Two Phase Flow Phase Change and Numerical Modeling Part 2 pdf

Two Phase Flow, Phase Change and Numerical Modeling 20 Input data: P L - laser power, f - focal distance of the focusing system, t on - laser pulse duration, t p - laser pulse period, p - additional gas pressure, g - material thickness, n - number of time steps that program are running for, t Δ - time step, M, N - number of digitization network in Ox and Oy directions, respectivelly. Both procedures (the main function and the procedure computing the boundaries) were implemented as MathCAD functions. 4. Numeric results The model equations were solved for a cutting process of metals with a high concentration of iron (steel case). In table 1 is presented the temperature distribution in material, computed in continuous regime lasers, with the following input data: L P1kW= (laser power), o 0.74η= (oxidizing efficiency), p0.8bar= (additional gas pressure), d 0.16mm= (focalized laser beam radius), D 10mm = (diameter of the generated laser beam), f 145mm = (focal distance of the focusing system), g 6mm= (material thickness) S A0.49= (absorbability on solid surface), L A0.68= (absorbability on liquid surface), 5 t10s − Δ= (time step), t 10ms = (operation time), M 8= (number of intervals on x direction), N 32= (number of intervals on y direction), T k 1000= (number of iterations). The iron material constants were taken into consideration, accordingly to the present (solid, liquid or vapor) state. The real temperatures in material are the below ones multiplied by 25. Temperature distribution was represented in two situations: at the material surface and at the material evaporating depth () z 4.192mm= (figure 3). Fig. 3. Temperature distribution, L P1kW,t10ms== The depths corresponding to the melting and vaporization temperatures are: top z 4.288mm= , respectively vap z 4.192mm= . The moments when material surface reaches the vaporization and melting temperatures are: 5 vap t 0.181 10 s − =⋅, respectively 5 top t 0.132 10 s − =⋅ . The temperature distributions at different depths within the material, for laser power L P 400W= , and processing time t 1ms= , are presented in figure 4. Modeling the Physical Phenomena Involved by Laser Beam – Substance Interaction 21 M N 1 2 3 4 5 6 7 8 9 1 120.3 120.3 120.3 120.3 120.3 71.6 45.0 21.4 1.0 2 120.3 120.3 120.3 120.3 71.6 71.6 45.0 21.4 1.0 3 120.3 120.3 120.3 120.3 71.6 71.7 44.8 21.3 1.0 4 120.3 120.3 120.3 120.3 71.6 71.6 44.7 21.3 1.0 5 120.3 120.3 120.3 120.3 71.6 71.6 44.3 21.1 1.0 6 120.3 120.3 120.3 120.3 71.6 68.4 42.1 20.1 1.0 7 120.3 120.3 120.3 120.3 71.6 64.9 40.0 19.1 1.0 8 120.3 120.3 120.3 120.3 71.6 61.7 38.0 18.2 1.0 9 120.3 120.3 120.3 120.3 71.6 59.0 35.4 17.4 1.0 10 120.3 120.3 120.3 120.3 71.6 56.8 35.0 16.8 1.0 11 120.3 120.3 120.3 120.3 71.6 54.9 33.9 16.3 1.0 12 120.3 120.3 120.3 120.3 71.6 53.4 33.0 15.8 1.0 13 120.3 120.3 120.3 120.3 71.6 52.2 32.3 15.5 1.0 14 120.3 120.3 120.3 120.3 71.6 51.3 31.7 15.2 1.0 15 120.3 120.3 120.3 120.3 71.6 50.3 31.0 14.9 1.0 16 120.3 120.3 120.3 94.9 64.4 47.2 29.5 14.2 1.0 17 120.3 120.3 120.3 71.6 64.0 42.5 26.0 12.5 1.0 18 120.3 120.3 120.3 71.6 57.3 38.3 23.5 11.4 1.0 19 120.3 120.3 120.3 71.6 53.1 35.2 21.4 10.3 1.0 20 120.3 120.3 120.3 71.6 47.4 29.6 17.4 8.4 1.0 21 120.3 120.3 71.6 61.2 37.5 23.2 13.5 6.5 1.0 22 120.3 120.3 71.6 45.0 25.8 14.7 8.0 3.9 1.0 23 120.3 86.0 39.3 18.7 9.2 5.0 2.9 1.7 1.0 24 25.6 7.6 4.2 2.7 1.9 1.5 1.2 1.1 1.0 25 1.5 1.3 1.2 1.1 1.1 1.0 1.0 1.0 1.0 26 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 33 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Table 1. Temperature distribution in material Two Phase Flow, Phase Change and Numerical Modeling 22 Fig. 4. Temperature distribution, L P 400W, t 1ms== The temperature distributions on the material surface (z 0)= are quite identical in both mentioned cases (figures 3 and 4). The material vaporization depth is depending on the processing time, and the considered input parameters as well. So, for a 10 times greater processing time and a 2.5 times greater laser power, one may observe