Free Flow Regime Research Articles

Dissipation instability of Couette-like adiabatic flows in a plane channel

The mixed convection flow in a plane channel with adiabatic boundaries is examined. The boundaries have an externally prescribed relative velocity defining a Couette-like setup for the flow. A stationary flow regime is maintained with a constant velocity difference between the boundaries, considered as thermally insulated. The effect of viscous dissipation induces a heat source in the flow domain and, hence, a temperature gradient. The nonuniform temperature distribution causes, in turn, a buoyancy force and a combined forced and free flow regime. Dual mixed convection flows occur for a given velocity difference. Their structure is analysed where, in general, only one branch of the dual flows is compatible with the Oberbeck–Boussinesq approximation, for realistic values of the Gebhart number. A linear stability analysis of the basic stationary flows with viscous dissipation is carried out. The stability eigenvalue problem is solved numerically, leading to the determination of the neutral stability curves and the critical values of the Péclet number, for different Gebhart numbers. An analytical asymptotic solution in the special case of perturbations with infinite wavelength is also developed.

Fully discrete, decoupled and energy-stable Fourier-Spectral numerical scheme for the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy flow regime of two-phase incompressible flows

In this paper, we introduce fully discrete Fourier-Spectral numerical scheme to solve the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy equations, which represent a phase-field model for two-phase incompressible flow in either the free flow regime or a Hele-Shaw cell. The proposed scheme achieves full decoupling while maintaining linearity and energy stability through a combination of the Scalar Auxiliary Variable (SAV) method, which discretizes the nonlinear potential, and the “Zero-Energy-Contribution” (ZEC) method, which handles the coupled nonlinear advective/surface tension terms. The efficiency of this scheme is attributed to its linear decoupling structure and the fact that it requires only a few elliptic equations with constant coefficients to be solved at each time step. We rigorously establish the scheme’s unconditional energy stability. Further, some numerical simulations are provided in both 2D and 3D to show its effectiveness, including its accuracy, stability, and efficiency.

Modeling of Brownian Force on a Spherical Particle Trajectory in Free Molecular Gas Flow Regime

Modeling of Brownian Force on a Spherical Particle Trajectory in Free Molecular Gas Flow Regime

Delta-perturbation expansion for critical flow depth problem in trapezoidal channels

For man-made and natural channels, the knowledge of the critical depth is an important parameter in the analysis of free surface flow regimes and backwater curves. For trapezoidal channels, a trial and error approach and large sequence computation (iterations or infinitely nested radicals) are needed due to the implicit character of the governing equation. In the present paper, an original analytical solution based on the Delta-perturbation expansion is proposed for the problem of critical depth computation in trapezoidal shaped channels. The obtained explicit analytical expression forms a very precise solution for practical purposes. A series of real canals are treated as examples to illustrate the application of the proposed approach.

Effects of Road Slope and Vehicle Weight on Truck Fuel Consumption

In this paper, we developed truck fuel consumption models for the particular assistance of professionals in charge of road project valuation in terms of predicting fuel used by trucks, which is an important topic on vehicle operating costs to be considered in the benefit–cost analysis of road projects. On the other hand, fuel consumption has a direct impact on emissions to the atmosphere, and thus future research can be conducted regarding estimations about emissions by trucks. In this research, we identified the effect of overall vehicle weight on truck fuel consumption in a free-flow regime. The methodology includes the design of experiments and factorial design as statistical techniques to obtain data, as well as linear and non-linear regressions to obtain models for two types of trucks: rigid (three axles) and articulated (six axles). Notably, there is no evidence of research previously conducted on the latter. We used statistical methods for the selection of trucks, equipment, road segments, and other aspects, obtaining good control in tests verifying the appropriate values for factors according to the planned ones. The results satisfy the expectations of the research, and it was demonstrated that the vehicle weight and roadway slope were significantly more important than speed alone, which was typically considered the main variable in other studies. On the other hand, longitudinal slopes higher than 5% were found to not be suitable for freight road corridors. It is recommended that 6-axle trucks instead of 3-axle trucks be used for a 16 t amount of cargo transported on a plain road (longitudinal slope under 3%). The HDM-4 model did not represent fuel consumption adequately for the current vehicle fleet operating on roads. Fuel consumption models must be updated, for instance, every 10 years, such that they can adapt to vehicle technological advances and the energetic improvement of fuels, including the proportion of biofuels and gas.

