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2 Acta Astronautica 66 (2010) Contents lists available at ScienceDirect Acta Astronautica journal homepage: Study of thermoconvective flows induced by vibrations in reduced gravity V. Shevtsova, Yu. Gaponenko, D. Melnikov, I. Ryzhkov, A. Mialdun Microgravity Research Center, Université Libre de Bruxelles, CP-165/62, Av. F.D. Roosevelt, 50, B-1050 Brussels, Belgium A R T I C L E I N F O A B S T R A C T Article history: Received 18 February 2009 Accepted 23 May 2009 Available online 5 July 2009 Keywords: Vibrations Convection Parabolic flight Heat transfer We report an experimental evidence of convection caused by translational vibration of non-uniformly heated fluid in low gravity. The theory of thermovibrational convection in weightlessness has been well developed but experimental proof of this type of motion was not enough convincing. An innovative point of the experiment is the observation of temperature field in front and side views of the cubic cell. In addition, particle tracing is employed. The evolution of temperature field is studied systematically in a wide range of frequencies and amplitudes. It is demonstrated that vibrational convection enhance the heat transfer in the system. The mean flow structures previously reported in numerical studies are confirmed Elsevier Ltd. All rights reserved. 1. Introduction It is known that the application of vibration to a fluid system with density gradient can cause relative flows inside the fluid. The effects of rotational vibration and translational vibration are different. Rotational vibration acts even on homogeneous fluids, where it generates periodic flow. It is a phenomenon that can be studied on Earth. Translational vibration affects only fluids with non-uniform density. If the density gradient results from non-uniform temperature field, these flows are called thermovibrational convection. A `pure' thermovibrational convective mechanism can be observed in weightlessness only. In terrestrial conditions, buoyant convection also acting on density inhomogeneities masks vibration-induced flows. The study of vibrational impact on fluids has fundamental and applied importance. Vibrational convection provides a mechanism of heat and mass transfer due to the existence of mean flows. In weightlessness, it is an additional way of transporting heat and matter similar to thermo and solutocapillary convection. Mean flows show some similarity Corresponding author. Fax: address: vshev@ulb.ac.be (V. Shevtsova). with gravity-induced convection and might serve as a way to control and operate fluids in space [1]. High-frequency vibrations onboard microgravity platforms such as ISS and satellites can disturb the experiments that require purely diffusive heat and mass transfer: crystal growth, measurement of transport coefficients, etc [2]. Vibrations can suppress or intensify gravitational convection depending on the mutual orientation of vibration axis and thermal (compositional) gradient [3]. There have been extensive theoretical studies of thermovibrational convection in various configurations and under different gravity levels. The fundamental treatise [4] comprises a systematic study of convective flows caused by high and finite frequency vibrations in closed and infinite cavities. Thermovibrational convection in a square (cubic) and rectangular cavities was widely investigated (see [2 6] and references therein). At the same time, experimental studies addressing vibrational phenomena in weightlessness are very limited. A well known series of experiments was carried out with the ALICE-2 instrument onboard MIR station [7,8]. The influence of vibrations on the propagation of a temperature wave from a heat source in a near-critical fluid (gas) was investigated. The study was based on observing the evolution of optical inhomogeneity caused by the distortion of temperature /$ - see front matter 2009 Elsevier Ltd. All rights reserved. doi: /j.actaastro

3 V. Shevtsova et al. / Acta Astronautica 66 (2010) field. The impact of residual accelerations onboard a spacecraft on convection in differentially heated cylindrical cavities was studied independently by Naumann et al. [9] and Babushkin et al. [10]. In these experiments, the temperature was monitored at several fixed points. We present the results of experiments on the observation of thermal vibrational convection in reduced gravity, conducted in the 46th and 48th Parabolic Flight Campaigns organized by the European Space Agency. The present work focuses on the comprehensive analysis of the experimental results in microgravity conditions of a parabolic flight (g 10 2 g 0 ). The preparation of this experiment was reported earlier by Melnikov et al. [11], while the first experimental results were concisely presented by Mialdun et al. [12,13]. These experiments constitute a preliminary and complementary step of the space experiment IVIDIL (influence of vibrations on