One-dimensional Flow Research Articles

Numerical Investigation on the length of the near-field region of smoke flow in tunnel fires

In a tunnel fire, smoke flow is often divided into two regions: the near-field and the far-field. The former is a three-dimensional radial flow region close to the fire source and the latter is a one-dimensional steady flow region generally formed a certain distance away from the fire. Although the efficiency of the smoke exhaust system is influenced by the region, limited research has been done to determine the demarcation point between the two regions. In this study, a total of 27 tunnel fire computer simulations were conducted to examine the effect of heat release rate (HRR) and the tunnel's cross-sectional dimensions on the location of the demarcation point. Rather than relying on the tunnel's height, which has been commonly used in previous tunnel fire studies to determine smoke flow characteristics, a hydraulic diameter of the tunnel's cross-section was employed in this study. An improved correlation for the location of the demarcation point is proposed by comparing a theoretical dimensionless model to numerical simulation results.

A thorough description of one-dimensional steady open channel flows using the notion of viscosity solution

Determining water surface profiles of steady open channel flows in a one-dimensional bounded domain is one of the well-trodden topics in conventional hydraulic engineering. However, it involves Dirichlet problems of scalar first-order quasilinear ordinary differential equations, which are of mathematical interest. We show that the notion of viscosity solution is useful in thoroughly describing the characteristics of possibly non-smooth and discontinuous solutions to such problems, achieving the conservation of momentum and the entropy condition. Those viscosity solutions are the generalized solutions in the space of bounded measurable functions. Generalized solutions to some Dirichlet problems are not always unique, and a necessary condition for the non-uniqueness is derived. A concrete example illustrates the non-uniqueness of discontinuous viscosity solutions in a channel of a particular cross-sectional shape.

Dynamics of A+B→C reaction fronts under radial advection in a Poiseuille flow.

A+B→C reaction fronts describe a wide variety of natural and engineered dynamics, according to the specific nature of reactants and product. Recent works have shown that the properties of such reaction fronts depend on the system geometry, by focusing on one-dimensional plug flow radial injection. Here, we extend the theoretical formulation to radial deformation in two-dimensional systems. Specifically, we study the effect of a Poiseuille advective velocity profile on A+B→C fronts when A is injected radially into B at a constant flow rate in a confined axisymmetric system consisting of two parallel impermeable plates separated by a thin gap. We analyze the front dynamics by computing the temporal evolution of the average over the gap of the front position, the maximum production rate, and the front width. We further quantify the effects of the nonuniform flow on the total amount of product, as well as on its radial concentration profile. Through analytical and numerical analyses, we identify three distinct temporal regimes, namely (i) the early-time regime where the front dynamics is independent of the reaction, (ii) the transient regime where the front properties result from the interplay of reaction, diffusion that smooths the concentration gradients and advection, which stretches the spatial distribution of the chemicals, and (iii) the long-time regime where Taylor dispersion occurs and the system becomes equivalent to the one-dimensional plug flow case.

Ventricular outflow tract obstruction: An in-silico model to relate the obstruction to hemodynamic quantities in cardiac paediatric patients.

BackgroundRight (R) or left (L) ventricular outflow tract (VOT) obstruction can be either a dynamic phenomenon or a congenital anatomic lesion, which requires a prompt and optimal timing of treatment to avoid a pathological ventricular remodelling.ObjectiveTo develop a simple and reliable numerical tool able to relate the R/L obstruction size with the pressure gradient and the cardiac output. To provide indication of the obstruction severity and be of help in the clinical management of patients and designing the surgical treatment for obstruction mitigation.MethodsBlood flow across the obstruction is described according to the classical theory of one-dimensional flow, with the obstruction uniquely characterized by its size. Hemodynamics of complete circulation is simulated according to the lumped parameter approach. The case of a 2 years-old baby is reproduced, with the occlusion placed in either the R/ or the L/VOT. Conditions from wide open to almost complete obstruction are reproduced.ResultsBoth R/LVOT obstruction in the in-silico model resulted in an increased pressure gradient and a decreased cardiac output, proportional to the severity of the VOT obstruction and dependent on the R/L location of the obstruction itself, as it is clinically observed.ConclusionThe in-silico model of ventricular obstruction which simulates pressure gradient and/or cardiac output agrees with clinical data, and is a first step towards the creation of a tool that can support the clinical management of patients from diagnosis to surgical treatments.