Molecular geometry effect on gas transport through nanochannels: Beyond Knudsen theory

Gas transport through nanochannels has gained increasing attention in membrane-based gas separations. Knudsen theory is the cornerstone to quantify the gas flux in the regime of free molecular flow, and gas molecules are usually treated as mass points and distinguished solely by molecular weight. However, recent experiments have shown that gases with similar molecular weight exhibit a remarkable difference in the flow rate, which cannot be interpreted by Knudsen theory. In this study, we ascertain the molecular geometry effect on the transport of various gases through nanochannels. Gas molecules with a complex geometry are more likely to experience multiple reflections on the surface, leading to the diffuse scattering and a reduced flux. During the collision, only the normal translational kinetic energy acts as a positive contribution to the successful reflection, while the vibrational, rotational and tangential translational kinetic energies are all ineffective in this process. The ratio of this ineffective energy to the initial kinetic energy is suggested as the criterion whether the gas can disengage from the wall after each collision. The proposed molecular geometry effect offers a new perspective to extend Knudsen theory for broader applications. Our findings also deepen the understanding of gas separation by nanoporous materials.

Comparative Validation of Spatial Interpolation Methods for Traffic Density for Data-driven Travel-time Prediction

In data-driven travel-time prediction, previous studies have mainly used speed as the input. However, from a traffic engineering perspective, given that speed varies little in the free-flow regime, traffic density, which can accurately represent traffic conditions from the free-flow regime to the congested-flow regime, is preferable as an input. In this study, we compared the accuracy of traffic densities spatially interpolated using spatial statistical and machine learning methods, and validated their effectiveness as inputs for travel-time prediction. The results show that even traffic density interpolated by simple spatial interpolation contributes to the accuracy of travel-time prediction and is superior to speed for early detection of traffic congestion.

Stationary states in two-lane traffic: Insights from kinetic theory.

Kinetics of dilute heterogeneous traffic on a two-lane road is formulated in the framework of Ben-Naim-Krapivsky model and stationary state properties are analytically derived in the asymptotic limit. The heterogeneity is introduced into the model as a quenched disorder in desired speeds of vehicles. The two-lane model assumes that each vehicle or platoon in a lane moves ballistically until it approaches a slow-moving vehicle or platoon and then joins it. Vehicles in a platoon are assumed to escape the platoon at a constant rate by changing lanes after which they continue to move at their desired speeds. Each lane is assumed to have a different escape rate. As the stationary state is approached, the platoon densities in the two lanes become equal, whereas the vehicle densities and fluxes are higher in the lane with lower escape rate. A majority of the vehicles enjoy a free flow if the harmonic mean of the escape rates of the lanes is comparable to average initial flux on the road. The average platoon size is close to unity in the free-flow regime. If the harmonic mean is lower than the average initial flux, then vehicles with desired speeds lower than a characteristic speed v^{*} still enjoy free flow while those vehicles with desired speeds that are greater than v^{*} experience congestion and form platoons behind the slower vehicles. The characteristic speed depends on the mean of escape times [R=(R_{1}+R_{-1})/2] of the two lanes (represented by 1 and -1) as v^{*}∼R^{-1/μ+2}, where μ is the exponent of the quenched disorder distribution for desired speed in the small speed limit. The average platoon size in a lane, when v^{*}≪1, is proportional to R^{μ+1/μ+2} plus a lane-dependent correction. Equationsfor the kinetics of platoon size distribution for two-lane traffic are also studied. It is shown that a stationary state with platoons as large as road length can occur only if the mean escape rate is independent of platoon size.

Average density estimation for urban traffic networks: Application to the Grenoble network

This paper deals with the problem of the average density estimation in large-scale traffic networks, without requiring to know the density of each individual road. This is achieved by the design of a reduced-order open-loop observer. In general, this type of observers requires some specific graph properties, but we show that it is possible to find a virtual representation of the network that satisfies these conditions, by diving each road into a number of cells of specific length. The virtual network is shown to provide close approximations to the average density of the real system for large enough networks. Algorithms to efficiently calculate the observer parameters are proposed. This approach is based on the assumption that traffic dynamics are linear, and is applied at first in free-flow regime. Using microscopic simulations and real data we evaluate the observer performance even when congestion is present in the network.

