Equilibrium Flow Model Research Articles

CFD-based shape optimization of flashing converging-diverging nozzles in pelton turbines for domestic carbon dioxide heat pumps including off-design conditions

A path to enhance the coefficient of performance (COP) of domestic heat pumps is to replace the throttling valve with a turboexpander. Designing this component requires addressing supersonic flashing flows localized within the nozzle. In particular, two-phase flows prevent the application of the method of characteristics to design efficient converging–diverging shapes. To overcome this issue, we propose a shape optimization combined with a homogeneous equilibrium flow model as a design tool. Kriging models are used as surrogates of the objective function and constraint to reduce the overall computational burden associated with shape optimization. The infilling criterion to improve surrogate accuracy involves the maximization of the constrained expected improvement. A multi-point optimization is formulated, including design and off-design conditions in both objective and constraint, for a total of four relevant operating conditions. The off-design conditions are derived from system analysis, accounting for variations in the evaporator temperature and outlet gas-cooler temperature. The optimized nozzle results in a COP improvement of 7.6%, compared to a 6.6% increase when replacing the throttling valve with a baseline geometry designed as recommended by the literature. The adoption of a multi-point optimization strategy ensures that this enhancement in design conditions is not offset by off-design performance decay, which is 0.3 percentage points over the three off-design conditions. Overall, replacing the throttling valve with the optimized expander leads to an average COP improvement of 8.6%.

In a state of flux: new insight into the transport processes that maintain bacterial metal homeostasis.

A new study by Nies et al. (J Bacteriol 206:e00080-24, 2024, https://doi.org/10.1128/jb.00080-24) provides a rich, quantitative data set of zinc accumulation by cells of Cupriavidus metallidurans, including of mutant bacterial strains lacking import or efflux genes, and comparison of zinc accumulation by cells previously starved of metal with those of zinc-replete cells. The data surprisingly demonstrate the concomitant activity of both active metal import and metal efflux systems. They present a flow equilibrium model to describe zinc homeostasis in bacteria.

Boundary Guidance Strategy and Method for Urban Traffic Congestion Region Management in Internet of Vehicles Environment

Accelerated urbanization has increased regional traffic congestion. To alleviate traffic congestion in a homogeneous road network, combined with the advantage of real-time traffic information obtained by the Internet of Vehicles (IoVs), a boundary guidance strategy for traffic congestion region is proposed. The strategy considers the optimal operation state of traffic congestion region and is divided into two categories according to different destinations of traffic demands. Meanwhile, a method for the boundary guidance strategy is presented in which the macroscopic fundamental diagram (MFD) is used to determine the optimal accumulation, a traffic flow equilibrium model is established to calculate the real-time accumulation, and a fuzzy adaptive PID control algorithm is designed to calculate the optimal traffic inflow of the traffic congestion region. Furthermore, an example is selected for simulation. The results show that the boundary guidance strategy can effectively improve the operational state of the road network and alleviate traffic congestion. Finally, the influence of connected vehicle penetration rate on the strategy is discussed. The simulation results show that the strategy can improve the operation state of the road network under mixed traffic flow, and the higher the penetration rate, the more significant its effect on alleviating traffic congestion.

Optimal polymer slugs injection profiles

The graded viscosity banks technology (tapering) for polymer flooding is studied for several different models of mixing zones behavior. Depending on the viscosity function the limiting polymer injection profile is rigorously derived for the transverse flow equilibrium model, for the Koval model and for the Todd–Longstaff model. The potential gain in the polymer quantity compared to the profile with a finite number of slugs is numerically estimated.

