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Table 1.1: Useful non-dimensional numbers

Table 1 1: Useful non-dimensional numbers

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Figure 1.1: Heat Rejection System (HRS) Radiators of the ISS.
Figure 1.1: Heat Rejection System (HRS) Radiators of the ISS.
Figure 1.2: Spacecraft power trend (M. R. Patel, 2004).
Figure 1.2: Spacecraft power trend (M. R. Patel, 2004).
Figure 1.3: General schematic of two phase capillary driven heat transfer devices (Mameli, 2012) 1.2.2 Classification Two phase passive systems can be classified considering whether a wick structure is present. Heat pipes (HP), capillary pumped loop (CPL) and loop heat pipes (LHP) belong to the wicked group. Termosyphons (TP), two phase/loop termosyphons (LTS) and pulsating heat pipes (PHP) belong instead to the wickless group. In appendix A, a brief historical excursus is pointed out, with particular emphasis on the invention and first space application, together with a brief operation description and main disadvantages.
Figure 1.3: General schematic of two phase capillary driven heat transfer devices (Mameli, 2012) 1.2.2 Classification Two phase passive systems can be classified considering whether a wick structure is present. Heat pipes (HP), capillary pumped loop (CPL) and loop heat pipes (LHP) belong to the wicked group. Termosyphons (TP), two phase/loop termosyphons (LTS) and pulsating heat pipes (PHP) belong instead to the wickless group. In appendix A, a brief historical excursus is pointed out, with particular emphasis on the invention and first space application, together with a brief operation description and main disadvantages.
Figure 1.4: Flow pattern map as observed by Triplett for a 1.45 mm diameter circular test section. The transition lines are only indicative (Triplett, Ghiaasiaan, Abdel-Khalik, and Sadowski, 1999)
Figure 1.4: Flow pattern map as observed by Triplett for a 1.45 mm diameter circular test section. The transition lines are only indicative (Triplett, Ghiaasiaan, Abdel-Khalik, and Sadowski, 1999)
Table 1.2: Critical diameter as proposed by different authors compared with the equivalent Edtvos number (a part from the last criterion) considers also the effects of inertia and viscosity. The criterion suggested is based on the critical value of the Weber number for the liquid phase:
Table 1.2: Critical diameter as proposed by different authors compared with the equivalent Edtvos number (a part from the last criterion) considers also the effects of inertia and viscosity. The criterion suggested is based on the critical value of the Weber number for the liquid phase:
Figure 1.5: Comparison of selected transition criteria for R134a as a function of reduced pressure (Baldassari and Marengo, 2013).
Figure 1.5: Comparison of selected transition criteria for R134a as a function of reduced pressure (Baldassari and Marengo, 2013).
Figure 1.6: Wickless Heat Pipes working principles in the light of the confinement criteria (Franco an Filippeschi, 2012). The classification herein showed is sharp, but does not completely correspond to reality. Considering the static and dynamic transition criteria, as showed in figure 1.7, it is possible to highlight an interesting discrepancy.
Figure 1.6: Wickless Heat Pipes working principles in the light of the confinement criteria (Franco an Filippeschi, 2012). The classification herein showed is sharp, but does not completely correspond to reality. Considering the static and dynamic transition criteria, as showed in figure 1.7, it is possible to highlight an interesting discrepancy.
Figure 1.7: Relation between confinement criterion and type of device operation.
Figure 1.7: Relation between confinement criterion and type of device operation.
Figure 1.8: PHP prototypes by Akachi (Acachi, 1993). The pulsating heat pipe is a two phase passive heat transfer device, firstly proposed by the Russian Smyrnov in 1971 (Smyrnov and Savchenkov, 1971) and later developed in its current form by the Japanese Acachi (Acachi, 1990, 1993). It is able to transfer great heat fluxes with low thermal resistance and a simple, cheap structure (showed in figure 1.8).
Figure 1.8: PHP prototypes by Akachi (Acachi, 1993). The pulsating heat pipe is a two phase passive heat transfer device, firstly proposed by the Russian Smyrnov in 1971 (Smyrnov and Savchenkov, 1971) and later developed in its current form by the Japanese Acachi (Acachi, 1990, 1993). It is able to transfer great heat fluxes with low thermal resistance and a simple, cheap structure (showed in figure 1.8).
Figure 1.9: Open (a) and closed (b) loop PHP; slug&plug regime.
Figure 1.9: Open (a) and closed (b) loop PHP; slug&plug regime.
Figure 1.10: Temporal evolution of evaporator wall and fluid temperature for different heat inputs (fluid: ethanol) in a circular PHP with d=2 mm, results of experimental measurement by Mameli (Mameli, 2012). if it is a closed one it can also circulate depending on the heat input level.
Figure 1.10: Temporal evolution of evaporator wall and fluid temperature for different heat inputs (fluid: ethanol) in a circular PHP with d=2 mm, results of experimental measurement by Mameli (Mameli, 2012). if it is a closed one it can also circulate depending on the heat input level.
Figure 1.11: The two types of termosyphons herein described. At high heating power input, because of the correspondingly large mass flow rate of the vapour, the liquid-vapour interfacial shear stress becomes increasingly relevant. Once the interfacial shear force overcomes the gravitational force on the liquid film, the liquid flow may be reversed and the flooding limit is reached. Many novel designs have been proposed to overcome the flooding limit, which include an internal physical barrier along the adiabatic section bypass line for liquid return, also known as a cross-overflow separator (Bezrodnyy, Volkov, and Alekseyenko, 1983). The main advantage of these designs is that the liquid and vapour flows have partially separated passages, which can result in a higher flooding-limited heat transfer capacity.
