Combustion, Explosion, and Shock Waves, Vol. 39, No. 1, pp. 23–30, 2003

Quality of a High-Enthalpy Flow upon Electric-Arc Heating

of Air in a Facility for Investigating Supersonic Combustion

UDC 536.45

V. A. Zabaikin

1

Translated from Fizika Goreniya i Vzryva, Vol. 39, No. 1, pp. 28–36, January–February, 2003.
Original article submitted March 20, 2002.

The quality of a high-enthalpy air flow is considered in terms of simulating full-scale
flow parameters in studying supersonic combustion. It is shown that the plasmatron
with gas-vortex stabilization of the arc, which was used in experiments, can provide,
in a wide range of pressures and temperatures, a level of specific erosion of electrodes
equal to 10

−7

–10

−9

kg/C and a concentration of nitric oxide lower than 0.06%, which

has almost no effect on the flow structure and basic characteristics of ignition and
combustion processes.

Key words: plasmatron, erosion, supersonic flow, hydrogen combustion.

Experimental investigations of combustion of liq-

uid and gaseous propellants under conditions of high
velocities and temperatures are of high scientific and
applied significance, in particular, for the development
of ramjets. This requires the use of aerodynamic facil-
ities providing a high stable level of heating of the test
gas (first of all, air), including the case of elevated pres-
sures. Significant issues for all heating methods are ob-
taining uniform temperature profiles at the test-section
entrance and introduction of minimum changes in air
composition, which includes both preservation of the
main components (O

2

and N

2

) and reduction of contam-

ination by alien impurities (first of all, nitrogen oxides
and products of erosion of heater elements).

High temperatures are usually reached by using fire

heating of the gas (either petroleum or kerosene, as in
[1], or hydrogen is burnt) and electric-arc heating with
a discharge of a capacitor in hot-shot facilities (in this
case, additional chemical heating is also possible). An
example of advanced implementation of energy addition
from capacitors is a high-enthalpy hot-shot wind tun-
nel with a pressure multiplier [2, 3]. Nevertheless, the
use of a wire evaporating during the discharge provides
contamination higher than 1.4

·10

−7

kg/C, leaving aside

erosion of electrodes and walls of the discharge chamber,
melting of the edges of the broken diaphragm, and for-

1

Institute of Theoretical and Applied Mechanics,
Siberian Division, Russian Academy of Sciences,
Novosibirsk 630090; [e-mail].

mation of nitrogen oxides. The estimates show [3] that
the mass fraction of oxygen decreases approximately by
1% during wind-tunnel starting. The specific features
of hot-shot facilities are also high electric discharge cur-
rents in the plenum chamber, reaching 10

6

A, which

leads to induction of strong electric and magnetic fields
and sometimes requires shielding of the models tested.

In the case of fire heating, the main contami-

nants are water vapors (especially, in the case of hy-
drogen heating); if petroleum or kerosene is used, ad-
ditional contaminants are CO

x

and, possibly, incom-

pletely burnt hydrocarbons. In any case, the influence
of the heating method on such parameters as the ig-
nition delay and the maximum reachable combustion
temperature can be quite noticeable [1]. As compared
to “pure” (Cowper) heating, the maximum tempera-
ture can differ by 200 K and the ignition delay can dif-
fer almost by an order of magnitude. Nevertheless, fire
heating has an advantage of comparative technical sim-
plicity, especially if subsequent addition of oxygen to
the flow is not performed.

An alternative method of heating is the use of an

electric arc in plasmatrons.

The advantages of this

method over the fire, Cowper, ohmic, and other meth-
ods of heating are the small time of flow stabilization,
the possibility of long-time continuous operation at high
temperatures, and the possibility of significant variation
of the air (gas) flow from one regime to another. At the
same time, the electric-arc heater is a rather compli-

0010-5082/03/3901-0023 $25.00 c

2003

Plenum Publishing Corporation

23

24

Zabaikin

Fig. 1. EAP layout (a) and its operation range (b):
1) cathode; 2) ejection of part of air; 3) anode; 4) arc-
swirling solenoid; 5) arc; 6) rings of tangential injection;
7) starting insert; 8) region of operation with the mini-
mum cathode erosion; 9) region of emergency operation
of the EAP.

cated device and requires a powerful source of electric
energy. Its operation in an air medium leads to the
formation of oxides and to surface erosion of structural
elements contacting the arc, which is responsible for the
appearance of alien admixtures and can affect the com-
bustion processes.