Research and application of the mathematical model for extreme weather event in coastal urban areas

Extreme weather event simulation in coastal urban areas is more complex and difficult due to their special geography and climate characteristics, different kinds of land uses, close-packed buildings, and large amounts of flood control works and drainage systems. Urban Flood Simulation Model (UFSM) was integrated in this study to simulate the extreme weather events in the Pudong flood protection area (Shanghai, China). The model is established based on two-dimensional unsteady flow theory and nonstructural and irregular mesh technique. A method based on one-dimensional unsteady flow theory is proposed to deal with small-scale river and road. The calculation of the pumping stations, the water gates is indicated based on the real scheduling discipline. The extreme weather event scenarios (typhoon+rainstorm+ astronomical high tide + upstream flood) are simulated. The results show that the flood risk is higher in the coastal area and the upstream of the Huangpu Rive, and UFSM is a suitable method for simulating the flood inundation of coastal urban areas.

Data-driven nonlinear constitutive relations for rarefied flow computations

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed first through the machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between responses of stress tensors and heat flux and feature vectors is established after the training phase. Through the obtained off-line training model, new test cases excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make the DNCR method to be an effective tool in the rarefied gas community, especially for hypersonic engineering applications.

Computational analysis to evaluate one-dimensional rectilinear steady filtration flow of incompressible fluid through homogeneous reservoirs as exemplified by the Yarega field

The paper is concerned with a computational analysis of one-dimensional rectilinear steady filtration flows of incompressible fluids through homogeneous strata as exemplified by the Yarega field. It provides dependence diagrams of key parameters required to characterize the field. Based on the resultant data, it highlights the importance of further studies to evaluate filtration incompressible flows with an aim of enhancing productive oil recovery.

Developing methods for mathematical modeling of a two-phase dielectric-electrolyte microsystem

In this paper, we propose a numerical solution to the problem of stability of a two-phase dielectric / electrolyte system under direct and alternating electric fields. The lower wall adjacent to the electrolyte is assumed to be a charged surface, while the upper one is electrically insulated. The charge on the lower surface is supposed to be stationary, and the surface charge on the free interface between liquids is assumed to be mobile. The model is described by a system of Nernst-Planck-Poisson-Stokes equations. The mathematical model is closed by the corresponding boundary conditions. The linear stability of the one-dimensional flow is investigated. At a constant electric field, and the presence of two types of instabilities is found: short-wave and long-wave.

The Momentum Conserving Scheme for Two-Layer Shallow Flows

This paper confronts the numerical simulation of steady flows of fluid layers through channels of varying bed and width. The fluid consists of two immiscible fluid layers with constant density, and it is assumed to be of a one-dimensional shallow flow. The governing equation is a coupled system of two-layer shallow water models. In this paper, we apply a direct extension of the momentum conserving scheme previously used for solving the one layer shallow water equations. Computations of various steady-state solutions are used to demonstrate the performance of the proposed numerical scheme. Under the influence of a given flow rate, the numerical steady interface is generated in a channel topography with a hump. The results obtained confirm the analytic steady interface of the two-layer rigid-lid model. Furthermore, the same scheme was used with an additional artificial damping to simulate the maximal exchange flow in channels of varying width. The numerical steady interface agreed well with the analytical steady solutions.