diffusion in liquids), which is performed in the frame of ESA physical sciences project and aimed at examining the influence of vibration stimuli on diffusive phenomena [14]. The main goals of the parabolic flight experiments are: (1) to observe and interpret the thermovibrational convection in microgravity, (2) to improve the experimental technique originally developed for IVIDIL and verify it in microgravity conditions and (3) to make an experimental verification of existing theoretical results. The cell is fixed to the linear motor, which performs translational harmonic oscillations in Xdirection (perpendicular to the temperature gradient). The linear motor is a single bearing stage of Baldor (cat. no. LSS1TE1CF08C012). It is driven by programmable controller that allows any custom designed motion profile. The mass of the moving part was m = 2.4 kg. The technical data sheet provided by manufacturer indicates the force F =116 N. The corresponding vibration acceleration is a vib =F/m=4.9g 0. An experimental curve of the linear motor performance is shown in Fig. 2. Different symbols correspond to the tests on the ground and in microgravity. The upper limit for frequency increases with decreasing the amplitude. As followsfrom Fig. 2, the work performance was better than foreseen at small amplitudes and worse for the large amplitudes. In the experiments, the frequency and amplitude were varied in the ranges 1 12 Hz and mm, respectively. The maximum vibrational acceleration Aω 2 = 5.8g 0 was achieved at A = 10 mm and f = 12 Hz (ω = 2πf ). 2. The experiment 2.1. Experimental setup To observe thermovibrational convection in microgravity, we have designed a special experimental setup. Scheme of the optical part is shown in Fig. 1a. The working liquid is placed in a cubic cell with transparent walls of internal size L=5 mm. The external walls of the cell are shaped in the form of two prisms (Fig. 1c) to allow optical observation (see the description below). The cell is made of quartz Suprasil. The top and bottom walls are kept at constant temperatures T hot and T cold, respectively, by the Peltier modules (3 cm 3cm). Fig. 2. Linear motor performance: amplitude frequency diagram according to the experimental tests. Fig. 1. The scheme of experimental setup (a), the cubic cell and coordinate system (b), and the top view of the experimental cell (c).

4 168 V. Shevtsova et al. / Acta Astronautica 66 (2010) Space Agency in November 2007 and March 2008, respectively. A plane following a parabolic trajectory (like a stone thrown into the air) is in the state of free fall. The parabolic flight maneuver is following: from the normal horizontal flight mode (1g 0 = 9.81 m/s 2 ), the nose of the plane is pulled up, until a slope of 47 with respect to the horizon is reached. In this phase the plane experiences hypergravity (1.8g 0 ) for 20 s. Then the plane enters the parabolic trajectory of approximately 22 s of reduced gravity with g 10 2 g 0. After free fall the plane dives downwards with 42. In this phase the plane experiences again the doubled gravity (1.8g 0 ) for 25 s until it gains back to normal flight mode (1g 0 ), see Fig. 4. During one day, a total of 31 parabolas is performed; each campaign includes three days. Fig. 5 shows a typical gravity profile during a single parabola. The microgravity period is delimited by the dashed lines. The residual gravity level is Fig. 3. Experimental rack is ready for boarding. The thermovibrational flows were monitored by measuring the temperature field inside the cell by optical digital interferometry. The setup is based on the concept of Mach Zehnder interferometer (Fig. 1). The light beam of He Ne laser (λ = nm) is enlarged by the beam expander and then splitted into two collimated beams of equal intensity by the beam splitter. One of the beams transverses the entire cell in two perpendicular directions. The lateral walls shaped in the form of two transparent prisms allow scanning the front and side views (planes YZ and XZ, respectively). The beam paths through the cell are shown by arrows. The temperature variations in the liquid create the spatial distribution of refractive index that modulates the wave-front of the emerging optical beam. After passing the mirror, this beam interferes with the reference one at the second beam splitter. The patterns are recorded by CCD camera (24 fps, pixels sensor) and processed by computer. Interferograms are reconstructed by performing 2D fast Fourier transform (FFT) of the fringe image, filtering a selected band of spectrum, performing the inverse 2D FFT of the filtered result and phase unwrapping. The knowledge of phase shift gives information about the gradient of refractive index, which is used to reconstruct 2D projections of temperature field on the front and side view planes. This method allows temperature measurement with the accuracy of 0.01 K. More details about optical digital interferometry can be found in [15]. The velocity