Calibrating Wiedemann-99 Model Parameters to Trajectory Data of Mixed Vehicular Traffic

We propose a new methodology for calibrating Wiedemann-99 vehicle-following parameters for mixed traffic (different conventional vehicle classes) based on trajectory data. The existing acceleration equations of the Wiedemann model are modified to represent more realistic driving behavior. Exploratory analysis of simulation data revealed that different Wiedemann-99 model parameters could lead to similar macroscopic behavior, highlighting the importance of calibration at the microscopic level. Therefore, the proposed methodology is based on optimizing performance measures at the microscopic level (acceleration, speed, and trajectory profiles) to estimate suitable calibration parameters. Further, the goodness of fit for the observed data is sensitive to the numerical integration method used to compute vehicles’ velocity and position. We found that the calibrated parameters using the proposed methodology perform better than other approaches for calibrating mixed traffic. The results reveal that the calibrated parameter values and, consequently, the thresholds that delineate closing, following, emergency braking, and opening regimes, vary between two-wheelers and cars. The window (in the relative speed versus gap plot) for the unconscious following is larger for cars while the free-flow regime is more extensive for two-wheelers. Moreover, under the same relative speed and gap stimulus, two-wheelers and cars may be in different regimes and display different acceleration responses. Thus, accurate calibration of each vehicle’s parameters is essential for developing micro-simulation models for mixed traffic. The calibration analysis results of strict and overlapping staggered car following signify an impact of staggered car following compared with strict car following which demands separate calibration for strict and staggered following.

Effects of modern marguerite-shaped inlets on hydraulic characteristics of swirling flow in shaft spillways

This study used model experiments to investigates hydraulic characteristics of flow at marguerite-shaped inlets with holes at the bottom of their lobes, known as modern marguerite-shaped inlets. This innovation reduces the swirling flow strength and improves the hydraulic performance of simple shaft spillways. Head–discharge relationships, flow circulation, threshold and critical submergence depths, and discharge coefficients are detailed for different flow regimes. The findings suggest that flow discharges through this type of inlet were approximately six, three, and two times greater than flow discharges through a simple shaft spillway, a circular piano key inlet, and a simple marguerite-shaped inlet, respectively. Increasing the outer length and height of inlets also uniformly distributed the flow around shaft spillways. The best hydraulic performance was observed in the inlets with an outer height of 1.25D and an outer length of 3.75D, where D is the diameter of the shaft spillway. Different equations, with high correlations and low errors, were derived to determine the threshold and critical submergence depths and the discharge coefficients for free and orifice flow regimes.

Traffic flow rate on Kigali roads: a case of national roads (RN1 and RN3)

Traffic flow study plays a key important in various functionalities of cities all over the world. The study of traffic flow is also viewed as an essential facility of the country when it wants to establish traffic operations patterns in the progress of road planning. Blockages are accountable for a sequence of harmful effects such as loss of time, scheduling difficulties, carbon dioxide production, and risks of accidents as well as external expenses. Besides, inadequate transportation facilities and increased traffic volume hamper urban development, especially in developing nations. The objective of the study was to assess the traffic flow state in two selected national roads of Kigali city. The traffic data were collected from 5 am to 8 pm on two National Roads (RN1 and RN3). The relationship between density and flow rate was analyzed using the fundamental diagram of traffic flow. It was found that the peak hours were from 6 am to 8 am and 5 pm to 8 pm. The highest number of vehicles counted were motorcycles due to shortcuts taken to reduce travel time. The results on RN3 revealed a proportion increase of traffic flow and density in the free-flow regime from 0 to maximum flow of 3346.6 veh/h correspondent to a critical density of 114.9 veh/km. However, in the congested zone regime, there was a decrease in traffic flow and an increase in density. It was found that the curve of flow versus density tended to increase on-road RN1. This study proposed the promotion of public transport and e-commerce as strategies to mitigate the congestion. Also, further research may be carried out on all roads of Kigali city, to provide the level of congestion useful for traffic deviation accordingly.