Figure 1.11: The two types of termosyphons herein described. At high heating power input, because of the correspondingly large mass flow rate of the vapour, the liquid-vapour interfacial shear stress becomes increasingly relevant. Once the interfacial shear force overcomes the gravitational force on the liquid film, the liquid flow may be reversed and the flooding limit is reached. Many novel designs have been proposed to overcome the flooding limit, which include an internal physical barrier along the adiabatic section bypass line for liquid return, also known as a cross-overflow separator (Bezrodnyy, Volkov, and Alekseyenko, 1983). The main advantage of these designs is that the liquid and vapour flows have partially separated passages, which can result in a higher flooding-limited heat transfer capacity.
Figure 1.12: Dynamic threshold diameters for FC-72 for different fluid temperatures evaluated at an average bulk velocity of the fluid equal to 0.1 m/s and a microgravity level of 0.01 m/s? (Mangini, Mameli, Georgoulas, Araneo, Filippeschi, and Marengo, 2015).
Figure 1.12: Dynamic threshold diameters for FC-72 for different fluid temperatures evaluated at an average bulk velocity of the fluid equal to 0.1 m/s and a microgravity level of 0.01 m/s? (Mangini, Mameli, Georgoulas, Araneo, Filippeschi, and Marengo, 2015).
algorithm exploiting an height function. They stated film boiling as the dominant heat transfer mechanism in liquid film region and found out heat transfer enhancement in liquid slugs due to recirculation (then: strong influence of bubble frequency). Moreover, they proposed a heat transfer coefficient theoretical correlation. A schematic of the flow proposed by these authors is reported i fig. 2.1. Figure 2.1: Scheme of the decomposition of the flow field within a microchannel, (M. Magnini, Pul- virenti, and J.R. Thome, 2013b).
algorithm exploiting an height function. They stated film boiling as the dominant heat transfer mechanism in liquid film region and found out heat transfer enhancement in liquid slugs due to recirculation (then: strong influence of bubble frequency). Moreover, they proposed a heat transfer coefficient theoretical correlation. A schematic of the flow proposed by these authors is reported i fig. 2.1. Figure 2.1: Scheme of the decomposition of the flow field within a microchannel, (M. Magnini, Pul- virenti, and J.R. Thome, 2013b).
Figure 2.2: Four nucleation sites: bubble growth, detachment and coalescence numerical visualization, (Georgoulas and Marengo, 2016). Georgoulas and Marengo (Georgoulas and Marengo, 2015, 2016) extensively modified and validated the open source CFD OpenFoam to improve its two phase flow in micro- channels simulation accuracy. They improved the interface curvature algorithm and implemented a model for phase change and dynamic contact angle.
Figure 2.2: Four nucleation sites: bubble growth, detachment and coalescence numerical visualization, (Georgoulas and Marengo, 2016). Georgoulas and Marengo (Georgoulas and Marengo, 2015, 2016) extensively modified and validated the open source CFD OpenFoam to improve its two phase flow in micro- channels simulation accuracy. They improved the interface curvature algorithm and implemented a model for phase change and dynamic contact angle.
Figure 2.3: Volume fraction visualization, Givler and Martinez. The first PHP CFD-VOF simulation was performed by Givler and Martinez (Givler and Martinez, 2009) of Sandia National Laboratory in 2009. They used the general purpose CFD software FLOW-3D in order to evaluate software capabilities used to model the coupled multiphysics processes inherent to PHPs. A single loop and a 2 turns PHPs were simulated. Visual results for the second case are shown in fig. 2.3. The authors did not describe the model and whether they adopted an interface sharpening technique to overcome VOF limitations. Moreover, following the criterion proposed by Gupta (Gupta, Fletcher, and Haynes, 2009), the mesh is too coarse to adequately capture the interface.
Figure 2.3: Volume fraction visualization, Givler and Martinez. The first PHP CFD-VOF simulation was performed by Givler and Martinez (Givler and Martinez, 2009) of Sandia National Laboratory in 2009. They used the general purpose CFD software FLOW-3D in order to evaluate software capabilities used to model the coupled multiphysics processes inherent to PHPs. A single loop and a 2 turns PHPs were simulated. Visual results for the second case are shown in fig. 2.3. The authors did not describe the model and whether they adopted an interface sharpening technique to overcome VOF limitations. Moreover, following the criterion proposed by Gupta (Gupta, Fletcher, and Haynes, 2009), the mesh is too coarse to adequately capture the interface.
Figure 2.4: Volume fraction of vapour obtained by Subash and Pachgare, (Nagwase and Pachghare, 2013). It is nearly impossible to recognize the interface.
Figure 2.4: Volume fraction of vapour obtained by Subash and Pachgare, (Nagwase and Pachghare, 2013). It is nearly impossible to recognize the interface.
Figure 2.5: Temperature results obtained by Lin et Al., (Lin, S. Wang, Shirakashi, and L. Zhang, 2013).
Figure 2.5: Temperature results obtained by Lin et Al., (Lin, S. Wang, Shirakashi, and L. Zhang, 2013).
Figure 2.6: Temperature results by Rudresha and Kumar, (Rudresha and Kumar, 2014) approximation, indeed, in cylindrical coordinates is the reduction of a 3D circular cylin- der (that is the geometry claimed in the article) while in cartesian to is the reduction of two parallel flat plates. Results are shown for temperature pattern, see fig. 2.5, and thermal resistance. Compared with the experimental results, the model was just able to capture thermal resistance trends.
