- Email: [email protected]
Boiling incipience in parallel micro-channels with low mass flux subcooled water flow
International Journal of Multiphase Flow 47 (2012) 150–159
Contents lists available at SciVerse ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Boiling incipience in parallel micro-channels with low mass flux subcooled water flow A. Mosyak, L. Rodes, G. Hetsroni ⇑ Department of Mechanical Engineering, Technion – Israel Institute of Technology, 32000 Haifa, Israel
a r t i c l e
i n f o
Article history: Received 17 April 2012 Received in revised form 12 July 2012 Accepted 13 July 2012 Available online 26 July 2012 Keywords: Micro-channel Subcooled boiling incipience Bubble dynamics Roughness
a b s t r a c t Here we present an investigation of boiling incipience in parallel micro-channels and compare the results with those reported for conventional channels. To provide additional insights into the role of surface roughness on the onset of nucleate boiling (ONB) in micro-channels, the roughness parameters were studied extensively. Onset of nucleate boiling is investigated in uniformly heated parallel rectangular micro-channels of Dh = 297 lm with subcooled water flow at mass flux of 15.4–77.1 kg/m2s. It is shown that in the literature significant disagreement between values of wall temperature and the average mass liquid temperature at ONB point is due to different experimental conditions. For the analysis of the conditions at which the ONB occurred, the parameter based on the relation of the difference between wall excess temperature and bulk fluid temperature at ONB to the difference between saturation temperature and fluid inlet temperature is developed. The experimental results indicate that parameters, which affect incipience of nucleation in micro-channels, such as cavity radius and wall excess temperature, are well predicted by the theoretical nucleation criteria, which were developed for conventional size channels. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Systems which provide liquid or two-phase flow through parallel channels of hydraulic diameter less than about 0.5 mm can be considered as micro-channels heat sinks. These systems are very well suited for cooling of devices where high heat flux is dissipated from a small surface area. Phase-change processes, particularly flow boiling, are important in the micro-scale and significant amount of research is performed in this area. The extend to which incoming liquid will be vaporized in the micro-channels, is a design parameter which depends on the intended application. In micro-scale refrigeration systems, the change in vapor quality may be substantial, e.g. of the order of 0.0–0.8. In electronic cooling applications, the equilibrium vapor quality may remain at zero or be very small to capture the high heat transfer coefficients of subcooled flow boiling without the need to incorporate a condenser. The onset of bubble nucleation usually requires that the temperature on the heated surface exceed the saturation temperature of the liquid corresponding to the prevailing pressure. However, there is significant disagreement between experimental results for conventional size channels due to different experimental conditions. For example, the wall has to be at relatively high excess temperature to initiate the nucleate boiling e.g. in the experiments by
⇑ Corresponding author. Tel.: +972 48 292058; fax: +972 48 238101. E-mail address: [email protected] (G. Hetsroni). 0301-9322/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.07.006
Hapke et al. (2000) compared to those reported by Sato and Matsumura (1964) and by Bergles and Rohsenow (1964). Only few experimental studies have considered the ONB in micro-channels. Qu and Mudawar (2002) performed experiments to measure the incipient boiling heat flux qONB in a heat sink containing 21 rectangular micro-channels 231 lm wide and 713 lm deep. It was shown that wall excess temperature (i.e. the temperature above the saturation temperature) is directly proportional to the heat flux. The onset of nucleate boiling in the flow of water through a micro-channel heat sink was investigated by Liu et al. (2005). Twentyfive micro-channels of 275 lm in width and 636 lm in height were cut into the top surface of the copper block. To complement the incipient heat flux results identified from the visualization approach, the micro-channel wall temperatures and pressure drop along the micro-channels were analyzed. The common results were obtained from temperature and pressure drop measurements. However, the roughness of the heated surface was not measured. The work by Lee et al. (2004) explored experimentally bubble dynamics in a single trapezoid micro-channel with a hydraulic diameter of 41.3 lm. Bubble nucleation, growth, departure size and frequency were observed using a high-speed camera. Their results may be predicted from the classical model with micro-sized cavities suggested by Hino and Ueda (1985) for subcooled boiling in conventional channels. Bubble nucleation in micro-channel flow boiling, using single artificial cavity with radius of 12.5–16.4 lm, was studied by Lee et al. (2011). Onset of nucleate boiling, bubble growth behavior
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
and flow boiling pattern were observed however, the heat flux was not specified. There is discrepancy between measured superheat required for onset of nucleation boiling in micro-channels reported by different investigators. For example, the flow boiling characteristics of subcooled water flowing through micro-channels with rectangular cross-section of 0.6 0.7 mm were experimentally investigated by Peng and Wang (1993). When the wall temperature was higher than the saturation temperature no bubbles were observed in micro-channels. The authors concluded that there is a ‘‘critical scale for liquid bulk to determine whether bubbles can grow in liquid’’. On the other hand, Lee et al. (2004) conducted experiments in a single trapezoid micro-channel with Dh = 41.3 lm. The bubble nucleation of this study may be predicted by a classical model for conventional size channels. To the best of our knowledge, experimental results of the fluid bulk temperature at ONB point under condition of subcooled boiling in micro-channels are not reported. It is difficult to measure liquid temperature around the bubble, which occurs when the wall temperature exceeds the saturation temperature by a certain amount. Systematic experiments addressing the onset of nucleate boiling, flow instability, and other related subcooled boiling phenomena in micro-channels are thus needed. The main purpose of the preset study is to highlight the phenomenon of boiling incipience in micro-channels and to compare it with conventional size channels. To estimate the value of the bulk liquid temperature at ONB the parameter taking into account the difference between saturation and inlet fluid temperature was developed.
2. Experimental facility and procedure 2.1. Experimental setup A scheme of the experimental apparatus is shown in Fig. 1. Filtered deionized water at a temperature of 20 °C was used as the working fluid. It was pumped from the entrance tank by a peristaltic pump through the inlet calming chamber, inlet manifold to the micro-channels in the test module, and from the microchannels through the outlet manifold, outlet calming chamber to the exit tank. The mass flow rate of the water was measured by a weighing method.
Fig. 1. Experimental facility.
151
2.2. Test module The test module, Fig 2, was fabricated of 14 mm 20 mm and 1.25 mm thick aluminum plate and placed into the heat sink housing. Twenty five micro-channels were machined on one side of this plate using a precision sawing technique. The micro-channels were of 200 lm wide, 580 lm deep and wall thickness of 200 lm. The lower part of heat sink housing was made from PEEK plate in order to decrease the heat loses to the environment and keep the inlet/ outlet manifolds temperature at constant values. The upper part, made of PEEK, was attached to the lower part by screws and served as a cover, which was used also for pressure drop measurements. During experiments of flow visualization this cover was replaced by a transparent one. The aluminum chip module combines precise mechanical sawing on one side and electric chromium evaporated resistor on the other, which are in common use to manufacture micro-electronic devices. The electrical insulation was an AlOx interlayer 35 lm thick, thermal conductivity of 10.2 W/mK, made by anodization process. The heater filament was made of pure chromium Cr 99.9% with resistivity of 13.2 lX cm (20 °C), thickness of 1720 A°, width of 1.257 mm, and length of 82 mm. To study the effect of axial heat flux due to conduction in the aluminum, calculations using CFD software were conducted by Mishan et al. (2007). At uniform heat flux of q = 4.4 W/cm2 and mass flux m = 8.33 kg/m2 s, numerical and experimental results agreed quite well: the difference between calculated and the measured maximum temperature on the heater was 0.1 K. Heat flux was controlled by a power supply. Several studies showed that the manifolds design played an important role in the liquid distribution between the parallel micro-channels, which can lead to span-wise temperature gradients on the device surface, increase thermal stresses and reduce the reliability. To optimize the design of the manifold configurations, a number of numerical calculations were conducted previously by Mishan et al. (2007). The calculations were carried out for three types of manifolds shown in Fig. 3. It was shown that the configuration of the manifold 1 ensures uniform velocity distribution at the entrance to the micro-channels. 2.3. Measurement apparatus The vapor–liquid pattern in the micro-channels was studied using a microscope and high-speed video camera. A microscope was connected to an external lighting arrangement. An additional camera joint was assembled to connect a high-speed camera to the microscope. The high-speed camera with maximum frame rate of 10,000 fps, was used to visualize the two-phase flow regimes in micro-channels. The way it works is by capturing video at high frame rate, which when it is played back at low speed, looks like it has been recorded in slow motion. The playback speed of the high- speed camera can be varied from a single frame to 1000 fps. A thermal high-speed imaging radiometer was utilized to study the temperature field on the electrical heater and the working fluid temperature distribution along the micro-channels. The IR camera is suitable for temperature measurements in the wavelength range of about 5 lm, it has a sensitivity of 0.1 K and a typical resolution of 256 pixels per line. The measurement resolution was of 0.03 mm. Using the radiometer one can obtain a quantitative thermal field in the line mode, an average temperature in the area mode, and a temperature of a given point in the point mode. The fluid temperature was measured at the entrance and exit of the test module by 0.3 mm type-T thermocouples. The heater was coated with a thin layer of black diffusive paint, with emissivity of 0.95. For pressure, drop measurements the holes, 0.6 mm in diameter, were connected to pressure transducers by needles. The pressure drop was measured directly at the central part of
152
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
Fig. 2. Experimental setup. (a) Test module, (b) pressure measurement, and (c) flow and thermal visualization.
