One-dimensional Unsteady Model Research Articles

Solution to the Unsteady Seepage Model of Phreatic Water with Linear Variation in the Channel Water Level and Its Application

For a semi-infinite aquifer controlled by a river channel boundary, when the Laplace transform is used to solve a one-dimensional unsteady seepage model of phreatic water while considering the influence of the vertical water exchange intensity ε with the change in the river channel water level f(t), a complicated and tedious integral transformation process is required. By replacing f(t) with an operator, this study first derived the analytic formula of the ε term based on the properties of the Laplace transform without the direct participation of f(t) in the transformation. By using f(t) in the form of several types of linear functions, the Laplace transform and inverse transform laws were summarized. The analytical solution to the problem was easily obtained by applying the “integral property” of the transformation to the linear function term with time t. The relative error between the numerical solution and the analytical solution of the example was less than 0.2%, which verified the rationality of the model linearization method and the reliability of the analytical solution. For different boundary conditions, the process of establishing and applying the inflection point method and the curve-fitting method for calculating the model parameters by using dynamic monitoring data for phreatic water is presented with examples.

A novel method for modeling the phase change of iron ore particles in the cohesive zone of a blast furnace

Cohesive zone plays a vital role in the stable operation of a blast furnace (BF), yet the complex phase change process of iron ore particles in this zone is still not well understood. In this study, a novel one-dimensional (1D) unsteady phase change model was developed to elucidate the heat transfer and melting mechanisms of iron ore particles. After model validation, the effects of several key operating parameters (e.g., particle diameter, gas velocity, initial temperature) on the phase change behavior of iron ore particles were analyzed, and the joint effect of multiple parameters was discussed. The results show that larger-sized iron ore particles possess lower specific surface areas, which in turn reduces their convective heat absorption capacity. Consequently, the distance from the solid-liquid phase interface to the particle surface increases, thereby slowing down the movement of the phase interface and prolonging the melting duration of the particles. Increasing the gas velocity and the initial temperature does not have a significant impact on reducing the duration of the complete melting process. Under the specified conditions, it is observed that increasing the gas velocity by 3-fold and 9-fold results in a reduction of the melting duration by 2.4% and 8.3%, respectively. Elevating the initial temperature of iron ore particles results in a decrease in the core-to-surface temperature difference, a slower heating rate, and a shorter duration to achieve melting. Among the factors affecting the melting process, the particle diameter is found to be the most significant in terms of the liquid phase precipitation, mushy zone thickness, and core-to-surface temperature difference of iron ore particles.

One-Dimensional Unsteady Numerical Model of Gas Suspension Flow Caused by Gravitational Sedimentation of Particles with a Constant Velocity

One-Dimensional Unsteady Numerical Model of Gas Suspension Flow Caused by Gravitational Sedimentation of Particles with a Constant Velocity

Interfacial heat transfer characteristics and thermal expansion behavior of heterostructure materials in arc-heated wind tunnel

Structural ceramics such as carbon fiber reinforced silicon carbide (C/SiC) are of great importance for supersonic aircraft, where thermal-mechanical coupling behavior of materials affects the service performance of structural ceramics. In order to advance the understanding of the high temperature thermal-mechanical coupling behavior of heterostructure materials (one typical type of structural ceramics), we adopted here an optical observation system to visualize the variation of the gap width between heterostructure materials in arc-heated wind tunnel test. The variation of the gap width (decreasing and then volatility increasing) was observed during the test. Numerical simulation shows that thermal conduction and thermal expansion between the substrate and specimens play a critical role in the evolution of the gap width, as evidenced by the experiments. Additionally, the variation of the gap width under various conditions was given and a one-dimensional unsteady thermodynamic model of double-layer plate was established to reveal the gap evolution mechanism of heterostructure materials. The results of theoretical model agree well with numerical simulation.

Energy Saving Analysis of Photovoltaic Roof Based on MATLAB

One-dimensional unsteady theoretical models of three different photovoltaic module installation modes are established. Through MATLAB modeling and simulation, the influence of photovoltaic modules on roof heat transfer in different layout modes is compared. Comparing with ordinary roof, the shading effect of photovoltaic roof in summer and heat preservation effect in winter was analyzed. The results show that the PV roof layout with ventilation channel is better in summer. The proof layout with closed flow channel is better in winter.