Methods of decreasing the “adverse” consequences

of using plasmatrons and results achieved thereby are
described in the present paper.

A linear electric-arc plasmatron (EAP) developed

at the Institute of Thermal Physics of the Siberian Divi-
sion of the Russian Academy of Sciences [4, 5] is used as
a heater in the supersonic combustion test bench of the
Institute of Theoretical and Applied Mechanics of the
Siberian Division of the Russian Academy of Sciences
(Fig. 1a). The general view of the test bench itself is
shown in Fig. 2.

The gas–air path of the facility operates on high-

pressure gas holders (up to 20 MPa) and includes an
air filter, several shutters and reductors, flow-metering

sectors, and a safety valve (not shown in Fig. 2). In the
facility itself, part of air enters directly the EAP where
it is heated, and part of air enters the mixing cham-
ber (plenum chamber, II in Fig. 2) where it is mixed
with hot air from the EAP and reaches a temperature
required for experiments. After the plenum chamber,
the air passes through a cooled adapter and nozzle and
enters the channel examined or the ambient space. The
adapter is designed for mounting replaceable axisym-
metric or plane nozzles. All axisymmetric nozzles are
contoured, have an identical exit diameter (50 mm), and
are designed for Mach numbers of 1.4, 2.2, 2.6, and 3.1.
Two first nozzles are most frequently used, since noz-
zles with M = 2.6 and 3.1 at stagnation pressures of
(4–10)

· 10

5

Pa (standard operation range) form a sig-

nificantly overexpanded jet (jet-pressure ratio n < 0.5).
The next upgrading of the facility implies an increase in
the operation range of pressures up to 40

·10

5

Pa. Plane

nozzles (for Mach numbers M = 1.5–3) are mounted to-
gether with a rectangular channel with a cross-sectional
size of 40

×60 mm; they are made of copper and are not

cooled. The channel has a step 40 mm high. The side
walls for optical observations have quartz glasses (the
description of the rectangular channel can be found in
[6, Chapter 8]).

Channels with axisymmetric nozzles are assem-

bled from separate sections 20–545 mm long and 50–
90 mm in diameter. Both constant-section and expand-
ing channels are used; the angle of expansion is 1–10

◦

.

Configurations of some typical axisymmetric channels
considered are described in [7]. Between the adapter
and nozzle block, it is possible to place an insert with
injectors for fuel injection along the nozzle centerline, as
is shown in Fig. 2. The fuel-injection methods used and
the corresponding burning patterns are described in [8].
At the end of the test section, there is a supersonic circu-
lar injector behind which the air enters a noise-damping
chamber and escapes into the atmosphere.

The most complicated and important element of

the air-heating system is the EAP. High requirements
are imposed onto the EAP, since it has to ensure:

— gas heating in a continuous regime (

≈1 min) in

the temperature range of 1300–2500 K at a pressure of
0.5–1 MPa;

— flow-stabilization time of

≤1 sec after starting;

— minimum amount of alien admixtures and prod-

ucts released in the course of heating;

— high reproducibility of operation regimes;
— large lifetime of the facility.
These requirements can be satisfied by a constant-

current EAP (hybrid layout) with a total power up to
2 MW. It is based on the construction of an ´

EDP-143

three-chamber plasmatron with a cylindrical cathode

Quality of a High-Enthalpy Flow upon Electric-Arc Heating of Air

25

Fig. 2. Layout of the supersonic combustion test bench: electric-arc heater (I), plenum chamber
(II), adapter (III), nozzle block (IV), channel examined or free space (V), exhaust system (VI);
1) ejection of the gas from the cathode area; 2, 3) places where admixtures are introduced up-
stream and downstream of the plenum chamber; 4) washer; 5) fuel injector; 6) orifices in the “flue
tube” for air injection for mixing (G

4

); 7) air injection into the ejector.

and an anode with an output step. The use of a step-
wise output electrode favors rapid equalization of tem-
perature and velocity profiles at the plasmatron exit [9].
A rather complicated flow structure with reverse flow re-
gions and flow rotation is formed in such a plasmatron.
The cathode and anode spots of the arc are unsteady;
they move over the circumferences of the cathode and
anode chambers, respectively. Continuous motion of the
arc-attachment spots ensures “smearing” of heat fluxes
over a greater surface area of the electrodes and, thus,
reduces the level of erosion and increases the lifetime
of electrodes. Rotation and stabilization of the cathode
spot are ensured by tangential injection of air (G

1

and

G

2

) through swirling rings. Rotation and stabilization

of the anode spot are provided both gas-dynamically,
due to tangential injection of air (G

3

) and its stalling be-

hind the step, and by means of induction of a solenoidal
magnetic field (3 and 4 in Fig. 1a).