A new network equilibrium flow model: User-equilibrium with quantity adjustment

Travelers’ route choice behaviors affect the distribution of network flow. The paper presents an unconventional equilibrium flow model that extends the well-known non-Walrasian equilibrium theory of economics to the analysis of route choice behavior. With the introduction of path residual capacity as the quantity signal, a quantity adjustment user equilibrium flow model depicts the route choice dynamics based on the maximum path residual capacity, and thus differs from the traditional traffic equilibrium pattern regulated by path travel time. An equivalent nonlinear complementary problem to the proposed model is developed, and further reformulated as an unconstrained mathematical program using a gap function, which permits many efficient solution algorithms. The maximum residual capacity path algorithm and the maximum residual capacity traffic assignment algorithm are developed, and the gradient descent algorithm is used to solve the unconstrained mathematical program. Numerical results show that the proposed model and solution algorithm are feasible and effective. The paper proposes that both price adjustment and quantity adjustment are special cases of the price-quantity adjustment principle, and the equilibrium flow model based on which can capture route choice behaviors that has not been modeled in previous studies.

Numerical Simulation of Cavitation and Damping Force Characteristics for a High-Speed Supercavitation Vehicle

In this study, an attempt has been made to investigate the supercavitation and hydrodynamic characteristics of high-speed vehicles. A homogeneous equilibrium flow model and a Schnerr–Sauer model based on the Reynolds-averaged Navier–Stokes method are used. Grid-independent inspection and comparison with experimental data in the literature have been carried out to verify the accuracy of numerical methods. The effect of the navigation speed and angle of attack on the cavitation morphology and dynamic characteristics has been investigated. It has been demonstrated that the angle of attack has a remarkable influence on the wet surface and hydrodynamic force, whereas navigation speed has little effect on the position force of the vehicle under the circumstance of no wet surface. The hydrodynamic force changes periodically with the swing of the vehicle, but its maximum is greater than that for the direct navigation state at the same attack angle. Moreover, the damping effect obviously affects the hydrodynamic force amplitude and movement trend.

Screening of resonant magnetic perturbation fields assuming various plasma flow models

A recently updated version of the MARS-F code [Y. Q. Liu et al., Phys. Plasmas 7, 3681 (2000); L. Li et al., Phys. Plasmas 25, 082512 (2018); and G. L. Xia et al., Nucl. Fusion 59, 126035 (2019)] is utilized to numerically investigate the plasma screening effect on the applied resonant magnetic perturbation (RMP) field, assuming various equilibrium flow models, including the toroidal flow, the parallel flow and their combinations, and poloidal and toroidal projections of the parallel flow. A parallel equilibrium flow with a uniform radial profile is found to have no effect on plasma screening of the RMP field. A sheared parallel flow, however, does change plasma screening. The poloidal projection of the parallel flow weakens plasma screening in the resistive-inertial regime. The effect on the favorable average curvature regime is found, however, to be non-monotonic. With the increasing flow speed, the poloidal projection first weakens Glasser-Green-Johnson (GGJ)-screening. Further increase in the flow speed results in enhanced GGJ-screening again. This non-monotonic behavior is related to the perturbed parallel shielding current, which appears also off the mode rational surface at fast flow due to additional resonances between the RMP perturbation and the sound wave continuum. These results indicate that flow induced plasma screening to the RMP field can have complicated characteristics, which, in turn, can have implications on the RMP field penetration into the plasma in experiments for controlling the edge localized modes.

Spectroscopic investigations on impurities and their effect on the electron number density in the shock tube

An accurate estimation of electron number density is significant in many plasma physics studies. In this paper, the effect of impurities in test gas on the electron number density of the plasma generated in the hypersonic flow of a free-piston driven hypersonic shock tube has been studied using optical emission spectroscopy. Emission spectra of argon plasma showed the presence of following impurities: sodium, potassium, nitrogen, oxygen and hydrogen. The electron number density calculated from the spectral broadening of argon emission lines, is one order of magnitude higher than the electron number density calculated from the thermochemical equilibrium flow model that does not include the impurities. Hence the results show that the presence of impurities has a significant impact on the shock tube plasma and warrants the need to include these effects in the thermochemical equilibrium flow model while investigating magneto-aerodynamic interaction flows and communication blackout studies in the hypersonic ground-based test facilities.

