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EXPERIMENTAL AND NUMERICAL INVESTIGATION OF ELECTRIC−ARC AIRSPIKES FOR BLUNT AND SHARP BODIES AT MACH 5 E. Schülein1, A.A. Zheltovodov2, E.A. Pimonov2 and M.S. Loginov2

1DLR, Institute of Aerodynamics and Flow Technology, 37073, Göttingen, Germany 2Khristianovich Institute of Theoretical and Applied Mechanics SB RAS,

630090, Novosibirsk, Russia Introduction The flow control by a localized heating (Fig. 1, a) is

the object of investigations at least since the beginning of the 20th century. In accordance with the review [1] in 1914 the Russian scientist E.A. Shilovskii performed the first experiments on drag reduction for blunted projectiles by burning phosphorus at the tip of an aero-spike, and starting from 1945 the studies of external combustion for aerodynamic forces and moments control performed in the USA, USSR and Europe. Similar to the effect of con-ventional solid aero-spike the flow heating upstream of blunt body reduces its wave drag and “burning” aero-spike can additionally increase the positive effect of a solid one (see, e.g. [1–3]).

a

Development of modern plasma technologies has stimulated high interest to their application for a remote energy deposition (ED) in the supersonic flows using electric, microwave and optical discharges. Analysis of their effectiveness for high speed flow control and drag reduction as well as understanding the main physical processes that lead to modifications of shock waves and global flowfield structure are the relevant problems (see, e.g. surveys [1, 4−8]). Considering development of the “thermal spike” concept we mention only few basic papers. As was noted in [9], ED by the use of beamed laser was suggested in [10] and later such the method was named as “directed energy airspike” (“DEAS”) or simply “airspike” [11]. The early numerical calculations [12] have demonstrated a possibility of wave drag reduction by steady ED ahead of blunt body. As was concluded, the realised flowfield structure in the case with small energy source as compared to the body diameter is similar to the one with conventional solid aero-spike. The “thermal spike” (or “hot spike”) conception has been also formulated for wave drag reduction of blunt body on a basis of discovered unsteady “forerunner” effect (an appearance of large-scale and wedge- or cone-shaped disturbance similar to a separation zone) in conditions of a shock wave/rarified channel interac-tion [13, 14]. Such “forerunner” model was used recently in [15, 16] for explanation of pulsations in front-separation regions in shock wave/heated layer interaction conditions, which appears in calcula-tions of localized ED upstream of blunt and sharpen axisymmetric bodies. Additionally, the model of a “steady isobaric front separation region” (SIFSR) [17, 18]) has been applied to determine the steady separation region geometry in the numerical calculations. It is to be noted that in [20] on the basis of a similar SIFSR model described earlier in [19] an analytic formula has been proposed for prediction of the separation shock wave strength and the “plateau” pressure level in 2-D separation zones in flows with and without ED.

Electricalconnection

Variable

Tungstenelectrodes

DC-arc

++__

Test model withInternal balance

b

Fig. 1. Supersonic flow past a blunt body with an airspike (a) and test model set-up with DC dis-

charge (b) realized in Ludwieg Tube Facility

The physics of high-temperature real gas flows within the thermal spikes is rather complex but the most important mechanisms are the decrease of the total pressure and Mach number downstream of lo-calized ED that remains noticeable in the interaction region with the bow shock (Fig. 1, a). In accor-dance with [21] a forerunner appears in the heated layer when its total pressure is smaller than the static pressure downstream of the shock wave. As was supposed in this paper, such a phenomenon is similar to a boundary layer separation.

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It is well known that conventional aero-spike mounted in front of blunt bodies can lead to distinct wave drag reductions of more than 50% and combustion on its tip can intensify this effect up to ap-proximately 80% [2, 3]. Nevertheless, in accordance with recent reviews (see, e.g. [1, 6]) only 40 – 45 % drag reduction could be achieved in experiments with using of counterflow plasma jets injection from blunt and sharpen bodies of revolution. As concluded, the greatest effect was reached in the con-tinuous mode of plasma generator and in conditions of the long penetration mode (LPM) regimes of plasma jet in the upstream direction. Approximately 50% drag reduction was achieved by using a repeti-tively pulsed laser-induced optical discharge (see additionally [22]). Numerical calculations performed in the framework of inviscid perfect gas model [23] indicate a more distinct wave drag reduction effect than observed in the mentioned experiment.

