One-dimensional Flow Model Research Articles

RELAP5 application for water hammer analysis in different thermal-hydraulic systems

• Causes of water hammers: rapid valve operation, void-induced, condensation-induced. • RELAP5 code may represent water hammer due to valve operation and appearance of void. • The developed modelling recommendations are based on comparative analysis. • Water hammer in nuclear, fusion and district heating systems possible due to fast valve actions. • Integrity of pipelines in nuclear, fusion and district heating systems remain not violated. The water hammer phenomenon investigations employing RELAP5 code with one-dimensional two-fluid six-equation models of water and steam flow were performed and the main results shared in this paper. The capability of RELAP5 code to simulate transients leading strong pressure pulses was investigated employing the measurement results of three test facilities for different water hammer types: PPP at UMSICHT, CWHTF at FZR Dresden and PMK-2 at AEKI. Based on the benchmarking results the recommendations for the modelling of piping systems, which could be affected by different types of water hammer were developed and tested. The recommendations cover selection of thermal-hydraulic system conditions, parameters of modelling and RELAP5 code correlations. These recommendations have enabled to develop a detail RELAP5 models for the simulation of water hammer effects in further research works. The applications of RELAP5 code for water hammer analysis in different thermal-hydraulic systems (RBMK-1500 reactor main circulation loop, targets cooling/heating circuit in Wendelstein 7-X experimental stellarator facility and pipelines in district heating system) are presented in this paper. The performed analyses of transients demonstrated that the pressure pulsations could appear in all these systems as results of check valve closures. However, pressure surges are not so strong due to specific of such systems and integrity of pipelines remains not violated.

External Surface Water Influence on Explosive Eruption Dynamics, With Implications for Stratospheric Sulfur Delivery and Volcano-Climate Feedback

Explosive volcanic eruptions can inject sulfur dioxide (SO2) into the stratosphere to form aerosol particles that modify Earth’s radiation balance and drive surface cooling. Eruptions involving interactions with shallow layers (≤500 m) of surface water and ice modify the eruption dynamics that govern the delivery of SO2 to the stratosphere. External surface water controls the evolution of explosive eruptions in two ways that are poorly understood: 1) by modulating the hydrostatic pressure within the conduit and at the vent, and 2) through the ingestion and mixing of external water, which governs fine ash production and eruption column buoyancy flux. To make progress, we couple one-dimensional models of conduit flow and atmospheric column rise through a novel “magma-water interaction” model that simulates the occurrence, extent and consequences of water entrainment depending on the depth of a surface water layer. We explore the effects of hydrostatic pressure on magma ascent in the conduit and gas decompression at the vent, and the conditions for which water entrainment drives fine ash production by quench fragmentation, eruption column collapse, or outright failure of the jet to breach the water surface. We show that the efficiency of water entrainment into the jet is the predominant control on jet behavior. For an increase in water depth of 50–100 m, the critical magma mass eruption rate required for eruption columns to reach the tropopause increases by an order of magnitude. Finally, we estimate that enhanced emission of fine ash leads to up to a 2-fold increase in the mass flux of particles < 125 μm to spreading umbrella clouds, together with up to a 10-fold increase in water mass flux, conditions that can enhance the removal of SO2 via chemical scavenging and ash sedimentation. On average, compared to purely magmatic eruptions, we suggest that hydrovolcanic eruptions will be characterized by reduced climate forcing. Our results suggest one possible mechanism for volcano-climate feedback: temporal changes with climate in surface distributions of water and ice may modify the relative global frequency or dominance of hydrovolcanic eruption processes, modulating, in turn, global patterns in volcano-climate forcing.

An Improved One-Dimensional Flow Model for Side Chambers of Centrifugal Pumps Considering the Blade Slip Factor

