Evaporation and Viscous Flow in Triangular Grooves in Micro Heat Pipes

Author(s):  
Mulugeta Markos ◽  
Vladimir S. Ajaev ◽  
G. M. Homsy

We develop a lubrication type model of a liquid flow in a wedge in the limit of small capillary numbers and negligible gravity. The model incorporates the effects of capillary pressure gradients and evaporation. Steady vapor-liquid interface shapes are found for a range of parameters. In the limit of weak evaporation the flow is the same in all cross-sections and can be controlled by changing the wedge angle. We find the wedge angle that results in the maximum value of the flow rate for a given contact angle. For high evaporation rates, both the flow rate and the amount of liquid in each cross-section along the wedge decrease until the point of dry-out is reached. The location of the dry-out point is studied as a function of evaporation. Practical suggestions about optimization of micro heat pipes are given.

Author(s):  
Mulugeta Markos ◽  
Vladimir Ajaev ◽  
G. M. Homsy

The paper presents a lubrication-type model of liquid flow and heat transfer in different groove structures in micro heat pipes under negligible gravity and small capillary number. In the adiabatic region the flow rate can be controlled by changing the shape of the cross-section. We have computed the flow rate as a function of geometric parameters. Determination of the vapor-liquid interface shape in the grooves requires coupling of fluid flow and heat transfer. We examined the shape of the interface when thermocapillary effect is insignificant and then consider the effect of thermocapilarity. Practical applications of our results are discussed in relation to the design and optimization of micro heat pipes.


Author(s):  
Christophe Vallée ◽  
Tobias Seidel ◽  
Dirk Lucas ◽  
Akio Tomiyama ◽  
Michio Murase

In order to investigate the two-phase flow behavior during countercurrent flow limitation in the hot leg of a pressurized water reactor, two test models were built: one at the Kobe University and the other at the TOPFLOW test facility of Forschungszentrum Dresden-Rossendorf (FZD). Both test facilities are devoted to optical measurement techniques; therefore, a flat hot leg test section design was chosen. Countercurrent flow limitation (CCFL) experiments were performed, simulating the reflux condenser cooling mode appearing in some accident scenarios. The fluids used were air and water, both at room temperature. The pressure conditions were varied from atmospheric at Kobe to 3.0 bars absolute at TOPFLOW. According to the presented review of literature, very few data are available on flooding in channels with a rectangular cross section, and no experiments were performed in the past in such flat models of a hot leg. Commonly, the macroscopic effects of CCFL are represented in a flooding diagram, where the gas flow rate is plotted versus the discharge water flow rate, using the nondimensional superficial velocity (also known as Wallis parameter) as coordinates. However, the classical definition of the Wallis parameter contains the pipe diameter as characteristic length. In order to be able to perform comparisons with pipe experiments and to extrapolate to the power plant scale, the appropriate characteristic length should be determined. A detailed comparison of the test facilities operated at the Kobe University and at FZD is presented. With respect to the CCFL behavior, it is shown that the essential parts of the two hot leg test sections are very similar. This geometrical analogy allows us to perform meaningful comparisons. However, clear differences in the dimensions of the cross section (H×W=150×10 mm2 in Kobe, 250×50 mm2 at FZD) make it possible to point out the right characteristic length for hot leg models with rectangular cross sections. The hydraulic diameter, the channel height, and the Laplace critical wavelength (leading to the Kutateladze number) were tested. A comparison of our own results with similar experimental data and empirical correlations for pipes available in literature shows that the channel height is the characteristic length to be used in the Wallis parameter for channels with rectangular cross sections. However, some limitations were noticed for narrow channels, where CCFL is reached at lower gas fluxes, as already observed in small scale hot legs with pipe cross sections.


1995 ◽  
Vol 117 (1) ◽  
pp. 195-201 ◽  
Author(s):  
L. W. Swanson ◽  
G. P. Peterson

Successful analysis and modeling of micro heat pipes requires a complete understanding of the vapor–liquid interface. A thermodynamic model of the vapor–liquid interface in micro heat pipes has been formulated that includes axial pressure and temperature differences, changes in local interfacial curvature, Marangoni effects, and the disjoining pressure. Relationships were developed for the interfacial mass flux in an extended meniscus, the heat transfer rate in the intrinsic meniscus, the “thermocapillary” heat-pipe limitation, as well as the nonevaporating superheated liquid film thickness that exists between adjacent menisci and occurs during liquid dry out in the evaporator. These relationships can be used to define quantitative restrictions and/or requirements necessary for proper operation of micro heat pipes. They also provide fundamental insight into the critical mechanisms required for proper heat pipe operation.