Additional experimental studies are important in search of optimal position and efficiency of ED for optimal supersonic flow control. Say, too small upstream distance between the energy deposition zone and the body leads to a not optimal effect of the “hot spike”. Another problem is a necessity to re-alize more or less “clean” tests without any measurement artefacts. So, the author of [24] claims that only 2/3 of deposited energy was measured as thrust power saved (negative energy efficiency) and pre-sents a theory about the “non-thermal” plasma effect on shock wave structures. Both these statements could be refuted by the new experimental results presented here.

Current joint experimental/numerical investigation is aimed to analyze effect of a localized DC-arc discharge located upstream of conically sharpened bodies and spherically blunted bodies of revolution on the flowfield structure and aerodynamic drag. The efficiency of ED in supersonic flow conditions is analyzed.

Test models, techniques, and test conditions

The experiments were conducted in the Ludwieg Tube Facility at DLR Göttingen [25]. The facility has the test section diameter of 0.5 m and a run time of about 0.35 s. The experiments were carried out at the free stream Mach number M∞ = 5 and the Reynolds number based on the body's diameter ReD = 1.03×106 (±4%), the stagnation pressure P0 = 10.9 ± 0.1 bar and stagnation temperature T0 = 430 ±10 K.

The used test model set-up is shown in Fig. 1, b. The conically sharpened and spherically blunted bodies of revolution with diameter D = 60 mm and a length of cylindrical part 200 mm have been used in experiments. The sharp bodies had different cone half-angles β = 35°, 45°, 55° and 65° to investigate effect of DC-arc discharge at different conical shock wave strength and for a comparison with a case with normal bow shock wave ahead of the sphere.

An internal 6-component balance of the TASK-Corporation was utilized for the aerodynamic force measurements. In the present work only the drag force coefficient is analyzed. As reference for its cal-culation the test model’s cross-sectional area is used. It is to be noted that presented experimental drag coefficients correspond to the over all drag force whereas only the wave drag is predicted by considered numerical calculations. Thus, the comparison between the data and calculations is only qualitative but it can be used as a good illustration of specific tendencies in influence of ED established by experiment. As was shown by repeated measurements with different test models, the nominal accuracy of their drag measurements in the nominal conditions (without DC-arc discharge) was about ±2%.

The DC-arc position upstream of the model nose was fixed at L = 210 mm that corresponds to a distance of 3.5 body diameters (L/D = 3.5). Shorter distances show steep rise of methodological prob-lems of influence of the viscous wakes from electrodes, which were noticeable due to their interaction with a bow shock, leading to a distinct wave drag reductions for the used test models even without ED. Thus, some examples considered at L/D = 2.5 and 3.25 in the abstract [26] are the illustrations of pre-liminary stage of this research.

The development of the stable and slim electrodes and sockets was the most important requirement for successful measurements. This work was iteratively conducted in the wind tunnel facility by means of "learning by doing". Initial set-up is shown in Fig.1, b. Several technical solutions were tested exten-sively, for the time being without energy deposition, until a more or less adequate variation was found. The construction selected is based on the horizontal positioning of both electrodes and their sockets up-stream of the blunt body. The “parasitic” profit in the wave drag of the blunt body, which was induced

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only by the electrodes wakes without energy supplement, could be reduced down to approximately 4% of the drag level without electrodes. In the comparison to the effect of energy deposition shown bellow is that an acceptable result. The electric power measurements of the arc used were made by the simulta-neous recording of the current and voltage in the arc-circuit during the wind tunnel run. DC-arc powers from approximately W = 1 kW up to 3 kW were realized in the tests. The length of longitudinal electric discharge (the distance between the electrodes) was l ≈ 5 mm and diameter of ED zone d ≈ 2 mm.

The effect of ED on the flowfield structure around the test body was visualized by the shadow-graph technique and quantified by direct force measurements. For the capturing of shadowgrams a high speed camera PHOTRON Ultima APX-RS 250K was used at a frame rate of 5 kHz and an exposure time of 4 µs. The zone of energy deposition (the DC-arc itself) could not be observed by the camera directly because the light intensity was too high and the CMOS-sensor would be overexposed otherwise.

Numerical technique

A numerical method described in details in [23] was employed in the simulations. The initial code is based on a 2-D axisymmetric formulation of nonstationary Euler equations written in conservative form and perfect gas model. A Godunov-type method was used, in which numerical fluxes at the current time level were obtained by solving a local one-dimensional Riemann problem by the HLLEM algo-rithm with a min-mod limiter and the third order MUSCL reconstruction. Time integration was per-formed with explicit third-order Runge – Kutta TVD scheme. The energy for unit mass per unit time supplied by ED was modelled by a source term in the energy equation.

