The Riemann problem for a dispersive blood flow model in arteries

This paper compares the two most frequently used approaches for the prediction of faecal coliforms in the effluent (FCe) of waste stabilization ponds (WSPs): the continuous stirred reactor (CSTR) model and the dispersed flow (DF) model. On the basis of theoretical and practical analysis, it is concluded that, under most conditions usually found in practice, the DF model can be expected to predict unrealistically low FCe. This trend is more pronounced the more the flow conditions in the pond(s) approach plug flow, and the higher the average retention time per pond. Model differences in FCe prediction typically deviate from one another by up to 1–2 log units. This can lead to the design of substantially different pond sizes, with footprint differences between the two models of 30–50% not being exceptional. Consequently, on the basis of usually applied model parameters, for the time being it appears safer to use the CSTR model for FCe prediction in WSP systems.

Of major interest, especially in city environments, and increasingly inside vehicles or industrial plants, is the drive to reduce human exposure to nitrogen oxides (NOx). This trend has drawn increasing attention to filtration, which has developed remarkably owing to the capabilities of recently developed mathematical models and novel filter concepts. This paper reports on the study of the kinetic modelling of adsorption of nitrogen dioxide (NO2), collected from the tailpipe of a diesel engine, reacting to calcium nitrate salt (Ca(NO3)2) on a surface flow filter consisting of a coating of fine ground limestone or marble (CaCO3) in combination with micro-nanofibrillated cellulose (MNFC) acting as binder and humectant applied onto a multiply recycled newsprint substrate. The coating and substrate are both porous, but on different pore size scales, with the coating having significantly lower permeability. To maximise gas-coating contact, therefore, the coating deposition is pixelated, achieved by pin coating. An axially dispersed gaseous plug flow model (dispersion model) was used to simulate the transport within the coating pore network structure, following earlier flow modelling studies, and a kinetic reaction model was used to examine NO2 to NO3- conversion in correlation with experimental results. Modelling results indicate a 60.38% conversion of exposed NO2 gas to Ca(NO3)2 under the specific conditions applied, with an absolute relative error between the predicted and experimentally estimated value being 0.81%. The model additionally enabled a prediction of effects of changing parameters over a limited perturbation range, thus assisting in predicting filter element consumption, with attention given to the active component CaCO3 surface as a function of particle size in relation to the gas contact exchange, promoting the reaction over time. It is intended that the Ca(NO3)2 formed from the reaction can go on to be used as a value-added fertiliser, thus contributing to circular economy.

Application of the mass transfer model for describing nonequilibrium transport of HOCs through natural geosorbents

Performance evaluation and mathematical modelling of coliform die-off in tropical and subtropical waste stabilization ponds

In order to perform a reasonable numerical prediction of two -phase flow based on a multi-fluid model, it is necessary for us to understand whether the model constitutes a well-posed or ill-posed initial-value problem. Otherwise, we cannot take appropriate measures for numerical instability caused by ill-posedness. Hence, mathematical characteristics of several multiphase models such as a one-dimensional three-fluid model, a two-dimensional two-fluid model and a dispersed flow model were examined in the present study. For this purpose, the existing mathematical method for evaluating the well-posedness was reviewed in detail. It was pointed out by this review that the existing method is applicable to a model of incompressible multiphase flow as well as compressible multiphase flow even though the coefficient matrix of the incompressible model is singular. Then, the well-posedness of several multi-fluid models and dispersed flow models was clarified.

Hydrodynamique d'un filtre biologique en systeme insature avec nitrification d'un effluent septique

The mechanism of the formation for cocurrent downflow pulse flow was studied experimentally in a packed bed of inert spheres of 3, 6, and 8 mm using an air−water flow. By measurement of the flow distance until pulses are observed, the spatial growth rate of convective disturbances within the pulsing flow regime were determined. Observations indicate that pulses form from trickling flow as the result of a global convective instability. Further, experiments indicate that an analogous transition exists for the formation of pulses from the dispersed bubble flow regime, except that pulses form as the flow rates are adjusted to become less severe. Existing global instability models based on averaged (dispersed flow) momentum equations were modified to explain experimental results. A key uncertainty in modeling pulse formation from trickle flow is the regularization (i.e., stabilization) force. Re-examination of this issue suggests some mechanistic inconsistencies with surface tension which had been used in previous studies. Consistent with the present experiments, it is proposed that gravity may be the primary restoring force. Incorporating gravity stabilization into the dispersed flow equations provides predictions that are at least as good as the previous models. A similar dispersed flow model is used to explain the bubbly flow to pulse transition. While predictions agree with experimental data for part of the range, model accuracy is limited by the accuracy of constitutive expressions for interaction forces between phases.