the micro-channels (not in the manifolds). Such a method makes it possible to avoid pressure drop losses associated with contraction and expansion at the micro-channels inlet and outlet. WYKO NT 1100 series optical profilometer was used to measure the surface topography from nanometer-scale roughness through millimeter-scale steps, with sub-nanometer resolution (Wyant and Greath, 1992). The average roughness of the channel bottom surface was measured and calculated according to Paul et al. (2003).
2.4. Procedure For a normal testing procedure, the pump was turned on and the electrical power to the heater was adjusted to a desired level by a variable voltage controller. The module was then allowed to reach a steady state, which was achieved within about 10 min from the moment the flow conditions were stabilised. At given test condition, video images and images of the temperature field on the heater were captured simultaneously. The flow pattern is visualized and recorded in the central part of the micro heat sink, which contains 10 micro-channels. Temperature and pressure drop variations with time are recorded simultaneously.
2.5. Data reduction The parameters used in the data reduction and analyses are summarized below. 2.6. Surface parameters To provide additional insights into the role of surface roughness on ONB in micro-channels roughness parameters were studied extensively. The roughness of the interior surface of the channels affects the flow parameters. The concept of roughness has statistical implications as it considers factors such as sample size and sampling interval. Widely used roughness parameters are: rms roughness, Thomas (1999).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z 1 L Rq ¼ yðxÞ2 dx L 0
ð1Þ
where L is the evaluation length; y(x) is the vertical distance from the mean line, height is assumed to be positive in the up direction, away from the bulk material; x is the distance along measurement or
Rq ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn 2 y i¼1 i n
ð2Þ
center-line average (CLA) roughness:
Ra ¼
1 L
Z
L
jyðxÞjdx
ð3Þ
0
or
Ra ¼
n 1X jy j n i¼1 i
ð4Þ
Surfface parameters may be characterized by maximum peak height Rp = max(yi), maximum valley depth Rv = min(yi), maximum height of the profile Rt = Rp Rv. 2.7. Heat flux
Fig. 3. Types of manifolds used for calculations.
To determine the heat flux from the heater to the working fluid, the heat losses due to conduction, convection and radiation were taken into account. There are several heat transfer surface areas that may be used in the calculations. The first is the plate area of the heat sink F = 1 1 cm2. The second, Fh, can be defined relative to mean heat flux along the heated perimeter. A comprehensive discussion on the application of these two definitions to evaluate
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
153
the mean heat flux is presented by Qu and Mudawar (2003). In the present study F = Fh, and the heat flux transferred to the fluid was defined as
uncertainty of 0.4 K in wall temperature is dominated by the error in the determination of TW,ONB.
q ¼ uIV=F h
3. Verification of the method
ð5Þ
where I and V are the input current and voltage, u is the ratio of the heat transferred to the working fluid to the local heat generation. For each set of experimental conditions an energy balance was performed, the average temperature of the heater and the average temperature of the cover were used to calculate the heat losses to ambient, and the value u was calculated. Mass flux: The mass flux, m, at the inlet to the test section was calculated as
m ¼ Q q=A
ð6Þ
where Q is the volumetric flow rate, q is the fluid density, and A is the overall cross-section of the micro-channels.Reynolds number: Re ¼ UDh =m, where m is the kinematic viscosity at the inlet water temperature, U is the mean flow velocity of the liquid phase, Dh the hydraulic diameter. Mass vapor quality at the outlet manifold was calculated from equation of change in the enthalpy of a liquid–vapor system during evaporation in the micro-channels. 2.8. Experimental uncertainty Errors depend on measurements of the following values: Dh – the hydraulic diameter of the channels, L – the length of the channels, pressure drop DP, wall temperature TW, saturation temperature TS. The error of the product Po = f Re is: d(fRe)/(fRe) = [(dDP/ DP)2 + (4dDh/Dh)2 + (dL/L)2 + (dm/m)2]0.5. It shows that the channel hydraulic diameter measurement introduces significant error into the uncertainty of the product Po = f Re. The error in determining the power, generated by Joule heating is due to errors of measurements of both electric current and electric voltage. The error in magnitude of the power transferred to the working fluid is due to uncertainties of the flow rate, specific heat of water, the difference between outlet and inlet temperatures Tout Tin. The error in the estimation of heat losses is due to correlations for calculation of natural convection and radiation heat transfer. The uncertainty of the measurements depends on the bias limit, which is an estimate of the magnitude of the constant error and on the precision limit, which is an estimate on the lack of repeatability caused by random errors. The uncertainty of components for an estimation of an error measurement was obtained according to the Guide to the Expression of Uncertainty of Measurement (1995). The uncertainties in determining various parameters in this study are given in Table 1. A careful analysis in the experimental uncertainty is critical to the interpretation of experimental data. As it will be showed below (Table 3), the average value of TW,ONB TS is in the range of 2.0–4.3 K. Table 1 shows that the Table 1 Experimental uncertainties (95% confidence level). N
Source of uncertainties
Symbol
Uncertainty
1. 2. 3. 4.
Hydraulic diameter Length of the test section Wall temperature Difference between wall and saturation temperatures Mass flow rate Pressure drop Heat flux Poiseuille number
Dh L TW TW - TS
1.0% 0.3% 0.4 K 0.6 K.
m DP q Po
1.0% 1.5% 4.4% 10.2%
5. 6. 7. 8.
3.1. Roughness measurements across the surface channels Measurements carried out along the channel at intervals approximately of 0.1 (mm) are shown in Fig. 4. As can be seen the surface is characterized by uniform cutting pattern all along the channel. WYKO has the software which controls the acquisition, analysis, storage and display of data collected and provides powerful measurement and analysis capabilities, including surface height statistics such as Rp, Rv, Rt, Rq, and Ra. The following data were deduced from the measurements: Rt = 148.95 lm, Rq = 8.72 lm and Ra = 4.01 lm. These parameters were used to calculate cannel cross-section, hydraulic diameter Dh and relative roughness ea = Ra/Dh and eq = Rq/Dh. The parameters are: Dh = 297 lm, ea = 1.1%, eq = 2.9%. 3.2. Pressure drop Fig. 5 shows the experimental data of Poiseuille number and values calculated from rectangular duct according to Shah and London (1978). The experimental results agree with analytical value within the data uncertainty. 3.3. Wall temperature It should be noted that small uncertainties in mass flux and heat flux can lead to relatively large uncertainties for the temperature at ONB point due to integral nature of the experiments. We used two methods to obtain parameters at ONB by maintaining the liquid flow rate constant: experiments that provide increase in wall temperature with increase in heat flux and experiments that provide behavior of pressure drop versus increasing heat flux. The experiments were repeated at least twice, to ensure reproducibility. The maximum temperature difference between average temperature at ONB obtained using two methods (pressure drop-heat flux and wall temperature-heat flux) was 0.7 K. 4. Results 4.1. Temperature on the heated wall Fig. 6 displays the average wall temperature versus the applied heat flux for both single-and two- phase flow. The experiments were conducted at various mass fluxes, which were calculated for the micro-channel array cros-section. For single-phase flow, at given values of mass flux, the temperature of the heater increased linearly with increasing heat flux. With the intention of obtaining the entire boiling curve, the power applied to the test module was increased by small increments, while the total fluid flow rate through the heat sink was maintained at a constant level. It can be seen that at cerain value of heat flux the slope of curves shown in Fig. 6 decreases. Such a phenomenon may be associated with the initiation of a two-phase boiling flow. The onset of nucleate boiling point can thus be specified as the point beyond which the gradients of two curves become noticeably different. 4.2. Flow instability Hetsroni et al. (2003, 2005, 2006) investigated a type of instability at low values of mass flux which took place in a heat sink which
154
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
Fig. 4. The roughness of the bottom channel.