a 10.94 times greater vaporization depth, compared with the previous case (z 0.383 mm)= . If comparing the obtained results, it results a quite small dimension of the liquid phase (difference between top z and vap z ) , within 0.006 ÷ 0.085 mm. Fig. 5. The vaporization speed variation vs. processing time Modeling the Physical Phenomena Involved by Laser Beam – Substance Interaction 23 Knowing the vaporization depth at a certain processing time allows evaluating the vaporization speed and limited processing speed. The vaporization speed variation as a function of processing time is presented in figure 5. It may be observed that vaporization speed is decreasing function (it decreases as the laser beam advances in material). The decreasing of the vaporization speed as the vaporization depth increases is owed to the laser beam defocusing effect, which augments once the laser beam advances in material. The processing speed is computed for a certain material thickness, as a function of vaporization speed corresponding to processing moment when vaporization depth is equal to material thickness. So, for a certain processing time, results the thickness of the material that may be processed, which is equal to vaporization depth. As a consequence of the mass-flow conserving law, in order to cut a material with a certain thickness, the time requested by moving the irradiated zone must be equal to the time requested by material breakdown. The following relation derives in this way, allowing evaluating the processing speed as a function of vaporization speed: Tvap 2d vv g =⋅ (98) In figure 6 are compared the processing speeds: analytically determined, experimentally determined and returned by the above presented method (Pearsica et al., 2010, 2008c). Fig. 6. Processing speed variation Two Phase Flow, Phase Change and Numerical Modeling 24 The experimental processing speeds were determined for a general use steel (OL 37), and iron material parameters were considered for the theoretical speeds. It may be observed in the presented figures that processing speed numerical results are a quite good approximation for the experimental ones, for the laser power L P 640 W= , the maximum error being 11.3% for p3bar= and, 17.28%, for p0.5bar= . In case of L P 320 W= , the numerical determined processing speed matches better the experimental one for small thickness of processed material (for g 1mm= , the error is 10.2%, for p0.5bar= , and 6.89%, for p3bar= ), the error being greater at bigger thickness (for g 3mm= and p0.5bar= the error is 89.4%, and for g 4mm= and p3bar= the error is 230.52%). According to the presented situation, it may be considered that, in comparison with the analytical processing speed, the numerical determined one match better the experiments. 5. Conclusion The computing function allowed determination of: temperature distribution in material, melting depth, vaporization depth, vaporization speed, working speed, returned data allowing evaluation of working and thermic affected zones widths too. The equations of the mathematical proposed model to describe the way the material submitted to laser action reacts were solved numerically by finite differences method. The algebraic system returned by digitization was solved by using an exact type method, known in literature as column solving method. The variables and the unknown functions were non-dimensional and it was chosen a net of equidistant points in the pattern presented by the substantial. Because the points neighboring the boundary have distances up to boundary different from the net parameters, some digitization formulas with variable steps have been used for them. An algebraic system of equation solved at each time-step by column method was obtained after digitization and application of the limit conditions. The procedure is specific to implicit method of solving numerically the heat equation and it was chosen because there were no restrictions on the steps in time and space of the net. Among the hypothesis on which the mathematics model is based on and hypothesis that