Overland-gully-sewer (2D-1D-1D) urban inundation modeling based on cellular automata framework

A new overland-gully-sewer (2D-1D-1D) urban inundation modeling is herein proposed. The authors have developed an integrated approach for overland-gully-sewer urban inundation simulations, which comprises 2D overland flow modeling (2D-OFM) by solving the two-dimensional non-inertia shallow water equations (2D-NISWEs), one-dimensional gully flow modeling (1D-GFM), and one-dimensional sewer flow modeling (1D-SFM). This approach can achieve good accuracy on urban inundation simulations. Nevertheless, such physically-based 2D overland flow modeling with the non-inertia SWEs (2D-OFM-NISWEs) requires substantial computational procedures, so that it is not suitable for real-time evaluation of inundation in urban areas. To resolve this limitation, the present study proposes a new integrated approach for overland-gully-sewer urban inundation modeling, in which the cellular automata (CA) framework is adopted for 2D-OFM to improve its suitability, and 1D-GFM and 1D-SFM are modeled by SWMM. A novel linkage among 2D-OFM-CA, 1D-GFM, and 1D-SFM is developed. A theoretical comparison of the governing equations and computational procedures between the two approaches is first conducted. Two historical flood events in Taipei city are next selected to perform the numerical accuracy verification and numerical efficiency evaluation. Analysis of inundation depths/velocities between the two approaches is conducted, and investigation of the drained and surcharged/inversed discharges of the two approaches is also made. The numerical comparisons between the two approaches indicate that the proposed approach can maintain good accuracy with significant reduction on its computing time. This newly proposed approach can finish a 3 hours short-duration urban inundation simulation on a case study with 335,621 cells within 12–17 mins. As a result, this CA-based approach is proved to be a useful tool for real-time urban inundation modeling.

Estimating output flow depth from Rockfill Porous media

Abstract To analyze the flow in a rockfill porous media using the Gradually Varied Flows theory (one-dimensional flow analysis) and solving the Parkin equation (two-dimensional flow analysis), calculation of the output flow depth as the downstream boundary condition is of great importance. In most previous studies, the output flow depth has been considered equal to the critical depth. In the rockfill porous media, unlike free surface channels, the fluid weight is exerted to the aggregates in addition to the flow, and therefore, the output flow depth from the rockfill is always greater than the critical depth (flow leaves the rockfill with a specific energy greater than the critical energy), and is expressed as a coefficient (Γ) of the critical depth. In the present study, using dimensional analysis and particle swarm optimization (PSO) algorithm and experimental data in different conditions (a total of 178 experimental data for rounded, crashed, Glass artificial materials with rhomboid structure, Glass artificial materials with cubic structure, sandy natural materials), an equation was presented to calculate the mentioned coefficient as a function of the physical characteristics of the rockfill porous media as well as the flow that can be used for all experimental conditions with high accuracy. If the output flow depth is considered to be equal to the critical depth, the mean relative error (MRE) in terms of using the experimental data of the mentioned materials separately and for the data of all the mentioned materials together was equal to 84.40, 83.81, 60.62, 67.68, 74.82 and 69.96%, respectively. In the case of using the proposed equation in the present study, the corresponding values of 5.49, 4.72, 6.24, 4.41, 6.42 and 8.99% were calculated, respectively.

Collaborating elite of Kalabagh and patterns of control in colonial Punjab, 1849–1939

ABSTRACT This article discusses the local dynamics of control by the rural elite in colonial Punjab over agricultural land, the informal credit market and labour supply. I argue, the landed elite in collaboration with bureaucratic patronage, developed linkages between indigenous institutions and imperial ideology, controlled and manipulated the means of power and wealth. This led to a one-dimensional flow of capital and profit, towards elite and state, causing a serious check on social mobility and economic development. In a local study of a rural town, Kalabagh, in the north-west of Pakistani Punjab, the article brings forward an understudied aspect of colonial policies which followed a different trajectory from the rest of the Punjab. The colonial state, instead of development, maintained the structure of society under feudal setup. Rais, the ruling elite of the town, as colonial collaborator, managed the moneylending system in his estate and trapped the wage labourers in complex debt bondage, perpetuating jajmani type relationship in the twentieth century. At one level this arrangement invigorated hierarchical differentiation and dispossession of rural proletariat, at another level, the social differentiation acted as an instrument to mobilize the community for collective action towards nationalist discourse.