contains a number of parallel micro-channels. Flow boiling in parallel channels was studied from the subcooled liquid entry at the inlet, to a liquid-vapor mixture flow at the outlet. Once the nucleation begins, the heat flux causes a sudden release of energy into the vapor bubble, which grows rapidly. Since the length of micro-channels is very small compared to conventional size channels, the rapid bubble grows pushes the liquid–vapor interface on both caps of the vapor slug at the upstream and dowmstream ends and leads to a reversed flow. When, in some parallel channels, the liquid on the upstream side is pushed back, the other parallel channels carry the resulting excess flow. The behavior of the long vapor
bubbles occuring in a microchannel is not similar to intermitted slugs of liquid between two long vapor trains. The periodic phenomenon described above leads to pressure and temperature fluctuations on the heated wall. Fig. 7 illustrates the temperature fluctuations and amplitude spectrum on the heated wall. Bubble formation in micro-channels may be responsible for such type of fluctuations. The frequency response of temperature measurements by infrared technique was analyzed by Hetsroni et al. (1996). The authors estimated that the maximal frequency xmax of the thermal process recorded by this method should not be over the value
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
xmax ¼ h=qcd
155
ð7Þ
where qcd are the density, thermal capacity and thickness of the heated substrate, h is the heat transfer coefficient. Estimation according to Eq. (7) for aluminum substrate of 0.5 mm thickness and heat transfer coefficient of 10,000 W/m2 K calculated for laminar single-phase flow shows that maximal frequency response is about 9 Hz. This value is about nine times as much as that measured in the present study shown in Fig. 7b. 4.3. Pressure drop
Fig. 5. The Poiseuille number.
Fig. 6. The dependence of the wall temperature on the heat flux.
The ONB phenomenon and associated with it instabilities can be analyzed based on the pressure drop-flow rate characteristics of heated channels. Fig. 8 shows a typical sequential images (from upper right corner to lower left corner) illustrating a bubble growing from inception to dimensions of about channel cross section. The appearance of vapor bubbles at observed central channels can be attributed to the the onset of nucleate boiling. Alternatively, the onset of nucleate boiling can be connected to the gradient of single-phase curve. When boiling occurs the pressure drop increases significantly with increasing heat flux. Typical characteristic curve is depicted in Fig. 9. The curve is obtained at different values of heat flux for a given constant value of mass flux. The onset of nucleate boiling point, ONB, on a characteristic curve can be specified as the point beyond which the gradients of the two curves (single-phase and two-phase) become noticeably different (Kennedy et al. 2000). The segment of the curve to the left of the ONB is stable. Pressure drop and temperature fluctuations can develop once the heat flux increases above the ONB point where the slope of the curve changes. Further increase in heat flux will lead to a sharp increase in the pressure drop. The liquid temperature variations in the experiments with heating are relatively large. They affect the liquid viscosity, thereby reducing the liquid single-phase friction factor and leading to smaller channel pressure drops. The
Fig. 7. The temperature fluctuations on the heated bottom wall, m = 46.3 kg/m2 s, q = 60 kW/m2. (a) Time variation and (b) amplitude spectrum.
156
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159 Table 2 Incipience of nucleation boiling in parallel micro-channels. Mass flux
U
Onset of nucleate boiling DT(ONB) (K)
St
(m/s)
Heat flux on the heater q 104 (W/m2)
€ (kg/m2 s) m 15.4 30.8 46.3 61.7 77.1
0.0155 0.030 0.045 0.060 0.077
2.4 3.7 6.0 7.5 9.5
2.0 2.5 3.5 3.9 4.3
19.6 16.0 17.0 16.0 16.0
by Bergles and Rohsenow (1964), Unal (1975), Kennedy et al. (2000), Table 3 Liu et al. (2005) as well as data obtained in the present study was performed. To estimate the value of the bulk liquid temperature at ONB, TB,ONB, the energy and continuity equations should be considered. In terms of mean mass temperature the thermal balance equation for rectangular channel with three heated walls shown in Fig. 10 is
qONB LONB ð2a þ bÞ
qU in C p ðT B;ONB T in Þab
¼1
ð8Þ
If the value of TB,ONB TS Eq. (8) takes the form
qONB LONB ð2a þ bÞ
qU in C p ðT S T in Þab
Fig. 8. Bubble growth from the time of onset of boiling nucleation m = 46.3 kg/m2 s, q = 60 kW/m2.
Fig. 9. The dependence of pressure drop on the temperature of the heated bottom wall. m = 46.3 kg/m2s.
average results on boiling incipience obtained from two methods described above are presented in Table 2. Table 3 lists the measured incipient heat flux for various fluid mass velocities. It indicates that incipient heat flux increases with increased fluid mass flux. The results are consistent with those reported by Qu and Mudawar (2002) and Liu et al. (2005) and with prediction by Yarin et al. (2008). 4.4. Fluid subcooling Due to the importance of accurately accounting for the influence of subcooling on ONB the analysis based on experimental data
¼1
ð9Þ
where a is the channel height, b is the channel width, Cp is the heat capacity of the liquid at constant pressure, LONB is the distance from the channel inlet to the cross section where ONB occurs, qONB is the heat flux at ONB, Tin, TB,ONB, TS, is the fluid temperature at the inlet, bulk temperature at the cross section where ONB occurs, and saturation temperature, respectively, TW,ONB is the wall temperature at ONB, Uin is the fluid velocity at the inlet, q is the fluid density. The bulk temperature TB,ONB is close to saturation temperature TS, when the value calculated using Eq. (9) does not differ significantly from unity. From the experimental results reported by Unal (1975), Kennedy et al. (2000), Liu et al. (2005) one may conclude that at ONB the parameter D ¼ T W T B =T S T in is of the order of 0.01. When the value D was in the range 0.1–0.2, as in experiments by Bergles and Rohsenow (1964), the onset of nucleate boiling occurred at values of bulk temperature, TB,ONB, significantly less than saturation temperature. Fig. 11 illustrates the dependence of fluid bulk temperature at ONB cross section on inlet flow temperature. The dark area corresponds to the region where the local fluid temperature T exceeds the saturation temperature TS. In this region, the maximum probability of the bubble embryo formation takes place. If the temperature TW,ONB does not differ significantly from saturation temperature, TS, a bubble nucleates in a low subcooled region, as observed here. Although the water temperature at the entry to the reservoir was 20 °C, the temperature at the inlet of micro-channels was significantly higher due to pressure fluctuations. Single-phase water flow in parallel channels is stable, since the flow rates and pressure drop levels are high enough. As heating is applied at low mass flow rates, and vapor is generated, the oscillatory motion of the liquid and vapor could be self-sustaining as long as certain heating conditions are maintained. The system departs from the stable operating conditions, and often transfers to flow regions where hydrodynamic instability becomes a possibility. The vapor jet moves not only downstream but also upstream, and the space that it occupied increases. In this case the temperature at the inlet of the micro-channels increases, Hetsroni et al. (2001).
157
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159 Table 3 Liquid subcooling at ONB point. Author and method of ONB detection
Heat flux qONB (MW/m2)
Inlet flow velocity Uin (m/s)
Pressure P (MPa)
Relative heated length LONB/d
Fluid subcooling DTsub ONB (K)
Unal (1975) High-speed photographic technique Bergles and Rohsenow (1964) The dependence of the wall excess temp. on the heat flux
0.38 0.45 9.774 9.774 6.67 5.67 2.145 2.145 1.5–4.0 1.5–3.0 1.5–3.0 1.5–3.0 1.5–3.0 1.5–3.0
2.121 2.121 19.2 19.2 9.54 9.54 3.74 3.74 1.0–4.0 1.3–2.6 3.5 1.3 2.0 4.3
13.9 15.8 0.261 0.261 0.261 0.261 0.261 0.261 1.034 1.034 0.69 0.69 0.344 0.344
1250 1250 29 48 29 48 29 48 137 110 137 110 137 110
4.3 4.1 108.3 66.6 103.3 50.0 92.2 56.6 5–12 13–19 4.0 4.0 5.0 5.0
Kennedy et al. (2000) The dependence of the pressure drop on the mass flux
4.5. The influence of surface roughness on boiling incipience We compared our results with macro-scale nucleation criterion of saturated boiling in terms of active nucleating cavity radius and wall excess temperature as reported in the literature. In the case where the upper limit of available cavity sizes was restricted to radius r max , the incipient boiling conditions according to Hino and Ueda (1985) are
qONB ¼
kL 2rkL T S DT ONB r max hLG qG ðr max Þ2
ð10Þ
Fig. 12 shows the nucleation criterion calculated for our experimental results using Eq. (10). According to (Collier and Thome, 1994) the bubble will nucleate from the cavity of critical size
Fig. 10. Rectangular channel with three heated walls.
rc;crit ¼
2rkL T S hLG qG qONB
0:5 ð11Þ
Calculation by Eq. (11) is also shown in Fig. 12. Comparison between the values of the surface roughness in the present study matches the theoretical effective cavity radius. Thus, the considerable agreement between experimental results and theory supports the idea that for subcooled boiling in micro-channels nucleation incipient conditions can be estimated by conventional theory. The experimental data obtained in the present study together with the main results appeared in the open literature in the last years are used in order to highlight incipient boiling conditions in conventional size and micro-channels. It is shown that the ONB in terms of heat flux, wall excess temperature, and the upper limit of available cavity does not depend on scaling effects. For this
Fig. 11. Dependence of fluid bulk temperature at ONB cross section on inlet flow temperature.
