One-dimensional Flow Research Articles

Mathematical model of killing an oil horizontal well

The physical picture of the killing fluid and the formation fluid movement in the process of killing a horizontal oil well has been described, a physical and mathematical model of the process has been developed and the limits of the model applicability have been indicated. It is recommended to conduct the killing process in two stages, separated by a technological break. During the first stage, the injected killing fluid fills the tubing, the annulus and the part of the horizontal wellbore. For the duration of the technological break, the denser tubing slowly displaces the formation fluid from the horizontal wellbore into the annulus where the formation fluid floats to the surface in the form of droplets. For the period of the second stage, the remaining amount of tubing is pumped into the well. The model is based on the well-known hydraulic equations for laminar flow of liquids, the solution of the flooded jet problem, as well as the model of one-dimensional vertical inertialess flow of a two-phase medium with incompressible phases. A closed system of equations has been formed taking into account the viscous friction losses on the walls of the horizontal pipe and at the interface between the formation fluid and the killing fluid flows. The solution of this system has been obtained and the values of the main process parameters have been found: velocities and flows of liquid gas and liquid coolant and time of complete replacement of liquid coolant by the killing fluid depending on the inclination angle of the horizontal pipe. It is shown that the character of the movement of the formation fluid drops in the pipe space depends on their volume fraction φ in the mixture with the killing fluid. With the value φ < 1/3 the jelly drops float up with a constant speed, while the jelly droplet radius and the speed of their floating up are unambiguously determined by the jelly stream size, density and viscosity of jelly and liquid hydrocarbon. The graphs of dependence of these parameters on the value of the formation fluid flow have been presented. On the basis of the research the recommendations for the process of killing horizontal oil wells have been formulated.

Symmetries of the one-dimensional hyperbolic Lagrangian mean curvature flow

Symmetries of the one-dimensional hyperbolic Lagrangian mean curvature flow

Modeling the effect of patient size on cerebral perfusion during veno-arterial extracorporeal membrane oxygenation.

A well-known complication of veno-arterial extracorporeal membrane oxygenation (VA ECMO) is differential hypoxia, in which poorly-oxygenated blood ejected from the left ventricle mixes with and displaces well-oxygenated blood from the circuit, thereby causing cerebral hypoxia and ischemia. We sought to characterize the impact of patient size and anatomy on cerebral perfusion under a range of different VA ECMO flow conditions. We use one-dimensional (1D) flow simulations to investigate mixing zone location and cerebral perfusion across 10 different levels of VA ECMO support in eight semi-idealized patient geometries, for a total of 80 scenarios. Measured outcomes included mixing zone location and cerebral blood flow (CBF). Depending on patient anatomy, we found that a VA ECMO support ranging between 67-97% of a patient's ideal cardiac output was needed to perfuse the brain. In some cases, VA ECMO flows exceeding 90% of the patient's ideal cardiac output are needed for adequate cerebral perfusion. Individual patient anatomy markedly affects mixing zone location and cerebral perfusion in VA ECMO. Future fluid simulations of VA ECMO physiology should incorporate varied patient sizes and geometries in order to best provide insights toward reducing neurologic injury and improved outcomes in this patient population.

Large-Scale Hydromorphological Characteristics Of The Proglacial River Katun (Ob Headwaters)

During the industrialization in Europe, rivers were straightened and designed to fit human activities, thus nowadays only a few natural river systems remain as reference conditions as well as guiding principles for river restoration projects. Therefore, the natural state of some river types is often described using historic records and maps. This study aims to analyze the key characteristics of a pristine proglacial river Katun in the Altai mountains and contribute to the knowledge about reference conditions. For this purpose, hydromorphological characteristics like slope, sinuosity and river width of the river Katun were analysed and summarized using different GIS techniques. Additionally, pebble counts were carried out to assess the changing sediment composition along the longitudinal continuum. Combined with River Habitat Surveys and a one-dimensional flow simulation using HEC-RAS it was possible to give a holistic overview of the dynamic fluvial system Katun in its upper, middle and lower reaches. The results confirmed the relationship between the river and its surrounding topography as they clearly show the lateral development of the Katun. As shown for the individual parameters (e.g., slope, width, depth, flow velocity, shear stress), they influence each other and are strongly dependent and characteristic for each river section. In the context of revitalisation of straightened and / or channelized river courses, it is important to focus on the processes of this interaction and provide suitable space for lateral expansion. The study can be seen as a recommendation on how to analyse hydromorphological characteristics of fluvial systems as well as to establish guiding principles in river restoration using remote sensing.

