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Thermophysics and Aeromechanics, 2013, Vol. 20, No. 6

Interfacial friction and mass transfer at gas flow into vacuum through a nozzle with a near-wall liquid film*

V.N. Yarygin, V.G. Prikhodko, I.V. Yarygin, and A.D. Nazarov

Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia

E-mail: [email protected]

(Received May 16, 2013)

The cycle of experiments on interaction between the co-current gas flow and the near-wall liquid film were carried out at high gas flow velocities, including the supersonic ones. The local parameters of the near-wall film were measured by the capacitance probes. It is shown that the co-current gas flow affects the near-wall film significantly, causing intensive wave formation, droplet detachment from the film surface, and their entrainment by the gas flow. It is determined that a relative amount of liquid entrained by the co-current flow is generalized by the Weber number of this gas flow.

Key words: near-wall film, co-current flow, droplets, mass transfer, interfacial friction.

Introduction

The liquid flow in the form of thin films (with the thickness of below 1 mm) is widely used in various heat-and-mass exchangers (condensation of immobile and moving vapor, gas absorption or desorption, drying, distillation, fractioning, chemical-engineering processes, etc.). Another important application of the film flows is protection of walls from the high-temperature gas flow (for instance, the use of the near-wall fuel film in the liquid-propellant engines for screening the combustion chamber and supersonic nozzle. The near-wall gas cooling is also used for these purposes [1].

Interaction of the near-wall film with the co-current gas flow is mainly determined by the parameters of this flow, such as velocity, density, and static pressure. Even at low flow ve-locities, the liquid film looses its stability, and capillary waves are formed on its surface, whe-reas, without the co-current flow, the film flow is waveless. An increase in velocity of the co-current gas flow facilitates interfacial interaction and leads to formation of 2D and 3D waves on the film surface. Starting from some values of gas flow velocity and density (Weber number), droplets are detached from the film surface and entrained by the co-current flow [2].

Another important feature is interaction of the near-wall film with the co-current gradient flow, for instance, in nozzles. A significant drop of the static pressure in the flow (approximately, by the factor of 2 for Mach numbers equal to 1, and by the factor of 30 for Mach numbers equal to 3) can cause the situation, when the static pressure in the flow above the film becomes lower than the pressure of saturated liquid vapors. This leads to film

* The work was financially supported by the Russian Foundation for Basic Research (Grant No.13-08-00410).

© V.N. Yarygin, V.G. Prikhodko, I.V. Yarygin, and A.D. Nazarov, 2013


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boiling-up and evaporation, and formation of a transverse vapor flow from the film surface to the boundary layer. By the analogy with injection through a permeable wall into the boundary layer, this vapor flow can essentially affect the value of interface friction causing a decrease in the shearing stress on the “gas-liquid” interface in comparison with the regimes of gas-film interaction with and without boiling. In literature there are almost no results, which give accu-rate and reliable data on the values of shearing stress on the “gas-liquid” interface under the conditions of high relative velocities of the co-current flow. This situation can be partially ex-plained by the fact that there are no approaches to direct measurement of friction at the interface, especially at intensive wave formation, droplet separation from the film surface, its boiling and evaporation. The estimates of this value are based on the measurements of other parameters, for instance, pressure reduction along the channel. However, this approach gives only the value of interfacial friction averaged along the channel length. For the high relative velocities of the co-current flow, there are no reliable methods for calculation of interfacial friction.

Now there are many publications on the liquid film flows [3]. The most extended studies deal with gravitation films. The stress film flows are described in many works. However, these experiments are carried out at relatively low velocities of the co-current flow of about 10 m/s. In the present work, we study interactions of the co-current gas flow with the near-wall liquid film at high gas flow velocities, including the supersonic ones.

The problem of external contamination of spacecraft, including the International Space Station (ISS), by the jets of control and orientation thrusters (OT), where a fuel film is used to cool the nozzle walls, initiated these studies [4]. Now the OTs on self-igniting fuel components (unsymmetrical dimethylhydrazine (UDMH, fuel) and nitrogen tetraoxide (amyl, oxidizer)) are mounted at the ISS. The elements of external surface of the ISS within the flow field of exhaust plume are subjected to the force, thermal and contaminating effect. Since the fuel components used in OT are toxic, possible penetration of combustion products deposited on the ISS exter-nal surface inside the station with astronaut suits during their space walks are of the great dan-ger.

