M.A. Ebadian

An experimental study of single-phase and two-phase flow pressure drop in annular helicoidal pipes

Abstract In this study, experimental investigations were conducted for single-phase and air/water two-phase flow in annular helicoidal pipes with vertical and horizontal orientations. Three test sections were investigated. The outer diameters of the inner tube were 12.7 mm, 9.525 mm, and 6.35 mm, and the inner diameters of the outer tube were 21.18 mm, 15.748 mm, and 10.21 mm, respectively. The experiments were performed for superficial water Reynolds numbers in the range of 210 to 23,000 and superficial air Reynolds numbers in the range of 30 to 30,000. The effects of coil geometry and the flow rates of air and water on single-phase and two-phase flow pressure drop were experimentally investigated for annular helicoidal pipes. The data were correlated as the relationship of the pressure drop multipliers versus Lockhart-Martinelli parameter for the two-phase flow. The average void fraction was also measured in the experiments by means of the quick acting valve method. Unlike two-phase flow in straight pipe, the pressure drop multipliers of two-phase flow in annular helicoidal pipes have been found to be dependent on the flow rate in addition to the Lockhart-Martinelli parameter for the annular helicoidal pipe with large diameter. Thus, the Lockhart-Martinelli correlation is not valid in the prediction. Correlations for two-phase flow in horizontal and vertical annular helicoidal pipes have been established for both single-phase and two-phase flow based on the present experimental data.

Developing turbulent convective heat transfer in helical pipes

Abstract A fully elliptic numerical study has been carried out to investigate three-dimensional turbulent developing convective heat transfer in helical pipes with finite pitches. The κ-e standard two-equation turbulence model is used to simulate turbulent flow. The governing equations are solved by a control-volume finite element method. Numerical results have been compared to the existing experimental data and a good agreement has been obtained. The results presented in this paper cover a Reynolds number range of 2.5 x 104∼ 1.0 x 105, a pitch range of 0.0 ∼ 0.6 and a curvature ratio range of 0.025 ∼ 0.050. The developments of effective thermal conductivity and temperature fields and local and average Nusselt numbers are given and discussed. It has been found that the examined parameters exert complex effects on developing thermal fields and heat transfer in the helical pipes. The Nusselt numbers for the helical pipes are oscillatory before the flow is fully developed, especially for the case of relatively large curvature ratio.

An exact solution of extended Graetz problem with axial heat conduction

Abstract The convective heat transfer properties of a hydrodynamically, fully developed viscous flow in a circular tube are analyzed without using any simplified assumption such as low Reynolds numbers or Peclet numbers. The pipe is then subjected to a step-change in wall temperature. A straightforward approach using the Fourier transform technique is utilized to obtain analytical expressions for temperature distribution, heat flux, and Nusselt numbers. The effects of axial heat conduction are included in these expressions in both the upstream and the downstream directions for Peclet numbers ranging from 0 to ∞. By first taking the Fourier transform of the temperature field and expanding the coefficients of the transformed temperature in terms of the Peclet number, the energy equation with discontinuous wall temperature and longitudinal heat conduction is transformed into a set of ordinary differential equations. This resulting set of equations is then solved successively. The representative curves illustrating the variations of bulk temperature, heat flux, and Nusselt numbers with pertinent parameters are plotted. The asymptotic Nusselt numbers for small, as well as large Peclet numbers, is obtained as 3.6565, compared to the exact classical value of 3.6568. The significance of each curve is also discussed.

Laminar forced convection in a helicoidal pipe with finite pitch

Abstract This paper presents a numerical investigation of fully developed laminar convective heat transfer in a helicoidal pipe with a finite pitch coiled pipe. Three major parameters are identified to affect laminar convective heat transfer in a helicoidal pipe: the Dean number, torsion and the Prandtl number. The results indicate that torsion will increase the temperature gradient on one side of the pipe wall and decrease the temperature gradient on the other side. In the case of a small Prandtl number fluid, the Nusselt number declines slightly as torsion increases. However, in the case of a large Prandtl number fluid, the Nusselt number is significantly reduced as torsion increases. The predicted results for the limiting cases are also compared with other numerical and experimental results.

Numerical investigations of liquid-solid slurry flows in a fully developed turbulent flow region

In this paper, a simplified 3D algebraic slip mixture (ASM) model is introduced to obtain the numerical solution in sand–water slurry flow. In order for the study to obtain the precise numerical solution in fully developed turbulent flow, the RNG K–e turbulent model was used with the ASM model. An unstructured (block-structured) non-uniform grid was chosen to discretize the entire computational domain, and a control volume finite difference method was used to solve the governing equations. The mean pressure gradients from the numerical solutions were compared with the authors experimental data and that in the open literature. The solutions were found to be in good agreement when the slurry mean velocity is higher than the corresponding critical deposition velocity. Moreover, the numerical investigations have displayed some important slurry flow characteristics, such as volume fraction distributions, slurry density, slip velocity magnitude, slurry mean velocity distributions, and slurry mean skin friction coefficient distributions in a fully developed section, that have never been displayed in the experiments. 2003 Elsevier Science Inc. All rights reserved.