Figure 2.6: Temperature results by Rudresha and Kumar, (Rudresha and Kumar, 2014) approximation, indeed, in cylindrical coordinates is the reduction of a 3D circular cylin- der (that is the geometry claimed in the article) while in cartesian to is the reduction of two parallel flat plates. Results are shown for temperature pattern, see fig. 2.5, and thermal resistance. Compared with the experimental results, the model was just able to capture thermal resistance trends.
Rudresha and Kumar executed an experimental and numerical analysis of a 4 turns PHP charged with different nanofluids. The numerical analysis makes use of ANSYS- Fluent (Rudresha and Kumar, 2014). The authors only showed the results and only for temperature, fig. 2.6. Figure 2.7: Volume fraction results by Pouryoussefy and Zhang: (a) 2D case (Pouryoussefi and Y. Zhang, 2015), (b) 3D case (Pouryoussefi and Y. Zhang, 2016). The poor resolution of the interface is clearly visible.
Rudresha and Kumar executed an experimental and numerical analysis of a 4 turns PHP charged with different nanofluids. The numerical analysis makes use of ANSYS- Fluent (Rudresha and Kumar, 2014). The authors only showed the results and only for temperature, fig. 2.6. Figure 2.7: Volume fraction results by Pouryoussefy and Zhang: (a) 2D case (Pouryoussefi and Y. Zhang, 2015), (b) 3D case (Pouryoussefi and Y. Zhang, 2016). The poor resolution of the interface is clearly visible.
Figure 2.8: Comparison between experimental and numerical results, Jiaqiang et Al. (Jiaqiang, X. Zhao, Deng, and H. Zhu, 2015). Pouryoussefi and Zhang numerically investigated the chaotic flow both in 2D (it is not clear wether the tube is circular and which coordinate system was used) PHP charged with water and 3D PHP charged with water and ethanol using ANSYS-Fluent (Poury- oussefi and Y. Zhang, 2015, 2016). The initial distribution in the tube is obtained filling it with separate liquid and vapour and let them evolve under the action of the present orces. An energy equation is added to the VOF in which the source term is said to be zero in the 2D case (no evaporation/condensation, but from results is clear that during the simulations evaporation and condensation took place) but different from zero in the 3D one. A contact angle is assumed a priori and used to refine the surface normal vec- tor near the wall. The authors assigned a constant temperature boundary condition at evaporator and condenser in the first case while in the second one they used the heat flux at evaporator. Moreover in the 2D case they used a constant time step of 107° s (not defined in the 3D one) while, in particular for multiphase flows, it is preferable an adjustable one w.r.t the local Courant number (ideally, it should not exceed an upper limit Cox0.5 in the region of the interface, p. 62 of ref. (Open, 2011b)). Volume fraction results are shown in fig. 2.7. The model is validated but it is clear that interface captur- ing is very poor because of the absence of interface sharpening and, in the 2D case, also because of a too coarse grid.
Figure 2.8: Comparison between experimental and numerical results, Jiaqiang et Al. (Jiaqiang, X. Zhao, Deng, and H. Zhu, 2015). Pouryoussefi and Zhang numerically investigated the chaotic flow both in 2D (it is not clear wether the tube is circular and which coordinate system was used) PHP charged with water and 3D PHP charged with water and ethanol using ANSYS-Fluent (Poury- oussefi and Y. Zhang, 2015, 2016). The initial distribution in the tube is obtained filling it with separate liquid and vapour and let them evolve under the action of the present orces. An energy equation is added to the VOF in which the source term is said to be zero in the 2D case (no evaporation/condensation, but from results is clear that during the simulations evaporation and condensation took place) but different from zero in the 3D one. A contact angle is assumed a priori and used to refine the surface normal vec- tor near the wall. The authors assigned a constant temperature boundary condition at evaporator and condenser in the first case while in the second one they used the heat flux at evaporator. Moreover in the 2D case they used a constant time step of 107° s (not defined in the 3D one) while, in particular for multiphase flows, it is preferable an adjustable one w.r.t the local Courant number (ideally, it should not exceed an upper limit Cox0.5 in the region of the interface, p. 62 of ref. (Open, 2011b)). Volume fraction results are shown in fig. 2.7. The model is validated but it is clear that interface captur- ing is very poor because of the absence of interface sharpening and, in the 2D case, also because of a too coarse grid.
Figure 2.9: Volume fraction (left) and temperature (right) results obtained by Liu and Chen, (X. Liu and Y. Chen, 2014). agreement with experimental ones (see fig. 2.8), the interface is poorly resolved and almost everywhere the thin liquid film is absent. These errors are due to the absence of interface sharpening and to a not fine enough grid.
Figure 2.9: Volume fraction (left) and temperature (right) results obtained by Liu and Chen, (X. Liu and Y. Chen, 2014). agreement with experimental ones (see fig. 2.8), the interface is poorly resolved and almost everywhere the thin liquid film is absent. These errors are due to the absence of interface sharpening and to a not fine enough grid.
Figure 2.10: Volume fraction results obtained by Wang et Al. (J. Wang, H. Ma, and Q. Zhu, 2015; J. Wang, H. Ma, Q. Zhu, Y. Dong, and Yue, 2016). Detail of the smooth PHP (left) and of the corrugated one (right). The second one shows a better interface resolution, probably due to a finer mesh or interface sharpening.
