LABORATOIRE PLASMA ET CONVERSION D’ENERGIE - UMR5213

Participants :

Post-Doc : B. Piaud

Permanent : M. Miscevic, P. Lavieille, S. Dutour

Partners, collaboration and contracts

GREPHE/LAPLACE is part of Microgravity Application Program (MAP) of the European Space Agency (ESA) with MRC/ULB (Belgium), Università di Padova (Italy), EPFL (Switzerland), IT SB RAS (Russia), Euro Heat Pipes S.A. and Lambda-X S.A.

Introduction

The condenser of cooling loops with capillary pumping plays an important role in the performance of the system. It affects stability in two ways : i) convective condensation can be intrinsically unstable, particularly when gravity plays a relatively minor role. ii) the position of the condensation front, directly related to the efficiency of the condenser, can lead to feedback in the loop and cause the system to oscillate. In order to put into relief the gravity influence on condensation phenomena, the convective condensation in tubes of various dimensions has been studied experimentally, providing visual data on the condensation flow patterns for three tubes with inner diameters of 10, 1.1 and 0.56 mm. These tube diameters have been chosen to obtain dimensions upper, nearly equal, and lower than the capillary length scale of the working fluid. This study exhibits various flow regimes according to the different diameters. A significant difference in the annular zone was observed for diameter scales lower than the millimeter. This observation allowed us to provide evidence of the respective influences of the gravity and capillary forces on the flow patterns.

Test facilities for microgravity-like study

One way of reducing the effects of gravity is therefore to decrease the channel diameter. In this aim, an experimental study was undertaken into the convective condensation of n-pentane in a channel with a circular cross section 560 μm in diameter and 10 cm long. Using a glass tube enabled the liquid and vapour phase distribution to be followed visually. The inlet conditions for the fluid entering the tube were imposed. The n-pentane was in the vapour phase and at a temperature slightly higher than its boiling point ; its flow rate was fixed with a syringe pump. The outlet was at atmospheric pressure. Cooling was obtained by a circuit of thermostated water at a sufficient flow rate for its temperature to be considered constant over the whole length of the microchannel. The results were analyzed mainly by using an ombroscopic method. Owing to the circular geometry of the interfaces, a ray tracing model was designed to correct the measurements made by image analysis. The process of optical correction is briefly resumed in the section.

Specific optical tools developed in the lab

The optical model developed assumes a two-dimensional pattern. Condensation occurs on the tube wall ; the liquid remains at the periphery, and the vapor in the core of the channel due to the relatively slight effect of gravity. Considering these hypotheses, an axisymmetric liquid film with a given thickness δ settles inside the pipe (Fig. 1). All the heat exchanger dimensions and the camera lenses characteristics are taken into account. The stroboscope light is represented here by a parallel source of 10 000 rays uniformly distributed over the whole height of the pipe. This number can be increased for more local analysis, notably for very thin liquid films. Ray propagation from the source to the camera follows the laws of optical geometry (Descartes laws). The ray trajectory is broken down into a succession of points, between which light propagation is straight. Indeed, the refractive index is considered to be homogeneous in each medium. Fig. 1 gives the main stages for determining the path of the ray from the source to the receiver (if its path allows this destination to be reached). This model allows predicting the observed image on the CDD sensor, and so to correct the optical deformations induced in particular by cylindrical shape of the tube wall and liquid-vapour interface. Using the deduced calibration curve, the observed thickness is converted into a ‘‘real’’ thickness.

Fig. 1. Example of ray propagation from the source to the receiver, and of the reconstructed image on the camera receiver.

Local void fraction profile

Thanks to image editing, it is possible to get the instantaneous or time averaged void fraction profiles as a function of the axial position. The mean void fraction in the two-phase zone reveals two major flow structures : an annular regime with a high void fraction equal to 0.85 and regimes presenting a release of bubbles with void fraction equal to 0.25. It appears that mean void fraction should be considered as constant for a given flow structure whatever the value of the mass flux considered in the present study. The profile of average void fraction α retranscribes the condensation flow structures observed. In the case of an annular (or capillary) regime, the time averaged void fraction is almost equal to 1. Then, it falls rapidly to 0 along the curvature of the meniscus (Fig. 2a). In the case of an annular wavy flow (Fig. 2b), the time averaged void fraction is close to 1 in the entry region. However, the presence of a wave along the liquid–vapor interface makes its value fall to 0.9. For these two regimes, the condensation lengths are short (few millimeters). For the regime introducing the release of spherical bubbles (Fig. 2c), the condensation zone length increases drastically (few centimeters). In the entrance region, the void fraction diminishes towards values ranging between 0.9 and 0.8. This is due to the presence of non-stationary waves. In contrast, once spherical bubbles are formed, the void fraction strongly decreases. In the case of a regime with elongated bubbles (Fig. 2d), the behavior differs. Indeed, a greater rise of the void fraction appears after the end of the annular zone. It corresponds to the formation, predominantly in this zone, of the elongated bubble. Then, the void fraction decreases sharply corresponding to the beginning of the bubbly zone.