field in the cell was observed with a help of isodense tracer particles (hollow ceramic microspheres with the diameter of 150 μm). The above described setup was arranged inside an experimental rack and installed onboard the Airbus A300 Zero-G, see Fig. 3. The dedicated rack was designed and developed by one of the authors of this paper (Mialdun) Microgravity environment The experiments were performed in parabolic flights during 46th and 48th campaigns organized by the European g x, g y 10 2 g 0, g z g 0. (1) Here the x and y axis lie in the plane of aircraft wings (positive x axis points towards the nose). The z axis is perpendicular to the wings plane and goes out the upper side of the vehicle. The orientation of the experimental cell with respect to the described coordinate system is shown in Fig. 1b. The gravity level during the flight was measured by the accelerometer with the sampling rate of 5 Hz. During the microgravity period, the residual gravity in z direction may change sign. So, it can stabilize or destabilize the flow inside the cell. The residual gravity in x and y directions, which are perpendicular to the temperature gradient, is always destabilizing. For successful observation of thermovibrational convection, the vibrational impact should be strong enough to suppress the influence of residual gravity. The scenario of the experiment is as follows. The temperature gradient is established in the cell during horizontal flight. To suppress convection, the cell is heated from above (the temperature gradient is co-directed with z axis of the aircraft and is opposed to the gravity vector). Vibration is switched on in the beginning of microgravity period and continues for 25 s. During this time, interferometric patterns are recorded by the camera. The motor is switched off at the end of microgravity period. The time of horizontal flight between two consecutive parabolas is around 2 min. A large number of available parabolas allowed us to perform repeated experiments with the same configuration as well as to investigate different vibrational regimes. 3. Choice of control parameters In the present study, we consider the case of highfrequency vibrations. It means that the vibration period is small in comparison with the characteristic hydrodynamic times (viscous and thermal time). In this case, the velocity, temperature and pressure fields can be presented as superpositions of mean (time-averaged) and oscillatory parts F = F + F.

5 V. Shevtsova et al. / Acta Astronautica 66 (2010) Fig. 4. Parabolic flight scenario. When the gravity force is present, its influence is described by the Rayleigh numbers Ra x,y,z = g X,Y,Zβ T ΔTL 3, (4) νχ where g x, g y, g z are the components of gravity vector. For successful observation of thermovibrational convection in microgravity during parabolic flight, the experiment should satisfy the following requirements: 1. The influence of convection caused by the residual gravity should be minimized. The relative importance of gravitational and vibrational convective mechanisms is described by the ratios of the Gershuni number to the corresponding Rayleigh number Gs = (Aω)2 β T ΔT. (5) Ra x,y,z 2g x,y,z L Fig. 5. Acceleration profiles during a parabolic flight manoeuvre (large scale). The mean quantities are defined by F(t) = 1 Π t+π/2 t Π/2 F(τ) dτ, (2) where Π is the period of vibrations. The dimensionless criterion that characterizes the vibrational impact is the vibrational Rayleigh number. Following [9], we suggest to call it Gershuni number to mark a significant contribution of Gershuni to the theory of thermovibrational convection [4] Gs = Ra vib = (Aωβ TΔTL) 2, (3) 2νχ where ΔT is the applied temperature difference, β T is the thermal expansion, ν is the viscosity, and χ is the thermal diffusivity. So, the vibrational velocity Aω, the thermal expansion β T and the applied temperature difference ΔT should be large, while the cell size L should be small. 2. Sustained oscillations of velocity and temperature fields should develop within microgravity time (20 s). So, the characteristic times (viscous time τ vs = L 2 /ν and thermal time τ th = L 2 /χ) should be as small as possible. 3. The oscillations of velocity and temperature should be observable by the available experimental technique (interferometry and particle tracing, see Section 1). For reliable registration of oscillations, the velocity magnitude and temperature variations should have the order of 1 mm/s and 10 1 K, respectively. 4. The working liquid should satisfy the safety requirements of parabolic flights. The formulated requirements pose a problem of choosing the control parameters of the experiment. The available parameters of the linear motor were described in Section 1.1. It can provide overloads up to 5.8g 0 and the maximal vibrational velocity Aω = 1.19 m/s at the amplitude A = 0.05 m and frequency f = 3.8 Hz. Concerning the cell size, it should not be too small to allow optical observation. Based