Solution of reactive flow in a rocket engine nozzle with Paraffin/Kerosene propellants

AbstractThis paper presents a simulation‐based solution for calculating rocket engine performance with liquid‐type propellants of Paraffin and Kerosene for oxidizer to fuel ratio that is given by a linear formula. The engine was divided into two main stages: combustion chamber and a nozzle. In the first phase, conditions were found in the combustion chamber, based on the assumption of equilibrium according to Barrere. Next, the flow in the nozzle was calculated based on the fluid in the combustion chamber. Three main theories were examined in order to find the flow conditions in the nozzle: equilibrium, frozen and mixed flows (Bray conditions). While the latter assumes the existence of the “Sudden Freezing Point” found by Bray, so that from this point to the end of the nozzle, the flow is assumed to be frozen. The use of the proposed simulation might contribute for multiple calculations performance (e.g., fuels with multiple intermediate reactions). Comparison between both types of fuels/propellants for the three described types of flow is presented alongside CEA software results, whereas good agreement between solutions was found. Also, the greater the ratio between hydrogen and carbon atoms, the better the engine performance for a particular oxidizer. Finally, it was found that an equilibrium flow model throughout the nozzle has a better nozzle performance compared to the other types of flows.

Coordinated Perimeter Control for Multiregion Heterogeneous Networks Based on Optimized Transfer Flows

Exploring efficient control strategies for heterogeneously congested urban networks remains a big research challenge. The theory of macroscopic fundamental diagram (MFD) provides a new perspective for network-wide congestion control decisions. This paper proposes a coordinated perimeter control strategy for multiregion heterogeneous networks based on optimized transfer flows. First, a two-layer network partitioning method is presented to capture spatial heterogeneity dynamics of urban networks. For this partition, traffic flow equilibrium model based on MFD and multiagent based hierarchical traffic management scheme are built. Then, an improved multinomial logit model is developed for deriving optimized transfer flows among multiple congested regions. A coordinated perimeter control strategy using model predictive control is further proposed, which is aimed at tracking desired accumulations of each congested region. As a case study, the proposed control strategy is applied to the downtown network of Jinan, China, using simulation analysis. The results demonstrate that it can achieve balanced network flow distribution and increased mobility.

Density Wave Instability Verification of CFD Two-Fluid Model

Thermally induced density wave instability (DWI) (Type-II) is an important phenomenon for two-phase flow industrial systems. Developing numerical tools and methods for the prediction of the DWI boundary is of importance in the design and safety of nuclear reactors. With the advent of computational fluid dynamics (CFD) in nuclear safety analysis, it is important to first verify the CFD results against existing theory and validate them with experimental data. In this work, a CFD two-fluid model (TFM) for DWI was implemented and verified against the theory of Ishii (1971). Closure relations were selected to approach the homogeneous equilibrium flow model. A steady-state verification of the model was carried out first. Then, dynamic verification was performed. Predictions of the stability boundary and the frequency of oscillations are in a good agreement with the theory. This study further verifies the dynamic capability of TFM CFD.

Optimal Evacuation Strategy for Parking Lots Considering the Dynamic Background Traffic Flows.

An optimal evacuation strategy for parking lots can shorten evacuation times and reduce casualties and economic loss. However, the impact of dynamic background traffic flows in a road network on the evacuation plan is rarely taken into account in existing approaches. This research develops an optimal evacuation model with total evacuation time minimization by dividing the evacuation process in a parking lot into two periods. In the first period, a queuing theory is used to estimate the queuing time, and in the second period, a traffic flow equilibrium model and an intersection delay model are employed to simulate vehicles’ route choice. To deal with these models, a modified ant colony algorithm is developed. The results of a numerical example prove that the proposed method has an advantage in improving evacuation efficiency. The results also show that background traffic flows affect not only vehicles’ average queuing time in parking lots but also optimal evacuation route choice. Additionally, a sensitivity analysis indicates that the minimum threshold of headway time that allows vehicles out of a parking lot to merge into the background traffic flows on the roads connecting the exits has a great impact on average queuing time, average travel time, and total evacuation time.