It is to be noted that such an algorithm has been used successfully to predict the flows over the spherically blunted and conically-sharp bodies with ED at the Mach number 2 and L/D = 2 (see [23]). Accordingly to experimental estimations, an elliptical-shaped energy source with semi-axes of 2.5 mm and 1 mm in longitudinal and transversal directions correspondingly was chosen. The employed grid had 600x600 points and it was refined exponentially towards axis of symmetry to resolve such the en-ergy source. By this reason grid cells were elongated in x-direction in a vicinity of symmetry axis and the sizes ratio along x and y directions were approximately equal to 20:1. To suppress a negative “car-buncular” effect [27], which damaged the numerical solution in the analyzed conditions with high shock waves strengths at Mach 5 and the used grid, more dissipative the first order HLL algorithm was de-cided to apply for preliminary calculations which are considered below.

Results and discussions

A series of experiments performed with conically sharp test models of different cone half-angles β = 35°, 45°, 55° and 65° in conditions without ED as well as with DC-arc discharge characterizes spe-cific features of the flowfield structure realized with increasing the strength of attached conical shock wave. The arc-discharge has in this case a fixed constant heated power W = 2.3 kW and was located at the distance L/D = 3.5 or L/δ0 ≈ 21, where δ0 ≈ 10 mm – the heated layer thickness immediately ahead of the cone tip. As shown in Fig. 2, the realized flowfield structure is very similar at β = 35° in condi-

a b

Fig. 2. Experimental flow shadowgraphs for 35° cone at M∞ = 5.

a – without ED, b - with DC-arc discharge (W = 2.27 kW) located at L/D = 3.5.

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tions without a DC-arc discharge (a) and with it (b). The attached shock wave is realized in both cases. It is to be noted that in the case without en-ergy addition the electrodes remained at the position investigated.

Increase of the cone angle up to β = 45° at fixed W level leads to an appearance of strongly unsteady “in-termittent” separation with periodic incipience of small separation zone ahead of the cone (Fig. 3, b), its dra-matically rise to some maximal size (Fig, 3, c) and its repeating disappear-ance. Observed process is periodic one with a frequency f ≈ 100 Hz and char-acterized by large-scale variations of the separation length LS between its extreme values LS/δ0 ≈ (0.5 – 5.3). As seen from the photograph, the wake breakdown caused by its interaction with initially attached conical bow shock wave (Fig. 3, a) stimulates de-velopment of a reversed flow region

ahead of the body with a weaker conical separated shock wave around it (Fig, 3, c). The crossed separa-tion and bow shocks form a λ - shock structure with a shear layer surface spreading from a triple point downstream. The moving compression waves (shocklets) are seen above the separated shear layer simi-lar to the ones observed and predicted in conditions of turbulent boundary layer separation in compres-sion ramp [28].

a b

c

Fig. 3. Experimental flow shadowgraphs for 45°-cone at M∞ = 5. a - without ED, b - with DC-arc discharge (L/D = 3.5, W = 2.27 kW).

It is to be noted that the discussed flowfield structure was well reproducible during all the stages of its development from a stage of incipient separation (Fig. 3, b) up to the stage of large-scale separation zone (Fig. 3, c) and during the following return evolution. The low-frequency fluctuations observed re-mind slightly of the ones that happen in conditions of turbulent boundary layer separation in the vicinity of compression ramp when the expansion/contraction of the separated flow from 2 to 4δ0 in extend ex-ists at a few hundred Hertz [29]. Such a variation of the separation region length corresponds to transi-tion from incipient intermittent separation regime to developed quasi-steady turbulent boundary layer separation regime in compression ramps (see [30, 31]). In accordance with [32] (see also [33]) namely the undisturbed boundary layer thickness δ0 upstream of the separation point is specific scale for the separated zone in compression ramp at the second regime. This type of separation occurs in the bound-ary layer at moderate ramp angles when at given Mach number the bow shock on a wedge of the same deflection angle is an attached oblique one. Thus, it would be logically to suppose that existence of any disturbances in the considered heated layer, like the total pressure and the Mach number spottiness, could be the reason of observed separation length variations. Taking into account very low level of the arc-current variations (1% between the values I = 71.0−71.6 A) any external disturbances, such as the test model or electrodes vibrations, could be considered as a more possible reasons for the separation-zone fluctuations. It is to be added that the weak flow asymmetries in some shadowgraphs show the ef-fects of the not-exactly positioning of the arc-discharge region relatively to the model axis. Already small lateral deviation from it influences the bow shock / wake – interaction and leads to attenuation of the energy deposition effect. Thus, such a factor can be by an additional source of the low-frequent dis-turbances. The importance to reach a reproducible positioning of the electrodes was really a technical problem that could not be solved completely in the wind tunnel tests.

