Thermo-hydraulic predictions for multi-pass evaporators by orthogonal collocation using a new flow pattern map

A recently published paper by this author [S. Thyageswaran, Analysis of multi-pass evaporators using orthogonal collocation, Int. J. Refrigeration doi:10.1016/j.ijrefrig.2007.06.011 (in press)], shows that orthogonal collocation is an effective alternative to traditional integration for the thermal analysis of multi-pass evaporators. The steady rate of heat exchanged (Q) and overall pressure drop (Δp), for an R-22 based chiller having one shell and eight tube passes, were predicted using the Kattan–Thome–Favrat and the Müller-Steinhagen and Heck models for the boiling R-22. While Q was over-predicted by 0.95%, Δp was over-predicted by 20.3%. In the present work, results have been obtained using state-of-the-art, unified heat transfer and pressure drop sub-models based upon an improved flow pattern map by Wojtan et al. [L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes, part 1: a new diabatic two-phase flow pattern map, Int. J. Heat Mass Transfer 48 (2005) 2955–2969; L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes, part 2: development of a new heat transfer model for stratified-wavy, dryout and mist flow regimes, Int. J. Heat Mass Transfer 48 (2005) 2970–2985], and Moreno Quibén and Thome [J.M. Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, part 1: diabatic and adiabatic experimental study, Int. J. Heat Fluid Flow 28 (5) (2007) 1049–1059; J.M. Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, part 2: new phenomenological model, Int. J. Heat and Fluid Flow 28 (5) (2007) 1060–1072]. The new predictions for Q and Δp are 141.76 kW and 13.3 kPa, respectively, compared to their rated values of 140.67 kW and 13.789 kPa.     

Computation of high Prandtl number turbulent thermal fields by the analytical wall-function

The extended version of the analytical wall-function (AWF) for rough wall turbulence by Suga et al. [K. Suga, T.J. Craft, H. Iacovides, An analytical wall-function for turbulent flows and heat transfer over rough walls. Int. J. Heat Fluid Flow 27 (2006) 852–866] is improved for high Prandtl number flows. The original AWF assumes a linear profile of turbulent viscosity near a wall though it is widely recognised that a theoretically correct cubic profile of the turbulent viscosity is essential for heat transfer of high Prandtl number flows. In order to predict thermal boundary layer of high Prandtl number fluid flows, the present approach thus employs a correct limiting profile of the turbulent viscosity in the analytical integration process. The presently proposed version of the AWF proves its good performance for predicting turbulent high Prandtl number thermal flows at Pr  4 × 10⁴ for smooth wall cases, and at least at Pr  10 for rough wall cases.     

Investigation of flow boiling in horizontal tubes: Part I—A new diabatic two-phase flow pattern map

Several important modifications to the flow pattern map of Kattan-Thome-Favrat [J. Heat Transfer 120(1) (1998) 140-147] made, resulting in a significantly new version of the map. Based on the dynamic void fraction measurements described in [Int. J. Multiphase Flow 30 (2004) 125-137], the stratified-wavy region has been subdivided into three subzones: slug, slug/stratified-wavy and stratified-wavy. Furthermore, annular-to-dryout and dryout-to-mist flow transition curves have been added and integrated into the new flow pattern map, identified by distinct trends of the heat transfer coefficient as a function of vapor quality and by flow pattern observations to determine (and then predict) the inception and completion of dryout in horizontal tubes.     

A modification of a Nusselt number correlation for forced convection in porous media

We report numerical simulations of forced convection heat transfer rates of a steady laminar flow in a two-dimensional model of porous media to elucidate the differences observed between the numerical predictions of Kuwahara et al. (2001) [Int. J Heat Mass Trans. 44, 1153–1159] and Gamrat et al. (2008) [Int. J Heat Mass Trans. 51, 853–864]. A modification in the correlation given by Kuwahara et al. (2001) is proposed to make the results of the three numerical studies comparable and in agreement with the experimental data.     