The chosen gas-dynamic layout of the heater pro-

vided comparatively low heat losses to the walls (de-
pending on the operation regime, the total efficiency
varied from 67 to 75%). This layout is responsible, to a
large extent, for the level of erosion of the heater itself
and, hence, the total amount of admixtures in the air
flow. The anode and, particularly, the cathode experi-
ence erosion at arc-attachment spots. As a result, an
annular groove (25–30 mm wide) with a typical granular
structure is formed on the electrode surface. The metal
evaporating from the arc-attachment zone is oxidized in
the plasmatron and then entrained to the plenum cham-
ber and further through the nozzle to the test section.
Since the electrodes are made of copper, the products
of their erosion are fine dust of copper oxides. In our
configuration, the specific erosion is determined by the
dynamics of motion of the cathode and anode spots,
which, in turn, depends on the amounts and flow rates

of air in various parts of the EAP, current, pressure, and
geometric dimensions of plasmatron chambers. Good
cooling of the most heat-loaded plasmatron elements is
also very important, which was paid much attention to
in the development of the EAP and test bench.

Figure 1b shows the ranges of satisfactory and

emergency (with unstable rotation of the arc and el-
evated erosion) operation regimes of the plasmatron,
determined experimentally. The minimum cathode ero-
sion (

≈10

−9

kg/C) corresponds to the ratio of flow rates

G

3

= (2–5)(G

1

+ G

2

) to the cathode and anode cham-

bers. (Usually, G

1

= G

2

, but the ratio of these flow

rates can be slightly changed if the central part of the
electrode is warn out, which shifts the erosion region
of the electrode and increases the total lifetime of the
EAP.)

An important issue for test facilities with arc heat-

ing is the workability and level of air contamination at
pressures above 10

5

Pa, since most plasmatrons are de-

signed for operation at atmospheric pressure. With in-
creasing pressure, stability of plasmatron operation and
stability of the arc decrease, and electrode erosion in-
creases. Operation of a plasmatron of the layout de-
scribed at atmospheric pressure allows actual sustain-
ing of specific erosion at a level of

≈10

−9

kg/C (Fig. 3)

in cathode chambers of diameters

≥0.06 m. However,

erosion rapidly increases with increasing pressure up to
0.4–0.5 MPa. By choosing proper geometric parameters
[diameters of the cathode chamber d

1

(0.07 m), starting

insert d

4

(0.02 m), anode spacer d

2

(0.039 m), and anode

d

3

(0.06 m)] and also the amounts and flow rates of air

G

1

, G

2

, and G

3

, we managed to ensure, in a wide range

of currents (i.e., actually, EAP power), the level of spe-
cific erosion in operation regimes less than 10

−7

kg/C

(Fig. 4) within the entire required range of operation pa-
rameters of the facility. In this case, the following rela-

26

Zabaikin

Fig. 3. Specific erosion of the copper electrode on the
current strength at atmospheric pressure: curves 1 and
2 refer to the cathode chamber diameter of 0.05 and
0.06 m [5], respectively.

Fig. 4. Specific erosion versus pressure for I =
650 (1), 1500 (2), 1570 (3), 1450 (4), and 1400 A (5);
G

1

+ G

2

= 69 (1 and 2), 85 (3), 90 (4), and

105 g/sec (5).

tions should be satisfied (in the SI system): d

4

≈ d

1

/2.5,

d

4

/d

2

≤ 0.6, d

3

≈ 1.5d

2

, (G

1

+ G

2

)/pd

1

> 2

· 10

−6

, and

G

3

= (2–5)(G

1

+ G

2

) [5].

