Search

With the development of gas well exploitation, the calculation of wellbore with single-phase state affected by single factor cannot meet the actual needs of engineering. We need to consider the simulation calculation of complex wellbore environment under the coupling of multiphase and multiple factors, so as to better serve the petroleum industry. In view of the problem that the commonly used temperature and pressure model can only be used for single-phase state under complex well conditions, and the error is large. Combined with the wellbore heat transfer mechanism and the calculation method of pipe flow pressure drop gradient, this study analyzes the shortcomings of Ramey model and Hassan & Kabir model through transient analysis. Based on the equations of mass conservation, momentum conservation and energy conservation, and considering the interaction between fluid physical parameters and temperature and pressure, the wellbore pressure coupling model of water-bearing gas well is established, and the Newton Raphael iterative method is used for MATLAB programming. On this basis, the relationship between tubing diameter, gas production, gas–water ratio, and wellbore temperature field and pressure field in high water-bearing gas wells is discussed. The results show that the wellbore temperature pressure coupling model of high water-bearing gas well considering the coupling of gas–liquid two-phase flow wellbore temperature pressure field has higher accuracy than Ramey model and Hassan & Kabir model, and the minimum coefficients of variation of each model are 0.022, 0.037 and 0.042, respectively. Therefore, the model in this study is highly consistent with the field measured data. Therefore, the findings of this study are helpful to better calculate the wellbore temperature and pressure parameters under complex well conditions.

Microbiologically influenced corrosion (MIC) often occurs at the bottom of shale gas-gathering pipelines. Under the condition of pipe flow, the synergistic behavior of SRB corrosion and other factors is not clear. Based on the home-made multiphase flow corrosion loop, the biofilm formation and corrosion of sulfate-reducing bacteria on the surface of a shale gas pipeline steel L360N at different liquid flow rates are studied. At low flow rates such as 0.2 m/s and 0.5 m/s, the SRB biofilm gradually thickens. When the flow rate is 1.0 m/s ~ 1.5 m/s, the existing SRB biofilm is stripped. With the increase in velocity, the average and local corrosion rates first increase and then decrease. The synergistic corrosion of MIC and flow rate in the pipe will change with the increase in flow rate. SRB dominated the corrosion of L360N steel at low flow rate. At high velocity, the corrosion of L360N steel is accelerated by flow erosion after the biofilm is stripped. This study clarifies the corrosion behavior of the interaction between SRB and flow rate, and this understanding has rarely been reported in the past literature and can provide a basis for corrosion protection of shale gas field.

This paper studies the transition to turbulence of pipe flow for a system rotating about the streamwise direction. The linearized Navier–Stokes equations are numerically solved using the Petrov–Galerkin discretization. Both destabilizing and stabilizing effects of the rotation are highlighted. We show that in comparison to the linear stability situation at the Reynolds number going up to $$10^7$$ , for the non-rotating case, pipe flow is linearly unstable to infinitesimal perturbations at low rotation numbers. By fixing the Reynolds numbers, small rotation numbers increase the amplitude of perturbations, which attain the maximum values in the region of the unstable modes. As they exceed their maximum values, these perturbations are attenuated. When the rotation number is increased further, perturbations are progressively damped until a critical value above which the flow becomes linearly stable. We determine the region in perturbation amplitude which separates perturbations that trigger instabilities and perturbations that decay toward the laminar profile. This study also reveals that the large values of rotation numbers cause a symmetric structure onto the flow, in a domain that is periodically continued in the axial direction.

Turbulent kinetic energy (TKE) equation based on the Reynolds averaging hypothesis was approximated in the near wall region of turbulent channel flows and an analytical solution for TKE was proposed by Absi for $$y^{ + } < 20$$ (R. Absi, Analytical solutions for the modeled k equation, Trans. ASME: J. Appl. Mech. 75 (2008) 044,501). While, comparisons with DNS data show very good agreement, some of the model approximations employed previously require revision which is the main motivation of this work. We here present an alternate formulation for the smooth near wall TKE budget and propose an improved method of solution. Results are compared against wide range of friction Reynolds numbers, Reτ DNS datasets and found to be in good agreement. Interestingly the proposed improved method reveals that beyond Reτ, = 5200 TKE profiles collapse meaning that the TKE remains independent of Reτ that is consistent with high Reynolds number turbulent characteristics reported in the DNS (Hultmark et. al., Turbulent pipe flow at extreme Reynolds numbers, Phys. Rev. Lett., 108 (2012) 094,501). Although there exist two parameters in the paresent work to be determined empirically from DNS data it is reported that these parameters become empirically free at high turbulent Reynolds numbers, Reτ → ∞.The other interesting aspect of this work is that one of these parameters may be sensitized to other additional effects viz., wall roughness, pressure gradient, magnetic field, etc. One of the potential advantages of these near wall smooth turbulent channel flow analytical solutions is to obviate the need for solving the TKE equation near the smooth wall in the RANS, hybrid RANS/LES closures thus resulting in quicker and accurate engineering computations.

This paper reports experimental research on the flow behavior of oil-water surfactant stabilized emulsions in different pipe diameters along with theoretical and computational fluid dynamics (CFD) modeling of the relative viscosity and inversion properties. The pipe flow of emulsions was studied in turbulent and laminar conditions in four pipe diameters (16, 32, 60, and 90 mm) at different mixture velocities and increasing water fractions. Salt water (3.5% NaCl w/v, pH = 7.3) and a mineral oil premixed with a lipophilic surfactant (Exxsol D80 + 0.25% v/v of Span 80) were used as the test fluids. The formation of water-in-oil emulsions was observed from low water fractions up to the inversion point. After inversion, unstable water-in-oil in water multiple emulsions were observed under different flow regimes. These regimes depend on the mixture velocity and the local water fraction of the water-in-oil emulsion. The eddy turbulent viscosity calculated using an elliptic-blending k-ε model and the relative viscosity in combination act to explain the enhanced pressure drop observed in the experiments. The inversion process occurred at a constant water fraction (90%) and was triggered by an increase of mixture velocity. No drag reduction effect was detected for the water-in-oil emulsions obtained before inversion.