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.

Numerical study of the effect of heat transfer on solid phase formation during decompression of CO2 in pipelines

CO2 solid phase formation accompanying rapid decompression of high-pressure CO2 pipelines may lead to blockage of the flow and safety valves, presenting significant hazard for safe operation of the high-pressure CO2 storage and transportation facilities. In this study, a homogeneous equilibrium flow model, accounting for conjugate heat transfer between the flow and the pipe wall, is applied to study the CO2 solid formation in a 50 mm internal diameter and 37 m long pipe for various initial thermodynamic states of CO2 fluid and wide range of discharge orifice diameters. The results show that the rate of CO2 solid formation in the pipe is limited by heat transfer at the pipe wall. The predicted amounts of solid CO2 are discussed in the context of venting of CO2 pipelines.

Vertical Equilibrium Flow Models with Fully Coupled Geomechanics for CO2 Storage Modeling, Using Precomputed Mechanical Response Functions

Vertical equilibrium (VE) models have proved to be attractive for simulation of CO2 storage scenarios. Their primary advantage is a substantial reduction in computational requirements compared to standard 3D simulation tools. In this work, we aim to include the effects of geomechanics on aquifer flow while preserving computational efficiency. When fluids are injected into a geological formation, changes in pore pressure leads to rock deformation, which influence the flow properties of the formation. To fully model this effect, a two way coupling between flow and mechanics equations is generally necessary, including the full under- and overburden. This leads to a computationally expensive system, thus reducing the computational advantage of using VE models. Within a linear poroelastic framework, the full effect of deformation on flow is captured through changes in volumetric strain, which can be precomputed for a given pressure basis at grid generation time and used directly in the flow equations during simulation. This allow us to model the full effect of geomechanics on aquifer flow while eliminating the need for solving the mechanics equations at simulation time. We demonstrate the approach on 2D and 3D examples, and compare with results obtained from a standard VE flow models and a model that includes the full poroelastic set of equations. Compared to the latter, we observe a significant computational benefit using our proposed approach. On the other hand, the impact of geomechanics appears to be primarily captured by a well-chosen rock compressibility coefficient, suggesting that a fully coupled model might not be required in many practical cases.

An iterative learning approach for anticipatory traffic signal control on urban networks

ABSTRACTTraffic signal control on urban road networks offers high opportunity to improve traffic operations. Among others, anticipatory control determines signal timings to optimize network performance, taking into account explicitly the route choice responses and resulting (equilibrium) network flow patterns. However, the optimal control decisions are usually calculated using equilibrium flow models that are in general only a coarse representation of reality. As a result, model–reality mismatch often leads to suboptimal conditions characterized by unexpected congestion effects. This paper presents a novel method to support control decisions for practical applications in real traffic systems that operate repeatedly, for instance from week to week, month to month, and in the presence of flow measurements. The proposed method generates a sequence of control settings to track the real flow response, by observing errors between modeled flows and the measurements. Improvement in the control performance is achieved by learning from this error information. A theoretical analysis on convergence of the control sequence is provided and the impact of different weighting parameters on the convergence performance is discussed. Numerical examples on a test network confirm the effectiveness of the proposed iterative learning approach in tackling modeling error, as well as a main role of model bias correction in tracking reality. The impact of weighting parameters on its convergence is also illustrated.