need a more thorough analysis is the hypothesis on boundaries formation between solid state and liquid state, respectively, the liquid state and vapor state, supposed to be known previously, parameters that characterize the boundaries being determined from the thermic regime prior to the calculus moment. The analytical model obtained is experiment dependent, because there are certain difficulties in oxidizing efficiency o η determination, which implies to model the gas-metal thermic transfer mechanism. As well, some material parameters S (c, k, , A , ) ρ (which were assumed as constants) are temperature dependent. Their average values in interest domains were considered. The indirect results obtained as such (the thickness of penetrating the substantial, the vaporization speed) certify the correctness of the hypothesis made with boundary formula. The results thus obtained are placed within the limits of normal physics, which constitutes a verifying of the mathematics model equation. 6. Acknowledgment This work was supported by The National Authority for Scientific Research, Romania – CNCSIS-UEFISCDI: Grant CNCSIS, PN-II-ID-PCE-2008, no. 703/15.01.2009, code 2291: Modeling the Physical Phenomena Involved by Laser Beam – Substance Interaction 25 “Laser Radiation-Substance Interaction: Physical Phenomena Modeling and Techniques of Electromagnetic Pollution Rejection”. 7. References Belic, I. (1989). A Method to Determine the Parameters of Laser Cutting. Optics and Laser Technology , Vol.21, No.4, (August 1989), pp. 277-278, ISSN 0030-3992 Draganescu, V. & Velculescu, V.G. (1986). Thermal Processing by Lasers, Academy Publishing House, Bucharest, Romania Dowden, J.M. (2009). The Theory of Laser Materials Processing: Heat and Mass Transfer in Modern Technology, Springer, ISBN 140209339X, New York, USA Dowden, J.M. (2001). The Mathematics of Thermal Modeling, Chapman & Hall, ISBN 1-58488- 230-1, Boca Raton, Florida, SUA Hacia, L. & Domke, K. (2007). Integral Modeling and Simulating in Some Thermal Problems, Proceedings of 5 th IASME/WSEAS International Conference on Heat and Mass Transfer (THE’07) , pp. 42-47, ISBN 978-960-6766-00-8, Athens, Greece, August 25-27, 2007 Mazumder, J. (1991). Overview of Melt Dynamics in Laser Processing. Optical Engineering, Vol.30, No.8, (August 1991), pp. 1208-1219, ISSN 0091-3286 Mazumder, J. & Steen, W.M. (1980). Heat Transfer Model for C.W. Laser Materials Processing. Journal of Applied Physics, Vol.51, No.2, (February 1980), pp. 941-947, ISSN 0021-8979 Pearsica, M.; Baluta, S.; Constantinescu, C.; Nedelcu, S.; Strimbu, C. & Bentea, M. (2010). A Mathematical Model to Compute the Thermic Affected Zone at Laser Beam Processing. Optoelectronics and Advanced Materials, Vol.4, No.1, (January 2010), pp. 4-10, ISSN 1842-6573 Pearsica, M.; Constantinescu, C.; Strimbu, C. & Mihai, C. (2009). Experimental Researches to Determine the Thermic Affected Zone at Laser Beam Processing of Metals. Metalurgia International, Vol.14, Special issue no.12, (August 2009), pp. 224-228, ISSN 1582-2214 Pearsica, M.; Ratiu, G.; Carstea, C.G.; Constantinescu, C.; Strimbu, C. & Gherman, L. (2008). Heat Transfer Modeling and Simulating for Laser Beam Irradiation with Phase Transformations. WSEAS Transactions on Mathematics, Vol.7, No.11, (November 2008), pp. 2174-2180, ISSN 676-685 Pearsica, M.; Ratiu, I.G.; Carstea, C.G.; Constantinescu, C. & Strimbu, C. (2008). Electromagnetic Processes at Laser Beam Processing Assisted by an Active Gas Jet, Proceedings of 10th WSEAS International Conference on Mathematical Methods, Computational Technique and Intelligent Systems , pp. 187-193, ISBN 978-960-474-012-3, Corfu, Greece, October 26-28, 2008 Pearsica, M.; Baluta, S.; Constantinescu, C. & Strimbu, C. (2008), A Numerical Method to Analyse the Thermal Phenomena Involved in Phase Transformations at Laser Beam Irradiation, Journal of Optoelectronics and Advanced Materials, Vol.10, No.5, (August 2008), pp. 2174-2181, ISSN 1454-4164 Pearsica, M. & Nedelcu, S. (2005). A Simulation Method of Thermal Phenomena at Laser Beam