Pipe flow is a classic hydrodynamic issue. Most pipelines contain bends, and bends cause energy loss and distort the flow because of secondary flow. Deflectors are often used to adjust the flow quality in a bend. In this study, a numerical simulation using ANSYS Fluent 19.0 is used to analyze the effects of the deflector number, location and angle on the flow characteristics of a square pipe with a 90° bend. The velocity non-uniformity and the head loss are analyzed quantitatively. The secondary flow is presented visually, and its evolution characteristics are assessed. An optimized installation scheme for the deflectors is discussed, and a reference is provided for controlling the flow quality in bends via deflectors.

Fissure flow (FF)-induced disasters are a basic scientific difficulty in the fields of rock mechanics and geological engineering disasters. Based on large collapse and landslide disasters in China’s southwestern mountainous karst region, this study focused on the nonlinear evolution of the transition from pipe flow (PF) to FF during the process of carbonate rock rupture, with a view to determining the mechanism by which the interactions between geological structures and karst PF cause disasters. An experiment was designed and conducted to visualize the PF–FF transition in a carbonate rock by X-ray imaging at a material scale. Multiple mechanical metrics for the carbonate rock as well as X-ray imagery of the flow were obtained. The effects of multistage loading on the PF regime and the fractal characteristics of the PF–FF morphology were investigated. On this basis, the mechanism of the nonlinear evolution from PF to FF during the carbonate rock rupture process was determined. The experiment result demonstrates the fractal characteristics of the nonlinear evolution from PF to FF during the carbonate rock rupture process.

As proven in a recently published paper [Messa GV, Matoušek V (2020) Analysis and discussion of two fluid modelling of pipe flow of fully suspended slurry. Powder Technol 30:747$$-$$ - 768.], the $$\beta$$ β -$$\sigma$$ σ two-fluid model is capable of accurately reproducing the main features of turbulent, fully-suspended slurry flows in horizontal pipes provided that suitable values of the two parameters $$\beta$$ β and $$\sigma$$ σ are chosen. At present, the case-specific nature of $$\beta$$ β and $$\sigma$$ σ and their lack of a clear physical meaning are the main obstacles that must be overcome to give the $$\beta$$ β -$$\sigma$$ σ two-fluid model value not only as interpretative tool, but also as a predictive one. An important preliminary step to achieve this goal is to disclose the mathematical essence of the $$\beta$$ β -$$\sigma$$ σ two-fluid model, namely, to interpret the fluid-dynamic solution on the grounds of the structure of the differential and discretized equations. Such a methodological approach is applied here to the benchmark case of turbulent slurry flow between two infinite, horizontal, parallel plates, focusing, in particular, on the influence of the bulk-mean velocity of the slurry and the volumetric concentration of the solids in the flow. The study provides not only deeper insight into the $$\beta$$ β -$$\sigma$$ σ model, but also indicates important implications for alternative two-fluid models.

This paper aims to analyze dimensionless parameters, Weber number and Reynolds number, to describe inception of droplets at the interface of liquid–liquid pipe flow. Experiments are conducted in a 15.9 mm diameter and 6 m long stainless-steel pipe using high viscous oils and water. An empirical Weber number correlation, adapted from gas–liquid flow and modified for liquid–liquid flow, is proposed to identify the formation of droplets at the interface. The analysis of the proposed Weber number correlation indicates that the droplets originate when Weber number ≈ 300 and higher. The experimental data from the literature of low and high viscous oil–water flows is also considered for the analysis. The analysis suggests that the Kelvin–Helmholtz instability singularly does not produce droplets at the interface but only when the fluids inertial forces exceed the interfacial tension forces by 300 times. The data from the literature provide sufficient evidence on the existence of wall originated fluctuations in at least one of the fluid phases before the advent of interfacial waves or interfacial droplets. Accordingly, the investigation of Reynolds number indicates that the droplets are found to form when either oil or water phase Reynolds number Reo or Rew attains ≈ 12,000 with the respective fluid mass fraction ≥ 0.2. However, for fluid mass fraction

Droplet breakage is a common phenomenon in converting a pipe flow to a swirl flow in a vane-type pipe separator (VTPS)’ inlet. The evaluation of the dispersed droplet sizes after breakage is crucial to the optimum design of the inlet structure and the estimation of the oil-water separation performance. This paper studies the droplet behavior in a swirl flow produced by guiding vanes. Experiments are performed with two different guiding vanes at the inlet of the VTPS. The sizes of the produced oil droplets at the downstream of the guiding vanes are measured in situ using a Malvern Insitec SX. The results indicate that the streamlined deflector is superior to the semi-elliptical plate for the VTPS’ optimization based on the comparison of the droplet sizes in their respective induced swirl flow fields, which can be explained by a modified T-model. Our study suggests that the use of the modified T-model is a reliable method to optimize the design of the guiding vane in the swirling generating stage.

Fractures in rocks often provide preferential fluid migration pathways and their geometrical properties are the main factors influencing the permeability of the rock mass. By taking into account the complex geometries of rock fractures, including tortuous features, highly variable fracture apertures, rough fracture wall surfaces and complex fracture intersections, a highly effective approach is proposed in this work to investigate the behaviour of fluid flows in laboratory-scale fractured rocks. The computed tomography (CT) scanning was used to capture the micro-structures of non-planar fractures in a sandstone specimen. An image processing method was then developed to extract the three-dimensional fracture network. The fractures and fracture network were represented using an equivalent pipe network model, taking into consideration the complex geometries mentioned above. The nonlinear flow is incorporated into the model through the consideration of a friction factor in the pipe flow method (PFM). The absolute difference of the derived permeability between PFM and finite volume method (FVM) is 3.45%, but the FVM needs 15 times more CPU computation time. Therefore, the proposed approach is better than FVM in terms of computational efficiency. In addition, the use of the friction factor was demonstrated to be effective and efficient to model nonlinear flow within the fracture network, where the flow nonlinearity is caused by high flow velocity and the formation of eddies in certain parts of the fracture network, leading to a decrease in the overall apparent permeability and an increase in the flow tortuosity. The proposed method was further validated against flow test data covering a wide range of linear and nonlinear flow regimes.