Firstly the problem of contaminating effects of thruster jets drew attention at MIR space station. In the framework of the space experiment “Dvicon”, held in the orbit in 1998, the presence of contaminants in different parts of the outer surface around OT on MIR station was determined. However, much attention was started paying to the contamination pollution problem only at the ISS. The question was so serious that the astronauts were prescribed spe-cific precautions when working in outer space [5].

In the present paper, we examine the problems of OT modeling in the vacuum chambers. The main attention is paid to the study of gas flow interaction with the near-wall film inside a nozzle.

Statement of research and modeling issues

From the viewpoint of problem statement we deal with the flow of near-wall liquid film with the co-current gas flow from a supersonic nozzle into vacuum. Certainly, we can speak only about approximate simulation, even if a full-scale OT is tested in a vacuum chamber. The problem becomes even more complicated when the model liquids are used instead of the propellants. It is really difficult to reproduce in a model experiment the true thickness of the film at the nozzle exit, its composition and temperature as well as parameters of high-temperature gas flow of combustion products. Nevertheless, even approximate modeling allows us to obtain the required information about the flow structure (primarily, of the liquid-droplet phase) at maximally possible reproduction of the determining parameters.

It was found experimentally in [6] that the near-wall liquid film flowing into vacuum from a nozzle turns by 180° at the exit nozzle edge and moves along the outer surface


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of this nozzle in opposite direction, forming the backflow (contaminating) of the droplet phase. Thus, it was concluded that the character of liquid film interaction with the wall and co-current gas flow determines dynamics of film behavior inside the nozzle and its further evolution, while flowing into vacuum.

Therefore, the film parameters in the outlet cross section of nozzle (its thickness δl and average velocity Vl, or thickness δl and shearing stress τ at the “gas-liquid” interface) can be taken as the main criteria for modeling the near-wall liquid film. Under the assumption

of linear distribution of velocity in the near-wall film ll l

l

2 ,VdV

dyτ μ μ

δ= = the measured values

of thickness and velocity relate to the shear stress value in the following manner [7]:

l ll

l

2,

G

d

μδπ ρ τ

= (1)

ll

l l

.2

GV

d

τπ ρ μ

= (2)

where Gl, ρl, and μl are the flow rate, density, and viscosity of liquid, respectively. Another important condition of the natural process modeling is the choice of

the main parameters of the supersonic nozzle: its geometry, Mach number, type of gas, its temperature and flow rate or stagnation pressure. Usually, the researchers try to reproduce

full-scale Mach number, Ma and the ratio of specific heat capacities γ. It is not difficult to

reproduce the Mach number, but reproduction of the natural value of γ for the high-temperature combustion products is problematic. In this case, it is reasonable to use the integral characteristics of jets flowing into vacuum. In our studies, we assume the concept

of modeling by the typical angle of jet divergence Θ determined in terms of the relative jet

impulse J [8, 9]:

0.51

arctan ,J

J

⎛ ⎞−Θ = ⎜ ⎟⎝ ⎠

(3)

0.5

2 2

1 21 1 ,

M ( 1) Ma a

Jγ γ

−⎛ ⎞⎛ ⎞

= + +⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟−⎝ ⎠⎝ ⎠ (4)

where max ,aJ J GV= Ja, G, and Vmax is the gas impulse in the nozzle cross section, gas flow

rate, and maximal velocity, respectively. At this approach, in the experiment it is necessary to reproduce the value of the relative impulse of a real OT. For orientation thrusters installed at

the ISS, this value is J = 0.87 (Ma = 4.3, γ = 1.24, total fuel flow rate is about 50 g/s). Then,

according to assumed modeling condition m nJ J= and using air (γ = 1.4) as the model gas,

the Mach number of the model nozzle is Ma = 2.94, and this corresponds to the ratio

of diameters of the outlet and critical cross sections of the nozzle Da /D∗ = 2. Other parameters

of the model nozzle, namely the diameter of critical cross section, gas and liquid flow rates, and other were chosen by the conditions of modeling the near-wall liquid film and metering parameters of the experimental setup.


