Relationship Between Pressure Drop and Heat Transfer of Fully Developed Flow in Smooth Horizontal Circular Tubes and Spiral Coiled Tubes in the Laminar Flow Regime

Studies on isothermal steady state frictional pressure drop for flow of petroleum base oil SN70, SN150, Diesel and water are carried out in spiral coils with diameter to length ratio, 0.00042, 0.00047, 0.00073, 0.00164, 0.00189, 0.003 and 0.0037. An attempt is made to correlate friction factors with a better and more appropriate dimensionless group for flow of Newtonian fluids through spiral coiled tubes. An innovative approach of correlating heat transfer data with the newly established dimensionless group is presented. Heat transfer experiments are performed for spiral coils with diameter to length ratio 0.000474, 0.00042, 0.001896, 0.00198, 0.000942, 0.00164 in laminar flow regime. Suitable correlations for friction factors and Nusselt numbers are proposed. Relationship between pressure drop and heat transfer is studied. The incapability of the conventional analogy equations to estimate the heat and momentum transfer coefficients for laminar flow through straight or curved tubes is explained based on the viscous and form drag existing in straight and curved pipe flow. The limitations of the existing analogy equations are examined critically. A new general analogy equation is derived for laminar flow through spiral and straight tubes considering the influencing geometrical parameters of the tube. Keywords: Forced Convection; Heat and Mass transfer; Heat Exchangers; Thermal Systems.

Experimental Investigation and Data Analytics of Annular Cutting Velocity in Inclined and Horizontal Pipes

The lack of cutting transportation during drilling operations especially in horizontal and inclined wells can lead to large amounts of non-productive time and costly solutions. This problem has been encountered very often in the field due mostly to settlement of the cuttings at the bottom side of the hole and especially around pipe joints. Moreover, adopted rheological models are limited to 60 deg. inclination angle to predict the flow behavior of cuttings transport in directional wells. Therefore, the objective of this paper is to investigate the effect of various parameters related to the well configuration (inclined vs. horizontal), operating conditions, pipe/tool joints configurations, and flow conditions on the cutting velocity through an extensive experimental study with data analytics. The experimental approach was analyzed through film software, which allowed for the cutting velocities to be estimated. Regression models of cutting velocity with respect to each dimensionless group were formed and validated through a statistical analysis. A new empirical model for the cutting velocity was developed using multiple linear regression analyses. A sensitivity analysis was conducted to highlight the contribution of each dimensionless group on the variation of the cutting velocity. The newly proposed model for cutting velocity was tested and the calculated cutting velocity of 0.532 ft/s (.162 m/s) fell within the range of study between 0.188 ft/s (.057 m/s) and 0.690 ft/s (.210 m/s).

Parametric Dimensional Analysis on a C-H2 Smelting Reduction Furnace with Double-Row Side Nozzles

Higher requirements for steel smelting technology have been put forward based on the increasing awareness of energy conservation and environmental protection. In the field of iron making, carbon reduction processes are often used. In this study, molten iron was smelted by designing a C-H2 smelting reduction method. Although previous researchers have studied this through a large number of physical and numerical simulations, they have not yet refined general laws from the perspective of dimensional analysis. In this paper, a double-row side blow hydraulics simulation was carried out in the C-H2 smelting reduction furnace, and an entire list of dimensionless groups of input and output parameters was proposed based on its hydraulics simulation data. The expressions between the dimensionless group of mixing time and dimensionless groups such as Capillary number (Ca) and Lagrange group (La1) were obtained by multiple linear regression based on the experimental research results and data analysis. By verifying the calculated and experimental values of the dimensionless group of mixing time, it can be seen that both have a good positive correlation. This study provides a better methodology for controlling key parameters and lays the foundation for the optimal design of the process parameters for the C-H2 smelting reduction furnace.