The concept of non-uniform heat flux distributions has emerged because of its potential to make the design of thermal systems more flexible. Therefore, the current study highlights the impact of non-uniform heat flux distributions on the thermal characteristics of a high Prandtl number fluid for forced convective laminar flow regime in a horizontal pipe. The steady-state 2-D simulations have been employed using ANSYS Fluent. The variations in heat flux distributions as a wall boundary condition are systematically analyzed while keeping the total heat transfer constant. The results obtained for various distributions are compared in terms of a dimensionless maximum wall temperature (hot spot), local and average Nusselt numbers, and entropy generation rate. The analysis showed that the heat flux distributions significantly affected the heat transfer pattern. It was found that the hot spot temperature was lower for the descending heat flux boundary conditions compared to the ascending type of distributions. However, a higher entropy generation rate was observed for descending distributions as compared to ascending ones. It was also found that the ascending heat flux distributions provided higher average Nusselt number values than the descending cases of heat flux.

Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly accepted formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers.

In this work, an efficient model for simulating bubble dispersion and coalescence due to turbulence is developed in the Euler-Lagrange framework. The primary liquid phase is solved on the Euler grid with the RANS turbulence model. Bubble motion is computed with the force balance equations. One-way coupling between two phases is assumed and the framework is designed for the computation of disperse bubbly flows at low Eötvös number. The turbulent dispersion of the dispersed phase is reconstructed with the continuous random walk (CRW) model. Bubble-bubble collisions and coalescence are accounted for deterministically. To accelerate the time-consuming search for potential collision partners in dense bubbly flows, the sweep and prune algorithm is employed, which can be utilized in arbitrary mesh types and sizes. Validation against experiments of turbulent pipe flows demonstrates that the one-way coupled EL-CRW dispersion model can well reproduce the bubble distribution in a typical dense bubbly pipe flow. Good agreement of the bubble size distribution at the pipe outlet between the simulation and the experiment is obtained.

In this paper, a wall-adapted anisotropic heat flux model for large eddy simulations of complex engineering applications is proposed. First, the accuracy and physical consistency of the novel heat flux model are testified for turbulent heated channel flows with different fluid properties by comparing with conventional isotropic models. Then, the performance of the model is evaluated in case of more complex heat and fluid flow situations that are in particular relevant for internal combustion engines and engine exhaust systems. For this purpose large eddy simulations of a strongly heated pipe flow, a turbulent inclined jet impinging on a heated solid surface and a backward-facing step flow with heated walls were carried out. It turned out that the proposed heat flux model has the following advantages over existing model formulations: (1) it accounts for variable fluid properties and anisotropic effects in the unresolved temperature scales, (2) no ad-hoc treatments or dynamic procedure are required to obtain the correct near-wall behavior, (3) the formulation is consistent with the second law of thermodynamics, and (4) the model has a similar prediction accuracy and computational effort than conventional isotropic models. In particular, it is shown that the proposed heat flux model is the only model under consideration that is able to predict the direction of subgrid-scale heat fluxes correctly, also under realistic heat and fluid flow conditions in complex engineering applications.

Subterranean soil erosion is a common form of soil failure that is caused by groundwater seepage. In this paper, we present a subterranean soil erosion model ideally supposed as pipe flow with four conditions. By using the theories of pipe flow, its critical expressions are derived, including the critical flow quantity (Qcr), the critical velocity (Vcr), and the hydraulic gradient (Icr). A simulating experiment is designed to test Qcr to calculate the other critical values. In a case study, 14 clay samples from Guiyang, Guizhou, China, are tested via a simulation experiment. As a result, the critical shear stress of samples is found to be 32.01 Pa. Furthermore, three critical values of suffusion, including Qcr, Vcr and Icr, are calculated with different diameters of soil pores by using the critical expressions. Analyzing the relationship among the values shows that the pore diameter and groundwater temperature influence the critical hydraulic condition of subterranean soil erosion.

Cellulose fibres are prone to flocculate and form aggregates that are deformable by the hydrodynamic stress. In this work I document for coiled pipe flow, known to have secondary motion in the pipe cross-sectional plane, an accumulation of fibre flocs and fibre aggregates at the outer bend. That is the segregation into a section in the pipe cross-section and hence presents a case of angular segregation. The segregation was studied for non-coherent crowded fibre flocs. For that, segregation benefited from fibre concentration and suffered from increased hydrodynamic stress expressed by increasing Reynolds number. Based on the observed segregation of fibres a flow splitter was designed that separated the flow at 1/3 of the tube diameter measured from the inner bend. The outer bend suspension length-weighted fibre length was found to increase. For the best case in this work, the difference between outer and inner bend relative to the feed fibre length was 22%. As for radial and axial segregation, which are known, also angular segregation is fibre-length sensitive. As such it can be exploited for length fractionation of networking and aggregating elongated particles, for example fibres.

In this paper, the idea of using the baffles to improve the performance of the coaxial geothermal heat exchanger (CGHE) has been proposed. Thermal and hydrodynamic analysis of two types of CGHE during heat injection and thermal recovery processes was investigated. A transient numerical model and turbulent model have been developed to study the CGHE. In this study, for both cases, the active borehole length was 165 m and the flow rate and the injected heat were 0.58 L s−1 and 6.4 kW, respectively. Augmentation of the heat transfer from the ground to the annular flow and reduction in the heat transfer rate between the annular flow and central pipe flow were the primary goals of this study. For this purpose, 40 baffles were considered inside the annular portion (over the central pipe). Comparisons between the obtained results and available data showed that the simulations were valid. The outlet (and inlet) temperatures of the baffled CGHE were 13.2% lower than those for the conventional CGHE. Also, the baffled CGHE had better thermal performance than the conventional CGHE and caused a quicker recovery of temperature, which is useful for improving the performances of the CGHE. Also, the pressure drop of the annular flow for the baffled CGHE was higher than the conventional CGHE, while the pumping powers for two CGHEs were not significantly different.