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Experimental setup and diagnostic methods

Now there are many methods of measuring the local characteristics of the near-wall films, especially their thicknesses. For instance, these methods are reviewed in [3]. In our study, the local parameters of the near-wall liquid film (film thickness and its velocity) were meas-ured by the capacitance probes. The schemes of the test sections are shown in Fig. 1. The near-wall film was formed by the liquid supply through a ring gap of 0.1 mm in the nozzle prechamber. De-spite the supersonic nozzle was the main working section, some experiments were carried out with a cylindrical tube (a type of sonic nozzle), which allowed the experiments at velocities of the co-current gas flow from 0 to 300 m/s, whereas the experiments with the supersonic nozzle could be carried out only at velocities of the co-current flow of about 540 m/s.

The coaxial capacitance probes with the diameter of external electrode of 1.6 mm and dia-meter of inner electrode of 0.5 mm were used in experiments. The probes were mounted flush with the inner surface of nozzle. To measure the film thickness four probes 1 were located in 90º over the nozzle perimeter at the distance of 2 mm from its exit edge. The readings were averaged by four probes, and this allowed improvement of measurement accuracy and reliability for the liquid film. To measure the velocity of the film front and wave velocity on its surface, two probes 1 and 2 were used. Probe 2 was located at the distance of 5 mm from probe 1. Measurement frequency of the probes was 1 kHz. The detailed description of measurement principles and methods can be found in [10].

In experiments, ethanol was used mainly as the working liquid; its physical properties are close to UDMH used in OT of the ISS for creation of a cooling liquid film. In some expe-riments, butanol was used as the working liquid; the pressure of saturated vapors of buta-nol at the room temperature is approximately one order lower than that of ethanol, and other properties, except viscosity, are almost the same.

Experimental studies were carried out at the vacuum gas-dynamic setup “VIKING” at Kutateladze Institute of Thermophysics SB RAS [11]. The large volume of vacuum chamber (of about 150 m3) gives wide opportunities for operation under the pulse conditions. As a rule, pulse duration did not exceed five seconds.

In experiments, the Reynolds number of the gas flow was determined in terms of the gas flow rate G as

gasgas

4Re ,

G

Dμ π ∗=

where μgas is gas viscosity, D* is diameter of the critical cross section of nozzle varied within

4⋅104 − 3.5⋅105. The Reynolds number of liquid film in the critical cross section of nozzle, de-termined in terms of the liquid flow rate Gl as

Fig. 1. Schemes of probe location. Probe location: in longitudinal nozzle cross section ⎯ in supersonic (on the left) and sonic (at the center) nozzles, in transversal nozzle cross section ⎯ in supersonic and sonic nozzles (on the right); 1, 2 ⎯ measurement probes.


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ll

l

Re ,G

Dμ π ∗=

was varied from 7 to 14 for ethanol and from 2.5 to 5.3 for butanol.

Experimental results and analysis

First of all, let us distinguish interaction features between the near-wall liquid film and the co-current gas flow under the conditions of considered problem.

Significant pressure drop in the co-current gas flow. As was mentioned above, for the selected nozzle (Ma = 3) and type of gas (air), the pressure in the co-current gas flow above the film decreases approximately by the factor of 30. This means that for gas pressure in the prechamber of p0 ≈ 103 mmHg, maximal for the conditions of the present study, the gas pressure at the nozzle edge pa is about 33 mmHg, and this is lower than the pressure of satu-

rated vapors of ethanol (psat ≈ 44 mmHg) at the room temperature. Formally this means that the ethanol film in the outlet nozzle cross section becomes overheated, and it should start evaporat-ing or boiling. For butanol (psat ≈ 5 mmHg), this effect can be shown in the flow at the pressures of an order lower than that for ethanol.