A flux reconstruction kinetic scheme for the Boltzmann equation

It is challenging to solve the Boltzmann equation accurately due to the extremely high dimensionality and nonlinearity. This paper addresses the idea and implementation of the first flux reconstruction method for high-order Boltzmann solutions. Based on the Lagrange interpolation and reconstruction, the kinetic upwind flux functions are solved simultaneously within physical and particle velocity space. The fast spectral method is incorporated to solve the full Boltzmann collision integral with a general collision kernel. The explicit singly diagonally implicit Runge-Kutta (ESDIRK) method is employed as time integrator and the stiffness of the collision term is smoothly overcome. Besides, we ensure the shock capturing property by introducing a self-adaptive artificial dissipation, which is derived naturally from the effective cell Knudsen number at the kinetic scale. As a result, the current flux reconstruction kinetic scheme can be universally applied in all flow regimes. Numerical experiments including wave propagation, normal shock structure, one-dimensional Riemann problem, Couette flow and lid-driven cavity will be presented to validate the scheme. The order of convergence of the current scheme is clearly identified. The capability for simulating cross-scale and non-equilibrium flow dynamics is demonstrated.

Experimental Study on the Characteristics of Adsorbed Gas and Gas Production in Shale Formations

Adsorbed gas and free gas both exist in shale reservoirs simultaneously due to the unique nanoscale pore structure, resulting in the complex flow mechanism of gas in the reservoir during the development process. The dynamic performance analysis of shale reservoirs has mostly been conducted by the numerical simulation and theoretical model, while the physical simulation method for relevant research is seen rarely in the literature. Thus, in this paper, an experiment system was designed to simulate the degraded development experiments of shale, coal, and tight sandstone to reveal the output law of gas in different occurrence states of shale reservoirs and clarify the pressure propagation rules of different reservoirs, and then, adsorption gas and free gas production laws were studied by theoretical models. Research indicated the following: (1) The gas occurrence state is the main factor that causes the difference of the pressure drop rate and gas production law of shale, coal, and tight sandstone. During the early stage of the development of shale gas, the free gas is mainly produced; the final contribution of free gas production can reach more than 90%. (2) The static desorption and dynamic experiments confirm that the critical desorption pressure of adsorbed gas is generally between 12 and 15 MPa. When the gas reservoir pressure is lower than the critical desorption pressure in shale and coal formation, desorption occurs. Due to the slow propagation of shale matrix pressure, desorption of adsorbed gas occurs mainly in the low-pressure region close to the fracture surface. (3) The material balance theory of closed gas reservoirs and the one-dimensional flow model of shale gas have subsequently validated the production performance law of adsorbed gas and free gas by the physical simulation. Therefore, in the practical development of shale gas reservoirs, it is recommended to shorten the matrix supply distance, reduce the pressure in the fracture, increase the effective pressure gradient, and enhance the potential utilization of adsorbed gas as soon as possible to increase the ultimate recovery. The findings of this study can help for a better understanding of the shale reservoir utilization law so as to provide a reference for production optimization and development plan formulation of the shale gas reservoirs.

Study on scramjet engines with complex inlet flow conditions

Scramjet engine is one of the key technologies to realize hypersonic flight. It has great research value for its performance under complex inlet flow conditions. In this paper, the free jet test model of RBCC aircraft is established, and the numerical simulation is carried out with Japanese NAL direct connected hydrogen fuel combustion chamber test. Aiming at the problems of coupling analysis accuracy and long calculation period, a one-dimensional internal flow coupling analysis method based on one-dimensional flow is proposed to solve the backpressure problem in the subsonic combustion state. The experimental results show that this method can predict the flow separation point in the isolation section well in the subsonic combustion mode, and the error is less than 10%, the prediction results of the peak pressure and the mean pressure along the passage are less than 23% and 10.4%, respectively. In the supersonic combustion mode, the accuracy of one-dimensional flow is higher, and the prediction error for the peak pressure in the combustion chamber is less than 3.79%, and the prediction error for the location of the peak pressure is less than 2.3%.