Turbulent co-current Taylor bubble flow was modeled with LES alongside the VOF interface tracking solver. The method is first validated in the context of single phase turbulent pipe flow and three distinct laminar Taylor bubble flow cases. The turbulent co-current Taylor bubble flow is simulated using a moving frame of reference which is attached to the bubble, allowing for a straight-forward time averaging and Dirichlet-type flow recycling inlet boundary condition. In contrast to periodic inlet and outlet boundary conditions, the Dirichlet one assures that small bubbles which are lost by the Taylor bubble are removed from the computation once they leave the domain, therewith not interfering with the nose of the Taylor bubble. The transient loss of small bubbles which is observed in our simulations implies that the problem is inherently unsteady. We therefore present an averaging strategy which consists of combined time, space and ensemble averaging. This strategy allows systematic comparison of results across different computational meshes. The results show that the approach captures distinct features of turbulent co-current Taylor bubble flow well, in the sense that good agreement is observed with experimental data from literature in terms of the toroidal vortex flow field in the wake of the Taylor bubble. Agreement with measured velocity fluctuation profiles in the wake of the Taylor bubble is less pronounced, and is discussed in the paper. Nevertheless, the simulation approach of co-current Taylor bubble flow proposed in this paper may serve as a tool that will provide deeper insights in two-phase turbulent flow for future research.

Velocity and concentration profiles in a pipe flow was measured downstream of injection of a tracer gas at the pipe centerline. The pipe had diameter D = 0.2 m and two Reynolds numbers, Re = 50000 and Re = 100000, were used. The profiles were measured at positions 5D and 10D downstream of the injection point. Three different industrial relevant geometrical configurations were used upstream of the injection point: a 10D straight pipe, two 10D pipes connected with a 90° bend or a straight 10D pipe with a mixer plate mounted 2D upstream the injection point. In all cases, air entered the pipe from the surroundings through a sharp-edged inlet. This represents many practical flow applications and is also a well-defined inlet condition that generates turbulence in the vena contracta in the inlet. The measurements were compared to predictions from three different computational models: two with Reynolds Averaged Navier-Stokes (RANS) and one with high-resolution Detached Eddy Simulation (DES). For RANS, the k-ω SST model had difficulty in predicting the turbulence created by the vena contracta. The k-ε model performed better, but gave completely wrong results for the inlet with a pipe bend. The DES was successful for all cases with only minor deviations from measurements.

This study aims to express an optimize temperature profile with the most heat transfer and least work loss by minimizing the total entropy generation of a pipeline under external magnetic field. This study has investigated in low Stokes number and low Reynolds number conditions. It shows that, the fluid’s shear stress increases around the wall (r* > 0.8), due to presence of magnetic field. As a consequence, the magnetic field boosts the dissipation term. However, the velocity gradient over a wide range of radius 0

An extensive a priori analysis has been carried out on data from Direct numerical simulation of fully developed heated turbulent pipe flow at high molecular Prandtl numbers $$Pr=10$$ P r = 10 /20, testing three popular modelling candidates for subgrid-scale closure in Large-Eddy simulation (LES). Aside from assessing the models’ capabilities to describe quantitatively the unresolved turbulent fluxes, a special focus is also put on the role of the numerical error, which arises from the discretization of the filtered advective fluxes on a coarse LES grid. The present analysis extends here previous studies on subgrid-scale momentum transport in a isothermal mixing layer and channel flow carried out by Brandt (J Numer Methods Fluids 51: 635–657, 2006) and Vreman et al. (J Eng Math 29: 299–327, 1995), respectively, to the subgrid-scale transport of heat at high Prandtl numbers. The statistical dependence between the individual contributions (resolved, subgrid-scale, numerical discretization error) constituting the filtered advective flux divergence in the LES formulation is investigated as well, in terms of corresponding cross-correlations. The sensitivity of the tested sgs-models to a grid refinement is further examined performing also a posteriori LES, where the basically more sophisticated candidates turn out to be more demanding in terms of required grid resolution.

Fluid in rock fractures continually induces geocatastrophes in water–rock system engineering. Intuitively observing fluid in fractures is the key method for revealing the interaction mechanism of water and rock under different engineering backgrounds and providing some insights for solving engineering issues. This study proposes a visualization method for fluid in rock fractures using enhanced X-ray image digital radiography (EXIDR) and carries out coupled hydromechanical tests on the basis of the material scale of carbonate rocks, red bed mudstone (RBM) and coal. The experimental results show the transition mechanism of pipe flow (PF) to fissure flow (FF) during carbonate rock failures. The flow regime undergoes an evolution process from laminar flow to turbulent flow, which also changes with the fractal characteristics of PF-FF in carbonate rocks under multilevel stress loading. Additionally, the damage coefficient of RBM under coupled hydrodynamics and multilevel stress loading nonlinearly increases. Therefore, the initial permeability of RBM under hydrodynamics is significant for geohazard prevention in engineering and is induced by seepage and diffusion effects. In addition, the mean square flow describes how the flow rate varies with fracture growth and extension, i.e., the fractional exponential evolution relationship transitions from superdiffusion flow to subdiffusion flow. This indicates that fluid in fractures shows the dual behaviors of anomalous diffusion and nonlinear flow during coal and rock failures.

Collection of landfill gas by horizontal perforated wells is studied. The problem combines flow through porous media in the landfill and unobstructed pipe flow in the well. Respective analytical solutions to flow equations are used in an iterative numerical procedure to solve the coupled system. Realistic landfill input parameters confirm the feasibility of estimates obtained with the model. The study identifies flow control parameters and furnishes tools to evaluate surface flux and radius of influence for this type of well.