Figure 2.10: Volume fraction results obtained by Wang et Al. (J. Wang, H. Ma, and Q. Zhu, 2015; J. Wang, H. Ma, Q. Zhu, Y. Dong, and Yue, 2016). Detail of the smooth PHP (left) and of the corrugated one (right). The second one shows a better interface resolution, probably due to a finer mesh or interface sharpening.
Table 2.1: Summary of PHP CFD simulations review
Table 2.1: Summary of PHP CFD simulations review
Table 3.1: Summary of pros and cons of the two software options considered
Table 3.1: Summary of pros and cons of the two software options considered
Figure 3.2: Comparison of numerical predictions between the original and the modified VOF solver for the BrackBill’s test case: (a) spurious currents dampening and (b) Laplace pressure difference. the calculation of the normal vectors and the curvature of the interface that are used for the calculation of the interfacial forces. These errors emerge from the fact that in the VOF method the interface is implicitly represented by the volume fraction values that encounter sharp changes over a thin region. To overcome this issue, smoothed volume fraction values @ are used in curvature calculation. This smoothing is achieved by the application of the following Laplacian filter: the calculation of the interfacial forces. ‘These errors emerge from the fact that in the
Figure 3.2: Comparison of numerical predictions between the original and the modified VOF solver for the BrackBill’s test case: (a) spurious currents dampening and (b) Laplace pressure difference. the calculation of the normal vectors and the curvature of the interface that are used for the calculation of the interfacial forces. These errors emerge from the fact that in the VOF method the interface is implicitly represented by the volume fraction values that encounter sharp changes over a thin region. To overcome this issue, smoothed volume fraction values @ are used in curvature calculation. This smoothing is achieved by the application of the following Laplacian filter: the calculation of the interfacial forces. ‘These errors emerge from the fact that in the
Figure 3.3: Qualitative comparison of experimental and numerical 3D bubble evolution An example of qualitative comparison between experimental and numerical results is shown in fig. 3.3.
Figure 3.3: Qualitative comparison of experimental and numerical 3D bubble evolution An example of qualitative comparison between experimental and numerical results is shown in fig. 3.3.
Figure 3.4: Distribution of the final source term in the computational domain. Considering this last definition, the source terms in all cells that do not contain pure iquid or pure vapour are set to zero. This cropping step is done to ensures that source terms are shifted into the pure vapour and liquid cells next to the interface (see fig. 3.4). The interface therefore is not subjected to any source term and is only transported by the calculated velocity field, and the transport algorithm for the volume fraction field as well as the associated interface compression, can work efficiently without interfering with the source term field.
Figure 3.4: Distribution of the final source term in the computational domain. Considering this last definition, the source terms in all cells that do not contain pure iquid or pure vapour are set to zero. This cropping step is done to ensures that source terms are shifted into the pure vapour and liquid cells next to the interface (see fig. 3.4). The interface therefore is not subjected to any source term and is only transported by the calculated velocity field, and the transport algorithm for the volume fraction field as well as the associated interface compression, can work efficiently without interfering with the source term field.
Finally, the final source term distribution is calculated using the above scaling factors in the following relationship: The remaining source term field is scaled individually on the liquid and the vapour side through the application of appropriate scaling coefficients. This scaling step ensures mass conservation:
Finally, the final source term distribution is calculated using the above scaling factors in the following relationship: The remaining source term field is scaled individually on the liquid and the vapour side through the application of appropriate scaling coefficients. This scaling step ensures mass conservation:
Figure 3.5: Droplet impact: comparison of numerical and experimental results for the spreading diameter. Simulations are performed using a static contact angle 0-=90° and the Kistler dynamic contact angle model (Criscione, Rohrig, Jakirlic, Roisman, and Tropea, 2012).
Figure 3.5: Droplet impact: comparison of numerical and experimental results for the spreading diameter. Simulations are performed using a static contact angle 0-=90° and the Kistler dynamic contact angle model (Criscione, Rohrig, Jakirlic, Roisman, and Tropea, 2012).
Figure 4.1: Zero-G Airbus A300 during parabolic flight descent. .2 ESA 65th Parabolic Flight Campaign (PFC-65)
Figure 4.1: Zero-G Airbus A300 during parabolic flight descent. .2 ESA 65th Parabolic Flight Campaign (PFC-65)
Figure 4.2: A schematic of MicroBo experimental facility. 4.3.2 Experimental Facility Description
Figure 4.2: A schematic of MicroBo experimental facility. 4.3.2 Experimental Facility Description
Figure 4.3: Picture of the actual MicroBo test section. The twelve thermocuples are highlighted with their names. The heated portion is the central one.
Figure 4.3: Picture of the actual MicroBo test section. The twelve thermocuples are highlighted with their names. The heated portion is the central one.
Figure 4.4: MicroBo mounted onboard the Zero-G A300. iM a The working fluid is perfluorohexane (CgFj4 brute chemical formula), a fluorinert liquid used in electronics cooling and widely used for experiments of boiling on parabolic flights. The experimental loop derives from the previous version of the experiment that flew during the PFC-59 and PFC-61 in November 2013 and September 2014, respectively. Many components, the hydraulic loop, the electrical system, and the electronics were the same components used in the previous parabolic flight campaigns.