Fig. 2. Time averaged void fraction profiles according to the flow structures observed (a) capillary flow (G = 3.4 kg/(m² s)), (b) annular wavy flow (G = 4.8 kg/(m² s)), © annular with spherical bubble (G= 8.9 kg/(m² s)), (d) annular with Taylor and spherical bubbles (G = 13.8 kg/(m² s)).

Time averaged void fraction profiles, as a function of the non-dimensional axial position y/Ld (where Ld is the condensation length) are represented in Fig. 3 considering different values of mass flux. The values 3.4 and 4.8 kg/(m² s) correspond to capillary regime while the mass fluxes equal to 8.9 and 13.8 kg/(m² s) lead to regimes with formation of bubbles. This representation exhibits a nearly constant profile according to the regime considered and the homothetic nature of the local void fraction variation along the two-phase zone.

Fig. 3. Time averaged void fraction versus the non-dimensional axial position (y/Ld). Ld represents the length of the condensation zone.

Heat transfer

The knowledge of flow pattern means that it is possible to make an enthalpy balance considering the condensation zone. The global heat transfer coefficient H in this zone can be obtained by enthalpy balance.

This value is calculated for each mass flux considering the values of the mean condensation length obtained by image analysis.

Fig. 4 : Global heat transfer coefficient of the micro condenser versus the imposed mass flux and associated phase distribution.

Figure 4 shows that the average heat transfer coefficient is nearly constant in the case of the annular regime. In this zone, the film thicknesses involved are very small. It leads to high values of the internal heat transfer coefficient. After reaching a critical flow rate, a change in the flow regime occurs. The meniscus breaks up producing a train of bubbles strongly reducing the mean heat exchange calculated over the whole 2-phase region (extended meniscus region + bubble region). Hence, the global exchange coefficient of the condenser is 4-fold lower when the flow rate is greater than the critical value compared to the case where the flow rate is low (Fig. 4).

Intrinsic instability in ‘microgravity’

According to the variation of the standard deviation of the pressure difference between the ends of the microchannel as a function of the mass flux (figure 5), three behaviors may be highlighted : for low value of G, the standard deviation is very low, indicating that the phase dsitribution is stable. For value of G between 5 and 7 kg.m^-2.s^-1, the standard deviation increases. Visualisations of the two-phase flow show that this increase is correlated with the appearance of non stationary phenomena leading to the displacement of waves. At flow rates higher than those considered above (i.e., G>Gc), the growth of the waves accelerates faster than their movement along the tube leading to the formation of a plug of liquid in the middle of the 2-phase zone (Figure 6). This cuts the meniscus in half, forming downstream a long bubble that condenses, rapidly becoming spherical. This phenomenon is at the origin of the formation of bubbles presented in figure 2. Thus, to predict the appearance of this type of regime, the phenomena leading to the formation of the liquid plug must be understood. Experimental analysis of this phenomenon carried out using visualisation by rapid video camera showed the exponential behaviour of the wave growth rate. This property is characteristic of a linear instability phenomenon. The experimental results obtained for different flows were then compared to the Rayleigh and the Rayleigh-Kelvin-Helmholtz instabilities in terms of wavelength and growth rate. Divergence between the experimental results and these two types of instabilities indicates the preponderant role of the effects of confinement and/or of phase change on this type of instability, which should be the object of further investigations.

Fig. 5 : Standard deviation of the pressure signal versus the mass velocity.

Fig. 6 : Photographs of phase distribution of n-pentane in the miniature condenser. The time between each photo is 0.25 ms.

Non-steady-state models of the flow should be designed to enable the prediction of the appearance of this type of regime. Retardation, be it active or passive, of flow regime transition could then be attempted.