The primary focus of this work is the coupling of dispersive free-surface flow models through the utilization of a thick interface coupling technique. The initial step involves introducing a comprehensive framework applicable to various dispersive models, demonstrating that classical weakly dispersive models are encompassed within this framework. Next, a thick interface coupling technique, well-established in hyperbolic framework, is applied. This technique enables the formulation of unified models across different subdomains, each corresponding to a specific dispersive model. The unified model preserves the conservation of mechanical energy, provided it holds for each initial dispersive model. We propose a numerical scheme that preserve the projection structure at the discrete level and as a consequence is entropy-satisfying when the continuous model conserve the mechanical energy. We perform a deep numerical analysis of the waves reflected by the interface. Finally, we illustrate the usefulness of the method with two applications known to pose problems for dispersive models, namely the imposition of a time signal as a boundary condition or the imposition of a transparent boundary condition, and wave propagation over a discontinuous bathymetry.

High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves

Numerical and experimental investigation on the performance of rapid ultrasonic-assisted nucleic acid extraction based on dispersive two-phase flow

An inverse dispersed multiphase flow model for liquid production rate determination

Wide use of natural circulation loops operating at low redused pressures generates the real need to develop reliable methods for predicting flow regimes and friction pressure drop for two-phase flows in this region of parameters. Although water–air flows at close-to-atmospheric pressures are the most widely studied subject in the field of two-phase hydrodynamics, the problem of reliably calculating friction pressure drop can hardly be regarded to have been fully solved. The specific volumes of liquid differ very much from those of steam (gas) under such conditions, due to which even a small change in flow quality may cause the flow pattern to alter very significantly. Frequently made attempts to use some or another universal approach to calculating friction pressure drop in a wide range of steam quality values do not seem to be justified and yield predicted values that are poorly consistent with experimentally measured data. The article analyzes the existing methods used to calculate friction pressure drop for two-phase flows at low pressures by comparing their results with the experimentally obtained data. The advisability of elaborating calculation procedures for determining the friction pressure drop and void fraction for two-phase flows taking their pattern (flow regime) into account is demonstrated. It is shown that, for flows characterized by low reduced pressures, satisfactory results are obtained from using a homogeneous model for quasi-homogeneous flows, whereas satisfactory results are obtained from using an annular flow model for flows characterized by high values of void fraction. Recommendations for making a shift from one model to another in carrying out engineering calculations are formulated and tested. By using the modified annular flow model, it is possible to obtain reliable predictions for not only the pressure gradient but also for the liquid film thickness; the consideration of droplet entrainment and deposition phenomena allows reasonable corrections to be introduced into calculations. To the best of the authors' knowledge, it is for the first time that the entrainment of droplets from the film surface is taken into consideration in the dispersed–annular flow model.

Numerical prediction of slug flow boiling heat transfer in the core-catcher cooling channel for severe accident mitigation in nuclear power plant

We construct numerical solutions for a dispersed isothermal two-phase flow model. The system is a weakly hyperbolic, isothermal system describing the evolution of mass, momentum as well as volume fraction for the dispersed particles as well as the carrier fluid. The dispersed phase is modeled pressureless. We construct a new HLL-type Riemann solver and perform numerical simulations on the homogeneous part of the model. In each time step, an approximate MUSCL–Hancock finite volume scheme is used in which intercell Riemann problems are solved using the new GHLL solver.

Narrow channel heat transfer technique is a new developing heat transfer technique in recent years. As the temperature of droplet, steam and wall are decided by forced convection heat transfer between the steam and the wall, between the droplet and the wall, between the steam and the droplet and radiation heat transfer, which makes heat transfer mechanism of dispersed flow be difficultly interpretative. Dispersed flow in narrow annular channel is analyzed in the paper, investigating the influence of all kinds of heat transfer processes on dispersed flow, building annular channel dispersed flow model using thermodynamic non-equilibrium model. Calculation results show heat transfer is mainly controlled by heat transfer process between steam and wall. When temperature is low, radiation can be ignored on heat transfer coefficient calculation. The calculation of model can provide a reference for engineering application of steam generator, refrigeration system and so on.