Investigation of flow boiling in horizontal tubes: Part II—Development of a new heat transfer model for stratified-wavy, dryout and mist flow regimes

The new version of the flow pattern map presented in Part I of this paper has been used to modify the dry angle in the heat transfer model of Kattan-Thome-Favrat [J. Heat Transfer, 120 (1) (1998) 156]. This significantly improves the heat transfer prediction in stratified-wavy flow. Moreover, a new heat transfer prediction method has been developed for the dryout and mist flow regimes, which extends the applicability of the heat transfer model to these flow regimes. An extensive flow boiling heat transfer database has been acquired for R-22 and R-410A to develop and validate the new heat transfer prediction methods. The new model also shows good agreement with the independent heat transfer data of Lallemand et al. [M. Lallemand, C. Branescu, P. Haberschill, Local heat transfer coefficients during boiling of R-22 and R-407C in horizontal smooth and microfin tubes, Int. J. Refrigeration, 24 (2001) 57-72].     

Modeling of turbulent heat transfer and thermal dispersion for flows in flat plate heat exchangers

In this paper, heat transfer and dispersion for both laminar and turbulent regimes in heat exchangers and nuclear cores are considered. Such hydraulic systems might be seen as spatially periodic porous media. The existence of a turbulent flow within a porous medium structure suggests the use of a spatial average operator, combined to a statistical average operator. Previous works [M.H.J. Pedras, M.J.S. De Lemos, Macroscopic turbulence modeling for incompressible flow through undeformable porous media, Int. J. Heat Mass Transfer 44 (2001) 1081–1093; F. Kuwahara, A. Nakayama, H. Koyama, A numerical study of thermal dispersion in porous medium, J. Heat Transfer 118 (1996) 756–761] have applied a double average procedure to the thermal balance equation, which led to a macroscopic turbulent transport and a subsequent macro-scale equation featuring dynamic dispersion. Considering the heat flux at the solid surfaces as a boundary condition for the fluid energy balance, the model proposed in this paper allows one to take into account this dispersion as the sum of two contributions. The first one is the classical dispersion due to velocity heterogeneities [G. Taylor, Dispersion of solute matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Lond. A 219 (1953) 186–203] and the second one is due to wall heat transfer. Applying Whitaker up-scaling method [S. Whitaker, Theory and applications of transport in porous media: the method of volume averaging, Kluwer Academic Publishers, 1999], a “closure problem” is then derived for a representative elementary volume, using the so-called Boussinesq approximation to account for small scale turbulence. The model is used to compute macro-scale heat transfer properties for turbulent flows inside a flat plate heat exchanger. It is shown that, for such flows, both dispersive fluxes strongly predominate over the macroscopic turbulent heat flux.     

Flow boiling in horizontal flattened tubes: Part I – Two-phase frictional pressure drop results and model

Experiments of diabatic two-phase pressure drops in flow boiling were conducted in four horizontal flattened smooth copper tubes with two different heights of 2 and 3 mm. The equivalent diameters of the flat tubes are 8.6, 7.17, 6.25, and 5.3 mm. The working fluids are R22 and R410A, respectively. The test conditions are: mass velocities from 150 to 500 kg/m² s, heat fluxes from 6 to 40 kW/m² and saturation temperature of 5 °C (reduced pressures p_r are 0.12 for R22 and 0.19 for R410A). The experimental results of two-phase pressure drops are presented and analyzed. Furthermore, the predicted two-phase frictional pressure drops by the flow pattern based two-phase pressure drop model of Moreno Quibén and Thome [J. Moreno Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, Part I: Diabatic and adiabatic experimental study, Int. J. Heat Fluid Flow 28 (2007) 1049–1059; J. Moreno Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, Part II: New phenomenological model, Int. J. Heat Fluid Flow 28 (2007) 1060–1072] using the equivalent diameters were compared to the experimental data. The model, however, underpredicts the flattened tube two-phase frictional pressure drop data. Therefore, correction to the annular flow friction factor was proposed for the flattened tubes and now the method predicts 83.7% of the flattened tube pressure drop data within ±30%. The model is applicable to the flattened tubes in the test condition range in the present study. Extension of the model to other conditions should be verified with experimental data.     