Hydraulics of the subcritical Ventury channels

The purpose of the research is to develop and verify the method of hydraulic calculation of the Venturi channel in the flooded outflow mode. The criterion that separates the flooded and free flow regimes is the ratio of the flow depth in the throat of the Venturi channel hm to the critical depth hc exceeding one (hm/hc > 1). The article theoretically and experimentally substantiates a method for determining the flow rate in a flooded Venturi canal using two control cross-sections, one of which is in the upper basin of the canal, the other in its throat. The differential equation for an uneven flow in a non-prismatic channel was obtained in the form (13). The analysis showed that in a flooded Venturi channel with a subcritical flow at Froude numbers less than one (Fr <1), the denominator of equation (13) is always greater than zero; therefore, at the entrance to the channel in the region of constriction, when db/dl < 0, the depth is downstream decreases (dh/dl < 0), and in the lower diffuser, where db/dl > 0, the flow depth increases (dh/dl > 0). Thus, the curve of the flow surface has a dip in the throat of the flooded Venturi channel. Integration of differential equation (13) made it possible to obtain the function of changing the Froude numbers in the flow along the length of the flooded Venturi channel (16), and then, using relations (17), to determine the depths and flow velocities. The verification showed that the calculated data are in good agreement with the experimental ones. The deviations between calculation and experiment do not exceed ±3%. This makes it possible to recommend the outlined methods for application in engineering practice.

Investigation on Hydraulic Characteristics of Turbine-Type Manhole Cover

Manhole cover is an important device of urban drainage infrastructures. The hydraulic characteristics of turbine-type manhole covers were studied through numerical simulations and physical experiments. The flow field characteristics and water surface were investigated. The drainage process is divided into two parts: free flow regime and submerged flow regime. Numerical and experimental results are in good agreement. It is indicated that the depth of water is constant in the later stage of unstable free drainage, while it changes with time and determines the discharge under the subsequent unstable submerged drainage condition. The influence of the depth on discharge is mainly reflected in the submerged drainage stage, in which period the discharge is linearly related to the square root of the depth. While in free flow regime, the discharge is affected by volume fraction of water with second order. The correlation between the depth and the discharge in the process of submerged flow is proposed based on dimensional harmony principle. With the characteristic of massive discharge, the design of turbine-type manhole cover provides one more choice in urban drainage construction.

Joint Route Guidance and Demand Management for Real-Time Control of Multi-Regional Traffic Networks

In this work, we propose a joint route guidance and demand management strategy for multi-region networks with macroscopic traffic dynamics. Route guidance is used to identify the optimal transfer flows between neighbouring regions so that the trip completion rate across all regions is maximized. Demand management is utilized to control the traffic flows entering the network by forcing a portion of the traffic flows to wait at their origin. Towards this direction, we develop a Model Predictive Control (MPC) framework that aims to minimize the total time spent by all vehicles in the network (including the waiting time at the origin) by jointly optimizing the demand flows allowed in the network and the transfer flows between regions. To solve the resulting nonconvex and nonlinear optimization problem, by relaxing the nonconvex constraints, we develop a novel Linear Programming formulation that provides tight lower bounds on the optimal solution, as well as a feasible solution through the proposed MPC framework. Furthermore, (in another formulation) we restrict each region to only operate in the free-flow regime of the macroscopic fundamental diagram, which enables the transformation of the problem to a linear MPC formulation which can be solved in real-time using standard solvers and which provides a feasible solution to the original MPC problem. Extensive simulation results demonstrate that the linear MPC schemes execute in real-time and yield near-optimal results even under heavy traffic scenarios.

A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function

The well-known Lighthill-Whitham-Richards (LWR) kinematic model of traffic flow models the evolution of the local density of cars by a nonlinear scalar conservation law. The transition between free and congested flow regimes can be described by a flux or velocity function that has a discontinuity at a determined density. A numerical scheme to handle the resulting LWR model with discontinuous velocity was proposed in [J.D. Towers, A splitting algorithm for LWR traffic models with flux discontinuities in the unknown, J. Comput. Phys., 421 (2020), article 109722]. A similar scheme is constructed by decomposing the discontinuous velocity function into a Lipschitz continuous function plus a Heaviside function and designing a corresponding splitting scheme. The part of the scheme related to the discontinuous flux is handled by a semi-implicit step that does, however, not involve the solution of systems of linear or nonlinear equations. It is proved that the whole scheme converges to a weak solution in the scalar case. The scheme can in a straightforward manner be extended to the multiclass LWR (MCLWR) model, which is defined by a hyperbolic system of \begin{document}$ N $\end{document} conservation laws for \begin{document}$ N $\end{document} driver classes that are distinguished by their preferential velocities. It is shown that the multiclass scheme satisfies an invariant region principle, that is, all densities are nonnegative and their sum does not exceed a maximum value. In the scalar and multiclass cases no flux regularization or Riemann solver is involved, and the CFL condition is not more restrictive than for an explicit scheme for the continuous part of the flux. Numerical tests for the scalar and multiclass cases are presented.