Fig. 12. The dependence of the radius of the activated cavity on the wall excess temperature.
158
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
reason, the trend to generate new correlations for the prediction of ONB in micro-channels does not stimulate any improvement of the knowledge of the physics of the problem. 4.6. Effect of inlet velocity on incipient boiling heat flux Variation of the boiling Stanton number, St ONB ¼ qONB = ½qL U in cp ðT S T in Þ, vs. the Reynolds number, based on inlet flow velocity and hydraulic diameter, is shown in Fig. 13. Fig. 13a illustrates the dependence of the boiling Stanton number at ONB point on the inlet flow velocity in the Reynolds number (Uin = 0.015– 0.072 m/s) obtained in the present study. Experiments carried out by Liu et al. (2005) at P = 1 bar, for different values of the inlet flow temperature that varied in the range Tin = 41.2–92.0 °C are shown in Fig. 13b. One can see that the value of the StONB does not change significantly with the Reynolds number in the discussed experiments. Analysis of the data shown in these figures makes it possible to illustrate the salient features of the dependence qONB on Uin. They may be approximated by the following lines (Fig. 14a): the solid line corresponds to the case of Tin TS the dotted line corresponds to the case of Tin TS. Experimental results reported by Liu et al. (2005), Fig. 14b, agree qualitatively with prediction shown in Fig. 14a. 5. Conclusions A study is reported here on the conditions under which bubble nucleation occurs in micro-channels with subcooled fluid flows at low mass flux. Also studied was the effect of the roughness of the bottom of the micro-channels. Two methods were employed to obtain the parameters at ONB while maintaining the liquid flow rate constant: experiments where an increase in the wall temperature due to an increase in the heat flux and experiments where the pressure drop increase while increasing the heat flux. The results were compared with those reported for conventional size channels.
Fig. 14. The variation of the incipient boiling heat flux with the inlet flow velocity: (a) analytical predictions and (b) experiments by Liu et al. (2005).
It was shown that reported in the literature significant disagreement between values of wall temperature and the average mass liquid temperature at ONB point is due to different experimental conditions. For the analysis of the conditions at which the ONB occurred the parameter D based on the relation of difference between wall excess temperature and bulk fluid temperature at ONB to difference between saturation temperature and fluid inlet temperature is developed When the value of D is of the order of 0.1 the onset of nucleate boiling occurs at values of the bulk temperature, TB,ONB, significantly lower than the saturation temperature. When D is of order 0.01, the onset of nucleate boiling occurs at values of the bulk temperature, TB,ONB, that are close to the saturation temperature. The experimental results indicate that parameters, which affect incipience of nucleation in micro-channels, such as cavity radius and wall excess temperature, are well predicted by the theoretical nucleation criteria, which were developed for conventional size channels. Acknowledgments This work was supported under Grant 890020 from the United States Israel Binational Science Foundation, which is gratefully acknowledged. The authors would also like to acknowledge very useful discussions with Professor A. Bar-Cohen, our partner to this investigation. References
Fig. 13. The variation of the boiling Stanton number, with the Reynolds number. (a) Present experiments and (b) experiments by Liu et al. (2005).
Bergles, A.E., Rohsenow, W.W., 1964. The determination of forced-convection surface-boiling heat transfer. Trans. ASME J. Heat Transfer 86, 365–372. Collier, J.G., Thome, J.R., 1994. Boiling and Condensation, third ed. Clarendon Press, Oxford, UK.
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159 Guide to the Expression of Uncertainty of Measurement, 1995. International Organization for Standartization, Geneva. Hapke, I., Boye, H., Schmidt, J., 2000. Onset of nucleate boiling in micro-channels. Int. J. Therm. Sci. 39, 505–513. Hetsroni, G., Rozenblit, R., Yarin, L.P., 1996. A hot-foil infrared technique for studying the temperature field of a wall. Meas. Sci. Technol. 7, 1418– 1427. Hetsroni, G., Mosyak, A., Segal, Z., 2001. Nonuniform temperature distribution in electronic devices cooled by flow in parallel micro-channels. IEEE Trans. Compon. Packag. Technol. 24 (1), 16–23. Hetsroni, G., Mosyak, A., Segal, Z., Pogrebnyak, E., 2003. Two-phase flow pattern in parallel micro-channels. Int. J. Multiphase Flow 29, 344–360. Hetsroni, G., Mosyak, A., Pogrebnyak, E., Segal, Z., 2005. Explosive boiling of water in parallel micro-channels. Int. J. Multiphase Flow 31, 371–392. Hetsroni, G., Mosyak, A., Pogrebnyak, E., Segal, S., 2006. Periodic boiling in parallel micro-channels at low vapor quality. Int. J. Multiphase Flow 32, 1141–1159. Hino, R., Ueda, T., 1985. Studies on heat transfer and flow characteristics in subcooled flow boiling – Part I. Int. J. Multiphase Flow 11, 269–281. Kennedy, J.E., Roach, G.M., Dowling, M.E., Abdel-Khalik, S.I., Chiaasiaan, S.M., Jeter, S.M., Quershi, Z.H., 2000. The onset of flow instability in uniformly heated horizontal micro-channels. Trans. ASME J. Heat Transfer 122, 118–125. Lee, P.S., Tseng, F.G., Pan, C., 2004. Bubble dynamics in micro-channels. Part I: Single micro-channel. Int. J. Heat Mass Transfer 47, 5575–5589. Lee, J.Y., Kim, M.H., Kaviany, M., Son, S.Y., 2011. Bubble nucleation in micro-channel flow boiling using single artificial cavity. Int. J. Heat Mass Transfer 54, 5139– 5148.
159
Liu, D., Lee, P.S., Garimella, S.V., 2005. Prediction of the onset of nucleate boiling in microchannel flow. Int. J. Heat Mass Transfer 48, 5134–5149. Mishan, Y., Mosyak, A., Pogrebnyak, E., Hetsroni, G., 2007. Effect of developing flow and thermal regime on momentum and heat transfer in micro-channel heat sink. Int. J. Heat Mass Transfer 50, 3100–3114. Paul, D.E., Black, J.T., Kohser, R.A., 2003. Materials and Processes in Manufacturing, ninth ed. Wiley, SL, ISBN:0-471-65653-4. Peng, X.F., Wang, B.X., 1993. Forced convection and flow boiling heat transfer for liquid flowing through micro-channels. Int. J. Heat Mass Transfer 36, 3421– 3427. Qu, W., Mudawar, I., 2002. Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. Int. J. Heat Mass Transfer 45, 3933–3945. Qu, W., Mudawar, I., 2003. Flow boiling heat transfer in two-phase micro-channel heat sinks – 1. Experimental investigation and assessment of correlation methods. Int. J. Heat Mass Transfer 46, 2755–2771. Sato, T., Matsumura, H., 1964. On the conditions of incipient subcooled-boiling with forced convection. Bull. Jpn. Soc. Mech. Eng. 7, 392–398. Shah, R.K., London, A.L., 1978. Laminar Flow Forced Convection in Ducts. Academic Press, New York, SV. Thomas, T.R., 1999. Rough Surfaces, second ed. Imperial College Press, London. Unal, H.C., 1975. Determination of the initial point of net vapor generation in flow boiling system. Int. J. Heat Mass Transfer 18, 1095–1099. Wyant, J.C., Greath, K., 1992. Advances in interferometric optical profiling. Int. J. Mach. Tools Manufact. 32, 5–10, Printed in Great Britain. Yarin, L.P., Mosyak, A., Hetsroni, G., 2008. Fluid Flow, Heat Transfer and Boiling in Micro-channels. Springer.