Strong interaction of the co-current gas flow with the near-wall liquid film, which causes wave formation and intensive droplet separation. The co-current flow un-der the experimental conditions should affect significantly the film, causing wave formation and droplet detachment from its surface. The high Weber numbers achieved in experiments are the formal basement for the above assumption. According to estimates, their maximal values are close to 200. These are relatively high Weber numbers, and according to review [2], under the current experimental conditions, there should be intensive droplet detachment.

Reduction of the liquid film thickness due to the geometrical factor. Since the supersonic part of nozzle is the diverging channel, formally, the film thickness should de-crease proportionally to 1/D, i.e., for the selected nozzles with Da /D∗ = 2 at liquid film motion

from the critical cross section to the outlet one, its thickness δl and Reynolds number Rel should be decreased twice.

Disruption of the near-wall film at low flow rates. It was noticed in experiments that with a decrease in the liquid flow rate, we observe at some moment separate rivulets at the nozzle edge, but not the continuous film. This effect limited the minimal liquid flow rate in experiments. We did not study the process of disruption in the present work because, particu-larly, it is difficult to observe the liquid flow over the inner surface of the nozzle. The effect of film disruption and dry spot formation in evaporating liquid films were studied in detail in [12, 13].

Now let us present the main results for the supersonic nozzle. The time diagrams of ethanol film thickness obtained at a change in pressure p0 almost by an order (from 820 to 100 mmHg) in the prechamber (and, respectively, the pressure in the flow above the film) are shown in Fig. 2. The Re number was the same under all four regimes, and it equaled Rel = 14. One can see that with a decrease in pressure in the flow above the film (from 24 mmHg for p0 = 820 mmHg to 3 mmHg for p0 = 100 mmHg), the influence of evaporation-boiling processes on the film behavior becomes more and more significant, causing more intensive fluctuations of the film surface and the growth of its average thickness. For buta-nol, this effect was less significant, and it was observed only at minimal pressure p0 = 100 mmHg.

The use of two successive probes allowed us to understand correlation of readings and to measure the velocity of the film front and large waves. A part of time diagram of the film thickness in the range from 700 to 1200 ms, determined by the readings of probes 1 and 2,


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is shown in Fig. 3. The moment of film arrival to the first and second probes can be clearly seen. We can note the reading correlation by signal amplitude and shape and the presence of some periodic wave structure with a characteristic time scale of ≈ 50 ms (with frequency of ≈ 20 Hz).

Fig. 2. Time diagrams of ethanol film thickness for different p0. p0 = 820 mmHg (a), 580 mmHg (b), 340 mmHg (c), and 100 mmHg (d).

Fig. 3. Thickness of ethanol film measured by two successive probes. Rel = 14; 1 ⎯ first probe (upstream), 2 ⎯ second probe (downstream).


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It can also be seen that the waves have a steep front, then there is a flat part, with smaller waves on its surface. The velocity of liquid film front and wave velocity on the film surface were determined by a time delay between probe readings. According to results analysis, the velo-city of the liquid film front is twice as less as the wave velocity on the film surface, and their charac-teristic values are 0.5 and 1 m/s, respectively.

The studies allowed us to determine the average film thicknesses in the supersonic nozzle. Corresponding experimental data for butanol and ethanol are shown in Figs. 4 and 5, respectively. The solid lines in these figures demonstrate the average film thicknesses calculated by formula (1) for the experimental conditions. For these calculations, it is necessary to know the value of shearing stressτ. As was mentioned before, there are no published data for determination of τ at the outer film boundary in the presence of the high-speed, including supersonic, co-current gas flow. However, due to a small thickness of the near-wall liquid film the value of shear stress τ on the outer film surface can be assumed in the first approximation as τw on the nozzle wall without the film. Despite the simplicity of the assumed model,

it allows an estimate of the film thickness and velocity at the motion inside the nozzle with the co-current gas flow. Corresponding dependences for τ in the supersonic gradient flow were taken from [14], and they were as follows:

** 1/ 62

20.0131Re ,fC

V

τρ

−= = (5)

where Re** is determined from equation

**7/6 3.752.75

0

0.0076Re .

x

V dxVυ

= ∫ (6)

The first thing that we should pay attention at analysis of results presented in Figs. 4 and 5, is that for butanol, the calculations are above the experimental data and vice versa for ethanol, and it can be explained as follows. At first, let us consider the results for butanol (Fig. 4).