Homogeneous turbulence evolution in a stably stratified flow—III. Near time span at low inverse Froude number and distant time span at arbitrary Froude number

This paper is the third and last part of work studying analytically and numerically the second-order turbulence model [B.A. Kolovandin, Modelling the dynamics of turbulent transport processes, in: Advances in Heat Transfer, vol. 21. Pergamon, 1991, pp. 185–234, and B.A. Kolovandin, V.U. Bondarchuk, C. Meola, G. De Felice, Modeling of the homogeneous turbulence dynamics of stably stratified media, Int. J. of Heat and Mass Transfer 36 (1993) 1953–1968] for homogeneous turbulence in stratified media. As in the two previous parts [V.A. Babenko, Homogeneous turbulence evolution in stably stratified flow—I. Internal gravity waves at low inverse Froude numbers, Int. J. of Heat and Mass Transfer 40 (1997) 1951–1961, and V.A. Babenko, Homogeneous turbulence evolution in stably stratified flow—II. Asymptotic regimes of large evolution time at low inverse Froude numbers. Int. J. of Heat and Mass Transfer 40 (1997) 1963–1976], the model is studied with asymptotic small parameter methods. In this part the inverse Froude number and the inverse evolution time are used for this purpose.     

Heat transfer in micro-channels: Comparison of experiments with theory and numerical results

This paper considers experimental and theoretical investigations on single-phase heat transfer in micro-channels. It is the second part of general exploration “Flow and heat transfer in micro-channels”. The first part discussed several aspects of flow in micro-channels, as pressure drop, transition from laminar to turbulent flow, etc. [G. Hetsroni, A. Mosyak, E. Pogrebnyak, L.P. Yarin, Fluid flow in micro-channels, Int. J. Heat Mass Transfer 48 (2005) 1982–1998]. In this paper, the problem of heat transfer is considered in the frame of a continuum model, corresponding to small Knudsen number. The data of heat transfer in circular, triangular, rectangular, and trapezoidal micro-channels with hydraulic diameters ranging from 60 μm to 2000 μm are analyzed. The effects of geometry, axial heat flux due to thermal conduction through the working fluid and channel walls, as well as the energy dissipation are discussed. We focus on comparing experimental data, obtained by number of investigators, to conventional theory on heat transfer. The analysis was performed on possible sources of unexpected effects reported in some experimental investigations.     

New prediction methods for CO2 evaporation inside tubes: Part II—An updated general flow boiling heat transfer model based on flow patterns

Corresponding to the updated flow pattern map presented in Part I of this study, an updated general flow pattern based flow boiling heat transfer model was developed for CO₂ using the Cheng–Ribatski–Wojtan–Thome [L. Cheng, G. Ribatski, L. Wojtan, J.R. Thome, New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside horizontal tubes, Int. J. Heat Mass Transfer 49 (2006) 4082–4094; L. Cheng, G. Ribatski, L. Wojtan, J.R. Thome, Erratum to: “New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside tubes” [Heat Mass Transfer 49 (21–22) (2006) 4082–4094], Int. J. Heat Mass Transfer 50 (2007) 391] flow boiling heat transfer model as the starting basis. The flow boiling heat transfer correlation in the dryout region was updated. In addition, a new mist flow heat transfer correlation for CO₂ was developed based on the CO₂ data and a heat transfer method for bubbly flow was proposed for completeness sake. The updated general flow boiling heat transfer model for CO₂ covers all flow regimes and is applicable to a wider range of conditions for horizontal tubes: tube diameters from 0.6 to 10 mm, mass velocities from 50 to 1500 kg/m² s, heat fluxes from 1.8 to 46 kW/m² and saturation temperatures from ?28 to 25 °C (reduced pressures from 0.21 to 0.87). The updated general flow boiling heat transfer model was compared to a new experimental database which contains 1124 data points (790 more than that in the previous model [Cheng et al., 2006, 2007]) in this study. Good agreement between the predicted and experimental data was found in general with 71.4% of the entire database and 83.2% of the database without the dryout and mist flow data predicted within ±30%. However, the predictions for the dryout and mist flow regions were less satisfactory due to the limited number of data points, the higher inaccuracy in such data, scatter in some data sets ranging up to 40%, significant discrepancies from one experimental study to another and the difficulties associated with predicting the inception and completion of dryout around the perimeter of the horizontal tubes.     