Erosion of anodes in plasmatrons with cylindrical

copper electrodes is substantially lower than erosion of
cathodes [10]. This fact was confirmed by experience of
using the plasmatron on the supersonic combustion test
bench: the cathode was replaced approximately three
times as often as the anode. The walls of the anode
cavity were worn out uniformly.

The process of plasmatron starting has some spe-

cific features. The most important of them is that it
is impossible to start up the plasmatron at operating
pressures. Starting of the plasmatron by an auxiliary
arc initiated by an oscillator, which is frequently used
(and was initially used on this test bench), is possible
up to pressures of 0.09 MPa only because of the neces-
sity of the discharge-gap breakdown, which was found
experimentally. After ignition of the auxiliary arc be-
tween the cathode and copper starting insert, the main
arc between the anode and cathode is ignited due to
ionization of air in the entire path of the plasmatron.
The total flow rate of air through the EAP is not large
(

≤80 g/sec, which is less than one quarter of the flow

rate in the operating regime), and the temperatures at
the EAP exit can exceed 5000 K. Erosion of electrodes
at this moment is also considerable. By means of subse-
quent addition of air, the plasmatron reaches a specified
regime. Thus, the total time of EAP operation in the
nonoptimal mode could be 5–10 sec (

≈0.5 sec is the

EAP starting itself, the remaining time is needed to
reach a given operating regime in terms of pressure).

Based on the accumulated experience, within the

framework of test-bench upgrading, a special moving
electrode was used instead of plasmatron starting by
means of the oscillator. This electrode short-circuited
the cathode and the starting insert for a short time,
thus, forming an auxiliary arc. This increased the reli-
ability of starting, simplified the whole system, reduced
electromagnetic noise affecting the registration equip-
ment, and, which is most important, allowed an increase
in the initial pressure in the air system up to 0.3 MPa
during starting. Since the pressure in the plenum cham-
ber rapidly increases (by 0.3–0.5 MPa) when the main
arc is ignited, this turned out to be sufficient to rapidly
reach a given operating regime (τ

≤ 0.5 sec). Note, in

operating with the channels considered, the duration of
steady operating regimes was usually about 10 sec.

Another significant moment of upgrading was or-

ganization of ejection of some part of the gas from the
cathode chamber (see 2 in Fig. 1) into the atmosphere
(in the initial variant, the gas was removed but then
again entered the overall flow upstream of the plenum
chamber).

In the later variant, the gas is removed

through orifices in the copper insert (7 in Fig. 1), sepa-
rate flow-metering section, and dielectric junction (see
1 in Fig. 2). This gas removal in the plasmatron plays
an important role in plasmatron workability. First, it
allows a significant (at least twofold) increase in the to-
tal flow rate of air G

1

+ G

2

into the cathode and, thus,

an increase in the current load (hence, power) and a
decrease in erosion to an acceptable level [5]. Second,
because of separation of particles to the electrode wall,

Quality of a High-Enthalpy Flow upon Electric-Arc Heating of Air

27

a

b

c

Fig. 5. Luminescence of aluminum powder added upstream (a) and downstream (b and c) of the plenum chamber
and its interaction with a hydrogen plume (a and c).

the major part of cathode-erosion products is entrained
from the cathode without entering the plenum chamber,
which reduces the overall level of air contamination.

The last important issue of improving flow quality

is the plenum chamber (mixing chamber) mounted im-
mediately behind the plasmatron. It consists of an ex-
ternal cylindrical force shell and an internal perforated
insert (“flue tube”). Cold air (G

4

) is injected closer to

the end of the plenum chamber, passes first between the
force shell and the flue tube, cooling the latter, and then
enters the plenum chamber through a number of orifices
(see 6 in Fig. 2). Here the cold air is mixed with hot air
going out of the plasmatron. The location and number
of orifices are chosen from the condition of providing a
uniform temperature profile and are verified by direct
measurements [11]. At the plenum chamber exit, there
is a washer (see 4 in Fig. 2) creating an annular step
with a recirculation zone, which additionally improves
the temperature profile. Note, molecules excited by the
plasmatron arc should completely relax in the course of
mixing with rather long-time motion of hot air along
the plenum chamber with a velocity of

≈50–70 m/sec,

which occurs, on the average, during 0.014–0.02 sec if
the chamber length (together with the adapter) is 1 m.
For such times of gas residence in the plenum chamber,
there occurs recombination or oxidation of chemically
unstable compounds possibly formed in the plasmatron.
Neutral compounds and inert gases do not affect sub-
sequent combustion processes in the test section of the
facility, as is shown in [12].