Figure 4.4: MicroBo mounted onboard the Zero-G A300. iM a The working fluid is perfluorohexane (CgFj4 brute chemical formula), a fluorinert liquid used in electronics cooling and widely used for experiments of boiling on parabolic flights. The experimental loop derives from the previous version of the experiment that flew during the PFC-59 and PFC-61 in November 2013 and September 2014, respectively. Many components, the hydraulic loop, the electrical system, and the electronics were the same components used in the previous parabolic flight campaigns.
Figure 4.5: Technical draw of MicroBo hydraulic loop.
Figure 4.5: Technical draw of MicroBo hydraulic loop.
Figure 4.6: Two shots from PFC-65 at the same conditions (except gravity). At the top, hyper-gravity, at bottom microgravity. The first category of results spans all the possible flow regimes inside a tube, from bubbly to annular flow and, sometimes, to dry out. The upper part of figure 4.6 shows the visualization results in hyper-gravity while the bottom part shows results in microgravity or the 4 mm ID test section. The two pictures were taken during the same parabola at the same conditions (except for gravity). The difference between the two is very clear: the first one is a bubbly flow regime with stratification while the second is a Taylor bubble flow (the present condition satisfies all the static confinement criterion explained in chapter ?? but diameter is slightly bigger than Gu one, about 3.73 mm, and much bigger than Garimella’s).
Figure 4.6: Two shots from PFC-65 at the same conditions (except gravity). At the top, hyper-gravity, at bottom microgravity. The first category of results spans all the possible flow regimes inside a tube, from bubbly to annular flow and, sometimes, to dry out. The upper part of figure 4.6 shows the visualization results in hyper-gravity while the bottom part shows results in microgravity or the 4 mm ID test section. The two pictures were taken during the same parabola at the same conditions (except for gravity). The difference between the two is very clear: the first one is a bubbly flow regime with stratification while the second is a Taylor bubble flow (the present condition satisfies all the static confinement criterion explained in chapter ?? but diameter is slightly bigger than Gu one, about 3.73 mm, and much bigger than Garimella’s).
Figure 4.7: Data acquired for the whole parabola 24. Description of measured temperature has been given in section 4.3.3; AccZ is acceleration along vertical axis given in multiples of g.
Figure 4.7: Data acquired for the whole parabola 24. Description of measured temperature has been given in section 4.3.3; AccZ is acceleration along vertical axis given in multiples of g.
Table 4.1: Data from parabola 24
Table 4.1: Data from parabola 24
n order to analyze and reproduce each bubble, they have been digitalized using the open-source software ImageJ. Not all the visualization domain has been considered in this process: the part chosen is the one in which the most part of bubbles has a diameter comparable to the channel one. In the present case, then, it has been considered as bubble "inlet" the space between the first and second couples of thermocouples (the red ine in figure 4.8). Finally, bubble considered in this process are the ones that, at bubble "inlet", have a diameter comparable to the channel one. Figure 4.8: Digitalization process with ImageJ. From the top: flow picture, mask of the selected bubbles, analysis and labelling of the selected bubbles. The red vertical line represents the bubble "inlet".
n order to analyze and reproduce each bubble, they have been digitalized using the open-source software ImageJ. Not all the visualization domain has been considered in this process: the part chosen is the one in which the most part of bubbles has a diameter comparable to the channel one. In the present case, then, it has been considered as bubble "inlet" the space between the first and second couples of thermocouples (the red ine in figure 4.8). Finally, bubble considered in this process are the ones that, at bubble "inlet", have a diameter comparable to the channel one. Figure 4.8: Digitalization process with ImageJ. From the top: flow picture, mask of the selected bubbles, analysis and labelling of the selected bubbles. The red vertical line represents the bubble "inlet".
Figure 5.1: Xenon Work Station hardware and operative system characteristics To acomplish the tasks of this thesis, the Xenon Work St of ] Energy, Systems, Land and Construction |] Pisa was used. The operative system is Ubunt shown in fig. 5.1. In particular, 24 CPUs were allowable. In eac was subdivided among the optimum number of cores according to the rule of thumb of distribution). Engineering (D1 ation (WS) of Department EST! u 15.10 and the hardware characteristics are EC) of the University of h simulation the domain 160.000 cells per core. This number is a trade-off between the decrease in computational time due to the higher number of CPUs used and the increase in communication time among processors (it is possible to verify the efficacy of this statement by comparing ExecutionTime and ClockTime output. The less the difference, the beeter the domain
Figure 5.1: Xenon Work Station hardware and operative system characteristics To acomplish the tasks of this thesis, the Xenon Work St of ] Energy, Systems, Land and Construction |] Pisa was used. The operative system is Ubunt shown in fig. 5.1. In particular, 24 CPUs were allowable. In eac was subdivided among the optimum number of cores according to the rule of thumb of distribution). Engineering (D1 ation (WS) of Department EST! u 15.10 and the hardware characteristics are EC) of the University of h simulation the domain 160.000 cells per core. This number is a trade-off between the decrease in computational time due to the higher number of CPUs used and the increase in communication time among processors (it is possible to verify the efficacy of this statement by comparing ExecutionTime and ClockTime output. The less the difference, the beeter the domain
Figure 5.2: Axysimmetric geometry using the wedge patch type of OpenFOAM.
Figure 5.2: Axysimmetric geometry using the wedge patch type of OpenFOAM.