A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels

We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These flows are described by a conditionally hyperbolic balance law with non-conservative products. A detailed description of the properties of the model is provided, including entropy inequalities and asymptotic approximations of the eigenvalues of the corresponding coefficient matrix. The scheme extends existing central-upwind semi-discrete numerical methods for hyperbolic conservation and balance laws and it satisfies two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water depth for each layer, and it is well balanced, i.e., the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. Along with the description of the scheme and proofs of these two properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.

Analysis of Thermal Effect in Thin Disk Laser: A Review

Since its first invitation in 1993, solid-state diode end-pumped thin-disk laser attracts much attention due to its significant improvements in the solid-state laser system. It had many advantages; it has high optical and electrical efficiency, high produced peak power, a simple cooling system, and high beam quality more than the usual solid-state diode laser system. The thin-disk laser (TDL) permits an effective pulse mode, which permits a new type of very short-pulsed laser system that could be used in the industry. Due to the influence of the many factors such as effective cooling system, the type of pumping, and the used thin crystal, a one-dimensional heat flow through thin-disk laser could be achieved which permits excellent enhancement in the beam quality. Finally, in this work, a review is made to the works devoted to discussing the basic principle and the solutions used to analyze the thermal effect in the thin disk laser.

Micropolar Fluid Flow Along with an Inclined Riga Plate Through a Porous Medium

This study presents the one-dimensional unsteady micropolar fluid flow set in a porous medium along with an inclined infinite Riga plate. This Riga plate is created an electric and magnetic field, where a transverse Lorentz force is generated that contributes a flow along with the plate. The explicit finite difference method is used to find the solution of the non-dimensional form of the governing equations and estimated results are analyzed in terms of Microrotation parameter, Suction parameter, thermal Grashof number, mass Grashof number, Permeability parameter, Hartmann number, Dufour number, Soret number, Schmidt number. Also, the effects of the pertinent parameters on the local and average shear stress, Nusselt number, and Sherwood number are reported numerically as well as graphically.

Modeling Two-Phase Water Hammer Flow Using Shock-Capturing Scheme

This article focuses on simulating two-phase water hammer flow. A mathematical formulation has been pointed out to describe the transient one-dimensional homogeneous flow, modelled by gas-liquid mixture flow through an elastic pipe. The governing equations obtained from conservation laws have been carried out. Richtmyer two steps scheme stabilized by the flux corrected transport method have been investigated in the numerical simulations. Despite the fact that the conservative form of the equations gives good results in the simulation, it is useful to present the comparison between the numerical solutions of conservative, semi-conservative and non-conservative forms of equations during the simulation in order to legitimate these approximations often countered and used in such equations. A comparison between obtained results and experimentally reported data indicates that even with non-conservative form, the methods have been in good agreement with experimental observations and are better than the method of characteristics widely used in numerical computation describing water hammer phenomena.

An Explicit Analytical Solution for Transient Two-Phase Flow in Inclined Fluid Transmission Lines

Due to the complex nonlinearity characteristics, analytical modeling of compressible flow in inclined transmission lines remains a challenge. This paper proposes an analytical model for one-dimensional flow of a two-phase gas-liquid fluid in inclined transmission lines. The proposed model is comprised of a steady-state two-phase flow mechanistic model in-series with a dynamic single-phase flow model. The two-phase mechanistic model captures the steady-state pressure drop and liquid holdup properties of the gas-liquid fluid. The developed dynamic single-phase flow model is an analytical model comprised of rational polynomial transfer functions that are explicitly functions of fluid properties, line geometry, and inclination angle. The accuracy of the fluid resonant frequencies predicted by the transient flow model is precise and not a function of transmission line spatial discretization. Therefore, model complexity is solely a function of the number of desired modes. The dynamic single-phase model is applicable for under-damped and over-damped systems, laminar, and turbulent flow conditions. The accuracy of the overall two-phase flow model is investigated using the commercial multiphase flow dynamic code OLGA. The mean absolute error between the two models in step response overshoot and settling time is less than 8% and 2 s, respectively.