Abstract The blade slip factor significantly influences the prediction accuracy of the self-closure one-dimensional flow model for side chambers of centrifugal pumps. Wiesner's and Stodola's slip factors, which are used to formulate the blade outlet pressure and served as the boundary condition for the model, are examined, which is an improvement of the previous study (Gu et al., 2020, “A Pressure Model for Open Rotor–Stator Cavities: An Application to an Adjustable-Speed Centrifugal Pump With Experimental Validation,” ASME J. Fluids Eng., 142(10), p. 101301). Both computational fluid dynamics (CFD) simulations and experiments for the centrifugal pump are conducted to support the improvement. A good agreement exists between the performance at the best efficiency points (BEPs) of different rotating speeds obtained by simulations and experiments. Through the CFD analysis, the flow in the impeller remarkably deviates from the blade-congruent flow, especially in the quasi-triangular regions downstream of the throats. Meanwhile, the reason for pressure over-predictions of the side chamber one-dimensional flow model that embeds Wiesner's slip factor (FMW) is that Wiesner's expression underestimates the impeller flow deflection and overestimates pressure boundary. By contrast, the side chamber one-dimensional flow model with Stodola's slip factor (FMS) is closer to CFD in terms of relative flow angle and chamber inlet pressure. Compared with the side chamber pressure measurements, the accuracy of FMS is upgraded approximately by 3.5% than FMW. At the BEPs of different rotating speeds, FMS generates lower shroud thrust coefficients but slightly greater volumetric efficiencies than FMW. This work provides a simple approach to better calculate flow characteristics in the side chambers.

Comparison of one-dimensional and three-dimensional glottal flow models in left-right asymmetric vocal fold conditions

While the glottal flow is often simplified as one-dimensional (1D) in computational models of phonation to reduce computational costs, the 1D flow model has not been validated in left-right asymmetric vocal fold conditions, as often occur in both normal and pathological voice production. It is unclear to what extent the 1D model approximates the effect of three-dimensional (3D) flow phenomena and fluid-structure interaction. In this study, we performed 1D and 3D flow simulations coupled with the two-mass vocal fold model and compared vocal fold vibration patterns at different degrees of left-right stiffness asymmetry. The flow and acoustic fields in 3D were predicted by solving the compressible Navier-Stokes equations using the volume penalization method and considering the moving vocal fold wall as an immersed boundary. The results showed that vocal fold vibration amplitudes and left-right phase differences in the 3D flow were predicted by the 1D flow model under conditions of small left-right asymmetry, while vocal fold vibration amplitudes were underestimated at conditions of large left-right asymmetry. This indicates that 1D flow models may be sufficient in modeling phonation under left-right asymmetric conditions, although the performance can be further improved by more accurately predicting air pressure on vocal fold surface.

Modeling of vapor-liquid interactions in condensing ejectors

Ejectors are compact mechanical devices that utilize the expansion of a high-pressure primary fluid to entrain and compress a low-pressure secondary fluid by means of momentum transfer between the two streams of fluid. Condensing ejectors feature both momentum and heat transfer through the interaction between the vapor and liquid streams. The goal of this paper is to develop and validate a one-dimensional slug flow model to simulate the vapor–liquid interactions in two types of condensing ejectors – one with primary liquid and secondary vapor flows (Type I), and the other with primary vapor and secondary liquid flows (Type II). Control volume analysis of the mass, momentum, and energy balance in each phase and across the interface was conducted for the ejectors. The slug flow models for both types of ejectors are validated with published results in the literature. The friction coefficient on the inner wall of the ejectors and the interfacial heat transfer coefficient are identified as controlling parameters for the ejector performance in terms of pressure and temperature distributions along the axis. The detailed parametric study shows that the liquid inlet velocity and mixing tube diameter have a significant impact on the performance of the Type I ejectors, and the performance of the Type II ejectors is mainly controlled by the secondary liquid flow inlet temperature.

Investigation of the Polymer Coextrusion Process: A Review.

A review of the different coextrusion processes and the related processing problems is presented. A one-dimensional bilayer coextrusion Poiseuille flow model is first developed with Newtonian and shear-thinning rheological behaviors. A transitory computation at the convergence between the two independent polymer layers shows that stationary interface position and velocity profile are established after a short distance of the order of the die gap which justifies the validity of the 1D stationary model. This model is then applied to multilayer temperature dependent coextrusion flows which correspond to realistic industrial coextrusion conditions. Marked interface instabilities may be observed depending on the rheology of the coextruded polymers and of their flow rate ratios. Experiments point clearly out that these instabilities may be amplified along the die land. Convective stability analysis as well as direct numerical computation discriminate flow situations which amplify or damp down instabilities. These 1D models are unable to account for the complex feedblock coat-hanger die geometries. A thin layer coextrusion model is then developed, based on the Hele-Shaw lubrication approximations already used for single layer extrusion problems. It allows to predict the location of the interfaces between the different layers in the whole die, and especially at die exit. This represents a major issue in feedblock die coextrusion. These thin layer approaches are unable to address the encapsulation of one polymer by the other in these complex die geometries with important gap thicknesses. Experiments conducted in dies of square section allow identifying the dynamics of encapsulation. 3D models are required to account for this phenomenon but the management of the sticking contact at the die wall poses difficult numerical problems.