Influence of the particle–turbulence modulation modelling in the simulation of a non-isothermal gas–solid flow

A gas–solid suspension upward flowing in a heated vertical pipe has been simulated numerically using both Eulerian–Eulerian and Eulerian–Lagrangian approaches. Particular attention has been paid to the influence of the modelling of the particle–turbulence interactions. A model based on a source-term formulation derived from a study by Crowe (Int. J. Multiphase Flow 26 (5) (2000) 719) allows predicting turbulence enhancement due to a strong particle influence in the core of the pipe flow. Calculations of suspension Nusselt numbers, characterizing the heat transfer between the pipe wall and the flow, have therefore been performed, with a satisfactory level of accuracy, compared with available experimental data. Some numerical difficulty remains however, especially due to the near-wall layer interactions which seem very difficult to simulate.     

Numerical solution of hyperbolic heat conduction in thin surface layers

The purpose of the present paper is to propose a new hybrid method investigating the effect of the surface curvature of a solid body on hyperbolic heat conduction. The difficulty encountered in the numerical solutions of hyperbolic heat conduction problems is the numerical oscillation in vicinity of sharp discontinuities. In the present study, we have developed a new hybrid method combined the Laplace transform, the weighting function scheme [Shong-leih Lee, Weighting function scheme and its application on multidimensional conservation equations, Int. J. Heat Mass Transfer 32 (1989) 2065–2073], and the hyperbolic shape function for solving time dependent hyperbolic heat conduction equation with a conservation term. Four different examples have been analyzed by the present method. It is found from these examples that the present method is in good agreement in the analytical solutions [Tsai-tse Kao, Non-Fourier heat conduction in thin surface layers, J. Heat Transfer 99 (May) (1977) 343–345] and does not exhibit numerical oscillations at the wave front and the surface temperature is modified by the surface curvature during the short period when the non-Fourier effect is significant. The curvature will increase or decrease the temperature of the wave front, depending on whether the surface is concave or convex.     

Generic features and puzzles of nucleate boiling

At high reduced pressures extremely high nucleate boiling heat transfer coefficients (HTC) were measured. A single mechanism, which presents a consistent explanation of such HTCs, is very high intensity of liquid evaporation at the periphery of dry spots (nucleation sites) at the heated wall. Due to very small size the nucleation sites can be considered as point heat sinks. Between them convective heat transfer occurs, which in its turn is governed by the inherent mechanisms of boiling. The above two mechanisms comprise a total heat flux from the heated wall in nucleate boiling. The predicting equation, which determines heat flux in boiling via the wall superheat and liquid properties, has been developed with accuracy to two universal numerical factors fitted to the experimental data. Although the equation developed is found to be in good agreement with numerous experimental data for different liquids and in the wide range of reduced pressures and heat fluxes there exists a problem in nucleate boiling, which has not been understood to the full even qualitatively. This problem is the dependence of nucleation site density on the physical properties of the liquid and on the controlling parameters. Some new experimental results by Theofanous et al. [T.G. Theofanous, T.N. Dinh, J.P. Tu, A.T. Dinh, The boiling crisis phenomenon. Part I: Nucleation and nucleate boiling heat transfer, Exp. Therm. Fluid Sci. 26 (2002) 775–792; T.G. Theofanous, T.N. Dinh, J.P. Tu, A.T. Dinh, The boiling crisis phenomenon. Part II: Dryout dynamics and burnout, Exp. Therm. Fluid Sci. 26 (2002) 793–810.] and Qi et al. [Y. Qi, J.F. Klausner, R. Mei, Role of surface structure in heterogeneous nucleation, Int. J. Heat Mass Transfer 47 (2004) 3097–3107; Y. Qi, J.F. Klausner, Heterogeneous nucleation with artificial cavities, J. Heat Transfer 127 (2005) 1189–1196; Y. Qi, J.F. Klausner, Comparison of nucleation site density for pool boiling and gas nucleation, J. Heat Transfer 128 (2006) 13–20.] require revising the traditional views on a nature of the active nucleation sites in boiling. These results remind the old question: why can the nucleation sites arise at low superheats of the absolutely wettable surface? Obtaining theoretical equation for nucleation site density remains the most significant challenge in nucleate boiling theory.     