A shock-capturing meshless method for solving the one-dimensional Saint-Venant equations on a highly variable topography

Abstract The Saint-Venant equations are numerically solved to simulate free surface flows in one dimension. A Riemann solver is needed to compute the numerical flux for capturing shocks and flow discontinuities occurring in flow situations such as hydraulic jump, dam-break wave propagation, or bore wave propagation. A Riemann solver that captures shocks and flow discontinuities is not yet reported to be implemented within the framework of a meshless method for solving the Saint-Venant equations. Therefore, a wide range of free surface flow problems cannot be simulated by the available meshless methods. In this study, a shock-capturing meshless method is proposed for simulating one-dimensional (1D) flows on a highly variable topography. The Harten–Lax–van Leer Riemann solver is used for computing the convective flux in the proposed meshless method. Spatial derivatives in the Saint-Venant equations and the reconstruction of conservative variables for flux terms are computed using a weighted least square approximation. The proposed method is tested for various numerically challenging problems and laboratory experiments on different flow regimes. The proposed highly accurate shock-capturing meshless method has the potential to be extended to solve the two-dimensional (2D) shallow water equations without any mesh requirements.

Thermodynamic Concepts in Civil Engineering

Thermodynamics is not always done well or usefully brought to bear in civil engineering. This paper addresses historical aspects of misunderstandings of thermodynamic concepts; applies the Second Law of Thermodynamics to applications including shock waves in compressible fluid flow, the tidal bore, spillway flow , and junction flow. Additional applications of thermodynamics in civil engineering are discussed. These include deriving hydraulic transient wave celerities for waterhammer analyses; the First Law of Thermodynamics for a closed system and for a control volume; one-dimensional flow, energy loss due to friction; parallel incompressible flow; application of the control volume to a pressure conduit; the modified Bernoulli equation; tees with small inflow and outflow branches; isentropic flow of a perfect gas and its application to flow metering, determination of choked flow conditions, and determination of the shaft power required to drive a blower.

Kinetic modelling of rarefied gas flows with radiation

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with internal degrees of freedom and radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability to capture the influence of intermolecular potentials, while the other adopts the relaxation time approximations, which has higher computational efficiency. In our kinetic model equations, not only the transport coefficients such as the shear/bulk viscosity and thermal conductivity but also their underlying relaxation processes are recovered. The non-equilibrium dynamics of gas flow and radiation are tightly coupled, where the transport properties of gas molecules and photons are correlatively dependent. The proposed kinetic models are validated by the direct simulation Monte Carlo method in several non-radiative rarefied gas flows (e.g. the normal shock wave, Fourier flow, Couette flow and the creep flow driven by the Maxwell demon), and the experimental data of planar heat transfer and normal shock waves in nitrogen. Then, the rarefied gas flows with strong radiation are studied based on the kinetic models, not only in the above one-dimensional gas flows, but also in the two-dimensional radiative hypersonic flow passing a cylinder. The characteristics of heat transfer in the tightly coupled fields of gas and radiation are systematically investigated, particularly the influence of the non-equilibrium photon transport and their interactions with gas molecules are revealed. It is found that the radiation makes a profound contribution to the total heat transfer in radiative hypersonic flow at an intermediate photon Knudsen number.