Computational Prediction of Paste Separation from Industrial Waste by a Dry Separator Equipped with a Rotor

Recycling of aggregates separated from industrial wastes becomes more important than ever because of increasing demand of urban redevelopment. The purpose of this study is to investigate the operating principle of a newly developed paste separator equipped with a rotor. We constructed one-dimensional model for the air flow and the particle motion is assumed to be governed by the air drag, centrifugal and gravitational forces. We demonstrate that there are several sections on the air flow route, where particle motions are stationary along the stream-wise direction while rotating in the azimuthal direction, called quasi-stagnant state. It was shown that it plays a key role in separation of particles. We report the critical curve in the parametric space where we can predict separation or non-separation of a given particle size, flow rate and rotor speed.

Phenomenological model of disturbance waves in annular two-phase flow

A new, phenomenological, model of disturbance waves in annular two-phase flow is presented. The model builds upon the three-field (gas, drops and film) one-dimensional model of annular two-phase flow by considering the disturbance waves as an additional fluid field, traveling over a thin liquid base film, along with its own mass, momentum and energy conservation equations. The waves are modeled as fluid particles characterized by basic macroscopic parameters such as the wave shape factor (amplitude/width) and the wave number density (spatial frequency of waves). Phase change is considered and relevant closure models are developed for the field mass and momentum exchange rates (drop entrainment/deposition and waves/base film interactions). A Boltzmann transport equation of wave number density is introduced to model the hydrodynamic non-equilibrium effects related to the wave creation, merging and splitting processes, characteristic of developing annular two-phase flows (due to e.g., inlet effect, phase change, geometrical change or transient). Finally, the base film mass and wave number density sink and source rates are modeled using a relaxation time approximation. The new model is motivated and fully documented in this paper and has been implemented in the latest version of the transient sub-channel analysis code MEFISTO-T. While the proposed model framework is generic for coherent disturbance waves, the required wave characteristic correlations are specifically developed and calibrated using high pressure steam/water experiments under equilibrium conditions relevant of Boiling Water Reactor operation. The model relaxation times are then estimated by comparing the model predictions against measured wave parameters downstream various flow perturbations (evaporation and film suction), along the channel recovery length toward equilibrium. For all considered experiments, the model predicts the averaged wave and base film parameters typically within +/-20% and is able to capture the axial development of disturbance wave characteristics. The consideration of non-equilibrium effects is found fundamental to the accurate simulation of axially developing annular two-phase flows.

A multi-objective optimal control model of cascade pumping stations considering both cost and safety

It is very important to reduce the operation cost and ensure the channel safety for open-channel water diversion projects with cascade pumping stations. In this study, a multi-objective optimal control model of cascade pumping stations is coupled with the one-dimensional unsteady flow model considering both cost and safety, and a case study is performed with the section from the Tuancheng lake to the Huairou reservoir of the Miyun Reservoir Regulation and Storage Project, China, with six pumping stations. Compared with the actual scheme (M0), the average water lifting cost is reduced by 4.54–12.14% for the optimization schemes (M1-M6); the average variation of water level is reduced by 2.94–26.47% for M1-M5 but increased by 7.35% for M6. When the downstream pumping station needs to be adjusted, the larger the discharge is, the lower the average unit water lifting cost and the larger the average variation of water level will be. However, step-by-step adjustment should be used when a large adjustment (>2 m3/s) is required, because the variation of water level is higher than 30 cm/d in this case.

Non-equilibrium simulation of energy relaxation for earth reentry utilizing a collisional-radiative model

A high-temperature air collisional-radiative model considering both vibrational and electronic excited states is established to investigate the plasma characteristics along the stagnation-line in the post-shock flow by coupling with the one-dimensional flow model. The results obtained by the model are in reasonable agreement with the experimental data and previous calculation results. The evolutions of different temperatures and energy relaxation processes are analyzed in detail for the height of 76.42 km and Mach number of 40.58. The vibrational and electronic excited modes play a critical role on the energy transfer. The vibrational excitation processes under heavy-particle impact can transfer the translational energy to the vibrational mode, then to the electrons by the vibrational de-excitation processes. The excitation of atoms by heavy-particle impact can gain energy from the translational mode, and the de-excitation processes of high-lying excited states under electron impact result in the energy transfer to electrons. The elastic collisions also play a role on the direct transfer from translational energy to electrons. The calculations are performed for a wide range of flight altitudes and Mach numbers to investigate the thermochemical state and energy relaxation. By comparing the energy transfer processes under different altitudes and Mach numbers, it is found that the energy transfer is dominated by vibrational processes for the low-Height low-Mach condition, and the contribution of electronic excited mode is negligible. The division of thermochemical state and chemical reactions in the Height-Mach number diagram is obtained, which provides the basis for the selection of thermochemical model required for atmospheric reentry calculation.