Irradiation, Proceedings of 10 th International Conference „Applied Electronics“, pp. 269-272, ISBN 80-7043-369-8, Pilsen, Czech Republic, September 7-8, 2005 Riyad, M. & Abdelkader, H. (2006). Investigation of Numerical Techniques with Comparison Between Anlytical and Explicit and Implicit Methods of Solving One- Two Phase Flow, Phase Change and Numerical Modeling 26 Dimensional Transient Heat Conduction Problems. WSEAS Transactions on Heat and Mass Transfer , Vol.1, No.4, (April 2006), pp. 567-571, ISSN 1790-5044 Shuja, S.Z.; Yilbas, B.S. & Khan, S.M. (2008). Laser Heating of Semi-Infinite Solid with Consecutive Pulses: Influence of Material Properties on Temperature Field. Optics and Laser Technology , Vol.40, No.3, (April 2008), pp. 472-480, ISSN 0030-3992 Steen, W.M. & Mazumder, J. (2010). Laser Material Processing, Springer-Verlag, ISBN 978-1- 84996-061-8, London, Great Britain 2 Numerical Modeling and Experimentation on Evaporator Coils for Refrigeration in Dry and Frosting Operational Conditions Zine Aidoun, Mohamed Ouzzane and Adlane Bendaoud CanmetENERGY-Varennes Natural Resources Canada Canada 1. Introduction The drive to improve energy efficiency in refrigeration and heat pump systems necessarily leads to a continuous reassessment of the current heat transfer surface design and analysis techniques. The process of heat exchange between two fluids at different temperatures, separated by a solid wall occurs in many engineering applications and heat exchangers are the devices used to implement this operation. If improved heat exchanger designs are used as evaporators and condensers in refrigerators and heat pumps, these can considerably benefit from improved cycle efficiency. Air coolers or coils are heat exchangers applied extensively in cold stores, the food industry and air conditioning as evaporators. In these devices, heat transfer enhancement is used to achieve high heat transfer coefficients in small volumes, and extended surfaces or fins, classified as a passive method, are the most frequently encountered. Almost all forced convection air coolers use finned tubes. Coils have in this way become established as the heat transfer workhorse of the refrigeration industry, because of their high area density, their relatively low cost, and the excellent thermo physical properties of copper and aluminum, which are their principal construction materials. Compact coils are needed to facilitate the repackaging of a number of types of air conditioning and refrigeration equipment: a reduced volume effectively enables a new approach to be made to the modular design and a route towards improving performance and size is through appropriate selection of refrigerants, heat transfer enhancement of primary and secondary surfaces through advanced fin design and circuit configurations. Circuiting, although practically used on an empirical basis, has not yet received sufficient attention despite its potential for performance improvement, flow and heat transfer distribution, cost and operational efficiency. In the specific case of refrigeration and air conditioning, a confined phase changing refrigerant exchanges heat in evaporators with the cold room, giving up its heat. The design and operation of refrigeration coils is adapted to these particular conditions. Geometrically they generally consist of copper tubing to which aluminum fins are attached to increase their external surface area over which air is flowing, in order to compensate for this latter poor convection heat transfer. Coils generally achieve relatively high heat transfer area per unit volume by having dense arrays of finned tubes and the fins are generally corrugated or occasionally louvered plates with variable spacing and number of passes. Internal heat transfer of phase changing refrigerant is high and varies Two Phase Flow, Phase Change and Numerical Modeling 28 with flow regimes occurring along the tube passes. Flow on the secondary surfaces (outside of tubes and fins) in cooling, refrigeration or deep freezing, becomes rapidly complicated by the mass transfer during the commonly occurring processes of condensation and frost deposition, depending on the air prevailing conditions. Overall, geometric and operational considerations make these components very complex to design and analyse theoretically. 