A hybrid 1D-2D Lagrangian solver with moving coupling to simulate dam-break flow

In dam-break problems, two-dimensional (2D) models on the vertical plane appropriately capture the non-hydrostatic pressure distribution but with a high computational cost. This study presents a hybrid Lagrangian solver of one-dimensional (1D) shallow water flow and a 2D large-eddy simulation with a sub-particle scale to simulate dam-break flows over frictional beds. The proposed 1D-2D hybrid scheme is a useful trade-off between the accuracy of the 2D models on the vertical plane and the computational efficiency of 1D shallow water equations models. The configuration of sub-domains is established so that the 1D solves the regions with dominantly hydrostatic pressure, while the 2D solver accounts for the non-hydrostaticity. A moving coupling method is introduced based on two-layer shallow water equations with a uniform velocity distribution that constructs two sub-domains, including inner and outer zones in the section coupling model (SCM), or upper and lower layers within the layer coupling model (LCM). Then, the region with high vertical accelerations is substituted by the 2D model in the SCM or mixed SCM-LCM in which the overlapping zone and boundary interface move with time, based on the 1D flow feature. Also, a new method is proposed to deal with irregular boundary interfaces in the LCM while satisfying the momentum transfer. The present hybrid model is advantageous as it meets mass conservation, and there is no need for typical inflow/outflow boundary conditions at the coupling interfaces for simulating dam-break waves. Moving particle simulation (MPS) is utilized to solve the Lagrangian equations, which is advantageous in dealing with free-surface problems with large deformation. The model validation reveals that the hybrid results of water depths are in very good agreement with observed data and those obtained from the 2D model for selected dam-break flows with the ratio of initial depths downstream to upstream up to 0.4. In this respect, the average root-mean-square-error (RMSE) is computed at 8.09 mm in the SCM, 8.16 mm in the mixed SCM-LCM, and 7.48 mm in the pure 2D model, while both hybrid models save the computational time by 55% compared to the 2D model. Moreover, the mixed SCM-LCM preserves the nonlinearity of the wavefront over long times, whereas the SCM converts the wavefront into a shockwave considering the same number of fluid particles.

A novel physics-based model for fast computation of blood flow in coronary arteries

Blood flow and pressure calculated using the currently available methods have shown the potential to predict the progression of pathology, guide treatment strategies and help with postoperative recovery. However, the conspicuous disadvantage of these methods might be the time-consuming nature due to the simulation of virtual interventional treatment. The purpose of this study is to propose a fast novel physics-based model, called FAST, for the prediction of blood flow and pressure. More specifically, blood flow in a vessel is discretized into a number of micro-flow elements along the centerline of the artery, so that when using the equation of viscous fluid motion, the complex blood flow in the artery is simplified into a one-dimensional (1D) steady-state flow. We demonstrate that this method can compute the fractional flow reserve (FFR) derived from coronary computed tomography angiography (CCTA). 345 patients with 402 lesions are used to evaluate the feasibility of the FAST simulation through a comparison with three-dimensional (3D) computational fluid dynamics (CFD) simulation. Invasive FFR is also introduced to validate the diagnostic performance of the FAST method as a reference standard. The performance of the FAST method is comparable with the 3D CFD method. Compared with invasive FFR, the accuracy, sensitivity and specificity of FAST is 88.6%, 83.2% and 91.3%, respectively. The AUC of FFRFAST is 0.906. This demonstrates that the FAST algorithm and 3D CFD method show high consistency in predicting steady-state blood flow and pressure. Meanwhile, the FAST method also shows the potential in detecting lesion-specific ischemia.

A Bio-Inspired MEMS Wake Detector for AUV Tracking and Coordinated Formation

AUV (Autonomous Underwater Vehicle) coordinated formation can expand the detection range, improve detection efficiency, and complete complex tasks, which requires each AUV to have the ability to track and locate. A wake detector provides a new technical approach for AUV cooperative formation warfare. Now, most of the existing artificial lateral line detectors are for one-dimensional flow field applications, which are difficult to use for wake detection of AUVs. Therefore, based on the pressure gradient sensing mechanism of the canal neuromasts, we apply Micro-Electro-Mechanical System (MEMS) technology to develop a lateral line-inspired MEMS wake detector. The sensing mechanism, design, and fabrication are demonstrated in detail. Experimental results show the detector’s sensitivity is 147 mV·(m/s)−1, and the detection threshold is 0.3 m/s. In addition, the vector test results verify it has vector-detecting capacity. This wake detector can serve AUVs wake detection and tracking technology, which will be promising in AUV positioning and coordinated formation.