Contents lists available at SciVerse ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Boiling incipience in parallel micro-channels with low mass flux subcooled water flow A. Mosyak, L. Rodes, G. Hetsroni ⇑ Department of Mechanical Engineering, Technion – Israel Institute of Technology, 32000 Haifa, Israel
a r t i c l e
i n f o
Article history: Received 17 April 2012 Received in revised form 12 July 2012 Accepted 13 July 2012 Available online 26 July 2012 Keywords: Micro-channel Subcooled boiling incipience Bubble dynamics Roughness
a b s t r a c t Here we present an investigation of boiling incipience in parallel micro-channels and compare the results with those reported for conventional channels. To provide additional insights into the role of surface roughness on the onset of nucleate boiling (ONB) in micro-channels, the roughness parameters were studied extensively. Onset of nucleate boiling is investigated in uniformly heated parallel rectangular micro-channels of Dh = 297 lm with subcooled water flow at mass flux of 15.4–77.1 kg/m2s. It is shown that in the literature significant disagreement between values of wall temperature and the average mass liquid temperature at ONB point is due to different experimental conditions. For the analysis of the conditions at which the ONB occurred, the parameter based on the relation of the difference between wall excess temperature and bulk fluid temperature at ONB to the difference between saturation temperature and fluid inlet temperature is developed. The experimental results indicate that parameters, which affect incipience of nucleation in micro-channels, such as cavity radius and wall excess temperature, are well predicted by the theoretical nucleation criteria, which were developed for conventional size channels. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Systems which provide liquid or two-phase flow through parallel channels of hydraulic diameter less than about 0.5 mm can be considered as micro-channels heat sinks. These systems are very well suited for cooling of devices where high heat flux is dissipated from a small surface area. Phase-change processes, particularly flow boiling, are important in the micro-scale and significant amount of research is performed in this area. The extend to which incoming liquid will be vaporized in the micro-channels, is a design parameter which depends on the intended application. In micro-scale refrigeration systems, the change in vapor quality may be substantial, e.g. of the order of 0.0–0.8. In electronic cooling applications, the equilibrium vapor quality may remain at zero or be very small to capture the high heat transfer coefficients of subcooled flow boiling without the need to incorporate a condenser. The onset of bubble nucleation usually requires that the temperature on the heated surface exceed the saturation temperature of the liquid corresponding to the prevailing pressure. However, there is significant disagreement between experimental results for conventional size channels due to different experimental conditions. For example, the wall has to be at relatively high excess temperature to initiate the nucleate boiling e.g. in the experiments by
⇑ Corresponding author. Tel.: +972 48 292058; fax: +972 48 238101. E-mail address: [email protected] (G. Hetsroni). 0301-9322/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.07.006
Hapke et al. (2000) compared to those reported by Sato and Matsumura (1964) and by Bergles and Rohsenow (1964). Only few experimental studies have considered the ONB in micro-channels. Qu and Mudawar (2002) performed experiments to measure the incipient boiling heat flux qONB in a heat sink containing 21 rectangular micro-channels 231 lm wide and 713 lm deep. It was shown that wall excess temperature (i.e. the temperature above the saturation temperature) is directly proportional to the heat flux. The onset of nucleate boiling in the flow of water through a micro-channel heat sink was investigated by Liu et al. (2005). Twentyfive micro-channels of 275 lm in width and 636 lm in height were cut into the top surface of the copper block. To complement the incipient heat flux results identified from the visualization approach, the micro-channel wall temperatures and pressure drop along the micro-channels were analyzed. The common results were obtained from temperature and pressure drop measurements. However, the roughness of the heated surface was not measured. The work by Lee et al. (2004) explored experimentally bubble dynamics in a single trapezoid micro-channel with a hydraulic diameter of 41.3 lm. Bubble nucleation, growth, departure size and frequency were observed using a high-speed camera. Their results may be predicted from the classical model with micro-sized cavities suggested by Hino and Ueda (1985) for subcooled boiling in conventional channels. Bubble nucleation in micro-channel flow boiling, using single artificial cavity with radius of 12.5–16.4 lm, was studied by Lee et al. (2011). Onset of nucleate boiling, bubble growth behavior
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
and flow boiling pattern were observed however, the heat flux was not specified. There is discrepancy between measured superheat required for onset of nucleation boiling in micro-channels reported by different investigators. For example, the flow boiling characteristics of subcooled water flowing through micro-channels with rectangular cross-section of 0.6 0.7 mm were experimentally investigated by Peng and Wang (1993). When the wall temperature was higher than the saturation temperature no bubbles were observed in micro-channels. The authors concluded that there is a ‘‘critical scale for liquid bulk to determine whether bubbles can grow in liquid’’. On the other hand, Lee et al. (2004) conducted experiments in a single trapezoid micro-channel with Dh = 41.3 lm. The bubble nucleation of this study may be predicted by a classical model for conventional size channels. To the best of our knowledge, experimental results of the fluid bulk temperature at ONB point under condition of subcooled boiling in micro-channels are not reported. It is difficult to measure liquid temperature around the bubble, which occurs when the wall temperature exceeds the saturation temperature by a certain amount. Systematic experiments addressing the onset of nucleate boiling, flow instability, and other related subcooled boiling phenomena in micro-channels are thus needed. The main purpose of the preset study is to highlight the phenomenon of boiling incipience in micro-channels and to compare it with conventional size channels. To estimate the value of the bulk liquid temperature at ONB the parameter taking into account the difference between saturation and inlet fluid temperature was developed.
2. Experimental facility and procedure 2.1. Experimental setup A scheme of the experimental apparatus is shown in Fig. 1. Filtered deionized water at a temperature of 20 °C was used as the working fluid. It was pumped from the entrance tank by a peristaltic pump through the inlet calming chamber, inlet manifold to the micro-channels in the test module, and from the microchannels through the outlet manifold, outlet calming chamber to the exit tank. The mass flow rate of the water was measured by a weighing method.
Fig. 1. Experimental facility.
151
2.2. Test module The test module, Fig 2, was fabricated of 14 mm 20 mm and 1.25 mm thick aluminum plate and placed into the heat sink housing. Twenty five micro-channels were machined on one side of this plate using a precision sawing technique. The micro-channels were of 200 lm wide, 580 lm deep and wall thickness of 200 lm. The lower part of heat sink housing was made from PEEK plate in order to decrease the heat loses to the environment and keep the inlet/ outlet manifolds temperature at constant values. The upper part, made of PEEK, was attached to the lower part by screws and served as a cover, which was used also for pressure drop measurements. During experiments of flow visualization this cover was replaced by a transparent one. The aluminum chip module combines precise mechanical sawing on one side and electric chromium evaporated resistor on the other, which are in common use to manufacture micro-electronic devices. The electrical insulation was an AlOx interlayer 35 lm thick, thermal conductivity of 10.2 W/mK, made by anodization process. The heater filament was made of pure chromium Cr 99.9% with resistivity of 13.2 lX cm (20 °C), thickness of 1720 A°, width of 1.257 mm, and length of 82 mm. To study the effect of axial heat flux due to conduction in the aluminum, calculations using CFD software were conducted by Mishan et al. (2007). At uniform heat flux of q = 4.4 W/cm2 and mass flux m = 8.33 kg/m2 s, numerical and experimental results agreed quite well: the difference between calculated and the measured maximum temperature on the heater was 0.1 K. Heat flux was controlled by a power supply. Several studies showed that the manifolds design played an important role in the liquid distribution between the parallel micro-channels, which can lead to span-wise temperature gradients on the device surface, increase thermal stresses and reduce the reliability. To optimize the design of the manifold configurations, a number of numerical calculations were conducted previously by Mishan et al. (2007). The calculations were carried out for three types of manifolds shown in Fig. 3. It was shown that the configuration of the manifold 1 ensures uniform velocity distribution at the entrance to the micro-channels. 2.3. Measurement apparatus The vapor–liquid pattern in the micro-channels was studied using a microscope and high-speed video camera. A microscope was connected to an external lighting arrangement. An additional camera joint was assembled to connect a high-speed camera to the microscope. The high-speed camera with maximum frame rate of 10,000 fps, was used to visualize the two-phase flow regimes in micro-channels. The way it works is by capturing video at high frame rate, which when it is played back at low speed, looks like it has been recorded in slow motion. The playback speed of the high- speed camera can be varied from a single frame to 1000 fps. A thermal high-speed imaging radiometer was utilized to study the temperature field on the electrical heater and the working fluid temperature distribution along the micro-channels. The IR camera is suitable for temperature measurements in the wavelength range of about 5 lm, it has a sensitivity of 0.1 K and a typical resolution of 256 pixels per line. The measurement resolution was of 0.03 mm. Using the radiometer one can obtain a quantitative thermal field in the line mode, an average temperature in the area mode, and a temperature of a given point in the point mode. The fluid temperature was measured at the entrance and exit of the test module by 0.3 mm type-T thermocouples. The heater was coated with a thin layer of black diffusive paint, with emissivity of 0.95. For pressure, drop measurements the holes, 0.6 mm in diameter, were connected to pressure transducers by needles. The pressure drop was measured directly at the central part of
152
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
Fig. 2. Experimental setup. (a) Test module, (b) pressure measurement, and (c) flow and thermal visualization.
the micro-channels (not in the manifolds). Such a method makes it possible to avoid pressure drop losses associated with contraction and expansion at the micro-channels inlet and outlet. WYKO NT 1100 series optical profilometer was used to measure the surface topography from nanometer-scale roughness through millimeter-scale steps, with sub-nanometer resolution (Wyant and Greath, 1992). The average roughness of the channel bottom surface was measured and calculated according to Paul et al. (2003).