Modeling It therefore appears important to understand the physical mechanisms intrinsic to condensation. With this aim, we modeled the extended meniscus region so as to be able to simulate the production of the stationary waves observed experimentally. The model is currently being extended to the unsteady state and should ultimately enable the prediction of flow regime transitions.

Fig. 7 : 3D calculated meniscus. The color bar represents the radial position of the liquid-vapor interface.

The stationary model developed is based on the theory of separate phase flow in which the variables used are the mean magnitudes across a section. This one-dimensional model assumes an axisymmetrical distribution of the liquid and vapour phases. The flow in the liquid phase is assumed to be laminar and the two phases are assumed to be saturated. The transfer of momentum at the interface through vaporization is assumed to be negligible for the range of fluxes studied. Finally, heat transfer in the liquid phase is taken as being purely radial. The spatial distribution of the liquid and vapour phases obtained by the model (fig. 7) proved to agree with the flow structure observed by ombroscopy. The axial distribution of the thickness of the liquid along the 2-phase region was well predicted by the model. This enabled, in particular, the reproduction of the stationary wave or waves that were observed depending on the operating conditions and the thermophysical properties of the fluid. Figure 8 represents the variation of the 2-phase length versus the imposed vapour flow rate, characterized by the Reynolds number of the single-phase flow of the vapour at the tube inlet. The numerical and experimental results agree although the validation range remained limited for two reasons. The first limit, explaining the absence of experimental data at low Reynolds numbers, is related to the fact that short spans of tube containing the 2-phase system cannot be visualized. This is due to the fact that owing to the design of the set-up, the 2-phase region remains masked for values of Revo lower than 276. The second limit arises from the impossibility for the numerical model to find stationary solutions for values of Revo greater than 365. This limit is not in disagreement with experimental observations. Indeed, for high Reynolds numbers, the waves are no longer stationary and moved along the 2-phase length.

Fig. 8 : Mean void fraction and condensation zone length versus the vapour Reynolds number at the channel inlet : comparison between experimental and numerical results

In the same figure, the mean void fraction over the whole 2- phase length is also represented. Again, good agreement is found between the numerical and the experimental results. It is also interesting to note that the model indicates that the mean void fraction is nearly constant, as already noted experimentally. This is caused by the homothetic properties of the axial distribution of the void fraction over the whole 2-phase length. The preponderant role of capillary phenomena in structuring this type of flow is illustrated in figure 9 which reports the axial distribution of the pressure in the liquid and vapour phases provided by the model. Owing to the low movement of mass in this type of flow, the pressure of the vapour remained more or less constant. In contrast, the pressure in the liquid is strongly driven by capillary processes. In the thin film layer, the interface having a quasi-cylindrical shape, the capillary pressure jump is approximately σ/Rt. However, at the end of the meniscus, the interface takes a spherical shape, with a radius which is almost equal to the radius of the tube. So, the capillary pressure jump is approximately equal to 2σ/Rt. This sharp variation of the pressure in the liquid is obtained by viscous dissipation in an area of film that has suddenly become very thin (fig. 7) and operates over a very short distance of about Rt/3. Indeed, in this short zone, the liquid velocity increase sharply as illustrated in fig. 10. This concentration of wall friction in a very restricted area stresses the dominant role of capillary forces upon flow.

Fig. 9 : Numerical profile of liquid, vapour and capillary pressure. The origin of the z abscissa is chosen at the bulk meniscus end

Fig. 10 : example of calculated velocity profiles

An example of the in-tude heat transfer coefficient considering n-pentane as the working fluid versus the axial position is reported on fig. 11. High values of this coefficient are reached due to the very thin liquid films encountered. Enhancement of heat transfer is thus possible by reducing the characteristic tube dimension when low mass fluxes are considered, i.e. when there’s no release of bubbles.

Fig. 11 : example of the internal heat transfer coefficient considering n-pentane as the working fluid versus the axial position

Recent Publications

[1] B. Médéric, M. Miscevic, V. Platel, P. Lavieille, J-L Joly, "Experimental study of flow characteristics during condensation in narrow channels : the influence of the diameter channel on structure patterns.", Superlattices and Microstructures, 35, pp. 573-586, 2004.

Abstract : The convective condensation in tubes of various dimensions has been studied experimentally, providing visual data on the condensation flow patterns for three tubes with inner diameters of 10, 1.1 and 0.56 mm. By means of a high speed camera, flow can be divided into three zones : an annular zone, a zone of Taylor’s bubbles and a zone with isolated spherical collapsing bubbles. The effect of gravity on the flow patterns is highlighted and our experimental results on flow structures are compared with the descriptions and characteristics found in the literature. Finally, flow laws have been established thanks to the measurement of pressure drops.