6 170 V. Shevtsova et al. / Acta Astronautica 66 (2010) on these considerations, the size L = mwaschosen. The applied temperature differences were 15 and 20 K. According to requirements 1 and 2, the working liquid should have large thermal expansion and small viscous and thermal times. In the preliminary study [11], we have considered five liquids (water, ethanol, methanol, isopropanol, pentane) and found that isopropanol is the most suitable liquid. The mean temperature of the experiment was 40 C. The physical properties of isopropanol relevant to our study are the thermal expansion β T = K 1, the viscosity ν = m 2 /s, and the thermal diffusivity χ = m 2 /s. The viscous and thermal times of the system are L 2 /ν = 14.5 s and L 2 /χ = s, respectively. It makes possible to observe the transient development of thermovibrational flow and its influence on the temperature field during 20 s of microgravity. We do not investigate stationary states since the thermal time is significantly larger than the microgravity time. With the chosen linear motor and the working liquid, we were able to obtain the following space of ratios (5): 0 < Gs/Ra x,y < 29, 0 < Gs/Ra z < 14. It allowed us to investigate configurations where the role of vibration was dominant and the influence of residual gravity was rather small. 4. Results and discussion We have performed a large number of experimental runs with frequencies and amplitudes in the ranges 1 12 Hz and mm, respectively. The corresponding values are presented in Table 1 The cases 8, 10, 14 do not fall into the high-frequency limit used in some theoretical studies [4]. They will be excluded from some plots. The experimental temperature field at the beginning and the end of parabola shows in Fig. 6 some deviations from a purely conductive state. Strong deformation of Table 1 The frequencies and amplitudes used in the experiment (ω = 2πf ). N f (Hz) A (mm) ΔT (K) Gs Aω 2 g 0 Number of runs Experiments in normal gravity temperature isolines at the end of parabola indicates the development of significant convection. The residual gravity during this parabola is shown at the bottom graph and was g X,Y /g , g Z /g Note that thin regions ( 0.2 mm) near the horizontal walls were inaccessible for optical measurements. One may get misleading impressions from these figures that the temperature of horizontal walls is not constant. In the experiment, the temperatures of two copper plates were perfectly uniform in space and time (copper has very high thermal conductivity) and they were controlled during the experiment. It should be noted that our preliminary numerical simulations as well as the previous results [2] showed that the oscillatory distortion (quick part) of the temperature field is very small (or even negligible) with respect to the timeaveraged distortion induced by the mean flow. So, the patterns in Fig. 6 represent the mean temperature field with a good accuracy. In the beginning of parabola (0 s), the situation is close to the conductive state. The development of thermovibrational flow causes the distortion of temperature field, which is growing with time. To prove unambiguously the existence of convection (non-zero mean flow) produced by vibration the experiments were performed under three different conditions: (1) microgravity and no vibrations; (2) microgravity and vibrations; (3) normal gravity and vibrations. The strength of thermoconvective flows could be characterized through the variations of a temperature field. Let us introduce a quantity DT, which corresponds to the maximum temperature deviation from linear profile along vertical line in the middle of the cell DT = max T exp (z) T lin (z) x=2.5 mm, T lin (z) = T z=0 + z L (T T z=0 ), (6) ΔT here T exp is experimentally measured temperature. Fig. 7 shows the evolution of DT over the time of one parabola with and without vibrations. Both curves are obtained at microgravity conditions. There are some deviations from purely conductive state when no vibration is applied (lower curve). It indicates the presence of heat fluxes through lateral walls, which are also visible in Fig. 6 at t = 0 s. Accordingly, the weak convection is caused by the residual gravity. The analysis of different parabolas showed that the deviations from conductive state are not large. The situation is strikingly different when vibration is applied to the system. Comparison of the curves with and without vibrations in Fig. 7 confirms appearance of the convection caused by vibrations. With increasing the Gershuni number, thermovibrational convection becomes more intensive and leads to the strong distortion of the thermal field, compare blue curves in Figs. 8 and 9. They correspond to Gs = and 56216, respectively. The development of thermovibrational convection is faster and stronger for the larger Gs number. The temperature field for the largest studied Gershuni number, Gs = 71149, is shown in Fig. 6 (Run 18 in Table 1). At this