Table 5.2: Boundary conditions
Table 5.2: Boundary conditions
Table 5.1: Saturation properties of perfluorohexane at inlet condition (pin=0.154 MPa) (Lemmon, Huber, and McLinden, 2007) reported in table 5.1. with NIST Refprop 8.0 (Lemmon, Huber, and McLinden, 2007) at inlet conditions. Given the inlet pressure (pj,=0.154 MPa), the corresponding values of input parameters are reported in table 5.1.
Table 5.1: Saturation properties of perfluorohexane at inlet condition (pin=0.154 MPa) (Lemmon, Huber, and McLinden, 2007) reported in table 5.1. with NIST Refprop 8.0 (Lemmon, Huber, and McLinden, 2007) at inlet conditions. Given the inlet pressure (pj,=0.154 MPa), the corresponding values of input parameters are reported in table 5.1.
Figure 5.3: Bubble dimensions. The upper one is for the saturated case; below it the one for one degree of subcooling. Since in the sub-cooled case there is condensation before entering the heated region, in order to have the same dimensions at heated region entrance as the saturated case a bigger bubble is needed upstream. Bubbles. Bubbles shape and frequency is taken from the experiment as mean of bubbles real shape (dimensions are showed in figure 5.3. Since in the sub-cooled case there is condensation before entering the heated region, bubbles are bigger) and frequency (10 bubbles/sec). The number of simulated bubbles is 7 (the same as the first experimental bubble train). All Bubbles are patched at the same location in the adiabatic region, i.e. at a distance from the inlet equal to three times the internal diameter.
Figure 5.3: Bubble dimensions. The upper one is for the saturated case; below it the one for one degree of subcooling. Since in the sub-cooled case there is condensation before entering the heated region, in order to have the same dimensions at heated region entrance as the saturated case a bigger bubble is needed upstream. Bubbles. Bubbles shape and frequency is taken from the experiment as mean of bubbles real shape (dimensions are showed in figure 5.3. Since in the sub-cooled case there is condensation before entering the heated region, bubbles are bigger) and frequency (10 bubbles/sec). The number of simulated bubbles is 7 (the same as the first experimental bubble train). All Bubbles are patched at the same location in the adiabatic region, i.e. at a distance from the inlet equal to three times the internal diameter.
Figure 5.4: Visualization results comparison. On the left, experiment images; in the middle their digitalization with ImageJ; on the right the simulated volume fraction.
Figure 5.4: Visualization results comparison. On the left, experiment images; in the middle their digitalization with ImageJ; on the right the simulated volume fraction.
Figure 5.5: Comparison between superheat in the experiment (black line) and in the simulation (red line).The super-heat degree is calculated as the difference between wall temperature and fluid bulk temperature
Figure 5.5: Comparison between superheat in the experiment (black line) and in the simulation (red line).The super-heat degree is calculated as the difference between wall temperature and fluid bulk temperature
Figure 5.6: Comparison between mean volume measured at same nose locations in the experiment (black line) and in the simulation (red line).
Figure 5.6: Comparison between mean volume measured at same nose locations in the experiment (black line) and in the simulation (red line).
It is worthwhile to remark here, before going on with more quantitative comparisons, the problem of dispersed bubble flow. As explained, there exist no models that take into account this phenomenon. However, as evident in the left part of figure 5.4, a lot of dispersed bubbles are present. This points out the needing for modelling also nucleate boiling phenomena and dispersed bubble flow. Figure 5.7: Comparison between mean tail (left) and nose (right) velocity measured at same locations in the experiment (black line) and in the simulation (red line).
It is worthwhile to remark here, before going on with more quantitative comparisons, the problem of dispersed bubble flow. As explained, there exist no models that take into account this phenomenon. However, as evident in the left part of figure 5.4, a lot of dispersed bubbles are present. This points out the needing for modelling also nucleate boiling phenomena and dispersed bubble flow. Figure 5.7: Comparison between mean tail (left) and nose (right) velocity measured at same locations in the experiment (black line) and in the simulation (red line).
Figure 5.8: Comparison between mean tail (left) and nose (right) velocity measured at same locations in the experiment (black line) and in the simulation (red line). The heat transfer coefficient (HTC) is for sure one of the most important parameters related to the design of thermal management system. Calculation of HTC is made using equation 4.3, considering as fluid bulk temperature the one measured on the tube axis. The following description is made with reference to figure 5.8. As for temperature, the first numerical thermocouple is out of range. It is placed 10 mm downstream the begin- ning of the heated region. Probably this distance is not sufficient to obtain a developed thermal boundary layer. Indeed, the second thermocouple (placed 20 mm downstream the beginning of the heated region) shows a more reasonable HTC. Neglecting the first thermocouple, HTC absolute values and trends comparison could be highlighted. HTC magnitudes are very different: the numerical one is at least twice the experimental one. HTC experimental trend is linear and also the numerical one is nearly linear. The slope of the experimental HTC curve is slightly steeper than the numerical one.