2. Previous research highlights An inherent characteristic of plate fin-and-tube heat exchangers being that air-side heat transfer coefficients are generally much lower than those on the refrigerant side, an effective route towards their performance improvement is through heat transfer enhancement. Substantial gains in terms of size and cost are then made, on heat exchangers and related units, during air dehumidification and frost formation. In the specific case of evaporators and condensers treated here, it is the primary and secondary surfaces arrangements or designs that are of importance i.e. fins and circuit designs. These arrangements are generally known as passive enhancement, implying no external energy input for their activation. Fins improve heat exchange with the airside stream and come in a variety of shapes. In evaporators and condensers, round tubes are most commonly encountered and fins attached on their outer side are either individually assembled, in a variety of geometries or in continuous sheets, flat, corrugated or louvered. For refrigeration, fins significantly alleviate the effect of airside resistance to heat transfer. Heat exchangers of this type are in the class of compact heat exchangers, characterized by area densities as high as 700 m 2 /m 3 . Heat transfer enhancement based on the use of extended surfaces and circuiting has received particular attention in our studies. By discussing some of the related current research in the context of work performed elsewhere, it is our hope that researchers and engineers active in the field will be able to identify new opportunities, likely to emerge in their own research. Our efforts are successfully articulated around experimentation with CO 2 as refrigerant for low temperature applications and novel modeling treatment of circuit design and frost deposition control. 2.1 Modeling Modeling of refrigeration heat exchangers for design and performance prediction has been progressing during the last two decades or so in view of the reduced design and development costs it provides, as opposed to physical prototyping. Most models handle steady state, dry, wet or frosting operating conditions. They fall into two main approaches: zone-by-zone and incremental. Zone-by-zone models divide the heat exchanger into subcooled, two-phase and superheated regions which are considered as independent heat exchangers hooked in series. Incremental methods divide the heat exchanger in an arbitrary number of small elements. They can be adapted to perform calculations along the refrigerant flow path and conveniently handle circuiting effects, as well as fluid distributions. Several models of both types are available in the literature for design and simulation, with different degrees of sophistication. Only a representative sample of existing research on heat exchanger coils is reported here and the main features highlighted. (Domanski, 1991) proposed a tube–by-tube computation approach which he applied to study the effect of non-uniform air distribution on the performance of a plate-and-tube heat exchanger. Based on the same approach, (Bensafi et al., 1997) developed a general tool for [...]... 4435 .2 80.7 % 1 52. 5 -22 .9 -30.0 CASE 2 FMT 4811.5 4914.1 89.0 % 149.6 -23 .5 -29 .9 - 75.0 % 1 32. 2 -22 .9 -29 .6 65.6 - Experiments 4471.0 - ISWS 14 02. 4 1379.1 32. 5 % 29 .3 -22 .6 -24 .5 CASE 3 FMT 1557 .2 1550.0 36.5 % 38.6 -22 .8 -24 .8 - 35.5 % 44.4 -22 .7 -24 .9 76.0 Experiments 1495.9 - ISWS 5588.8 5590.6 45.3% 195.0 -19.4 -26 .6 - CASE 4 FMT 5869.4 5683.8 47.5% 398.9 -19.8 -30.8 - 43.5 % 303.4 -19.1 -28 .8... range of the measurements and because of the limited number of data points it is not possible at this stage to identify a variation tendency Circulation ratio N=1.0 N=1 .23 N=1.50 N =2. 90 N=5. 