2.4. Procedure For a normal testing procedure, the pump was turned on and the electrical power to the heater was adjusted to a desired level by a variable voltage controller. The module was then allowed to reach a steady state, which was achieved within about 10 min from the moment the flow conditions were stabilised. At given test condition, video images and images of the temperature field on the heater were captured simultaneously. The flow pattern is visualized and recorded in the central part of the micro heat sink, which contains 10 micro-channels. Temperature and pressure drop variations with time are recorded simultaneously.
2.5. Data reduction The parameters used in the data reduction and analyses are summarized below. 2.6. Surface parameters To provide additional insights into the role of surface roughness on ONB in micro-channels roughness parameters were studied extensively. The roughness of the interior surface of the channels affects the flow parameters. The concept of roughness has statistical implications as it considers factors such as sample size and sampling interval. Widely used roughness parameters are: rms roughness, Thomas (1999).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z 1 L Rq ¼ yðxÞ2 dx L 0
ð1Þ
where L is the evaluation length; y(x) is the vertical distance from the mean line, height is assumed to be positive in the up direction, away from the bulk material; x is the distance along measurement or
Rq ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn 2 y i¼1 i n
ð2Þ
center-line average (CLA) roughness:
Ra ¼
1 L
Z
L
jyðxÞjdx
ð3Þ
0
or
Ra ¼
n 1X jy j n i¼1 i
ð4Þ
Surfface parameters may be characterized by maximum peak height Rp = max(yi), maximum valley depth Rv = min(yi), maximum height of the profile Rt = Rp Rv. 2.7. Heat flux
Fig. 3. Types of manifolds used for calculations.
To determine the heat flux from the heater to the working fluid, the heat losses due to conduction, convection and radiation were taken into account. There are several heat transfer surface areas that may be used in the calculations. The first is the plate area of the heat sink F = 1 1 cm2. The second, Fh, can be defined relative to mean heat flux along the heated perimeter. A comprehensive discussion on the application of these two definitions to evaluate
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
153
the mean heat flux is presented by Qu and Mudawar (2003). In the present study F = Fh, and the heat flux transferred to the fluid was defined as
uncertainty of 0.4 K in wall temperature is dominated by the error in the determination of TW,ONB.
q ¼ uIV=F h
3. Verification of the method
ð5Þ
where I and V are the input current and voltage, u is the ratio of the heat transferred to the working fluid to the local heat generation. For each set of experimental conditions an energy balance was performed, the average temperature of the heater and the average temperature of the cover were used to calculate the heat losses to ambient, and the value u was calculated. Mass flux: The mass flux, m, at the inlet to the test section was calculated as
m ¼ Q q=A
ð6Þ
where Q is the volumetric flow rate, q is the fluid density, and A is the overall cross-section of the micro-channels.Reynolds number: Re ¼ UDh =m, where m is the kinematic viscosity at the inlet water temperature, U is the mean flow velocity of the liquid phase, Dh the hydraulic diameter. Mass vapor quality at the outlet manifold was calculated from equation of change in the enthalpy of a liquid–vapor system during evaporation in the micro-channels. 2.8. Experimental uncertainty Errors depend on measurements of the following values: Dh – the hydraulic diameter of the channels, L – the length of the channels, pressure drop DP, wall temperature TW, saturation temperature TS. The error of the product Po = f Re is: d(fRe)/(fRe) = [(dDP/ DP)2 + (4dDh/Dh)2 + (dL/L)2 + (dm/m)2]0.5. It shows that the channel hydraulic diameter measurement introduces significant error into the uncertainty of the product Po = f Re. The error in determining the power, generated by Joule heating is due to errors of measurements of both electric current and electric voltage. The error in magnitude of the power transferred to the working fluid is due to uncertainties of the flow rate, specific heat of water, the difference between outlet and inlet temperatures Tout Tin. The error in the estimation of heat losses is due to correlations for calculation of natural convection and radiation heat transfer. The uncertainty of the measurements depends on the bias limit, which is an estimate of the magnitude of the constant error and on the precision limit, which is an estimate on the lack of repeatability caused by random errors. The uncertainty of components for an estimation of an error measurement was obtained according to the Guide to the Expression of Uncertainty of Measurement (1995). The uncertainties in determining various parameters in this study are given in Table 1. A careful analysis in the experimental uncertainty is critical to the interpretation of experimental data. As it will be showed below (Table 3), the average value of TW,ONB TS is in the range of 2.0–4.3 K. Table 1 shows that the Table 1 Experimental uncertainties (95% confidence level). N
Source of uncertainties
Symbol
Uncertainty
1. 2. 3. 4.
Hydraulic diameter Length of the test section Wall temperature Difference between wall and saturation temperatures Mass flow rate Pressure drop Heat flux Poiseuille number
Dh L TW TW - TS
1.0% 0.3% 0.4 K 0.6 K.
m DP q Po
1.0% 1.5% 4.4% 10.2%
5. 6. 7. 8.
3.1. Roughness measurements across the surface channels Measurements carried out along the channel at intervals approximately of 0.1 (mm) are shown in Fig. 4. As can be seen the surface is characterized by uniform cutting pattern all along the channel. WYKO has the software which controls the acquisition, analysis, storage and display of data collected and provides powerful measurement and analysis capabilities, including surface height statistics such as Rp, Rv, Rt, Rq, and Ra. The following data were deduced from the measurements: Rt = 148.95 lm, Rq = 8.72 lm and Ra = 4.01 lm. These parameters were used to calculate cannel cross-section, hydraulic diameter Dh and relative roughness ea = Ra/Dh and eq = Rq/Dh. The parameters are: Dh = 297 lm, ea = 1.1%, eq = 2.9%. 3.2. Pressure drop Fig. 5 shows the experimental data of Poiseuille number and values calculated from rectangular duct according to Shah and London (1978). The experimental results agree with analytical value within the data uncertainty. 3.3. Wall temperature It should be noted that small uncertainties in mass flux and heat flux can lead to relatively large uncertainties for the temperature at ONB point due to integral nature of the experiments. We used two methods to obtain parameters at ONB by maintaining the liquid flow rate constant: experiments that provide increase in wall temperature with increase in heat flux and experiments that provide behavior of pressure drop versus increasing heat flux. The experiments were repeated at least twice, to ensure reproducibility. The maximum temperature difference between average temperature at ONB obtained using two methods (pressure drop-heat flux and wall temperature-heat flux) was 0.7 K. 4. Results 4.1. Temperature on the heated wall Fig. 6 displays the average wall temperature versus the applied heat flux for both single-and two- phase flow. The experiments were conducted at various mass fluxes, which were calculated for the micro-channel array cros-section. For single-phase flow, at given values of mass flux, the temperature of the heater increased linearly with increasing heat flux. With the intention of obtaining the entire boiling curve, the power applied to the test module was increased by small increments, while the total fluid flow rate through the heat sink was maintained at a constant level. It can be seen that at cerain value of heat flux the slope of curves shown in Fig. 6 decreases. Such a phenomenon may be associated with the initiation of a two-phase boiling flow. The onset of nucleate boiling point can thus be specified as the point beyond which the gradients of two curves become noticeably different. 4.2. Flow instability Hetsroni et al. (2003, 2005, 2006) investigated a type of instability at low values of mass flux which took place in a heat sink which
154
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
Fig. 4. The roughness of the bottom channel.