1999 ◽  
Vol 597 ◽  
Author(s):  
Roger J. Becker

AbstractThere is a maximum value for any nonlinear process, which can be found on the basis of fundamental quantum mechanics. With regard to single photon processes, there is a maximum absorption cross section, σa, which any molecule may reach. The maximum is 1.13 × 10-17 λ is the wavelength of the light, n is the refractive index of the host medium, and Q is the quality factor ascribed to the absorption line width. Thus large cross sections can only be obtained at the expense of a narrow operating range. The maximum is set by fundamental physics. Since nonlinear phenomena are highly resonant, the maxima of higher-order processes are also a strong function of the width of the resonance and the peak wavelength. In the case of twophoton absorption the peak value of the maximum cross section, σ2N or δ, is roughly 3.5 × 10-32 λ4nQ cm4/GW, or about 7 × 10-57 λ3 nQ cm4/photon. No value for a nonlinear coefficient is meaningful in the absence of the width of the resonance, the wavelength, and the refractive index of the medium at the wavelength of the measurement.The basic quantity of interest is the linear electronic polarizability. This fundamental quantity determines not only the absorption for the various processes of interest, but also the surface tension and the closely related solubility parameter. All scale with the polarizability a. The polarizability has a maximum value of e2/mω2; consequently the absorption cross sections have a corresponding ceiling. The maximum value for the peak in a resonant polarizability curve is set by a balance between the Coulomb potential energy of the electron and its kinetic energy. Hence it is an inherent property of the electron itself, irrespective of the molecular orbital in which it finds itself. All that the particular quantum configuration of the molecule does is partition the line strength for absorption among various possible transitions. The extreme case is when virtually all the strength is concentrated in a single transition, an inherently resonant condition.


2013 ◽  
Vol 731 ◽  
pp. 142-161 ◽  
Author(s):  
B. Figliuzzi ◽  
C. R. Buie

AbstractMany technological applications rely on the phenomenon of wicking flow induced by capillarity. However, despite a continuing interest in the subject, the influence of the capillary geometry on the wicking dynamics remains underexploited. In numerous applications, the ability to promote wicking in a capillary is a key issue. In this article, a model describing the capillary rise of a liquid in a capillary of varying circular cross-section is presented. The wicking dynamics is described by an ordinary differential equation with a term dependent upon the shape of the capillary channel. Using optimal control theory, we were able to design optimized capillaries which promote faster wicking than uniform cylinders. Numerical simulations show that the height of the rising liquid was up to 50 % greater with the optimized shapes than with a uniform cylinder of optimal radius. Experiments on specially designed capillaries with silicone oil show a good agreement with the theory. The methods presented can be useful in the design and optimization of systems employing capillary-driven transport including micro-heat pipes or oil extracting devices.


1991 ◽  
Vol 44 (6) ◽  
pp. 677 ◽  
Author(s):  
M EI-Shabshiry ◽  
SY EI Bakry ◽  
AH Moussa ◽  
MA Abdel-Raouf

Positron-lithium inelastic scattering is studied at positron energies ranging from 0�005 to 20 eV using the coupled static model. Two channels are open namely the elastic and positronium formation. The polarisation potentials of the Li atom in the first channel and that of the positronium atom in the second channel are taken into consideration in calculating the corresponding cross sections. The partial cross sections in each channel are calculated for eight values of the total angular momentum (0 ~.e ~ 7). In the elastic channel the total cross section Ull has its maximum value at the lowest energy, and decreases with an increase in positron energy Ki. The total positronium formation cross section has a small dip at 0�1 eV, and maximum value at Ki = 1 �4 eV, and then decreases smoothly with e+ energy. We compare our results with those of Ward et al. (1989) where positronium formation is ignored. The agreement in elastic cross sections improves with e+ energy, while the total collisional cross sections have the closest agreement at 1�0 eV. From this comparison, we find that positronium formation is important in the very low energy region, and the role of the excitation cross section increases steadily with e+ energy.


1980 ◽  
Vol 33 (2) ◽  
pp. 259 ◽  
Author(s):  
MT Elford

The momentum transfer cross section for electrons in mercury vapour has been derived over the energy range 0�1-5 eV from the drift velocity data of Elford (1980). The cross section has a resonance at 0�5 eV with a maximum value of 180 A 2 (1� 8 x 10-18 m2). It is shown that previous cross sections derived either from experimental data or obtained by ab initio calculations are incompatible with the drift velocity data.


1990 ◽  
Vol 68 (7-8) ◽  
pp. 582-586 ◽  
Author(s):  
D. C. Santry ◽  
R. D. Werner

The cross section of the 93Nb(n,2n)92mNb reaction has been studied by use of the activation method from the threshold energy of 8.8–19.8 MeV. Measurements are relative to the known cross-section values for the reactions H(n,n)H, 32S(n,p)32p, and 27Al(n,α)24Na. The cross-section value increases smoothly with energy and reaches a maximum value of 444 ± 18 mb at about 14.5 MeV then decreases to values of 293 ± 14 mb at 19.8 MeV. An effective cross-section value for a fission neutron spectrum calculated from the results is 0.321 ± 0.019 mb. The activation of Nb as a transfer standard for 14 MeV neutrons is discussed.


1999 ◽  
Vol 385 ◽  
pp. 63-78 ◽  
Author(s):  
M. S. HOWE

Rayleigh's (1926, Appendix A) method for the approximate calculation of potential flow from the open end of a semi-infinite flanged cylinder is applied to obtain analytical representations of Green's function describing the generation of sound waves within a flanged cylinder by sources located in the neighbourhood of the open end. Detailed results are given for the circular cylinder considered by Rayleigh and extension made to a flanged cylinder of rectangular cross-section. The validity of various approximations is assessed by comparison with the exact solution available (by the method of conformal transformation) for potential flow from a two-dimensional, flanged duct. The results are used to compare the profiles and the pressure gradients of compression waves generated when a high-speed train enters tunnels of circular and rectangular cross-sections.


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