Fig. 4. Experimental and calculation data at dif-ferent Regas along the thickness of butanol film. Rel = 5.3; pa ⎯ pressure in the flow above the film at the measurement point; 1 ⎯ experiment, 2 ⎯ calculation.

Fig. 5. Experimental and calculation data at dif-ferent Regas along the thickness of ethanol film. Rel = 14; pa ⎯ pressure in the flow above the film at the measurement point; 1 ⎯ experiment, 2 ⎯ calculation.


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Perhaps, we can assume that under the considered conditions, the main interaction processes between the co-current flow and butanol film are wave formation and droplet detachment, and the effect of film boiling is insignificant and obvious only at low p0 (low Regas in Fig. 4). Both

wave formation and droplet detachment should increase τ at the interface in comparison with τ

set in calculations on a smooth solid wall. Since l ~ 1 ,δ τ consideration of higher τ by

the calculation model will lead to a decrease in calculated values of δl and their convergence with experimental data.

Now let us consider the experimental data for ethanol (Fig. 5). Here the main difference from butanol is ethanol film boiling, especially at low p0, as can be seen in Fig. 2. Other two effects (wave formation and droplets detachment) are also available, but boiling (film swelling) is, probably, predominant. The main question is how it affects τ. It follows from comparison of calculation and experimental data shown in Fig. 5 that at film boiling, τ should decrease, i.e., change in the opposite direction in comparison with a change in τ at wave formation and droplet separation. These arguments seem realistic, if we accept the existence of the analogy between the processes of evaporation and substance injection through a permeable wall. As an illustration in Fig. 6, taken originally from [15], there is distribution of the heat transfer coefficient (Nusselt number) along the length of the supersonic nozzle. It is obvious that the heat transfer coefficient is maximal in the critical cross section of the nozzle. The shearing stress should behave similarly. It is also known that injection decreases the heat transfer coeffi-cient; therefore, evaporation from the interface should attenuate the force interaction between the co-current gas flow and the near-wall liquid film, and vice versa at vapor condensation from the flow on the film surface.

Some experiments studied liquid detachment from the film surface in the form of droplets and their following entrainment by the co-current flow. The amount of liquid detached from the film surface was determined in the following way. The initial liquid flow rate was meas-ured. The amount of liquid stayed in the film was determined by the measured values of the average liquid film thickness and its velocity in the outlet cross section of the channel. The difference between the initial and final liquid flow rates was assumed as the amount of liquid entrained by the co-current flow. These studies were carried out mainly for a cylindrical channel because only in this case it was possible to change the velocity of the co-current gas flow (vary-ing pressure in the vacuum chamber) in a wide range from 0 to 300 m/s; while the velocity of gas

in the outlet cross section of the supersonic nozzle was constant and equaled 540 m/s. Ac-cording to experiments, the amount of liquid, detached and entrained by the co-current flow, can be up to 70 % of its initial flow rate. It was determined that as in [2] the amount of liquid entrained by the co-current gas flow can be generalized by the Weber number:

2gas gas l

We ,2

Vρ δσ

=

where ρgas is gas density, Vgas is gas velocity,

Fig. 6. Distribution of Nusselt number along the nozzle [15]. In the upper part of the figure line ⎯ calculations, symbols ⎯ experimental data.


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δl is measured value of the average liquid film thickness, σ is the surface tension coefficient. Corresponding results are shown in Fig. 7.

Conclusion

Although experimental results are obtained in application to modeling the operation condi-tions of OT at the ISS, they represent an independent value for understanding the interaction features between the near-wall liquid film and the high-velocity co-current gas flow. The studies allowed us to determine parameters of the film in the outlet cross section and its evolution at its ejection into vacuum. Further, the methods and devices, which allow a signifi-cant decrease (by some orders) in contaminating effect of OT plumes on the external surface of the ISS, were proposed [16].