Acquisition of Key Vacuum-Assisted Resin Transfer Molding Parameters through Reverse Scanning for Application in the Manufacturing of Large Fiber-Reinforced-Plastic Products

Software-based mold flow analysis is often performed to confirm optimized resin pipe arrangements. In this study, the GeoDict software and reverse scanning were employed to develop a method for performing rapid porosity and permeability estimation. A comparison of the results from one-dimensional resin flow and Easyperm tests revealed a 10% variation in the porosity and permeability parameters obtained through the proposed rapid estimation method. In addition, the obtained parameters were substituted into a Moldex3D model to simulate the resin flow on the personal watercraft hull during vacuum-assisted resin transfer molding (VARTM). A comparison of simulation results and hull infusion results revealed that the integration of the proposed rapid estimation method with Moldex3D allowed for the accurate simulation of the resin flow in large fiber-reinforced-plastic (FRP) products (variation <8%). The proposed method can be applied to large wind turbine FRP parts and large FRP yacht components to increase process planning efficiency and product stability.

Semi-analytical method for blood flow model with source terms

This article discusses a semi-analytical method for solving modelling equations for blood flow through compliant vessels. He's method, also called the variational iteration method (VIM), is used to find an approach to a solution in an explicit form. The chosen problem has been handled by an asymptotic reduction of the associated incompressible Navier–Stokes equations, to obtain a one-dimensional nonlocal blood flow model with source terms. Numerical examples were chosen based on experimentally valued parameters and were used to highlight and illustrate the benefits of VIM. The results obtained from the blood flow model were compared to a numerical reference method.

Bimodal star formation in simulations of strongly magnetized giant molecular clouds

ABSTRACT We present the results of a set of radiation magnetohydrodynamic simulations of turbulent molecular clouds in which we vary the initial strength of the magnetic field within a range (1 ≲ μ ≲ 5) consistent with observations of local giant molecular clouds (GMCs). We find that as we increase the strength of the magnetic field, star formation transitions from unimodal (the baseline case, μ = 5, with a single burst of star formation and Salpeter IMF) to bimodal. This effect is clearest in the most strongly magnetized GMC (μ = 1): a first burst of star formation with duration, intensity, and IMF comparable to the baseline case, is followed by a second star formation episode in which only low-mass stars are formed. Overall, due to the second burst of star formation, the strongly magnetized case results in a longer star formation period and a higher efficiency of star formation. The second burst is produced by gas that is not expelled by radiative feedback, instead remains trapped in the GMC by the large-scale B-field, producing a nearly one-dimensional flow of gas along the field lines. The trapped gas has a turbulent and magnetic topology that differs from that of the first phase and strongly suppresses gas accretion onto protostellar cores, reducing their masses. We speculate that this star formation bimodality may be an important ingredient to understand the origin of multiple stellar populations observed in massive globular clusters.

Numerical approximation of living-man steady state solutions for blood flow in arteries using a well-balanced discontinuous Galerkin scheme

This study developed a well-balanced discontinuous Galerkin method for the one-dimensional blood flow model capable of preserving zero and non-zero velocity steady state solutions. The strategy used was to incorporate the source term into the flux function to rewrite the law of balance in a conservative form, in terms of global equilibrium variables that remained constant in space and time under steady states. Subsequently, the conservative variables were recalculated using the equilibrium variables. Recently, this concept was applied to shallow water and the Euler equations of gas dynamics. Numerical tests verified the well-balanced property of the designed scheme and its ability to capture small steady-state perturbations on relatively coarse meshes accurately.