Condensation of R134a flowing inside helicoidal pipe

Condensing heat transfer and pressure drop characteristics of an ozone-friendly refrigerant HFC-134a (hydrofluorocarbon 134a) flowing inside a 12.7 mm helicoidal tube were investigated experimentally to obtain heat transfer data and correlations. For long helicoidal pipe, heat transfer measurements were performed for the refrigerant flow mass fluxes from 100 to 400 kg/m 2 /s, in the cooling water flow Reynolds number range of 1500< Rew < 9000 at fixed system temperature (338C) and cooling tube wall temperature (128C and 228C). With the increase of mass flux, the overall condensing heat transfer coeAcients of R134a increased, and slowly the pressure drops also increased. However, with the increase of mass flux (or the cooling water flow Reynolds number), the refrigerant side heat transfer coeAcients decreased. The eAects of cooling wall temperature on heat transfer coeAcients and system pressure drops were considered. Predictive correlations valid over the above water flow Reynolds number ranges and refrigerant flow mass flux were proposed. Helicoidal pipe heat transfer characteristics were compared with data for horizontal straight pipe from literature reports. 7 2000 Elsevier Science Ltd. All rights reserved.

Turbulent forced convection in a helicoidal pipe with substantial pitch

Fully developed turbulent convective heat transfer in a circular cross-section helicoidal pipe with finite pitch is numerically studied. The κ-e model is used to model the turbulent behavior. The time averaged momentum and energy equations are derived in the helicoidal coordinate system. The results indicate that the temperature distribution in the cross-section will be asymmetric as the pitch of the coil increases. Unlike that in laminar flow, an increase in the Prandtl number will reduce the torsion effect on the heat transfer in a helicoidal pipe. The results also indicate that the pitch effect will be enhanced as the flow rate increases.

Combined laminar forced convection and thermal radiation in a helical pipe

Abstract The interaction phenomena between laminar forced convection and thermal radiation in a participating medium inside a helical pipe were studied numerically. The P-1 radiation model was applied to the combined convection–radiation simulations. The three-dimensional governing equations for laminar flow and heat transfer were solved with a control-volume finite difference method (CVFDM) with second-order accuracy, and the O-type structure grid was adopted in this study. The effects of thermal radiation on the convective flow and heat transfer were measured by comparing the numerical results with and without thermal radiation. The comparison showed that under the conditions examined in this paper, although the thermal radiation had no significant influence for flow and temperature fields, especially in a fully developed region, it substantially enhanced the total heat transfer in the helical pipe.

Laminar forced convection in the entrance region of helical pipes

Abstract In the present study, three-dimensional laminar forced flow and heat transfer in the entrance region of helical pipes have been investigated using a fully elliptic numerical method. Laminar flow and heat transfer were assumed to develop from the inlet to the outlet simultaneously. The governing equations were solved by means of a control-volume finite element method. The results presented in this paper cover a Reynolds number range of 250–2000, a pitch range of 0.0–0.6, and a curvature ratio range of 0.025–0.20. The present elliptic numerical results are compared with previous experimental data and parabolic numerical data. The developments of temperature field, main and secondary velocity fields, local and average friction factors, and local and average Nusselt numbers are given and discussed. It has been found that both the friction factor and Nusselt number are oscillatory in the entrance region of helical pipes. The pitch and Reynolds number exert different effects on the developments of the friction factor and Nusselt number than the curvature ratio.

Turbulent heat transfer to near-critical water in a heated curved pipe under the conditions of mixed convection

Abstract Numerical modeling was performed to investigate the developing turbulent flow and heat transfer characteristics of water near the critical point in a curved pipe. The renormalization group (RNG) κ – ϵ model was used to account for the turbulent flow and heat transfer in the curved pipe at a constant wall temperature with or without buoyancy force effect. A control volume finite element method (CVFEM) was used to solve the three-dimensional full elliptic governing equations for the problem numerically. Due to the great variation in physical properties of water near the critical point, the turbulent flow heat transfer can be significantly altered compared with the pure forced convection in the curved pipe. This study explored the influence of the near-critical pressure and wall temperature on the development of fluid flow and heat transfer along the pipe. The numerical results for forced convective flow and heat transfer were compared with experiments available in the literature. Based on the results of this research, the velocity, temperature, heat transfer coefficient, friction factor distribution, and effective viscosity are presented graphically and analyzed.