Figure 5.8: Comparison between mean tail (left) and nose (right) velocity measured at same locations in the experiment (black line) and in the simulation (red line). The heat transfer coefficient (HTC) is for sure one of the most important parameters related to the design of thermal management system. Calculation of HTC is made using equation 4.3, considering as fluid bulk temperature the one measured on the tube axis. The following description is made with reference to figure 5.8. As for temperature, the first numerical thermocouple is out of range. It is placed 10 mm downstream the begin- ning of the heated region. Probably this distance is not sufficient to obtain a developed thermal boundary layer. Indeed, the second thermocouple (placed 20 mm downstream the beginning of the heated region) shows a more reasonable HTC. Neglecting the first thermocouple, HTC absolute values and trends comparison could be highlighted. HTC magnitudes are very different: the numerical one is at least twice the experimental one. HTC experimental trend is linear and also the numerical one is nearly linear. The slope of the experimental HTC curve is slightly steeper than the numerical one.
is at saturation temperature. This means that heat is transferred mainly by liqu id film evaporation. On the contrary, in the experimental case the liquid is sub-cooled. | - Evapo- ration of the liquid film is present but there is also non-negligible sensible heat transfer to raise liquid film temperature. In these conditions, the evaporative mass flux is pattern transition. As a consequence, the superheat degree in the simulation was than the experimental one. higher in the simulated case, and for so reaches higher void fraction and shows a semi-annular flow pattern while the experimental flow pattern is always slug and plug. Then, the simulated HTC is higher than the experimental one for the heat transfer process exploits atent heat of evaporation rather than sensible heat. Moreover, the simulated flow pat- tern (semi-annular) is known to be more efficient (Mameli, 2012). In the experiment, not even the contribution of nucleate boiling and bubbles merging is able to induce flow higher Figure 5.9: Heat transfer processes in the simulation channel (a) and in the experimental channel (b) pattern transition. As a consequence, the superheat degree in the simulation was higher
is at saturation temperature. This means that heat is transferred mainly by liqu id film evaporation. On the contrary, in the experimental case the liquid is sub-cooled. | - Evapo- ration of the liquid film is present but there is also non-negligible sensible heat transfer to raise liquid film temperature. In these conditions, the evaporative mass flux is pattern transition. As a consequence, the superheat degree in the simulation was than the experimental one. higher in the simulated case, and for so reaches higher void fraction and shows a semi-annular flow pattern while the experimental flow pattern is always slug and plug. Then, the simulated HTC is higher than the experimental one for the heat transfer process exploits atent heat of evaporation rather than sensible heat. Moreover, the simulated flow pat- tern (semi-annular) is known to be more efficient (Mameli, 2012). In the experiment, not even the contribution of nucleate boiling and bubbles merging is able to induce flow higher Figure 5.9: Heat transfer processes in the simulation channel (a) and in the experimental channel (b) pattern transition. As a consequence, the superheat degree in the simulation was higher
Table 5.3: Values used in the evaluation of Ap in Clapeyron equation and correspondent result. in which he, is latent heat of vaporization and v is the specific volume of the two phases at the specified temperature. This equation describes the variation of pressure with temperature along the equilibrium liquid-vapor saturation curve. Considering the present case (with data showed in table 5.3), the expected pressure variation is Ap=4844.4 Pa. Pressure for the case is plotted in picture 5.10 from 0.1 to 0.3 seconds. Data are taken 60 mm after the position of bubble patching in order to show better details of residual fluctuation. As visible, two peaks in pressure occured in this period and they exactly happened after patching a bubble. The magnitude of these peaks is slightly different from time to time and the values in the vicinity of the patched bubble are reported in table 5.4.
Table 5.3: Values used in the evaluation of Ap in Clapeyron equation and correspondent result. in which he, is latent heat of vaporization and v is the specific volume of the two phases at the specified temperature. This equation describes the variation of pressure with temperature along the equilibrium liquid-vapor saturation curve. Considering the present case (with data showed in table 5.3), the expected pressure variation is Ap=4844.4 Pa. Pressure for the case is plotted in picture 5.10 from 0.1 to 0.3 seconds. Data are taken 60 mm after the position of bubble patching in order to show better details of residual fluctuation. As visible, two peaks in pressure occured in this period and they exactly happened after patching a bubble. The magnitude of these peaks is slightly different from time to time and the values in the vicinity of the patched bubble are reported in table 5.4.
Figure 5.10: Presure trend 60 mm after the patching site. The two peaks corresponds to a patched bubble. It is visible the residual pressure fluctuation between the two patching events. Since the model adopts the hypothesis of incompressible flow, p=0 is the reference value for pressure and for so negative pressure appears.
Figure 5.10: Presure trend 60 mm after the patching site. The two peaks corresponds to a patched bubble. It is visible the residual pressure fluctuation between the two patching events. Since the model adopts the hypothesis of incompressible flow, p=0 is the reference value for pressure and for so negative pressure appears.
Figure 5.11: Presure trend 60 mm after the patching site. No bubbles were patched in the period showed. Two very strong peaks are visible, the first negative, the second positive. All the other fluctua- tions (that are present) are not visible due to the magnitude of these peaks. the last patching, two strong variation of pressure, much stronger than the previously explained ones, broke bubbles. This is due to a limitation in the code implementation. As explained in section 3.6.2, the interface resistance exploits an accomodation factor to be calculated. This factor depends on whether evaporation or condensation is happening. As an example, in literature its value is suggested to be 1 in case of evaporation and 0.05 in case of condensation (Kunkelmann, 2011; M. Magnini, 2012). In the present case, when bubbles enters the heated region, evaporation and condensation took place at the same time. Two different values of this parameter should be given to the software together with a sub-routine to select which of the two must be used in the considered cell (in this case, 1 for evaporating cells, 0.05 for condensing one). At present, the implemented code allows to load only one value for this factor and that is the reason for the appearance of a non-physical pressure that breaks bubbles up.