A mathematical model is presented to study the main characteristics of severe slugging in a downward inclined pipeline followed by a catenary riser. In this model, both simplified transient model and phase distribution model are included so that the flow characteristics of each stage for severe slugging can be accurately reproduced, especially for blowout stage. The results show that the flow features of severe slugging can be simulated by the proposed mathematical model. A good agreement between the experimental data and the numerical results is observed. The model can predict the transient fluctuation of many respects, such as the superficial gas velocity at the bottom of the riser and the average velocity at the outlet of the riser.

A brief introduction of the time-filtered Navier–Stokes (TFNS) equations for very large eddy simulation (VLES) and its distinct features is presented. A set of nonlinear subscale models and their advantages over the linear subscale eddy viscosity models are described. A guideline for conducting a TFNS/VLES simulation is also provided. In this paper, we present simulations for three turbulent flows. The first one is the turbulent pipe flow at both low and high Reynolds numbers to illustrate the basic features of TFNS/VLES; the second one is the swirling turbulent flow in an LM6000 single injector to further demonstrate the differences between the results from nonlinear models versus linear viscosity models; the third one is a more complex turbulent flow generated in a single-element lean direct injection combustor, which demonstrates that the current TFNS/VLES approach is capable of predicting dynamically important, unsteady turbulent structures even with a relatively coarse mesh grid.

In the present study, the heat transfer and hydrodynamic analysis of flow through single-pipe heat exchangers of circular and square cross-sectional configurations were performed. The experimental and numerical investigations were conducted to evaluate the performance of two metallic oxides (Al2O3 and SiO2) and two carbon-based nanostructured nanofluids (KRG and GNP) in comparison with the distilled water (DW). The data obtained from the experimental runs with DW as a working fluid in both test sections were used to validate the 3-D numerical models for the square and circular pipe heat exchangers. The flow in both test sections is considered as a fully developed turbulent flow with the Reynolds number range of 6000–11,000, and both the test sections were subjected to a uniform heat flux at their outer surfaces. The concentrations of all nanofluids used in the present study were in the range of (0.025–0.1 mass%). The test rig was firstly validated during the water run by using different empirical correlations for the evaluation of pressure drop and Nusselt number and showing a very good agreement, and then, the numerical models were validated with the data obtained experimentally and the errors were less than 10% for both models. For the square tube flow, the average errors between the numerical and experimental findings of Nusselt number and pressure drop were 6.8% and 2.49%, respectively, and for the circular pipe flow, the evaluated errors were 9.34% and 5.92% for Nusselt number and pressure drop, respectively. The performance index for all the nanofluids was calculated to obtain the convective heat transfer coefficients and friction losses of the fluids in both the tubes. The results showed that the non-covalent graphene–DW is not suitable for heat transfer applications due to its higher viscosity. The results also showed a different enhancement of heat transfer for the same nanofluid in circular and square tube flows, whereas the performance index of the same nanofluid appears nearly the same for flow through both the cross sections.

A visualization of thermal diffusion in a horizontal pipe flow is conducted to elucidate the axial diffusion characteristics of two fluids of differing temperatures, particularly those flows between the laminar and turbulent flow regimes. Tracer particles are used to detect the thermal diffusion interface as well as to measure streamwise velocity profiles. We found that the Hagen–Poiseuille parabolic velocity profile established a long axial diffusion length that drives thermal convection in the pipe cross-sectional plane. This situation results in a 3D interface at Reynolds number, Re = 600, and a vertically stratified interface at Re = 1900. In turbulent flows at Re = 5700, an anti-diffusion spot appears in the front section before undergoing rapid mixing under turbulence. From the visualized particle images, the apparent axial coefficients of diffusion were measured and compared with the friction properties of the pipe. Furthermore, particle image velocimetry (PIV) explored the two-way coupling mechanism of between the temperature and the velocity within the thermal diffusion process.

A numerical study was conducted by using the finite difference technique to investigate the mechanism of the fully developed turbulent flow and heat transfer in a circular tube in company of large Reynolds number with constant heat flux and at constant wall temperature condition. The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form in order to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas’ algorithm, a program in FORTRAN version 95 was developed in order to numerically solve the discretized form of the system of equations describing the problem. Finally, thanks to this elaborate program, we were able to play on some parameters involved such as the Reynolds number, the number of Peclet, and the longitudinal coordinate to obtain important results of the treated thermal model which are discussed and well detailed of this work. Comparison between the literature correlation data and the calculated simulation indicates that it is a good match of the results.

This study describes the application of two main improvements in highly viscous fluid simulations using the smoothed particle hydrodynamics (SPH) method: an implicit time integration scheme to overcome the problem of impractically small time step restriction and the introduction of air ghost particles to fix problems regarding the free surface treatment. This study adopts the incompressible SPH as a basis for the implementation of these improvements, which guarantees a stable and accurate pressure distribution. We verified the proposed implicit time integration scheme with simulations of pipe flow and the free surface treatment with a simple hydrostatic problem. As a result, the free surface of the hydrostatic problem became very smooth and stable. In addition, we conducted a variety of dam-break simulations to validate this proposed SPH method, as well as to analyze the density and divergence error. Finally, we demonstrate the potential of this method with the highly viscous vertical jet flow over a horizontal plate test, which features a complex viscous coiling behavior.

Part 2 of the paper applies interplant water network synthesis using the novel principal pipe representation introduced in part 1 of this paper Alnouri et al. (PIOS 2(4):413–434, 2018). The concept of a principal pipe is presented as a shared pipeline structure that can be assigned several different functions, such as water collection, distribution, or both. A number of principal pipe categories and design aspects have been explored in this study, including pipe routing options, pipe flow directions, pipe sharing scenarios, and pipe water quality. To demonstrate the design of interplant water networks via principal pipes, a non-linear problem (NLP) has been implemented using an economic objective function, so as to allow a cost-optimal selection process for different types of principal pipes within industrial clusters. The proposed approach is illustrated using several examples that involve water regeneration and reuse. The benefits of the proposed methodology are quantified and discussed.