A rapid method for counter-flow heat regenerator calculation

A new rapid method of counter-flow heat regenerators performance prediction is presented. This method is based on analytical equation (15) which can be applied for regenerators operating in broad range of period time length. The accuracy of the method has been compared for slim regenerators with the robust method by Hill and Willmott [A. Hill, A.J. Willmott, A robust method for regenerative heat exchanger calculations, Int. J. Heat Mass Transfer 30 (1987) 241] and for corpulent regenerators with the solution by Hill and Willmott [A. Hill, A.J. Willmott, Accurate and rapid thermal regenerator calculations, Int. J. Heat Mass Transfer 32 (1989) 465].     

Nucleate boiling heat transfer from a structured surface – Effect of liquid intake

A model of the suction evaporation mode in nucleate boiling from tunnel and pore structures is presented. The model is based on the analysis by Nakayama et al. [W. Nakayama, T. Daikoku, H. Kuwahara, T. Nakajima, Dynamic model of enhanced boiling heat transfer on porous surfaces – Part II. Analytical model, ASME J. Heat Transfer 102 (3) (1980) 451–456] and L.H. Chein and R.L. Webb [A nucleate boiling model for structured enhanced surfaces, Int. J. Heat Mass Transfer 41 (14) (1998) 2183–2195]. Additionally, a detailed phenomenological model of liquid refill has been developed. It has been shown that the process of liquid refill and the time needed for it is strongly dependent on pool height. Effect of liquid pool height on bubble frequency has also been discussed. Finally, a generalized methodology is given for the prediction of boiling data from a structured surface.     

Performance of 2D scheme and different models in predicting flow turbulence and heat transfer through a supersonic turbine nozzle cascade

A number of turbulence models were employed to investigate the heat transfer and aerodynamic characteristics through a nozzle cascade of a high-pressure gas turbine. Isentropic Mach number and Nusselt number around the vane were predicted and compared to existing experimental data obtained at a supersonic flow condition. According to the result presented by different models, possible source of the prediction error was identified; and the performance of different turbulence closures in predicting the heat transfer characteristics around the vane was discussed. It shows that the calculated heat transfer result was affected directly by the predicted turbulence transportation throughout the boundary layer. Finally considering the computational cost and the performance of the models, the suitable model(s) are recommended for the further 3D applications.     

Ammonia two-phase flow in a horizontal smooth tube: Flow pattern observations,diabatic and adiabatic frictional pressure drops and assessment of prediction methods