A multi-class urban traffic model considering heterogeneous vehicle composition: An extension of the S model

In this paper a new multi-class urban traffic model is proposed based on the features of a single-class urban traffic model and the characteristics of a multi-class freeway traffic model. The heterogeneous traffic flow is represented using the concept of Passenger Car Equivalent (PCE) for congestion and free-flow regimes separately. The proposed multi-class urban traffic model is intended for model-based control applications. The single-class model and the proposed multi-class traffic model are compared with microscopic simulation data obtained using the SUMO (Simulation of Urban MObility) open-source simulator. The two models are calibrated through optimal parameter estimation and their performance is evaluated and compared by taking into account the error index between the models and the simulation data. Simulation results show that the multi-class model gives a significantly better fit.

An Analytical Model and Performance Evaluation of Multihomed Multilane VANETs

Motivated by the potentially high downlink traffic demands of commuters in future autonomous vehicles, we study a network architecture where vehicles use Vehicle-to-Vehicle (V2V) links to form relay network clusters, which in turn use Vehicle-to-Infrastructure (V2I) links to connect to one or more Road Side Units (RSUs). Such cluster-based multihoming offers improved performance, e.g., in coverage and per user shared rate, but depends on the penetration of V2V+V2I capable vehicles and possible blockage, by legacy vehicles, of line of sight based V2V links, such as those based on millimeter-wave and visible light technologies. This paper provides a performance analysis of a typical vehicle's connectivity and throughput on a highway in the free-flow regime, exploring its dependence on vehicle density, sensitivity to blockages, number of lanes and heterogeneity across lanes. The results, backed up by simulations of realistic vehicular traffic, show that even with moderate vehicle densities and penetration of V2V+V2I capable vehicles, such architectures can achieve substantial improvements in connectivity and reduction in per-user rate variability as compared to V2I based networks. The typical vehicle's performance is also shown to improve considerably in the multilane highway setting as compared to a single lane road. This paper also sheds light on how the network performance is affected when vehicles can control their relative positions, by characterizing the connectivity-throughput tradeoff faced by the clusters of vehicles.

Persistent oscillations in a traffic model with decision-making

This work explores the nonlinear behaviour in a congestion charge model, which emphasizes the correlation between drivers’ response and optimal traffic flow. The model assumes that all drivers follow the same common rules of rational thinking to avoid the congestion. There are two regimes in the model system. In free flow regime, the system has only one branch. In congested regime, the system bifurcates into two branches. Counter-intuitive behaviour of the model is caused by the oscillatory instability between two branches. Persistent oscillations reflect the intrinsic properties of decision-making process. Rational thinking provides limited adaptation capabilities to reach the optimal traffic flow. More past experiences and current options provide only marginal increase in capabilities to adapt to traffic situations. The idealized situations are also discussed.

A re-examination of the role of friction in the original Social Force Model

The fundamental diagram of pedestrian dynamics gives the relation between the density and the flow within a specific enclosure. It is characterized by two distinctive behaviors: the free-flow regime (for low densities) and the congested regime (for high densities). In the former, the flow is an increasing function of the density, while in the latter, the flow remains on hold or decreases. In this work, we perform numerical simulations of the pilgrimage at the entrance of the Jamaraat bridge (pedestrians walking along a straight corridor) and compare flow-density measurements with empirical measurements made by Helbing et al. (2007). We show that under high density conditions, the basic Social Force Model (SFM) does not completely handle the fundamental diagram reported in empirical measurements. We use analytical techniques and numerical simulations to prove that with an appropriate modification of the friction coefficient (but sustaining the SFM) it is possible to attain behaviors which are in qualitative agreement with the empirical data. Other authors have already proposed a modification of the relaxation time in order to address this problem. In this work, we unveil the fact that our approach is analogous to theirs since both affect the same term of the reduced-in-units equation of motion. We show how the friction modification affects the pedestrian clustering structures throughout the transition from the free-flow regime to the congested regime. We also show that the speed profile, normalized by width and maximum velocity yields a universal behavior regardless of the corridor dimensions.