We have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 2250. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Barkley et al., Nature 526, 550–553, 2015; Barkley et al., 2015). We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum energy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at that location. We collected a snapshot-ensemble (10000 time instances, snapshots) of the velocity fields acquired over T = 2000D/U time interval inside the moving window. The cross-plane velocity field inside the puff showed the dynamics of a developing turbulence. In particular, the analysis of the cross-plane radial motion yielded the illustration of the production of turbulent kinetic energy directly from the mean flow. A snapshot-ensemble averaging over 10000 snapshots revealed azimuthally arranged large-scale (coherent) structures indicating near-wall sweep and ejection activity. The localized puff is about 15-17 pipe diameters long and the flow regime upstream of its upstream edge and downstream of its leading edge is almost laminar. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities, Reynolds shear stress, skewness and flatness factors, become similar to a fully-developed turbulent pipe flow in the vicinity of the puff upstream edge. In the puff core, the velocity profile becomes flat and logarithmic. It is shown that this “fully-developed turbulent flash” is very narrow being about two pipe diameters long.

Nuclear magnetic resonance (NMR) has long been used for measuring flows, as it has the unique advantage of being a truly non-invasive method by which to do so. In this paper, we describe our use of a magnet with a large constant gradient to measure two decades of average velocities (0.002–0.7 m/s), principally using a measurement method developed by Osan et al. that uses the initial decay of a Carr–Purcell–Meiboom–Gill sequence to determine the mean flow velocity. Thanks to the repeatability afforded by the stable gradient, we reliably pinpoint the transition to turbulence for pipe flow through the magnet.

In this paper, turbulent pipe flows laden with finite-size particles are investigated, using the direct numerical simulations based on the lattice Boltzmann method. Our focus is on the modulation of turbulence statistics in the pipe due to the presence of finite-size neutrally buoyant particles, and the question if the characteristics of modulation differ from those in a turbulent channel flow under comparable system parameters in order to reveal the effect of curved walls in the pipe. The mechanisms responsible for modulations of the turbulent intensity in the pipe flow are clarified through a quantitative budget analysis of the turbulent kinetic energy.

Fractional and non-Newtonian calculus are an extension of classical calculus, usually known for providing new mathematical tools useful in science, developed from alternative approaches. Among fractional calculus, Riemann-Liouville and Caputo fractional derivatives have been the most popular operators employed in spite of their complexity. In this work, two novel and compact methods are presented as an alternative to the fractional calculation options. To test the feasibility of proposed methods, three classical fluid mechanic problems are studied: the flow through circular pipe, parallel plates and annulus, by modifying the constitutive equations into their fractional equivalent. On the other hand, a new weighted non-Newtonian derivative is proposed to extend the possibilities to model fluid viscosity based on the influence of nonadjacent layers, using the pipe flow as an example. Results show that proposed fractional models can describe shear-thinning and shear-thickening behaviors depending on the fractional order of the derivative, while the weighted derivative allows to expand the way viscosity is modeled, demonstrating the suitability of these approaches to describe physical problems.

A novel pressure reconstruction method is proposed to use the uncertainty information to improve the instantaneous pressure fields from velocity fields measured using particle image velocimetry (PIV) or particle tracking velocimetry (PTV). First, the pressure gradient fields are calculated from velocity fields, while the local and instantaneous pressure gradient uncertainty is estimated from the velocity uncertainty using a linear-transformation-based algorithm. The pressure field is then reconstructed by solving an overdetermined linear system which involves the pressure gradients and boundary conditions. This linear system is solved with generalized least squares (GLS) which incorporates the previously estimated variances and covariances of the pressure gradient errors as inverse weights to optimize the reconstructed pressure field. The method was validated with synthetic velocity fields of a 2D pulsatile flow, and the results show significantly improved pressure accuracy. The pressure error reduction by GLS was 50% with 9.6% velocity errors and 250% with 32.1% velocity errors compared to the existing baseline method of solving the pressure Poisson equation (PPE). The GLS was more robust to the velocity errors and provides greater improvement with spatially correlated velocity errors. For experimental validation, the volumetric pressure fields were evaluated from the velocity fields measured using 3D PTV of a laminar pipe flow with a Reynolds number of 630 and a transitional pipe flow with a Reynolds number of 3447. The GLS reduced the median absolute pressure errors by as much as 96% for the laminar pipe flow compared to PPE. The mean pressure drop along the pipe predicted by GLS was in good agreement with the empirical estimation using Darcy–Weisbach equation for the transitional pipe flow.

Mixed convection flow of aluminium-oxide nanoparticles in water through a circular tube was modelled using the discrete phase model and implemented on ANSYS-Fluent 17.0 through customised user-defined functions. The inclination angle was varied to study its effect on the migration and deposition of the nanoparticles. Experimentally determined thermo-physical properties were used in the analysis instead of theoretical or empirical models from the literature. Varying inclination angles were found to significantly affect the migration and deposition of nanoparticles. A critical angle of maximum deposition of approximately 30° was found for volume concentrations 1%, 3% and 5%. The effect of varying inclination angle on the heat transfer coefficient was minimal for low angles of inclination between 0 and 35% and decreased significantly after 40%. The effect of Saffman’s lift, thermophoretic, Magnus and Brownian effects were also investigated, and results show that thermophoretic and Brownian effects were most dominant effects.

This paper presents a novel representation and formulation for the synthesis of interplant water networks with the goal of achieving low-cost and simple water network designs in industrial clusters or eco-industrial parks. Building upon a spatial representation of the problem, we introduce a new interplant connectivity representation that channels water flows collectively through sets of principal pipes. These principal pipes are represented as shared pipelines that can have different functions, i.e., water collection, water distribution, or water collection and distribution. Different principal pipe categories may be structured by selecting a combination of different initial/final/feeding/receiving entities which are allowed to be connected, to form a principal pipe. Moreover, several design aspects can also be explored within a principal pipe category such as (1) the selection of a prescribed water quality, (2) pipe routing options, (3) pipe flow directions, and (4) pipe sharing scenarios. Part 1 of the paper presents the backbone of the methodology that entails the assembly of different principal pipe categories, and also demonstrates how different design aspects may be accounted for in the design process.