CO2 Plume Migration With Gravitational, Viscous, and Capillary Forces in Saline Aquifers

In this study, we attempt to consider three forces of gravitational, viscous and capillary forces, simultaneously when CO2 is injected in saline aquifers. In order to conduct it, we propose a dimensionless group in the form of combination of Capillary number and Bond number. This dimensionless group is a function of CO2 saturation, in which the pattern of CO2 flow regimes can be determined. By the analysis of the acquired each trapping mechanism from flow regimes, optimum CO2 injecting scheme can be designed for maximizing the solubility and residual trappings as stable mechanism. With utilizing the proposed dimensionless group, we conducted several numbers of simulations using 2D vertical heterogeneous system with respect to CO2 flow rate, interfacial tension between CO2 and water, and brine salinity. From the simulation results, when gravitational and viscous forces with respect to capillary force are described by two individual dimensionless groups of Capillary number and Bond number, CO2 saturation profiles are variously generated. These are not satisfactory correlations in the dependence of CO2 saturation on Capillary number and Bond number for the variable terms of density differences between CO2 and water and CO2 injection rates. With the proposed dimensionless group, the universal profile of CO2 saturation was obtained in describing CO2 flow behaviors for the variables. Thus, considering two variables of density differences and CO2 injection rates simultaneously, that is, when three forces considering at the same time, more realistic CO2 flow behavior can be analyzed. This study helps to determine the most secure conditions of CO2 injection and storage according to building the pattern of CO2 flow regimes which is classified by the range of a dimensionless group.

Experiments on Liquid Pressure-Drop in Rectangular Microchannels, Subject to Non-Unity Aspect Ratio and Finite Roughness

We concentrate in this contribution onto the pressure-drop in rectangular stainless steel microchannels with a hydraulic diameter of dh ≈ 133 μm. Three aspect ratios are engaged, namely 1:1, 1:2, 1:5, whereas the hydraulic diameter is maintained constant. The roughness of the channel walls is around r ≈ 1.3 μm, the Reynolds number is up to Re ≈ 4000. We investigate all microchannels in two different lengths to infer highly-accurate correlations for fully-developed flow conditions from pressure difference measurements between the inlet- and outlet plenum. We find with this new technique pressure drop correlations for the fully-developed flow, which agree, both in the laminar and the turbulent regime, reasonably with conventional (macroscopic) correlations. In all cases the laminar/turbulent transition is in the range Rec ≈ 1800–2300, consistent with findings in macroscopic channels. The influence of roughness is found to be particularly strong for the microchannel of aspect ratio 1:5. This raises the question, whether the dimensionless group (r/dh) remains the responsible parameter for roughness at extreme aspect ratios.

A Parametric Analysis of the Thermal Shear Localization in Elastohydrodynamic Lubrication Films

Experiments and computer simulations have revealed some unusual results of elastohydrodynamic lubrication (EHL) associated with a high degree of thermally induced inhomogeneous shear across the lubricant film, or thermal shear localization. The results include the development of a sizable film dimple in the central EHL region and a dramatic reduction in EHL traction. In this study, a theoretical analysis is carried out to determine the conditions under which the thermal shear localization may develop in EHL films. For a Newtonian lubricant obeying the Barus law of viscosity, a dimensionless group-parameter is identified that fully governs the degree of the thermal inhomogeneous shear. Results are presented that show the critical range of values of this parameter corresponding to the onset of the shear localization. The analysis is also extended to lubricants with non-Newtonian behavior. Results suggest that the same dimensionless group-parameter may be used to measure the degree of the shear localization when the lubricant viscosity in the parameter is replaced by an effective viscosity that accounts for the non-Newtonian effect.

A Parametric Analysis of the Thermal Shear Localization in EHL Films

Experiments and computer simulations [1] have revealed some unusual results of elastohydrodynamic lubrication (EHL) associated with a high degree of thermally induced inhomogeneous shear across the lubricant film, or thermal shear localization. The results include the development of a sizable film dimple in the central EHL region [2] and a dramatic reduction in EHL traction [3, 4]. In this study, a theoretical analysis is carried out to determine the conditions under which the thermal shear localization may develop in EHL films. For a Newtonian lubricant obeying the Barus law of viscosity, a dimensionless group-parameter is identified that fully governs the degree of the thermal inhomogeneous shear. Results are presented that show the critical range of values of this parameter corresponding to the onset of the shear localization. The analysis is also extended to lubricants with non-Newtonian behavior. Results suggest that the same dimensionless group-parameter may be used to measure the degree of the shear localization when the lubricant viscosity in the parameter is replaced by an effective viscosity that accounts for the non-Newtonian effect. Reference [5] presents details of the theoretical formulation and results analysis.