contains a number of parallel micro-channels. Flow boiling in parallel channels was studied from the subcooled liquid entry at the inlet, to a liquid-vapor mixture flow at the outlet. Once the nucleation begins, the heat flux causes a sudden release of energy into the vapor bubble, which grows rapidly. Since the length of micro-channels is very small compared to conventional size channels, the rapid bubble grows pushes the liquid–vapor interface on both caps of the vapor slug at the upstream and dowmstream ends and leads to a reversed flow. When, in some parallel channels, the liquid on the upstream side is pushed back, the other parallel channels carry the resulting excess flow. The behavior of the long vapor
bubbles occuring in a microchannel is not similar to intermitted slugs of liquid between two long vapor trains. The periodic phenomenon described above leads to pressure and temperature fluctuations on the heated wall. Fig. 7 illustrates the temperature fluctuations and amplitude spectrum on the heated wall. Bubble formation in micro-channels may be responsible for such type of fluctuations. The frequency response of temperature measurements by infrared technique was analyzed by Hetsroni et al. (1996). The authors estimated that the maximal frequency xmax of the thermal process recorded by this method should not be over the value
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
xmax ¼ h=qcd
155
ð7Þ
where qcd are the density, thermal capacity and thickness of the heated substrate, h is the heat transfer coefficient. Estimation according to Eq. (7) for aluminum substrate of 0.5 mm thickness and heat transfer coefficient of 10,000 W/m2 K calculated for laminar single-phase flow shows that maximal frequency response is about 9 Hz. This value is about nine times as much as that measured in the present study shown in Fig. 7b. 4.3. Pressure drop
Fig. 5. The Poiseuille number.
Fig. 6. The dependence of the wall temperature on the heat flux.
The ONB phenomenon and associated with it instabilities can be analyzed based on the pressure drop-flow rate characteristics of heated channels. Fig. 8 shows a typical sequential images (from upper right corner to lower left corner) illustrating a bubble growing from inception to dimensions of about channel cross section. The appearance of vapor bubbles at observed central channels can be attributed to the the onset of nucleate boiling. Alternatively, the onset of nucleate boiling can be connected to the gradient of single-phase curve. When boiling occurs the pressure drop increases significantly with increasing heat flux. Typical characteristic curve is depicted in Fig. 9. The curve is obtained at different values of heat flux for a given constant value of mass flux. The onset of nucleate boiling point, ONB, on a characteristic curve can be specified as the point beyond which the gradients of the two curves (single-phase and two-phase) become noticeably different (Kennedy et al. 2000). The segment of the curve to the left of the ONB is stable. Pressure drop and temperature fluctuations can develop once the heat flux increases above the ONB point where the slope of the curve changes. Further increase in heat flux will lead to a sharp increase in the pressure drop. The liquid temperature variations in the experiments with heating are relatively large. They affect the liquid viscosity, thereby reducing the liquid single-phase friction factor and leading to smaller channel pressure drops. The
Fig. 7. The temperature fluctuations on the heated bottom wall, m = 46.3 kg/m2 s, q = 60 kW/m2. (a) Time variation and (b) amplitude spectrum.
156
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159 Table 2 Incipience of nucleation boiling in parallel micro-channels. Mass flux
U
Onset of nucleate boiling DT(ONB) (K)
St
(m/s)
Heat flux on the heater q 104 (W/m2)
€ (kg/m2 s) m 15.4 30.8 46.3 61.7 77.1
0.0155 0.030 0.045 0.060 0.077
2.4 3.7 6.0 7.5 9.5
2.0 2.5 3.5 3.9 4.3
19.6 16.0 17.0 16.0 16.0
by Bergles and Rohsenow (1964), Unal (1975), Kennedy et al. (2000), Table 3 Liu et al. (2005) as well as data obtained in the present study was performed. To estimate the value of the bulk liquid temperature at ONB, TB,ONB, the energy and continuity equations should be considered. In terms of mean mass temperature the thermal balance equation for rectangular channel with three heated walls shown in Fig. 10 is
qONB LONB ð2a þ bÞ
qU in C p ðT B;ONB T in Þab
¼1
ð8Þ
If the value of TB,ONB TS Eq. (8) takes the form
qONB LONB ð2a þ bÞ
qU in C p ðT S T in Þab
Fig. 8. Bubble growth from the time of onset of boiling nucleation m = 46.3 kg/m2 s, q = 60 kW/m2.
Fig. 9. The dependence of pressure drop on the temperature of the heated bottom wall. m = 46.3 kg/m2s.
average results on boiling incipience obtained from two methods described above are presented in Table 2. Table 3 lists the measured incipient heat flux for various fluid mass velocities. It indicates that incipient heat flux increases with increased fluid mass flux. The results are consistent with those reported by Qu and Mudawar (2002) and Liu et al. (2005) and with prediction by Yarin et al. (2008). 4.4. Fluid subcooling Due to the importance of accurately accounting for the influence of subcooling on ONB the analysis based on experimental data
¼1
ð9Þ
where a is the channel height, b is the channel width, Cp is the heat capacity of the liquid at constant pressure, LONB is the distance from the channel inlet to the cross section where ONB occurs, qONB is the heat flux at ONB, Tin, TB,ONB, TS, is the fluid temperature at the inlet, bulk temperature at the cross section where ONB occurs, and saturation temperature, respectively, TW,ONB is the wall temperature at ONB, Uin is the fluid velocity at the inlet, q is the fluid density. The bulk temperature TB,ONB is close to saturation temperature TS, when the value calculated using Eq. (9) does not differ significantly from unity. From the experimental results reported by Unal (1975), Kennedy et al. (2000), Liu et al. (2005) one may conclude that at ONB the parameter D ¼ T W T B =T S T in is of the order of 0.01. When the value D was in the range 0.1–0.2, as in experiments by Bergles and Rohsenow (1964), the onset of nucleate boiling occurred at values of bulk temperature, TB,ONB, significantly less than saturation temperature. Fig. 11 illustrates the dependence of fluid bulk temperature at ONB cross section on inlet flow temperature. The dark area corresponds to the region where the local fluid temperature T exceeds the saturation temperature TS. In this region, the maximum probability of the bubble embryo formation takes place. If the temperature TW,ONB does not differ significantly from saturation temperature, TS, a bubble nucleates in a low subcooled region, as observed here. Although the water temperature at the entry to the reservoir was 20 °C, the temperature at the inlet of micro-channels was significantly higher due to pressure fluctuations. Single-phase water flow in parallel channels is stable, since the flow rates and pressure drop levels are high enough. As heating is applied at low mass flow rates, and vapor is generated, the oscillatory motion of the liquid and vapor could be self-sustaining as long as certain heating conditions are maintained. The system departs from the stable operating conditions, and often transfers to flow regions where hydrodynamic instability becomes a possibility. The vapor jet moves not only downstream but also upstream, and the space that it occupied increases. In this case the temperature at the inlet of the micro-channels increases, Hetsroni et al. (2001).
157
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159 Table 3 Liquid subcooling at ONB point. Author and method of ONB detection
Heat flux qONB (MW/m2)
Inlet flow velocity Uin (m/s)
Pressure P (MPa)
Relative heated length LONB/d
Fluid subcooling DTsub ONB (K)
Unal (1975) High-speed photographic technique Bergles and Rohsenow (1964) The dependence of the wall excess temp. on the heat flux
0.38 0.45 9.774 9.774 6.67 5.67 2.145 2.145 1.5–4.0 1.5–3.0 1.5–3.0 1.5–3.0 1.5–3.0 1.5–3.0
2.121 2.121 19.2 19.2 9.54 9.54 3.74 3.74 1.0–4.0 1.3–2.6 3.5 1.3 2.0 4.3
13.9 15.8 0.261 0.261 0.261 0.261 0.261 0.261 1.034 1.034 0.69 0.69 0.344 0.344
1250 1250 29 48 29 48 29 48 137 110 137 110 137 110
4.3 4.1 108.3 66.6 103.3 50.0 92.2 56.6 5–12 13–19 4.0 4.0 5.0 5.0
Kennedy et al. (2000) The dependence of the pressure drop on the mass flux
4.5. The influence of surface roughness on boiling incipience We compared our results with macro-scale nucleation criterion of saturated boiling in terms of active nucleating cavity radius and wall excess temperature as reported in the literature. In the case where the upper limit of available cavity sizes was restricted to radius r max , the incipient boiling conditions according to Hino and Ueda (1985) are
qONB ¼
kL 2rkL T S DT ONB r max hLG qG ðr max Þ2
ð10Þ
Fig. 12 shows the nucleation criterion calculated for our experimental results using Eq. (10). According to (Collier and Thome, 1994) the bubble will nucleate from the cavity of critical size
Fig. 10. Rectangular channel with three heated walls.
rc;crit ¼
2rkL T S hLG qG qONB
0:5 ð11Þ
Calculation by Eq. (11) is also shown in Fig. 12. Comparison between the values of the surface roughness in the present study matches the theoretical effective cavity radius. Thus, the considerable agreement between experimental results and theory supports the idea that for subcooled boiling in micro-channels nucleation incipient conditions can be estimated by conventional theory. The experimental data obtained in the present study together with the main results appeared in the open literature in the last years are used in order to highlight incipient boiling conditions in conventional size and micro-channels. It is shown that the ONB in terms of heat flux, wall excess temperature, and the upper limit of available cavity does not depend on scaling effects. For this
Fig. 11. Dependence of fluid bulk temperature at ONB cross section on inlet flow temperature.