[2] E. Pouzet, J.L. Joly, V. Platel, J.Y. Grandpeix, C. Butto, "Dynamic response of a capillary pumped loop subjected to various heat load transients", International Journal of Heat and Mass Transfer, 47, pp. 2293–2316, 2004.

Abstract : An experimental capillary pumped loop (CPL) device has been developed in order to study its fundamental response mechanisms following steps of applied power. A global model including all the loop elements and the essential physical processes has been designed, with a sole control parameter for fitting experiments and simulations. By comparing experimental results and simulations for upward and downward steps of heat load, the response mechanisms within the loop can be analyzed. This analysis has revealed a particularly good agreement for damped oscillations of low frequency observed during the undershoots ; it also provides an explanation as to the two-phase loop reacts badly to abrupt decreases of applied power.

[3] B. Médéric, P. Lavieille, M. Miscevic, "Void fraction invariance property of complete condensation flow inside a capillary glass tube", International Journal of Multiphase Flow, 31, issue 9, pp. 1049-1056, 2005.

Conclusions (no abstract) : A specific experimental setup has been designed to visualize the condensation flow inside a capillary tube. The transparency of the condenser allows the visualization of four condensation regimes for the range of mass fluxes considered. Thanks to image editing, it is possible to get the instantaneous or time averaged void fraction profiles as a function of the axial position. Moreover, the time averaged void fraction as a function of the non-dimensional axial position reveals a particular type of profile according to the flow structure considered. As a consequence, the mean void fraction in the two-phase zone reveals two major flow structures : a regime with a high void fraction equal to 0.85 and regimes presenting a release of bubbles with void fraction equal to 0.25. It appears that mean void fraction should be considered as constant for a given flow structure whatever the value of the mass flux considered in the present study.

[4] B. Médéric, P. Lavieille, M. Miscevic, "Heat transfer analysis according to condensation flow structures in a minichannel", Experimental Thermal and Fluid Science, 30, Issue 8, pp. 785-793, 2006.

Abstract : An experimental investigation of complete condensation flow is undertaken for a range of mass flow rates between 3.4 and 13.8 kg/ m² s. The associated flow regimes are visualized using an ombroscopic technique. Two major flows are observed (with or without release of bubbles). A critical value of the mass flow rate is obtained at the transition between these two regimes. The visualization also enables a local parameter to be determined : the void fraction. The influence of the presence of a bubbly zone is highlighted by the heat transfer and pressure drops. Finally, the dependence of the critical value of the mass flow rate on the temperature of the secondary flow is obtained.

[5] B. Médéric, M. Miscevic, P. Lavieille, J-L. Joly, "Experimental investigation of condensation flow in a minichannel by means of local void fraction determination", International Journal of Heat Exchangers, 7, n° 1, pp. 15-32, 2006.

Abstract : Convective condensation of n-pentane working fluid inside a 0.56 mm borosilicate round tube is presented for a range of mass flow rates from 0 to 18 kg/(m²s). The transparency of the condenser allows the visualization of the condensation flow structures. Three flow regimes are observed according to the flow rate, corresponding to annular or annular-wavy, annular-bubbly and annular intermittent-bubbly flow. A procedure is presented for the experimental determination of the void fraction profile. The variation of the condensation length versus mass flow rate is also proposed. In the last part, the average condensation pressure drop is investigated.

[6] M. Miscevic, B. Médéric, P. Lavieille, U. Soupremanien, V. Serin, "Condensation in Capillary-Driven Two-Phase Loops", Microgravity Science and Technology, 19, n° 3-4, pp. 116-120, 2007.

Abstract : This paper deals with certain aspects of convective condensation phenomena and condenser behaviour in capillary-driven cooling loops (CPL or LHP) studied in the LAPLACE laboratory, Toulouse. The effects of phase distribution, in the condenser, on the stability and the reliability of the whole system were studied. A model is proposed for convective condensation at low mass fluxes in a microgravity-like situation. The numerical results are in good agreement with experimental data. On increasing the mass flux, both numerical and experimental results suggest that the stationary state no longer exists, and intrinsic instabilities occur and develop in the condenser. The effects of such instabilities, as well as flow regime transitions, on loop behaviour remain an open question.