The present study illustrates new experimental two-phase flow pattern observations together with diabatic boiling and adiabatic two-phase frictional pressure drop results for ammonia (R717) flowing inside a 14-mm internal diameter, smooth horizontal stainless steel tube. The flow pattern observations were made for mass velocities of 50, 100 and 160 kg s^?1 m^?2 and saturation temperatures of ?14, ?2 and 12 °C for vapor qualities ranging from 0.05 to 0.6. The flow patterns observed during the study included: stratified-wavy, slug-stratified-wavy, slug, intermittent and annular. For all the experimental conditions, the flow structure observations were compared against the predictions of the flow pattern map model of Wojtan et al. [L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes: part I – a new diabatic two-phase flow pattern map, Int. J. Heat Mass Transfer 48 (2005) 2955–2969] and showed very good correspondence. The frictional pressure drop measurements were obtained for vapor qualities from 0.05 to 0.6, saturation temperatures from ?14 to 14 °C, mass velocities from 50 to 160 kg s^?1 m^?2 and heat fluxes from 12 to 25 kW m^?2. The experimental results show the traditional pressure drop trends: the frictional pressure drop increases with vapor quality and mass velocity. Moreover, the results also show that both diabatic and adiabatic frictional pressure drop values are similar, that is, the boiling process in itself does not affect the frictional pressure drop. The correlations of Friedel [L. Friedel, Improved friction drop correlations for horizontal and vertical two-phase pipe flow, in: European Two-Phase Flow Group Meeting, paper E2, Ispra, Italy, 1979], Lockhart and Martinelli [R.W. Lockhart, R.C. Martinelli, Proposed correlation of data for isothermal two-phase two-component in pipes, Chem. Eng. Process 45 (1949) 39–48] and Müller-Steinhagen and Heck [H. Müller-Steinhagen, K. Heck, A simple friction pressure correlation for two-phase flow in pipes, Chem. Eng. Process 20 (1986) 297–308] predicted only 54%, 52% and 60% of the experimental data within ±30%, respectively. The correlation of Grönnerud [R. Grönnerud, Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type of evaporators, part iv: two-phase flow resistance in boiling refrigerans, in: Annexe 1972-1, Bull. de l’Inst. Froid, 1979] predicted 93% of the data and the flow pattern based method of Moreno Quibén and Thome [J. Moreno Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part II: new phenomenological model, Int. J. Heat Fluid Flow 28 (2007) 1060–1072] predicted more than 97% of the experimental data within the same error band, while the latter method captures almost 89% of the data within ±20%.     

Predictions of Flow and Heat Transfer in Low Emission Combustors

Flow and heat transfer predictions in modern low emission combustors are critical to maintaining the liner wall at reasonable temperatures. This study is the first to focus on a critical issue for combustor design. The objective of this paper is to understand the effect of different swirl angle for a dry low emission (DLE) combustor on flow and heat transfer distributions. This paper provides the effect of fuel nozzle swirl angle on velocity distributions, temperature, and surface heat transfer coefficients. A simple test model is investigated with flow through fuel nozzles without reactive flow. The fuel nozzle angle is varied to obtain different swirl conditions inside the combustor. The effect of flow Reynolds number and swirl number are investigated using FLUENT. Different RANS-based turbulence models are tested to determine the ability of these models to predict the swirling flow. For comparison, different turbulence models such as standard k ? ε, realizable k ? ε, and shear stress transport (SST) k?ω turbulence model were studied for non-reactive flow conditions. The results show that, for a high degree swirl flow, the SST k?ω model can provide more reasonable predictions for recirculation and high velocity gradients. With increasing swirl angle, the average surface heat transfer coefficient increases while the average static temperature will decrease. Preliminary analysis shows that the k?ω model is the best model for predicting swirling flows. Also critical is the effect of the swirling flows on the liner wall heat transfer. The strength and magnitude of the swirl determines the local heat transfer maxima location. This location needs to be cooled more effectively by various cooling schemes.     

Effect of lateral fin profiles on turbulent flow and heat transfer performance of internally finned tubes

Heat transfer performance of internally finned tubes with blocked core-tube was numerically investigated by the realizable k–ε turbulence model with wall function method using a commercial software FLUENT. Three kinds of lateral fin profiles, that is, S-shape, Z-shape and V-shape, were studied and compared. The corresponding correlations of Nusselt number and friction factor for different-shape internally finned tubes were obtained. The comprehensive performances of the studied tubes were compared under identical mass flow rate, identical pumping power and identical pressure drop conditions. It was found that tubes with S-shape fins and Z-shape fins were superior to that with V-shape fins, and moreover, tube with Z-shape fins had the best performance. The fin outer curvature radius R near the inner surface of out-tube for the S-shape finned tube had appreciable effect on heat transfer, whereas the fin inner curvature radius r near the outer surface of blocked core-tube had little impact on heat transfer. Hence, when manufacturing the internally finned tube with S-shape fins, it is better to select the outer curvature radius R as smaller as possible.