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a b Fig. 4. Experimental flow shadowgraphs for 55°-cone at M∞ = 5. a - without ED, b - with DC-arc discharge (L/D = 3.5, W = 2.27 kW).

It is necessary to note that an abruptly change of the quasi-stationary full-length spike separation to a smaller separation on a part of the spike was observed at gradual length-variation of the conventional aero-spike ahead of blunt bodies (see, e.g. [3]). The hysteretic effect on the transition event from the one regime to the other has been observed in these experiments during an alternating change of the aero-spike length. As shown in [2] and confirmed later in [3], the combustion near the spike’s tip caused some increase of a cross size of the full-length spike separation zone comparing to the case with the hy-drogen jet from a tip of the aero-spike but without combustion as well as some increase in the length of limited separation around the long spike. The last phenomenon is qualitatively similar to the predicted in [20, 35] gradual increase of the separation zone with heating power at a supersonic Mach number in the heated wake. As shown in these papers, the separation zone penetrates the flow up to the energy source in conditions of subsonic Mach number in the heated wake.

Considered above both the regimes in the cases with long spikes have been quasi-steady. As known, periodic flow self-oscillations appear in the vicinity of short conventional spikes (see, e.g. [34, 36]). Significant transformation of the flow in the separation zone was observed in such conditions under influence of periodic penetration of supersonic external flow into this zone. As shown below, qualitatively similar features arise at heated wake interaction with detached normal bow shock wave ahead of the sphere on the stage of development relatively small intermittent separation zones.

a

c

b Increasing of the cone half-angle up to a value β = 55°

accompanied by suppression of the noted above large-scale fluctuations leads to a flow structure (Fig. 4, b) that is similar to a large scale quasi-steady turbulent separation in the vicin-ity of compression ramp (see [30, 31]) or to the flow around the body with a long conventional aero-spike. The small (∼δ0) intermittent separation region with high-frequency (tens of kHz) separation-shock fluctuations is localized in the vicinity of the averaged stagnation-point position in the heated wake. Similar flowfield and separation zone properties arised also at β = 65°.

Results of performed numerical calculation for some considered cases are presented in Fig. 5 by the density gradi-ents in the vertical axial sections. As seen from Fig. 5, a, the calculated steady flowfield structure at β = 35° is in good agreement with that obtained experimentally (Fig. 2, b). In conditions of highly unsteady flow (“an intermittent separa-tion regime”) at β = 45° (see Figs. 3, b, c) the calculations

Fig. 5. Calculated density gradients at M∞ = 5 in conditions of steady ED in the vicinity of conically

sharpened body (L/D = 3.5, W = 2.3 kW). a − β = 35°, b − β = 45°, c − β = 55°.

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also demonstrate the flow without separation zone and very small transformation of the conical shock wave in the heated wake (Fig. 5, b). The large-scale separation zone is predicted by the calculations in the regimes of a quasi-steady separation at β = 55° (Fig. 5, c) and the flowfield structure is in good qualitative agreement with the observed in experiment (see Fig. 4, b). It is to be emphasized that the considered preliminary numerical calculations are used only for qualitative comparison to indicate spe-cific tendencies in the flow transformations and drag variations under influence of ED. Modeling of the factual velocity deficit and distributions of other parameters in the wake as well as the unsteady effects at big distances between ED zone and bodies are very important and supposed to be done on the next stage of research.