7 V. Shevtsova et al. / Acta Astronautica 66 (2010) Fig. 6. (Online color) The temperature field (side view) at the beginning and at the end of parabola with vibration: f = 4Hz, A = 45 mm, ΔT = 20 K (Run 18 in Table 1). Below: g Z /g 0 gravity profile where first and last points indicating the times at which the temperature fields are shown. case the vibrational convective mechanism significantly dominates the gravitational one Gs/Ra x,y = and Gs/Ra z = 9.52, and leads to strong thermovibrational flows. The data in Figs. 6 9 are subtracted from side view images. The temperature distortion in the front view is much smaller than that in the side view due to the specific structure of the side pattern, see [12]. Note that the thermal field in the front (side) view is a superposition of patterns in the planes of constant x (y). Finally, several experiments were carried out in normal gravity for various vibrational excitations (during horizontal flights). We observed that gravity drastically suppresses vibrational convection, see red curves in Figs. 8 and 9. One may draw a conclusion that for examination of vibrational convection the microgravity experiments are unavoidable. On the other hand, vibrations produce the convection playing role of artificial gravity in Space and they may be used for management of fluids and life-support systems [1]. In addition, two regimes of vibrational impact were considered: (a) (interrupted vibrations) vibrations are applied only during 22 s of microgravity and (b) (continuous vibrations) vibrations are applied continuously including the period between two successive parabolas. The latter case allows us to study thermovibrational convection in microgravity and terrestrial conditions and observe the transition between the corresponding regimes. It follows from Fig. 10 Fig. 7. Maximum temperature deviation from linear profile along vertical line x = 2.5 mm over duration of parabola with and without vibrations. Runs 2 and 10 in Table 1. that there is no significant difference between these regimes. Small variations are attributed to the quality of microgravity level. In case interrupted vibrations CCD camera was switched on slightly earlier than vibrations. The collective results of numerous experiments are demonstrated in Fig. 11. To characterize the intensity of mean flow, the average temperature deviation from conductive profile (observed in the absence of vibration) is

8 172 V. Shevtsova et al. / Acta Astronautica 66 (2010) Fig. 8. Maximum temperature deviation from linear profile along vertical line x = 2.5 mm over duration of parabola in microgravity and normal gravity with the same vibrations. Runs 10 and 19 in Table 1. Fig. 11. Temperature deviation vs. Gs (i.e. the intensity of mean flow as a function of periodic excitation). Fig. 9. Maximum temperature deviation from linear profile along vertical line x = 2.5 mm over duration of parabola in microgravity and normal gravity with the same vibrations. Runs 16 and 20 in Table 1. and plotted as a function of Gershuni number (the results correspond to ΔT = 20 K). For relatively small vibrational stimuli, the heat/mass transfer is controlled by residual gravity (Gs < 10 4 ). As the Gershuni number increases, the thermal deviation grows indicating the dominant role of vibration. The scattering of the experimental points is attributed to the quality of parabolas. Note the distortion of isotherms in the case of horizontal flight (1g 0 ) was even smaller than in the case f = 0. For comparison, δt for Gs = in normal gravity. We would like to emphasize that among existing experimental works (which are very limited), there are no experiments where the thermal field and its evolution were measured inside the cell. In this respect, the present experiment is unique: it reveals the structure of mean flow and its impact on heat transfer. The obtained results show a close agreement with numerous numerical simulations. 5. Conclusions Fig. 10. Maximum temperature deviation from linear profile along vertical line x = 2.5 mm over duration of parabola in microgravity for different vibrational regimes. Runs 10 in Table 1. introduced by δt = 1 ΔTL L 0 T T cond x=l/2 dz, We have reported the direct experimental evidence of thermovibrational convection in low gravity. The temperature field in the fluid is measured in two perpendicular directions and its evolution in time is investigated systematically in a wide range of frequencies and amplitudes. A strong heat transport attributed to the mean flow is found under vibration in low gravity. This transport is significantly weaker in the absence of vibration (only residual gravity) and negligibly small in normal gravity for the studied levels of vibration. The present experiment can be considered as a significant step forward since we were able to measure the temperature field quantitatively. These results could be of considerable interest for a large number of theoreticians working in the field.