42 5.1 6 .23 7.6 14.7 27 .5 Tin (C) -24 .1 -24 .3 -24 .1 -24 .1 -24 .1 x (%) (exit) 100.0 82. 8 68.8 36 .2 19.7 ΔP (kPa) 10.0 19.5 27 .8 45.3 78.1 Tairin ( C) -20 .0 -19.95 -20 .0 -20 .2 -20 .3 Mass flow rate (g/s) 605.1 589... the end of the evaporation process and result in correspondingly high departures of the pressure drop outside the range covered by the correlations used CO2 CO2 Air CO2 Outlet relative humidity (%) Air ISWS 4091.0 41 12. 9 52. 8 % 170 .2 -22 .4 -29 .4 - CASE 1 FMT 4438.3 4530.6 58.0 % 195 .2 -23 .0 -29 .9 - 51.4 % 171.6 -22 .4 -29 .6 66.0 - Capacity (W) Air Experiments 4083.3 CO2 - Outlet quality ΔP (kPa) Outlet... (Ouzzane & Aidoun, 20 07) Geometry and conditions Circulation ratio 1 2 3 4 m CO2 (g / s) 11.6 23 .2 34.8 46.4 x (%) (exit) 99.66 55.48 37.99 29 .89 ΔP (kPa) 82. 66 164. 02 220 .74 28 8 .26 Q (kW) 3.551 3.774 3.749 3.6 72 ΔTCO2 1.744 3.533 4.81 6.3944 • Inner diameter = 8.7mm Ext diameter = 9.5mm Fins (27 .8×31.8×0.19) 118 fins/m, L = 90 m Tco2=-30C, Tairin= -24 C • m air = 1.105 (kG / s) CO2 Table 4 Calculation results... material on circuit and frost modeling, as well as analysis results will be introduced For a detailed review of operational details and data under different conditions, the reader is referred to (Seker et al., 20 04a, 20 04b), (Wang et al., 1996) and (Wang et al., 1997)  32 Two Phase Flow, Phase Change and Numerical Modeling 3 Research at CanmetENERGY 3.1 Theoretical approach Two essential and most uncertain... Table 2 Comparison of numerical results from two resolution procedures and experiments Numerical Modeling and Experimentation on Evaporator Coils for Refrigeration in Dry and Frosting Operational Conditions Air inlet in coil Fig 8 Pictures showing the frost formed on tubes and fins Fig 9 Variation of the frost thickness with time Air outlet in coil 43 44 Two Phase Flow, Phase Change and Numerical Modeling. .. temperature between air inlet and outlet Ac : total air side heat transfer area (14) 36 Two Phase Flow, Phase Change and Numerical Modeling Amin: minimum free flow area through which air passes across the coil β: ratio of free -flow to frontal area The air friction factor fa is calculated by the correlation proposed by (Wang et al., 20 02) f3 fa = 0 .22 8Re ( tan θ ) fl Dc f2 f4  Fs   S 1   f5  ... to inlet and outlet of the coil: air flows from one compartment to the other through a duct enclosing the coil Air circulation is maintained by a blower The compartments are well insulated in order to reduce infiltration of outside air and moisture Fig 4 Flow chart of the computing procedure for FMT 40 Two Phase Flow, Phase Change and Numerical Modeling Means of adjusting air temperature and humidity... junction between two tubes; the coordinates I and K indicate the direction of flow: incoming and destination, respectively The values of J(I,K) are: 38 Two Phase Flow, Phase Change and Numerical Modeling 0 no connection between I and K tubes J(I,K) =  1 connection between I and K tubes Index 1 for I or K is allowed only for the exit or entry to the system (Fig 3) shows an example of a heat exchanger with...      m r  =   m r  and  ou  in  •   ma   ou  •  = m a   in (1) Equation of momentum Pressure losses are calculated in tubes and return bends as follows: For tubes: (P ) r For return bends: ou = ( Pr )in − ( ΔPr ) l (2a) 34 Two Phase Flow, Phase Change and Numerical Modeling (P ) r ou = ( Pr )in − ( ΔPr )b (2b) For single phase, subcooled liquid and superheated vapour, the Darcy-Weisbach . 16.3 1.0 12 120 .3 120 .3 120 .3 120 .3 71.6 53.4 33.0 15.8 1.0 13 120 .3 120 .3 120 .3 120 .3 71.6 52. 2 32. 3 15.5 1.0 14 120 .3 120 .3 120 .3 120 .3 71.6 51.3 31.7 15 .2 1.0 15 120 .3 120 .3 120 .3 120 .3 71.6. 16 120 .3 120 .3 120 .3 94.9 64.4 47 .2 29.5 14 .2 1.0 17 120 .3 120 .3 120 .3 71.6 64.0 42. 5 26 .0 12. 5 1.0 18 120 .3 120 .3 120 .3 71.6 57.3 38.3 23 .5 11.4 1.0 19 120 .3 120 .3 120 .3 71.6 53.1 35 .2 21.4. 21 M N 1 2 3 4 5 6 7 8 9 1 120 .3 120 .3 120 .3 120 .3 120 .3 71.6 45.0 21 .4 1.0 2 120 .3 120 .3 120 .3 120 .3 71.6 71.6 45.0 21 .4 1.0 3 120 .3 120 .3 120 .3 120 .3 71.6 71.7 44.8 21 .3 1.0 4 120 .3