Fig. 12. The dependence of the radius of the activated cavity on the wall excess temperature.
158
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159
reason, the trend to generate new correlations for the prediction of ONB in micro-channels does not stimulate any improvement of the knowledge of the physics of the problem. 4.6. Effect of inlet velocity on incipient boiling heat flux Variation of the boiling Stanton number, St ONB ¼ qONB = ½qL U in cp ðT S T in Þ, vs. the Reynolds number, based on inlet flow velocity and hydraulic diameter, is shown in Fig. 13. Fig. 13a illustrates the dependence of the boiling Stanton number at ONB point on the inlet flow velocity in the Reynolds number (Uin = 0.015– 0.072 m/s) obtained in the present study. Experiments carried out by Liu et al. (2005) at P = 1 bar, for different values of the inlet flow temperature that varied in the range Tin = 41.2–92.0 °C are shown in Fig. 13b. One can see that the value of the StONB does not change significantly with the Reynolds number in the discussed experiments. Analysis of the data shown in these figures makes it possible to illustrate the salient features of the dependence qONB on Uin. They may be approximated by the following lines (Fig. 14a): the solid line corresponds to the case of Tin TS the dotted line corresponds to the case of Tin TS. Experimental results reported by Liu et al. (2005), Fig. 14b, agree qualitatively with prediction shown in Fig. 14a. 5. Conclusions A study is reported here on the conditions under which bubble nucleation occurs in micro-channels with subcooled fluid flows at low mass flux. Also studied was the effect of the roughness of the bottom of the micro-channels. Two methods were employed to obtain the parameters at ONB while maintaining the liquid flow rate constant: experiments where an increase in the wall temperature due to an increase in the heat flux and experiments where the pressure drop increase while increasing the heat flux. The results were compared with those reported for conventional size channels.
Fig. 14. The variation of the incipient boiling heat flux with the inlet flow velocity: (a) analytical predictions and (b) experiments by Liu et al. (2005).
It was shown that reported in the literature significant disagreement between values of wall temperature and the average mass liquid temperature at ONB point is due to different experimental conditions. For the analysis of the conditions at which the ONB occurred the parameter D based on the relation of difference between wall excess temperature and bulk fluid temperature at ONB to difference between saturation temperature and fluid inlet temperature is developed When the value of D is of the order of 0.1 the onset of nucleate boiling occurs at values of the bulk temperature, TB,ONB, significantly lower than the saturation temperature. When D is of order 0.01, the onset of nucleate boiling occurs at values of the bulk temperature, TB,ONB, that are close to the saturation temperature. The experimental results indicate that parameters, which affect incipience of nucleation in micro-channels, such as cavity radius and wall excess temperature, are well predicted by the theoretical nucleation criteria, which were developed for conventional size channels. Acknowledgments This work was supported under Grant 890020 from the United States Israel Binational Science Foundation, which is gratefully acknowledged. The authors would also like to acknowledge very useful discussions with Professor A. Bar-Cohen, our partner to this investigation. References
Fig. 13. The variation of the boiling Stanton number, with the Reynolds number. (a) Present experiments and (b) experiments by Liu et al. (2005).
Bergles, A.E., Rohsenow, W.W., 1964. The determination of forced-convection surface-boiling heat transfer. Trans. ASME J. Heat Transfer 86, 365–372. Collier, J.G., Thome, J.R., 1994. Boiling and Condensation, third ed. Clarendon Press, Oxford, UK.
A. Mosyak et al. / International Journal of Multiphase Flow 47 (2012) 150–159 Guide to the Expression of Uncertainty of Measurement, 1995. International Organization for Standartization, Geneva. Hapke, I., Boye, H., Schmidt, J., 2000. Onset of nucleate boiling in micro-channels. Int. J. Therm. Sci. 39, 505–513. Hetsroni, G., Rozenblit, R., Yarin, L.P., 1996. A hot-foil infrared technique for studying the temperature field of a wall. Meas. Sci. Technol. 7, 1418– 1427. Hetsroni, G., Mosyak, A., Segal, Z., 2001. Nonuniform temperature distribution in electronic devices cooled by flow in parallel micro-channels. IEEE Trans. Compon. Packag. Technol. 24 (1), 16–23. Hetsroni, G., Mosyak, A., Segal, Z., Pogrebnyak, E., 2003. Two-phase flow pattern in parallel micro-channels. Int. J. Multiphase Flow 29, 344–360. Hetsroni, G., Mosyak, A., Pogrebnyak, E., Segal, Z., 2005. Explosive boiling of water in parallel micro-channels. Int. J. Multiphase Flow 31, 371–392. Hetsroni, G., Mosyak, A., Pogrebnyak, E., Segal, S., 2006. Periodic boiling in parallel micro-channels at low vapor quality. Int. J. Multiphase Flow 32, 1141–1159. Hino, R., Ueda, T., 1985. Studies on heat transfer and flow characteristics in subcooled flow boiling – Part I. Int. J. Multiphase Flow 11, 269–281. Kennedy, J.E., Roach, G.M., Dowling, M.E., Abdel-Khalik, S.I., Chiaasiaan, S.M., Jeter, S.M., Quershi, Z.H., 2000. The onset of flow instability in uniformly heated horizontal micro-channels. Trans. ASME J. Heat Transfer 122, 118–125. Lee, P.S., Tseng, F.G., Pan, C., 2004. Bubble dynamics in micro-channels. Part I: Single micro-channel. Int. J. Heat Mass Transfer 47, 5575–5589. Lee, J.Y., Kim, M.H., Kaviany, M., Son, S.Y., 2011. Bubble nucleation in micro-channel flow boiling using single artificial cavity. Int. J. Heat Mass Transfer 54, 5139– 5148.
159
Liu, D., Lee, P.S., Garimella, S.V., 2005. Prediction of the onset of nucleate boiling in microchannel flow. Int. J. Heat Mass Transfer 48, 5134–5149. Mishan, Y., Mosyak, A., Pogrebnyak, E., Hetsroni, G., 2007. Effect of developing flow and thermal regime on momentum and heat transfer in micro-channel heat sink. Int. J. Heat Mass Transfer 50, 3100–3114. Paul, D.E., Black, J.T., Kohser, R.A., 2003. Materials and Processes in Manufacturing, ninth ed. Wiley, SL, ISBN:0-471-65653-4. Peng, X.F., Wang, B.X., 1993. Forced convection and flow boiling heat transfer for liquid flowing through micro-channels. Int. J. Heat Mass Transfer 36, 3421– 3427. Qu, W., Mudawar, I., 2002. Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. Int. J. Heat Mass Transfer 45, 3933–3945. Qu, W., Mudawar, I., 2003. Flow boiling heat transfer in two-phase micro-channel heat sinks – 1. Experimental investigation and assessment of correlation methods. Int. J. Heat Mass Transfer 46, 2755–2771. Sato, T., Matsumura, H., 1964. On the conditions of incipient subcooled-boiling with forced convection. Bull. Jpn. Soc. Mech. Eng. 7, 392–398. Shah, R.K., London, A.L., 1978. Laminar Flow Forced Convection in Ducts. Academic Press, New York, SV. Thomas, T.R., 1999. Rough Surfaces, second ed. Imperial College Press, London. Unal, H.C., 1975. Determination of the initial point of net vapor generation in flow boiling system. Int. J. Heat Mass Transfer 18, 1095–1099. Wyant, J.C., Greath, K., 1992. Advances in interferometric optical profiling. Int. J. Mach. Tools Manufact. 32, 5–10, Printed in Great Britain. Yarin, L.P., Mosyak, A., Hetsroni, G., 2008. Fluid Flow, Heat Transfer and Boiling in Micro-channels. Springer.