Figure 5.11: Presure trend 60 mm after the patching site. No bubbles were patched in the period showed. Two very strong peaks are visible, the first negative, the second positive. All the other fluctua- tions (that are present) are not visible due to the magnitude of these peaks. the last patching, two strong variation of pressure, much stronger than the previously explained ones, broke bubbles. This is due to a limitation in the code implementation. As explained in section 3.6.2, the interface resistance exploits an accomodation factor to be calculated. This factor depends on whether evaporation or condensation is happening. As an example, in literature its value is suggested to be 1 in case of evaporation and 0.05 in case of condensation (Kunkelmann, 2011; M. Magnini, 2012). In the present case, when bubbles enters the heated region, evaporation and condensation took place at the same time. Two different values of this parameter should be given to the software together with a sub-routine to select which of the two must be used in the considered cell (in this case, 1 for evaporating cells, 0.05 for condensing one). At present, the implemented code allows to load only one value for this factor and that is the reason for the appearance of a non-physical pressure that breaks bubbles up.
Figure 5.12: 3D reconstructed volume fraction results three milliseconds after the second peak.
Figure 5.12: 3D reconstructed volume fraction results three milliseconds after the second peak.
Figure A.1: Schematic of a TS (D. Reay, McGlen, and P. Kew, 2013)
Figure A.1: Schematic of a TS (D. Reay, McGlen, and P. Kew, 2013)
Figure A.2: Schematic of a HP (D. Reay, McGlen, and P. Kew, 2013)
Figure A.2: Schematic of a HP (D. Reay, McGlen, and P. Kew, 2013)
Figure A.3: Schematic of a LHP (Ku, 1999)
Figure A.3: Schematic of a LHP (Ku, 1999)
Figure A.4: Schematic of a RTS (Filippeschi, 2006) The drawback of these devices resides in the expensive wick structure needed to operate. A single cycle of periodic heat and mass transfer can be divided into two main parts: a transfer time, where the liquid is transferred from the evaporator to the accumulator through the condenser and a return time, where the liquid collected in the accumulator comes back to the evaporator. Different ways to obtain this process have been proposed so far: decreasing pressure in the evaporator (periodical interruption of heat supply to
Figure A.4: Schematic of a RTS (Filippeschi, 2006) The drawback of these devices resides in the expensive wick structure needed to operate. A single cycle of periodic heat and mass transfer can be divided into two main parts: a transfer time, where the liquid is transferred from the evaporator to the accumulator through the condenser and a return time, where the liquid collected in the accumulator comes back to the evaporator. Different ways to obtain this process have been proposed so far: decreasing pressure in the evaporator (periodical interruption of heat supply to
Table A.1: Heat performance comparison of different two phase heat transfer devices PHP has not even been completely under- Vapor :**"** stood and tested in space but its unique fea- bubble : tures makes it the best candidate for present “ {¥ T Evan and future heat transfer challenges: it is sim- ple, cheaper than HP and LHP ao pense Figure A.5: Schematic of a wick inside), light and flexible, with low ther- q, oll, 2004) mal resistance and high heat flux transfer capability.
Table A.1: Heat performance comparison of different two phase heat transfer devices PHP has not even been completely under- Vapor :**"** stood and tested in space but its unique fea- bubble : tures makes it the best candidate for present “ {¥ T Evan and future heat transfer challenges: it is sim- ple, cheaper than HP and LHP ao pense Figure A.5: Schematic of a wick inside), light and flexible, with low ther- q, oll, 2004) mal resistance and high heat flux transfer capability.
The major drawback of TS is its complexity (layout and needs for control electronics).
The major drawback of TS is its complexity (layout and needs for control electronics).
Figure B.2: Variation of heat flux and heat transfer coefficient with wall superheat in boiling as reported by Nukiyama (Nukiyama, 1984)
Figure B.2: Variation of heat flux and heat transfer coefficient with wall superheat in boiling as reported by Nukiyama (Nukiyama, 1984)
Figure B.3: Boundary conditions for CLPHP operation
Figure B.3: Boundary conditions for CLPHP operation
Figure C.1: Lumped parameters model control volumes
Figure C.1: Lumped parameters model control volumes
Figure C.2: (a) Schematic view of pulsating heat pipe with 5 turns. Black and white portions represent liquid slugs and vapor plugs, respectively. The PHP is heated in the evaporator section (red) and cooled in the condenser section (blue). (b) Mass-spring-damper representation of the PHP. The location of the evaporator, adiabatic and condenser sections are indicated by the colored inner ring (Giirsel, Frijns, Homburg, and Steenhoven, 2015)
Figure C.2: (a) Schematic view of pulsating heat pipe with 5 turns. Black and white portions represent liquid slugs and vapor plugs, respectively. The PHP is heated in the evaporator section (red) and cooled in the condenser section (blue). (b) Mass-spring-damper representation of the PHP. The location of the evaporator, adiabatic and condenser sections are indicated by the colored inner ring (Giirsel, Frijns, Homburg, and Steenhoven, 2015)
Figure C.3: Iso-level curves from a level-set formulation. The zero value iso-level curve (highlighted in blue) locates the phases interface
Figure C.3: Iso-level curves from a level-set formulation. The zero value iso-level curve (highlighted in blue) locates the phases interface
Figure C.4: (a) Schematic illustration of the VOF method, (b) close-up of the free interface region. a is the volume fraction
Figure C.4: (a) Schematic illustration of the VOF method, (b) close-up of the free interface region. a is the volume fraction
Related topics:
Electronic Cooling SystemCFD AnalysisFluid flow and heat transfer in MicrochannelsParabolic Flight ExperimentsPulsating Heat PipeHeat Transfer Fluid Mechanics CFD
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