The one-dimensional turbulence (ODT) model resolves a full range of time and length scales and is computationally efficient. ODT has been applied to a wide range of complex multi-scale flows, such as turbulent combustion. Previous ODT comparisons to experimental data have focused mainly on planar flows. Applications to cylindrical flows, such as round jets, have been based on rough analogies, e.g., by exploiting the fortuitous consistency of the similarity scalings of temporally developing planar jets and spatially developing round jets. To obtain a more systematic treatment, a new formulation of the ODT model in cylindrical and spherical coordinates is presented here. The model is written in terms of a geometric factor so that planar, cylindrical, and spherical configurations are represented in the same way. Temporal and spatial versions of the model are presented. A Lagrangian finite-volume implementation is used with a dynamically adaptive mesh. The adaptive mesh facilitates the implementation of cylindrical and spherical versions of the triplet map, which is used to model turbulent advection (eddy events) in the one-dimensional flow coordinate. In cylindrical and spherical coordinates, geometric stretching of the three triplet map images occurs due to the radial dependence of volume, with the stretching being strongest near the centerline. Two triplet map variants, TMA and TMB, are presented. In TMA, the three map images have the same volume, but different radial segment lengths. In TMB, the three map images have the same radial segment lengths, but different segment volumes. Cylindrical results are presented for temporal pipe flow, a spatial nonreacting jet, and a spatial nonreacting jet flame. These results compare very well to direct numerical simulation for the pipe flow, and to experimental data for the jets. The nonreacting jet treatment overpredicts velocity fluctuations near the centerline, due to the geometric stretching of the triplet maps and its effect on the eddy event rate distribution. TMB performs better than TMA. A hybrid planar-TMB (PTMB) approach is also presented, which further improves the results. TMA, TMB, and PTMB are nearly identical in the pipe flow where the key dynamics occur near the wall away from the centerline. The jet flame illustrates effects of variable density and viscosity, including dilatational effects.

Erosion damage is one of the main factors leading to failure of pipeline in oil field, especially for sudden contraction section under solid–liquid two-phase flow in hydraulic fracturing. In this article, a laboratory experiment was carried out to analyze the effects of pipe flow velocity, particle concentration and pipe inner diameter ratio on particle erosion of the reducing wall in high-viscosity liquid. The results show that the erosion rate and erosion distribution are different not only in radial direction but also in circumferential direction of the sample. The upper part of sample always has a minimum erosion rate and erosion area. Besides, the erosion rate of reducing wall is most affected by fluid flow velocity, and the erosion area is most sensitive to the change in the diameter ratio. Meanwhile, the erosion rate of reducing wall in cross-linked fracturing fluid is mainly determined by the fluid flowing state due to the high viscosity of the liquid. In general, the increase in flow velocity and diameter ratio not only causes the expansion of erosion-affected flow region in sudden contraction section, but also leads to more particles impact the wall.

Little efforts were done on the heat and mass transfer characteristics of superheated steam (SHS) flow in the horizontal wellbores. In this paper, a novel numerical model is presented to analyze the heat and mass transfer characteristics of SHS in horizontal wellbores with toe-point injection technique. Firstly, with consideration of heat exchange between inner tubing (IT) and annuli, a pipe flow model of SHS flow in IT and annuli is developed with energy and momentum balance equations. Secondly, coupled with the transient heat transfer model in oil layer, a comprehensive mathematical model for predicting distributions of pressure and temperature of SHS in IT and annuli is established. Then, type curves are obtained with numerical methods and iteration technique, and sensitivity analysis is conducted. The results show that (1). The decrease in SHS temperature in annuli caused by heat and mass transfer to oil layer is offset by heat absorbtion from SHS in IT. (2). SHS temperature in both IT and annuli increases with the increase in injection pressure. (3). IT heat loss rate decreases with the increases in injection pressure. (4). Increasing pressure can improve development effect.

On May 10th, 2012, 41 sinkholes collapsed the southern suburbs of Liuzhou, Guangxi Province, China, damaging 143 houses, eight factories buildings, and three commercial buildings. Lei (2013) revealed that groundwater dynamics, contributed to by the daily rainfall of 169.7 mm, led to soil particles running off (seepage erosion) resulting in the sinkholes. It is crucial to identify the critical parameters of seepage erosion that forms sinkholes. This paper analyzes critical parameters in the study site, establishes the pipe flow model of seepage erosion, and deduces parameter expression using its theories. We devised experimental equipment designed to simulate the process of seepage erosion and test the critical shear stress (τcr) of soil samples from the field. Additionally, we measured the diameter (d) of pores in the field soil using a scanning electron microscope, and calculated the critical groundwater velocity (Vcr). As the result, we found that the collapsed sinkholes in the study site were formed by groundwater with a velocity of 7.652 × 10−5 m/s (or 0.459 cm/min).

A dual-technique-based inline strategy was investigated in this study as a sustainment to conventional-technique skills in terms of limitation of wave oscillation period spread-out. Instead of the single polymeric short section employed by the latter technique, the former is based on replacing an up- and downstream short section of the primitive piping system using another couple made of polymeric pipe-wall material. Numerical computations used the method of characteristics for the discretization of unconventional water-hammer model based on the Vitkovsky and the Kelvin–Voigt formulations. The efficiency of the dual technique was considered for two operating conditions associated with up- and downsurge frames. Moreover, two pipe-wall material types were utilized for short-section pipe wall, namely the HDPE or LDPE materials. Additionally, the conventional technique was also addressed in this study, for comparison purposes. First, analyses of pressure-head, circumferential-stress and radial-strain wave patterns, along with wave oscillation periods examination, confirmed that the dual technique could improve the efficiency of the conventional one, providing acceptable trade-off between the attenuation of pressure-head and circumferential-stress peaks (or crests), and limitation of period spreading and radial-strain amplification. Second, a parametric study of the sensitivity of the wave damping to the employed short-section dimensions was performed in terms of short-section length and diameter. This parametric study helped estimate the near-optimal values of the short-section dimensions.