9 V. Shevtsova et al. / Acta Astronautica 66 (2010) Acknowledgments This work is supported by the PRODEX programme of the Belgian Federal Science Policy Office. The authors are grateful to Dr. Vladimir Pletser (ESA), Prof. J.C. Legros (MRC,ULB) and NOVESPACE personnel for continuing support and assistance during Parabolic Flight Campaigns. References [1] D. Beysens, Europhysicsnews 37 (3) (2006) 22. [2] R. Savino, R. Monti, Fluid-dynamics experiment sensitivity to accelerations prevailing on microgravity platforms, in: R. Monti (Ed.), Physics of Fluids in Microgravity, vol. 178, Taylor & Francis, London, [3] R. Savino, R. Monti, M. Piccirillo, Thermovibrational convection in a fluid cell, Comput. Fluids 27 (8) (1998) 923. [4] G.Z. Gershuni, D.V. Lyubimov, Thermal Vibrational Convection, Wiley, New York, [5] K. Hirata, T. Sasaki, H. Tanigawa, Vibrational effects on convection in a square cavity at zero gravity, J. Fluid Mech. 445 (2001) 327. [6] V.M. Shevtsova, D.E. Melnikov, J.C. Legros, The study of stationary and oscillatory weak flows in space experiments, Microgravity Sci. Technol. XV-1 (2004) 49. [7] A.V. Zyuzgin, A.I. Ivanov, V.I. Polezhaev, G.F. Putin, E.B. Soboleva, Convective motions in near-critical fluids under real zero-gravity conditions, Cosmic Res. 39 (2) (2001) 175. [8] Y. Garrabos, D. Beysens, C. Lecoutre, A. Dejoan, V. Polezhaev, V. Emelianov, Thermoconvectional phenomena induced by vibrations in supercritical SF 6 under weightlessness, Phys. Rev. E 75 (2007) [9] R.J. Naumann, G. Haulenbeek, H. Kawamura, K. Matsunaga, The JUSTSAP experiment on STS-95, Microgravity Sci. Technol. 13 (2) (2002) 22. [10] I.A. Babushkin, G.P. Bogatyrev, A.F. Glukhov, A.F. Putin, S.V. Avdeev, A.I. Ivanov, M.M. Maksimova, Investigation of thermal convection and low-frequency microgravity by the DACON sensor aboard the MIR orbital complex, Cosmic Res. 39 (2) (2001) 161. [11] D.E. Melnikov, I.I. Ryzhkov, A. Mialdun, V. Shevtsova, Thermovibrational convection in microgravity: preparation of a parabolic flight experiment, Microgravity Sci. Technol. 20 (1) (2008) 29. [12] A. Mialdun, I.I. Ryzhkov, D.E. Melnikov, V. Shevtsova, Experimental evidence of thermal vibrational convection in a nonuniformly heated fluid in a reduced gravity environment, Phys. Rev. Lett. 101 (2008) [13] A. Mialdun, I.I. Ryzhkov, D.E. Melnikov, V. Shevtsova, Experimental evidence of thermovibrational convection in reduced gravity, Space Res. Today 171 (2008) 4. [14] V. Shevtsova, D. Melnikov, J.C. Legros, Y. Yan, Z. Saghir, T. Lyubimova, G. Sedelnikov, B. Roux, Influence of vibrations on thermodiffusion in binary mixture: a benchmark of numerical solutions, Phys. Fluids 19 (2007) [15] A. Mialdun, V. Shevtsova, Development of optical digital interferometry technique for measurement of thermodiffusion coefficients, Int. J. Heat Mass Transfer 51 (2008) 3164.