Special experiments on the action of chemically ac-

tive solid particles confirmed the positive influence of
the plenum chamber.

The admixture was aluminum

powder with a particle size of 3–6 µm. The powder was
added upstream or downstream of the plenum chamber
(see 2 and 3 in Fig. 2). In the first case, injection was
performed into the high-temperature jet at the junc-
tion of the plasmatron and plenum chamber (the dis-
tance from the nozzle exit was 1070 mm). In the sec-

ond case, injection was performed in the subsonic part
of the nozzle (220 mm from the exit, similar to [12]).
Being added in the cross section of 1070 mm, the pow-
der burned completely inside the chamber, and a two-
phase supersonic air flow with hot inert Al

2

O

3

particles

was formed at the nozzle exit. Upon subsequent axial
injection of hydrogen, visual observations and registra-
tion of hydrogen-plume radiation intensity by an optico-
mechanical scanner did not reveal any differences from
the pattern observed without the powder (Fig. 5a). If
aluminum powder is added at a distance of 220 mm
(i.e., downstream of the plenum chamber), the pattern
becomes drastically different. Aluminum does not have
enough time to react completely over this length, and
a bright plume of burning metal is seen at the nozzle
exit (Fig. 5b, which shows the plume without injection
of hydrogen). In the case of additional injection of hy-
drogen along the axis of this plume, intense interaction
is observed, which is manifested in a significant expan-
sion of the burning jet (Fig. 5c). This is not observed
if aluminum powder is added upstream of the plenum
chamber (1070 mm).

The most typical stable compound formed by the

arc discharge is NO. The data of [13] allow us to be-
lieve that the influence of nitrogen monoxide on the
hydrogen-oxidation reaction (induction time) becomes
noticeable if NO concentration exceeds 2%, and the in-
duction period for a stoichiometric mixture increases
more than by an order of magnitude for NO concentra-
tions of 3–5%. The inhibiting action of NO is significant
at low temperatures; at T > 1200 K, however (by es-
timates of the same authors), nitrogen monoxide even
reduces the ignition delay, but this reduction is insignifi-
cant. A number of factors affecting the air-stream qual-
ity were experimentally verified on the test bench. A gas
analysis was performed in the exit section of the EAP
during its verification. Oxygen concentration was mea-
sured (the first experiments are described in [11]), which
allows indirect evaluation (by the decrease in O

2

concen-

28

Zabaikin

a

b

Fig. 6. Luminescence of dust (a) illuminated by the plasmatron arc and the hydrogen plume (b) at an air-jet
temperature equal to 2600 K.

tration) of possible appearance of oxides (NO

x

+ oxides

of metals, such as CuO, etc.) and the upper boundary
of their concentrations. Samples taken at three points
did not demonstrate any changes in O

2

concentration

(the measurement error was 0.01%). A decrease in O

2

concentration was observed in the EAP jet core (two
sampling points), but this decrease was less than 0.02–
0.03%, which may indicate that NO concentration here
is about 0.06% in the most adverse case. Taking into
account the data of [13], the effect of nitrogen monox-
ide on the accuracy of experiments with hydrogen com-
bustion can be considered as insignificant. In addition,
this is NO concentration in the central region, which
is the most contaminated one. Without allowance for
the entire flow, the mean concentration is lower. NO
concentration also decreases significantly after the gas
passes through the plenum chamber: the flow rate of
the gas added to the plenum chamber (G

4

), depending

on the operating mode, is 30–45% of the total flow rate
of the gas through the EAP: G

1

+ G

2

+ G

3

. Exactly

this scheme (heating of air in the EAP to a high tem-
perature and its subsequent mixing with pure cold air)
was recommended in [1] to reduce the concentration of
NO

x

. Note, the gas analysis was performed for the plas-

matron layout without ejection of some part of the gas
from the cathode chamber into the atmosphere (the first
EAP variant). The ejection makes air contamination by
alien admixtures even lower.

Another factor of contamination caused by us-

ing the EAP is the products of its erosion.