Non-unique solutions for flow depth and velocity estimations in free-surface annular-channel for single-phase viscous flows

Flow depth and mean velocity estimations for partially filled annular ducts are performed using a one-dimensional free-surface flow formulation. The formulation considers a Newtonian fluid flowing in a closed channel with a circular annular cross-section, in steady-state and uniform regimes. The Darcy–Weisbach friction factor, combined with the Churchill equation and hydraulic-diameter approach, is used. Expressions for the flow cross-section area and the wetted perimeter of the partially full annular channel flow, both terms of hydraulic-diameter definition, are derived from trigonometric rules as a function of the flow depth. In contrast to partially filled pipe flow where a bi-univocal and monotonic trend solution between flow depth and flow rate occurs, for annular-channel, multiple values for the flow depth satisfy the formulation for a single flow rate value. Multiple solutions existence is accounted for the abrupt changes in the flow geometry, mainly related to the wetted perimeter, when (i) the flow height enters in contact with the internal duct, (ii) the internal duct becomes completely submerged, and (iii) the flow completely fills the duct cross-section. Calculations for a broad range of geometries and flow conditions (inclination angles: 15°–85°, viscosity: 0.001–0.576 Pa s., and Reynolds numbers: 101–8×105) show errors up to 47% can be reached for flow velocity and flow depth estimations. Specifically, for turbulent flows, discrepancies are lower, being less than 10%. Thus, the higher the inclination angle and viscosity, the more significant errors. The paper outlines the implication of the flow depth and velocity estimations using a well-accepted formulation that impacts on industrial systems’ design and operation stages. We draw attention to the existence of non-unique solutions for free-surface flows in annulus and the need for experiments to elucidate which of these solutions is physically possible and consequently improve predictions for the flow depth and mean velocity in this kind of flow.

Reduced order 1 + 3D numerical model for evaluating the performance of solar borehole thermal energy storage systems

This study presents a computationally efficient numerical model for solving the fluid flow and heat transfer phenomena in co-axial boreholes heat exchangers arranged on a rectangular grid (N × N) drill hole pattern. Such systems of boreholes are an integral component of a Solar-Borehole Thermal Energy Storage System for seasonal thermal storage application. The numerical model couples a one-dimensional fluid flow and convective heat transfer model in the heat exchanger with a three-dimensional model of conductive heat transfer in the strata. In addition to solving mass and heat transfer in borehole systems, it integrates a solar thermal collector system and building dynamic thermal load to design a Solar- Borehole Thermal Energy Storage system for a 182-unit residential apartment building. Simulation also considers and evaluates the conductive, convective, and radiative thermal losses of the system. The model is validated using experimental data from a coaxial borehole heat exchanger and compared to the results of a commercial finite volume solver for multiple co-axial boreholes. The computational cost of developed numerical model is reduced by a factor of 194 compared to a commercial finite volume solver. Solar- Borehole Thermal Energy Storage system simulation is performed for a period of five years considering hourly fluctuations in solar irradiance and building dynamic thermal energy demand. Parametric study is performed on depth and spacing of boreholes, and mass flowrate in the solar thermal collectors. It is found that a system of 100 boreholes, each 100 m deep, linked to 674 solar thermal collectors can provide the heating for the building with a total thermal demand of 5600 GJ per year.

Study on the effect of viscosity and fluid flow on buckling behavior of nanoplate with surface energy

In this article, the buckling of a nanoplate at the bottom of a tank over which the fluid passes with a one-dimensional flow was investigated. Navier-Stokes equations were used to obtain the applied force from the fluid to the nanoplate. Surface effects theory was used to consider nanoscale effects. By solving this problem using Galerkin's weighted residual method, the effect of fluid viscosity and flow velocity was studied, and also the way surface effects change the critical buckling load of the nanoplates placed in the fluid was investigated. The results reported in this research are very helpful for developing and improving the performance of fluid-coupled nanostructures that have buckling potential.