Fracture propagation control in CO2 pipelines: Validation of a coupled fluid–structure model

Existing engineering methods to ensure fracture propagation control in natural-gas transmission pipelines have been shown to be non-applicable when dense-phase CO2 is transported. To overcome this, a coupled fluid–structure interaction model has been developed. It consists of a homogeneous equilibrium flow model, coupled with the Span–Wagner equation of state and including solid-phase formation, and a finite-element model of the pipe taking into account large deformations and fracture propagation through a local fracture criterion.Model predictions are compared with data from two medium-scale crack-arrest experiments with dense-phase CO2. Good agreement is observed in fracture length, fracture-propagation velocity and pressure. Simulations show that, compared to natural-gas pipelines, the pressure level at the opening fracture flaps is sustained at a much higher level and at a much longer distance behind the moving fracture tip. This may be one important reason why the existing engineering methods do not work for dense-phase CO2.

Sensitivity Analysis the Ticket Price of Hangzhou to Shaoxing Intercity Line Based on the Equilibrium Model

Intercity rail transit's ticket prices as the key sensitive factors affect passenger flow, which is related to the accuracy of the prediction.This paper provides a model based on equilibrium price sensitivity analysis method. In order to make clear the relationship between the intercity rail transit ticket price and passenger flow, analysing the average operation time, cost and other influence factors, establishing the utility function to calculate the utility value, according to the equilibrium flow model of passenger flow, we can get the passenger flow of all kinds of transportation under the equilibrium traffic, on this basis, the sensitivity analysis model is used to get the connection between the traffic and the travel ticket in different modes of transport, In the end ,taking Hang-Shao intercity rail transit for example to analysis the sensitivity of the price. The research results show that the model and the algorithm has the higher reliability.

Modeling cavitation flow of cryogenic fluids with thermodynamic phase-change theory

Cavitation is the formation of vapor bubbles within a liquid where the flow dynamics causes the local static pressure to drop below the vapor pressure. The so-called full cavitation model (FCM) developed by Singhal has been widely used in numerical modeling of the cavitation flow for thermosensible and non-thermosensible fluids. Within the FCM, the bubble size is taken to be equivalent to the maximum possible value to forego the calculation of bubble number density. We developed a new cavitation model by re-calculating the bubble radius in FCM to account for the effects of local pressure. The new model was obtained by combining the thermodynamic phase-change theory and the Young-Laplace equation with the assumption of thermodynamic equilibrium during the cavitation process. The cavitation calculations were performed based on the mathematical framework of the homogeneous equilibrium flow model and the transport-equation-based model for vapor phase mass fraction. The model was validated by modeling the cavitating flow of liquid nitrogen and liquid hydrogen through NASA hydrofoil and Ogive with consideration of the phase-change thermal effects. The temperature and pressure distributions with the new model are found to agree well with data from existing experimental studies, as well as the simulations with the FCM.

Spatial and temporal dynamics of water flow and solute transport in a heterogeneous glacial till: The application of high-resolution profiles of δ18O and δ2H in pore waters

Summary The heterogeneity and dynamic of water flow and solute transport processes were investigated in the upper 6 m of a surficial, glacial till in southern Saskatchewan, Canada. Continuous core samples from three vertical sites located over a maximum spatial distance of 65 m were collected and analyzed for particle size distribution, porosity, and water content. High-resolution (0.2 m) profiles of δ18O and δ2H in pore waters were also measured for the three sites on a seasonal basis. Depth profiles of all measured parameters indicate highly heterogeneous structures in the upper 6 m. In two coreholes, depleted water isotopes measured at different depths below ground (0.7 and 3 m) were in the range of winter precipitation values, suggesting preferential flow of meltwater in spring accompanied by a rising water table. A one-dimensional equilibrium flow and transport model failed to simulate the isotope-depth distributions with depleted winter values, and could not reproduce the measured values even when accounting for vertical, preferential flow. A conceptual model was created, based on the consistency of all measured data and assuming preferential lateral flow as the controlling flow and transport mechanism after snowmelt. In the model, water from surface runoff (after snowmelt) drains into an ephemeral depression that crosses the study site. As this water infiltrates, it forms a water table mound that slowly propagates away from the depression. As the water table propagates outwards, dynamic vertical flow processes result in net upward and downward fluxes.