Exact Riemann solutions for the drift-flux equations of two-phase flow under gravity

The exact Riemann solutions are constructed in completely explicit forms for the drift-flux equations of the one-dimensional inviscid, compressible and isentropic liquid-gas two-phase flow model in an inclined pipeline under gravity. It is found that the curved delta shock wave and vacuum state are involved in the Riemann solutions for the pressureless situation with the adiabatic exponent being one. It is proved rigorously that this curved delta shock wave solution satisfies the pressureless drift-flux equations in the sense of distributions. Finally, the asymptotic limits of Riemann solutions are investigated in detail when the adiabatic exponent tends to one, in which the concentration phenomenon can be observed when the non-self-similar Riemann solution consisting of curved 1-shock wave, 2-contact discontinuity and 3-shock wave converges to this curved delta shock wave solution. In addition, the cavitation phenomenon can also be inspected that all the states in the two rarefaction wave fans become the vacuum states in the limiting situation.

Local existence for viscous reactive micropolar real gas flow and thermal explosion with homogeneous boundary conditions

In this paper, we prove that the one-dimensional model of reactive micropolar real gas flow and thermal explosion has a solution locally in time. We first define the notion of a generalized solution for the governing initial-boundary value problem. We prove the claim of local existence by deriving a sequence of approximate problems obtained by Faedo-Galerkin projections. A priori estimates allow us to choose small enough time interval of existence, and show that the sequence of approximations is bounded in certain functional spaces, and therefore has a convergent subsequence. In the end, we show that it is precisely this limit that is the solution to the observed problem.

New permafrost is forming on the exposed bottom of Zonag Lake on the Qinghai-Tibet Plateau

Most lakes on the Qinghai-Tibet Plateau have expanded in recent years. Zonag Lake, a critical habitat for Tibetan antelopes in the continuous permafrost zone, burst and overflowed after several years of expansion, resulting in a reduction of approximately 100 km2 in the lake area. Observations have revealed new permafrost is forming on the exposed bottom, accompanied by various periglacial landscapes. The permafrost aggradation on the exposed bottom is rapid, and the permafrost base reached 4.9 m, 5.4 m, and 5.7 m in the first three years, respectively. In this study, the future changes and influencing factors of recently formed permafrost are simulated using a one-dimensional finite element model of heat flow. The simulated results indicate that the permafrost on the exposed bottom is likely to continue to develop, appearing first quick back slow trend. Besides the surface temperature, the annual amplitude is also an important factor in affecting the aggradation of permafrost. The unidirectional permafrost aggradation in the study area is different from the bidirectional permafrost aggradation on the closed taliks around the Arctic. Additionally, snow cover and vegetation are two important factors influencing the future development of permafrost on the exposed lake bottom.

Kinetic discretization of one-dimensional nonlocal flow models

We show that one-dimensional nonlocal flow models in PDE form with Lighthill-Whitham-Richards flux supplemented with appropriate in- and out-flow terms can be spatially discretized with a finite volume scheme to obtain formally kinetic models with physically meaningful reaction graph structure. This allows the utilization of the theory of chemical reaction networks, as demonstrated here via the stability analysis of a flow model with circular topology. We further propose an explicit time discretization and a Courant-Friedrichs-Lewy condition ensuring many advantageous properties of the scheme. Additional characteristics, including monotonicity and the total variation diminishing property are also discussed.

Optimization in a traffic flow model as an inverse problem in the Wasserstein space

We address an inverse problem for a dynamical system in the space of probability measures, namely, the problem of restoration of the time-evolution of a probability distribution from certain given statistical information. The dynamics of the distribution is described by a nonlocal continuity equation in the Wasserstein space of probability measures. For the simplest version of this problem, associated with a toy one-dimensional model of traffic flow, we derive a necessary optimality condition and design, on its base, a numerical algorithm of the type of gradient descent. We also discuss some technical aspects of the realization of the elaborated algorithm, and present the results of computational experiments implementing an eloquent numeric scenario.