Estimating the combined risks of sea level rise and storm surges using a numerical model: Application to Macao

The storm surges caused by tropical cyclones may lead to overtopping floods in low-lying coastal communities, which will be further exacerbated by sea level rise. In this study, a numerical model is developed that can simulate the two-dimensional surface flow and one-dimensional drainpipe flow simultaneously. Then this model is validated and applied to Macao Peninsula. The compound flood scenarios of storm surge and sea level rise are therefore forecasted, with storm surge return periods of 5-, 10-, 20-, 50-, 100-, and 200-years, and sea level rises by 0 m, 0.5 m and 1.0 m. The overtopping floods caused by storm surges are mainly distributed in the west and northwest of Macao Peninsula. When the sea level rises by 1.0 m, the backflow occurs 2 h earlier than that does under the current sea level. Adding pumping station can reduce backflow and improve drainage efficiency significantly. The effectiveness of the drainage system during floods can be quantified using backflow coefficient and drainage efficiency coefficient, which both decrease as the storm tide level increases. In the worst-case scenario of 200-year-return-period storm surge and 1-m sea level rise, the flooding area accounts for 41.1% of the land area, and the population at risk reaches 68.4% of the total population. The storm-surge-prone area overlaps with densely populated area in western Macao Peninsula, where the effects of storm surge and sea level rise are intensified.

Preliminary Design and Numerical Investigation of a Centrifugal Compressor for Supercritical Carbon Dioxide Operating in the Vicinity of Its Critical Thermodynamic State

Waste heat recovery is one of the main practices used to reduce the carbon footprint of the industrial sector regarding environmental concern. The supercritical carbon dioxide (s-CO2) cycle is one of the most attractive heat-to-power technologies; due to the abrupt variation in CO2 properties in the vicinity of its critical point, small compression work is required and finally a high cycle efficiency is achieved. In the literature, among the various proposed layouts, the recompression s-CO2 Brayton cycle is considered to be the most efficient one. The most critical component of such a cycle is definitely the main compressor, as the related usual design procedures have been developed in the past for ideal gas as a working fluid. This study presents a methodology for the preliminary design of a centrifugal compressor with a vaned diffuser, suitable for fulfilling the desired operating requirements of a particular supercritical CO2 recompression Brayton cycle. Furthermore, it demonstrates the numerical investigation of the three-dimensional (3D) flow phenomena occurring in it, focusing on the investigation of possible condensation. To this end, a one-dimensional flow model was developed to provide information regarding the geometry of the compressor and predict its prospective performance. Commercial computational fluid dynamics (CFD) software was then employed to examine the three-dimensional flow. The effect of accuracy in the evaluation of real gas properties approaching the critical point was examined, showing that a look-up table with more points around the critical point can reduce the numerical relative error by up to 0.3% for the value of specific heat capacity. In addition, the possibility of condensation occurrence was investigated at the impeller’s inlet, where the flow is accelerated. The supersaturation pressure ratio was defined and implemented in order to identify regions where static pressure is lower than saturation pressure, possibly leading to local two-phase flow.

A time-relaxed Monte Carlo method preserving the Navier-Stokes asymptotics

In this paper, a new time-relaxed Monte Carlo (TRMC) method is proposed for the inhomogeneous Boltzmann equation. Compared to the standard TRMC scheme, the proposed method performs the same convection operator, however, divides the collision operator by a micro-macro decomposition. The continuous part of the collision operator is constructed based on the first-order Chapman-Enskog expansion and solved by an explicit second-order scheme, while the numerical solution of the rest nonequilibrium part is still provided by the standard TRMC scheme. In this way, the new TRMC method demonstrates the same accuracy as the standard TRMC scheme in the kinetic limit, however, preserves Navier-Stokes asymptotics and the second-order accuracy in the fluid limit. Several numerical cases of inhomogeneous flows, such as the one-dimensional Poiseuille flow, Sod tube flow, the shock wave and two-dimensional hypersonic flow past a cylinder, are calculated and compared with direct simulation Monte Carlo (DSMC) or Navier-Stokes solutions. It is noted that the new TRMC scheme is more accurate and efficient than the standard TRMC and DSMC methods for simulations of multi-scale gas flows.