This is

indirectly evidenced by high-temperature experiments
(T

0

≥ 2500 K). In such regimes, the picture at the su-

personic nozzle exit sometimes reveals individual ele-
ments of the gas-dynamic structure of the off-design air
jet, which are usually discernible with the use of shad-
owgraphy only (see Fig. 6a, which shows the photograph
made by a computer-vision camera with the maximally
open diaphragm; the exposure time was τ

≈ 10

−2

sec).

It is most probable that this is luminescence of dust
present in air and erosion products of plasmatron elec-
trodes. In hot air, incandescent particles can glow by

themselves or be illuminated by the plasmatron arc
through the nozzle. Nevertheless, the luminescence in-
tensity of particles is so low that their spectrum could
not be registered even with the maximum sensitivity of
the instrument and its tuning to the brightest region of
luminescence.

Under similar conditions (T

0

= 2500–2600 K), the

flame spectrum was registered in the visible wavelength
range. The principle of hydrogen injection along the
axis of a supersonic nozzle is shown in Fig. 2 and de-
scribed in detail in [8]. The radiation spectra in the first
“barrel” close to the ignition site and also in the far-off
region of the plume are shown in Fig. 7a and b, re-
spectively (hydrogen-injection method is a sonic cocur-
rent jet, air-breathing injector [8]; the photograph of
the plume is shown in Fig. 6b). Note, the hydrogen–air
plume without admixtures in the visible range of the
spectrum has not radiation lines [14]. In practice, how-
ever, alien admixtures in the form of dust of versatile
composition yield a continuous spectrum (see Fig. 7).
Sources of solid particles can be only high-pressure air
from gas holders, hydrogen from containers, and the
EAP itself.

The spectrum of radiation of the initial

part of the plume in Fig. 7a contains a peak belonging
to sulphur (S

2

), which most often gives a blue color to

the hydrogen flame. Sulphur in uncontrollable amounts
is always present in hydrogen containers and can some-
times be used for optical measurements of the hydrogen-
plume parameters [6]. Yet, because of the variable con-
centration, the sulphur peak in the spectrum can be
clearly visible (Fig. 7a) or be absent (Fig. 7b and c).

A comparison of flame spectra in the visible range

with an operating plasmatron (stagnation temperature
of the heated air T

0

≈ 2600 K; see Fig. 7a and b) and

without heating (T

0

≈ 290 K; see Fig. 7c) showed that

the spectra have a similar character. The only differ-
ence is that the maximum of radiation intensity of the
continuous spectrum is slightly shifted toward the long-
wave range, which could be expected with decreasing
temperature.

Quality of a High-Enthalpy Flow upon Electric-Arc Heating of Air

29

Fig. 7. Hydrogen-flame spectrum in hot (a and b)
and cold (c) air: zone of intense combustion behind
the normal shock in the first “barrel” (a) and com-
bustion far from the nozzle (b).

This means that the main source of flow contam-

ination that can cause some measurement error is the
solid particles in the gases used, whereas the influence
of copper and other products of plasmatron erosion on
hydrogen combustion is insignificant. The luminescence
of gas-dynamic structures in Fig. 6a is caused by dust,
which becomes visible under intense illumination by the
plasmatron arc through the nozzle. In standard operat-
ing regimes, the three-chamber EAP construction does
not affect the flow structure and basic characteristics of
ignition and combustion processes; the degree of purifi-
cation of the fuel and air used may be more important.

Thus, electric-arc heaters can be reasonably used

in aerodynamic test benches that require long-time op-
eration at temperatures of 1000–2500 K, including sit-
uations where admixtures should produce no effect on
combustion kinetics.

Nevertheless, it is necessary to

use some design and exploitation measures to improve
the quality of the high-enthalpy flow. The most impor-
tant measures are the choice of the plasmatron of an
appropriate layout, determination of operating regimes
with the lowest erosion, the presence of an extended
section between the EAP and test sections, and pro-
vision of additional mixing of cold air at this section.
With these requirements fulfilled, the EAP becomes a
reliable instrument to be used in test benches model-
ing high-temperature processes at high velocities and
pressures, including those complicated by chemical re-
actions. Facilities with such electric-arc heaters may be
more preferable than fire heaters in terms of air purity
and may be better than Cowper and ohmic heaters in
terms of temperatures reached.

The

author

is

grateful

to

´

E.

K.

Urbakh,

P. K. Tret’yakov, and S. S. Vorontsov for valuable con-
sultations and assistance in work.

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