The flow transformation described is accompanied by significant aerodynamic drag reduction with appearance of separation zone in the heated wake in front of the bodies. In Fig. 6 the results of drag force measurements are presented for considered values of β at the fixed ED power W = 2.3 kW. In ac-cordance to these measurements a significant decrease in the total drag coefficient is achieved at the maximal values β of 55° and 65° in conditions of the large-scale quasi-steady separation (Fig. 6, a). It is to be noted that the measured drag value at highly unsteady “intermittent” regime at β = 45° is practi-cally the same as in the case without separation at β = 35°. Taking into account that the frequency re-sponse of the used balance is limited by 60 Hz the mentioned above large scale fluctuations of the sepa-ration zone with frequency of about 100 Нz could not be resolved. The balance gives a roughly aver-aged mean value, which could not be equal to the valid one. Thus, we must be careful to the quantitative correctness of Cx/Cx0 values in the regimes of “intermittency” separation starting from β ≈ 45°. The ex-act left and right boundaries of the observed intermittent separation regimes must be specified by addi-tional research. The measurements can be considered as quantitatively correct in the conditions of a quasi-steady separation at β ≈ 55°− 65°. As seen, the numerical calculations of the wave drag (Fig. 6, a) are in good qualitative agreement with experiment and indicate a tendency to significant wave drag de-

crease at the large-scale separation. The saved thrust power pre-

sented in Fig. 6, b corresponds to a given test model and flow condi-tions in the wind tunnel. It was cal-culated by the measured drag force decrease and the freestream velocity in the test-section (U∞ = 830 m/s). Obtained results are very impres-sive and show the strong increase in the effectiveness of the local flow heating in considered condi-tions at β ≈ 55°and 65°. The maximal power effectiveness ratio, calculated as ratio of thrust power saved to deposited power W into the flow, achieved the values up to 30 − 40 (Fig. 6, b). The dashed line is a free-hand drawn tendency of the measured data. As seen, the numerical prediction is in good qualitative agreement with data and demonstrates a tendency similar to that observed in the experiment.

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Development of the airspike effect upstream of the spherically blunted body with increasing the heating power level (W = 1.325, Fig. 6. Drag reduction (a) and saved power effectiveness (b) of conically shaped test

models at M∞ = 5

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1.998 and 2.573 kW) is shown by experi-mental shadowgraphs (Fig. 7). All specific features of the realized flowfield structure are marked in Fig. 7, c. As noted above, weak flow asymmetries in some shadow-graphs (see, e.g. Fig. 7, b) show the effects of the not-exactly positioning of the arc-discharge region relatively to the model axis. Even such small lateral deviations ef-fected the bow shock/wake interaction and attenuated the energy deposition effect.

As obtained in the experiment, high-frequency unsteadiness is typical for limited intermittent separation regimes in the vicin-ity of the detached normal shock ahead of the hemisphere (see, e.g. Fig. 8). Periodic penetration of the external supersonic flow into the separation zone downstream the λ-shock stimulates an appearance of an inter-nal shock wave (SW, Figs. 8, a, b), which moves after the separated shock in upstream direction. Such internal SW disappears with achieving some maximal separation length when the flow reattachment region shifts to the shoulders of the blunt body (the stage in Fig. 8, c and the flows in Fig. 7, b, c). It is to be noted that qualitatively similar phenome-non was observed in the vicinity of a flat-nosed cylinder model with a short conven-tional aero-spike [34] and predicted numeri-cally in [36]. Evolution of the flow structure in this case reminds of unsteady forerunner, which was predicted in [37] and reproduced in [15, 16]. Qualitatively similar tendency was observed in additional experiments at β = 90° performed preliminary in the present work. Nevertheless, the analysis of details of the instantaneous shock structures past the blunt bodies on the basis of shadowgraphs acquired in the present investigation with a relatively long exposure time of 4µs is not free from interpretation errors.

a

b

1 2 3

4

c

5

Fig. 7. Experimental shadowgraphs of flow over hemisphere-cylinder model at M∞ = 5 with DC-arc (L/D = 3.5).

a − W = 1.325 kW, b − 1.998 kW, c −2.573 kW (1 – the heated wake; 2 – separa-tion zone; 3 – separated shock; 4 – bow shock wave, 5 – moving shocklets).

In accordance with performed experiments described intermittent regimes with supposed the inter-nal SW were distinctly observed with increasing level up to approximately W ≈ 1.7 – 2.0 kW. The quasi-stationary large-scale separation appeared at W ≥ 2 kW when the reattached flow was tangent locally to the hemisphere surface (Fig. 7, c).

SW SW

a b c

Fig. 8. The stages of separation zone development ahead of sphere at M = 5, W = 1.325 kW

8

a d

b

As seen from Fig. 9, a–c, the calculated steady flowfield structures for considered cases are in qualitative agreement with the experimental shadowgraphs in conditions of a quasi-steady flow regime. Demonstrated experimental tendency to increasing of the forward separation zone with increasing heat-ing-power W is also seen in the calculations. Nevertheless, calculated separation zones length were steady over-predicted distinctly at W = 1.325 and 1.998 kW.