Based on the theory of thermodynamically compatible systems, we formulate the governing equations of a gas-liquid compressible pipe flow and develop the Runge–Kutta–TVD and Runge–Kutta–WENO high accuracy methods. The computational model is used to solve a series of test cases demonstrating its efficiency and capability to be applied to slug flows modeling.

A methodology to identify the partial blockages in a simple pipeline using genetic algorithms for non-harmonic flows is presented in this paper. A sinusoidal flow generated by the periodic on-and-off operation of a valve at the outlet is investigated in the time domain and it is observed that pressure variation at the valve is influenced by the opening size of blockage and its location. In this technique, the unsteady (steady oscillatory) pressure time series at only one location is required to identify two blockages. In the proposed methodology, the solution of the governing hyperbolic PDEs of pipe flow is obtained using the method of characteristics. For any piping system similar to the hypothetical pipe system used in the simulations, generalized best amplitude and best frequency of the valve operation are determined, which give maximum deviation in pressure responses for a specific blockage at different locations for a given constant-head reservoir. The generalized best amplitude and best frequency of the valve operation are also obtained for two blockages. Accuracy of the proposed methodology in identifying blockages in a hypothetical simple pipe system with increased noise in the simulated measurements is studied. A non-dimensional variable is proposed to determine whether the proposed methodology is applicable to isolate partial blockages in a piping system. Finally, the proposed methodology is experimentally validated on a laboratory piping system for a single blockage and two blockages.

Although many literatures have been focused on the underneath flow and loss mechanism, very few experiments and simulations have been done under the engines’ representative working conditions or considering the real cavity structure as a whole. This paper aims at realizing the goal of design of efficient turbine and scrutinizing the velocity distribution in the vicinity of the rim seal. With the aid of numerical method, a numerical model describing the flow pattern both in the purge flow spot and within the mainstream flow path is established, fluid migration and its accompanied flow mechanism within the realistic cavity structure (with rim seal structure and considering mainstream & secondary air flow’s interaction) is used to evaluate both the flow pattern and the underneath flow mechanism within the inward rotating cavity. Meanwhile, the underneath flow and loss mechanism are also studied in the current paper. The computational results show that the sealing air flow’s ingestion and ejection are highly interwound with each other in both upstream and downstream flow of the rim seal. Both the down-stream blades’ potential effects as well as the upstream blades’ wake trajectory can bring about the ingestion of the hot gas flow within the cavity, abrupt increase of the static pressure is believed to be the main reason. Also, the results indicate that sealing air flow ejected through the rear cavity will cause unexpected loss near the outlet section of the blades in the downstream of the HP rotor passages.

We propose new formulas for calculating the friction factor in pipes with smooth walls and relations between the mean and the maximum fluid flow velocity in a pipe. The formulas are in better agreement with experimental data than the literature relations. An expression for the friction factor suitable for all flow conditions is proposed. The results of this work can be used in calculating the hydraulic resistance of pipes, as well as in calculating the heat and mass transfer processes in apparatuses incorporating tubular elements.

Flow of Bingham plastics through straight, long tubes with non-circular cross-sections is studied by means of an analytical method that allows to model a wide spectrum of tube geometries. Shear stress normal to equal velocity lines, velocity field and plug zones are explored, in particular in a tube with equilateral triangular cross-section for small values of the Bingham number Bi, and they are compared with corresponding numerical solutions. We show that a circular plug is present at the center of the triangular tube cross-section, consistent with numerical simulations as well as with previous results in the literature, if calculations up to and including first order in the shape perturbation parameter $$\epsilon$$ are taken into account. However with the inclusion of the second order terms in the algorithm this structure is no longer present and no plug zone is predicted for the same pressure drop. We find that in that case normal shear stresses are always greater than the yield stress of the fluid. As a result, the central region becomes a pseudo-plug since it presents small but non-vanishing relative deformations and does not move as a rigid core. The energy dissipation function for the Bingham fluid flow is written in terms of natural coordinates. Its distribution depends only on the normal shear stress at any point with Bingham number as a parameter.

Three-dimensional direct numerical simulations of a solid-body rotation superposed on a uniform axial flow entering a rotating constant-area pipe of finite length are presented. Steady in time profiles of the radial, axial, and circumferential velocities are imposed at the pipe inlet. Convective boundary conditions are imposed at the pipe outlet. The Wang and Rusak (Phys. Fluids 8:1007–1016, 1996. doi: 10.1063/1.86882 ) axisymmetric instability mechanism is retrieved at certain operational conditions in terms of incoming flow swirl levels and the Reynolds number. However, at other operational conditions there exists a dominant, three-dimensional spiral type of instability mode that is consistent with the linear stability theory of Wang et al. (J. Fluid Mech. 797: 284–321, 2016). The growth of this mode leads to a spiral type of flow roll-up that subsequently nonlinearly saturates on a large amplitude rotating spiral wave. The energy transfer mechanism between the bulk of the flow and the perturbations is studied by the Reynolds-Orr equation. The production or loss of the perturbation kinetic energy is combined of three components: the viscous loss, the convective loss at the pipe outlet, and the gain of energy at the outlet through the work done by the pressure perturbation. The energy transfer in the nonlinear stage is shown to be a natural extension of the linear stage with a nonlinear saturated process.

Water distribution systems with complex configurations are important urban facilities and the hydraulic analysis is essential for system design, optimization and management. Hydraulic analysis involves the procedure of calculating the hydraulic parameters of nodal pressure heads and pipe flow rates under steady-state condition. The equations governing the heads and flows are nonlinear and the most popular method for solving the equations is the Newton-Raphson method, which is the basis of existing hydraulic simulator (EPANET 2). In this paper, fixed point iteration method is proposed for hydraulic analysis after transformation of the original nonlinear equations. Compared to EPANET 2, the proposed method can analyze a water distribution system without differentiation for the convergence for some problems which cannot be solved by EPANET 2. Three test networks were analyzed by the proposed method and EPANET 2. It is proved that the proposed method could get the convergence after a series of iterations, even in cases that EPANET 2 fail. And the initial values of nodal pressure heads and the specified calculation accuracy are considered to have influences on the calculation procedure.