyfrom experimental data (in considering the corresponding dependences of l ⁄ d on x presented in Fig. 3).

The distribution of the Mach number along the free jet axis, needed for calculations by Eq. (2), was deter-mined with allowance for the shock layer thickness (see Fig. 4) and from the dependence of the stagnation pressurep0 on the distance to the nozzle obtained experimentally for sensors of diameter 14 mm (Fig. 6). In this case, the for-mula from [6] was used:

p0

pch

= ⎛⎜⎝

K + 1

2KM2 − K + 1

⎞⎟⎠

1K−1

⎡⎢⎣

⎢⎢

(K + 1) M2

2 + (K −1) M2

⎤⎥⎦

⎥⎥

KK−1

,

where pch is the pressure in the electric arc chamber of the plasmatron.The stagnation pressure depends on the sensor diameter and increases with the latter. Therefore, in construct-

ing the dependence of the Mach number on the distance in a free jet it is necessary to subtract the shock layer thick-ness from the barrier coordinate, since the stagnation pressure is determined by the Mach number ahead of the shockwave (rather than by the coordinate of the barrier position).

The stagnation enthalpy on the jet axis

H0 = H (p, T) + M

2a

2 (p, T)2

was calculated at a distance of 15 mm from the nozzle cut from the thermodynamic temperature measured by thespectral method (the average value is 7000 K) at a static pressure in the jet equal to p = 0.5⋅105 N ⁄ m2 found fromthe formula

ppch

= ⎡⎢⎣1 +

(K − 1) M2

2

⎤⎥⎦

− K

k−1 .

Fig. 6. Dependence of the stagnation pressure and of the Mach number on thedistance from the barrier to the nozzle cut: 1) d = 14 mm; 2) 20; 3) 30.

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The value of the stagnation enthalpy was H0 � 41⋅106 J ⁄ kg.We investigated the influence of the sensor diameter on the heat flux in the vicinity of the stagnation point

of the barrier. An increase in the size of a sensor leads, on the one hand, to an increase in the stagnation pressure,and, on the other, to a decrease in the gas velocity gradient in the vicinity of the stagnation point. The measurementsof the heat flux made by the exponential method showed that as a result of the differently directed action of theseparameters the heat flux to the barrier is practically independent of the diameter of sensors (14 and 20 mm) (Fig. 7).

2. Results of Investigation of the Destruction of Specimens Made from Glass Fiber STE′F andPolytetrafluoroethylene F4 and Their Discussion. Under the conditions of high thermomechanical loadings, an inves-tigation of the destruction of cylindrical specimens made from glass fiber STE′F was carried out which showed that thevelocity of their entrainment is practically independent of the specimen diameters (d = 14 mm and 20 mm). Under thesame conditions of testing, the data on the velocity of linear entrainment of polytetrafluoroethylene F4 depends some-what on the specimen diameter, since the mechanism underlying the destruction of this material differs fundamentallyfrom the complex mechanism of the destruction of glass fiber (Fig. 8).

Since the jet parameters change rapidly with distance from the nozzle, with the aid of the system of tracingand supply of a specimen its end was held in the assigned cross section of the jet, which ensured the destruction ofthe material at constant thermal and dynamic impacts. The radiance temperature of specimens from glass fiberamounted to about 2800 K.

Specimens from glass fiber were investigated also under other conditions. Instead of the copper cooled nozzle,at the exit from the plasmatron a bushing from glass fiber STE′F with a diameter of the critical cross section of 7 mmwas installed. At the moment of the plasmatron start-up the working gas pressure in the discharge chamber increasedup to 22 bar and thereafter, as the critical cross section of the nozzle changed (ablation of the nozzle material), beganto decrease.

An analysis of the results of investigations shows that the mechanism of ablation of glass-reinforced plastic intesting of bushings and of cylindrical specimens is different. Thus, for example, the thickness of the coked layer in thecritical cross section of the bushing is about 0.7 mm; on the end of a cylindrical specimen there is practically nocharred layer. In this case, the heat flux and pressure in the critical cross section of the bushing is higher than on thesurface of the cylindrical specimen (p � 2–5 bars).

Conclusions. The investigations carried out into the characteristics of a high-temperature supersonic plasma-tron jet related to the stagnation pressure, heat flux, Mach number, and the shock layer thickness made it possible toelucidate the distinctive features of their mutual influence and complete the diagnostics of the jet parameters. The re-sults obtained are sufficient for selecting the corresponding regimes of testing on a plasmatron in investigation of theheat-protecting properties and characteristic features of the destruction of materials under the conditions of high ther-mal and aerodynamic loadings.

Fig. 7. Variation of the heat flux along the jet axis: 1) d = 14 mm; 2) 20.

Fig. 8. The velocity of entrainment of materials vs. the heat flux; F4 (1) d =10 mm; 2) 20); STE′F (3) 14; 4) 20; 5) nozzle).

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NOTATION

a, speed of sound, m ⁄ s; d, diameter of sensors, mm; dnoz, diameter of plasmatron nozzle, mm; H, stream en-thalpy, 106 J ⁄ kg; H0, stagnation enthalpy, 106 J ⁄ kg; K, adiabatic coefficient; L, distance from the plasmatron nozzlecut, mm; l, shock layer thickness, mm; M, Mach number; p, static pressure of air in a plasma jet, 105 N ⁄ m2; p0, stag-nation pressure, 105 N ⁄ m2; pch, pressure in the electric arc chamber of the plasmatron, 105 N ⁄ m2; q, heat flux towardthe barrier, 107 W ⁄ m2; T, air temperature in a plasma jet, K; V, velocity of material entrainment, mm ⁄ s; x, distancefrom the plasmatron nozzle cut to the barrier, mm; δ, magnitude of displacement of the Mach disk along the axis, mm;ε = ρ1

⁄ ρ2, ratio of gas densities before and behind the shock wave. Indices: ch, chamber; noz, nozzle; 0, stagnation.

REFERENCES

1. V. V. Chuprasov, M. S. Tret’yak, and A. F. Klishin, Experimental rig for investigating the interaction ofplasma jets with a substance, in: Abstracts of the Int. Conf. "Materials and Coatings under Extreme Conditions:Investigations, Application, Ecologically Pure Technologies of the Production and Utilization of Products," Sep-tember 22–26, 2008, Large Yalta, Zhukovka, Autonomous Republic of Crimea, Ukraine, Izd. Dom "Akadempe-riodika" NAN Ukrainy, Kiev (2008), p. 342.

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