The existence of reversed flow in forward separation zone is shown for the last case at W = 2.573 kW (Fig. 9, d). As seen from calculations (Fig. 9, e), the total pressure sharp drop (NS) on the line 2 is caused by the normal shock in the heated wake upstream of “separation” point located on a symmetry axis (see Figs. 9, a–c). This point is located downstream of the normal shock where the total pressure (line 2, Fig. 9, e) is nearly equal to the static pressure (line 1). This normal shock is also seen in some photographs (see, for example, Fig. 7, a, and 8). Nevertheless, it is difficult to observe this shock with decreasing its strength at the higher W values (Figs. 7, b, c), although the Mach number along the wake axis is supersonic in accordance with estimations on a basis of performed preliminary calculations. Ex-isting high-frequency fluctuations of this shock in the vicinity of the separation point with amplitude close to the heated layer thickness as well as the density heterogeneity similar with turbulence spottiness can be by the reason that it is not seen sometimes. This is in agreement with conclusions presented in [38].

As known, the specific scale of a boundary-layer separation switched between the cross-size of the obstacle (height or diameter) in cases of maximal-length separations, and the local boundary layer thickness δ0 in cases of small-scale separations e.g. in compression ramps. As discussed before, the de-tached normal shock stimulates development of an unsteady “forerunner” effect. Thus, it can be sup-posed that the total pressure or the Mach number spottiness in the heated layer downstream the arc-discharge can stimulate significant fluctuations of separation length under the change of specific scale for the separation zone. That can be the reason for the different prevailing fluctuation frequencies ob-served in the regimes with initially attached and detached shock waves.

As described above, the flow transformation analyzed is accompanied by significant aerodynamic drag reduction. In Fig. 10, a the results of drag force measurements are presented as effect of arc power W. Slow decreasing of Cx/Cx0 in the range approximately 1 < W < 2 kW corresponds to the strongly un-steady “intermittent” regimes of separation upstream of the sphere. Quasi-stationary regimes arise at approximately W < 2 kW. As seen the calculations are in qualitative agreement with the experimental

Fig. 9. Calculated density gradients in conditions of steady ED in the vicinity of sphere at M∞ = 5, L/D = 3.5

a − W = 1.325 kW, b − 1.998 kW, c, d, e − W = 2.573 kW (d − flow streamlines, e − the static pressure p/p∞ (1) and total pressure pt /p∞ (2) distributions along symmetry axis).

c

x, mm

p/p∞

1

2 e

NS

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data. Nevertheless, they demonstrate quantitatively a significant underesti-mation at conditions of high flow-unsteadiness and tend to the level ob-served only at quasi-stationary re-gimes.

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The saved thrust power corre-sponds to given model and flow condi-tions in the wind tunnel tests. The ten-dencies found in experiments and cal-culations are qualitatively similar (Fig. 10, b). Nevertheless, compared to the experiment the calculation gives a proper tendency in power effective-ness ratio not until the quasi-stationary regime occurred (Fig. 10, c). The ex-perimental results are very impressive and show a strong increase in the ef-fectiveness of the local flow heating up to power-levels of approximately 2.5 kW. The power effectiveness ratio achieves values up to 13. The point with the biggest arc-power is unfortu-nately measured not sure enough, be-cause the wake flow hints in this run the model not exactly on the axis. In-dependently from it, they should al-ready expect a saturation of the effect similar to the effect of spike length well known from the earlier investiga-tions. At low heating powers the effect should begin obviously at a finite threshold value of arc power needed to realize a steady low voltage discharge in the flow, which is a function of the flow conditions and electrode-gaps. The next problem by the definition of the energy deposited into the flow in the experiments is the lack of informa-tion about the losses occurring at arc generation.

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Fig. 10. Drag reduction (a) and saved trust power effectiveness of spherically blunted body at M = 5.

Conclusions Performed investigation highlights influence of ED with a use of DC-arc discharge located up-

stream of sharp and blunt bodies. The flowfield structure, which arises in conditions of the shocks trans-formations and thermal wake breakdown, was analyzed. A consideration of the highly unsteady separa-tion regimes as well as the real distribution of parameters in the wake should improve the numerical prediction in the next stage of research. High efficiency in drag reduction and saved power effectiveness was demonstrated.

A part of the experimental study was supported by German Research Foundation (DFG) with grant 436RUS17/13/06.

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