References

1. E.P. Volchkov, Near-Wall Gas Cooling, Nauka, Novosibirsk, 1983. 2. I.I. Gogonin, Heat transfer in condensation of vapor moving inside vertical tubes (review), J. Engng. Phys.

Thermoph., 2004, Vol. 77, No. 2, P. 454−470. 3. S.V. Alekseenko, V.E. Nakoryakov, and B.G. Pokusaev, Wave Flow of Liquid Films, Begell House, New

York, 1994. 4. Yu.I. Gerasimov and V.N. Yarygin, Problems of gas-dynamical and contaminating effect of exhaust plumes

of orientation thrusters on space vehicles and space stations, in: Proc. 25th Int. Symp. On Rarefied Gas Dynamics (RGD25), St. Petersburg, Russia, 21–28 July 2006, Novosibirsk, 2007, P. 805−811.

5. I.B. Afanasiev, Insiduous “Kromka”, Novosti kosmonavtiki, 2004, No. 4, P. 15−16. 6. V.G. Prikhodko and V.N. Yarygin, Arising of a return flow in a wall liquid film expelled into vacuum from

a cylindrical channel, Thermophysics and Aeromechanics, 2000, Vol. 7, No. 4, P. 443−445. 7. I.V. Yarygin and V.F. Levchenko, Measurement and calculation of thickness and velocity of a near-wall liquid

film at motion with a co-current gas flow in a supersonic nozzle, in: Proc. XII Intern. Conf. on the Methods of Aerophysical Research ICMAR’2004, Novosibirsk, 2004, Part 4, P. 314−319.

8. Yu.I. Gerasimov, Dimensionless numbers in the problem of the interaction of a freely expanding jet with a plate, Fluid Dynamics, 1981, Vol. 16, No. 2, P. 294−298.

9. I.N. Murzinov, Similarity parameters for the escape of a strongly underexpanded jet into a flooded space, Fluid Dynamics, 1971, Vol. 6, No. 4, P. 675−680.

10. S.V. Kotov, A.D. Nazarov, A.N. Pavlenko, N.I. Pecherkin, A.F. Serov, and V.Yu. Chekhovich, Capacitance meter of the local thickness of liquid film, Instruments and Experimental Techniques, 1997, Vol. 40, No. 1, P. 136−139.

11. V.G. Prikhodko, G.A. Khramov, and V.N. Yarygin, A large-scale cryogenic vacuum plant for gas-dynamic re-search, Instruments and Experimental Techniques, 1996, Vol. 39, No. 2, P. 309−311.

12. A.N. Pavlenko and V.V. Lel, Heat transfer and crisis phenomena in falling films of cryogenic liquid, Russian J. Engng. Thermophys., 1997, Vol. 7, No. 3−4, P. 177−210.

13. A.N. Pavlenko, V.V. Lel, A.F. Serov, A.D. Nazarov, and A.D. Matsekh, The growth of wave amplitude and heat transfer in falling intensive evaporating liquid films, Russian J. Engng. Thermophysics, 2002, Vol. 11, No. 1, P. 7−43.

14. Theoretical Foundations of Heat Engineering, Thermophysical Experiment. Hand-Book, Edit. by V.A. Gri-goriev and V.M. Zorin, Energoatomizdat, Moscow, 1988.

15. S.S. Kutateladze and A.I. Leontiev, Turbulent Boundary Layer in Compressible Gases, Academic Press and Arnold, New York, 1964.

16. V.N. Yarygin, Yu.I. Gerasimov, A.N. Krylov, L.V. Mishina, V.G. Prikhod’ko, and I.V. Yarygin, Gas dynamics of spacecraft and orbital stations (review), Thermophysics and Aeromechanics, 2011, Vol. 18, No. 3, P. 333−358.

Fig. 7. Amount of entrained liquid (ethanol) vs. Weber number. Rel = 10; ρ0 = 735 mmHg (1), 600 mmHg (2), 300 mmHg (3).

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