Rivers in reverse: Upstream-migrating dechannelization and flooding cause avulsions on fluvial fans

AbstractThe process of river avulsion builds floodplains and fills alluvial basins. We report on a new style of river avulsion identified in the Landsat satellite record. We found 69 examples of retrogradational avulsions on rivers of densely forested fluvial fans in the Andean and New Guinean alluvial basins. Retrogradational avulsions are initiated by a channel blockage, e.g., a logjam, that fills the channel with sediment and forces water overbank (dechannelization), which creates a chevron-shaped flooding pattern. Dechannelization waves travel upstream at a median rate of 387 m/yr and last on average for 13 yr; many rivers show multiple dechannelizing events on the same reach. Dechannelization ends and the avulsion is complete when the river finds a new flow path. We simulate upstream-migrating dechannelization with a one-dimensional morphodynamic model for open channel flow. Observations are consistent with model results and show that channel blockages can cause dechannelization on steep (10−2 to 10−3), low-discharge (~101 m3 s−1) rivers. This illustrates a new style of floodplain sedimentation that is unaccounted for in ecologic and stratigraphic models.

Prediction Capabilities of a One-dimensional Wall-flow Particulate Filter Model

This work is focused on the formulation of a numerical model for prediction of flow field inside a particulate filter. More specifically, a one-dimensional mathematical model of the gas flow in a particulate trap-cell is deduced and solved numerically. The results are given in terms of velocity, pressure, and filtration velocity. In addition, the dependence of the pressure drop on the main governing parameters has been investigated. More specifically, the permeability of the porous medium and the hydraulic diameter play a fundamental role in the pressure drop.

Deep Radiostratigraphy Constraints Support the Presence of Persistent Wind Scouring Behavior for More Than 100 Ka in the East Antarctic Ice Sheet

The characterization of unconformities in wind-scoured areas of the Antarctic Ice Sheet (AIS) is important for the accurate estimation of Antarctic mass balance and can provide constraints on climate models. Here we apply radar data collected by the Chinese National Antarctic Research Expedition in the vicinity of the Dome A region in East Antarctica to trace six isochronous internal reflecting horizons. We identify 39 unconformities and map englacial stratigraphy 500 m below the ice surface through cross-validation among the data from several austral summer campaigns using different ice-penetrating radars. By estimating erosion time of buried unconformities using a one-dimensional ice flow model along local ice flowlines, we identify persistent wind-scoured zones on the scale of ten thousand years. We identify the earliest truncated climatic record through interpretation of the radar images and find that erosional activity can be dated back to approximately 100,000 years before present; all of the persistent wind scouring behaviors we present here began during the Last Interglacial- Last Glacial (128 ~ 10 ka B.P.). High-resolution records such as this that reveal englacial unconformities and englacial structural characteristics associated with erosion contribute to improved understanding of climate variability and ice sheet dynamics during the Late Pleistocene.

On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media

Abstract In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L ∞ {L}^{\infty } stability under appropriate CFL conditions and BV {\rm{BV}} estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L 1 {L}^{1} . Results of numerical experiments are presented to validate the theoretical analysis.

Examples on Simulation Model

Abstract: A new methodology was developed Further real-time determination gate control operations of a river-reservoir system to minimize flooding conditions. The methodology is based upon an optimization-simulation model approach interfacing the genetic algorithm within simulation software for short-term rainfall forecasting, rainfall–runoff modeling (HEC-HMS), and a one-dimensional (1D), two-dimensional (2D), and combined 1D and 2D combined unsteady flow models (HEC-RAS). Both realtime rainfall data from next-generation radar (NEXRAD) and gaging stations, and forecasted rainfall are needed to make gate control decisions (reservoir releases) in real-time so that at timet, rainfall is known and rainfall over the future timeperiod(∆t)totimet+ ∆t can be forecasted. This new model can be used to manage reservoir release schedules (optimal gate operations) before, during, and after a rainfall event. Through real-time observations and optimal gate controls, downstream water surface elevations are controlled to avoid exceedance of threshold flood levels at target locations throughout a riverreservoir system to minimize the damage. In an example application, an actual river reach with a hypothetical upstream flood control reservoir is modeled in real-time to test the optimization-simulation portion of the overall model. Keywords: Simulation – Random numbers- Steps for simulation – Problems.