Paleoflood evidence for an upper limit of the maximum flood magnitudes along the Gold Gorge, the upper Hanjiang River, China

This paper provides an important archive of the largest paleoflood event along the Gold Gorge of the upper Hanjiang River, with a review of regional extraordinary flood magnitudes using historical, gauged, and paleoflood datasets. Paleoflood slackwater deposit (SWD) was identified using the sedimentological criteria and high-resolution physicochemical indexes. End-member model demonstrates the paleoflood SWD was dominated by sand component. Optical chronology indicates the paleoflood event was dated to 1000–900 a BP, corresponding to the North Song Dynasty (AD 960–1127). Paleoflood magnitudes derived from one-dimensional unsteady model vary between 23,000 and 34,000 m3/s. The paleoflood data provide a good representation of extraordinary flood event with a 10,000-years return period and greatly improve current flood frequency estimations. Moreover, the envelope curve for extraordinary floods was first established as Q = 50D0.65 and the paleoflood peak discharges are approximately 2–2.5 times of the largest gauged floods within the catchment. These results provide an upper limit of the maximum flood magnitudes along the upper Hanjiang River and also expand our understanding of rare and large magnitude floods in the middle Yangtze River valley.

Water Flow Simulation of Tigris River Between Samara and Baghdad Based on HEC-RAS Model

This work aims to use the digital elevation model (DEM) or 3-Dimensional surface to model and analyze the water flow in the Tigris River. The first stage of this study is based on filed data acquisition survey at 38 stations. These stations were adopted to implement the one-dimensional steady and unsteady numerical flow models. The HEC-RAS software was used to implement these models. The most important results of the steady-state model were that the maximum discharge and velocity and minimum flow area were 638.17 m3/sec, 2.12 m/sec and 301.42 m2 respectively. These values occurred at station 66+700. While, the minimum discharge and velocity and maximum flow area were 504.5 m3/sec, 0.13m/sec and 4758.13 m2 respectively. The results of unsteady state were analyzed based on the recorded discharge in the year 2018. The maximum and minimum discharge (flow velocity) were 638.12 m3/sec (2.42 m/sec) at the stations 94+666+7 and 635.57 m3/sec(0.14 m/sec) at station 00+00, respectively. The maximum and minimum Froude number were 0.52 and 0.02 at stations 94+666+7 and 04+800, respectively. These results help to identify the flow choking areas that cause defects. In addition, it can be the base for determining the critical sedimentation stations in which the bed level rises and aggravate the flow choking problem within the considered reach of the Tigris River.

Controlling the Salt Wedge Intrusion in Shatt Al-Arab River by a Barrage

Shatt Al-Arab River in Al Basrah, Iraq, has recently recorded massive levels of TDS values (Total Dissolved Solids) in the water as a result of reduced fresh water discharge from sources, causing the river to become salinized due to salt wedge intrusion. Therefore, a block dam in the south reach is required to salt intrusion prevention. The main objective of this research is to simulate the hydraulic impact of a suggested barrage in Ras Al Besha on the Shatt Al-Arab River. The HEC-RAS (5.0.7) model was used to develop a one-dimensional unsteady model to gaining an understanding of the proposed barrage's influence on river behaviour. The daily discharges of the Tigris River provided as the upstream boundary conditions, while the hourly water levels of the Shatt Al-Arab River provided as the downstream boundary conditions. The model was initially run on the basis of daily discharges in Aug 2018 and March 2020 for the model's calibration and verification. Then, a model was run with a proposed barrage, Four cases of discharge were chosen which were the low and moderate discharge that equal to (20-50-100 and 250) m3/s with adopted spring tide cycle. The operation scenarios were examined under the influence of three cases of barrage gates (fully opened, 50% open and programmed opening). The results indicate that the investigated discharges will cause a significant problems in navigation depths, especially in the case of the programming of gates opening where the stages drop range between 2.01-3.3m comparing with the normal case. Furthermore, the velocity indicators show that the significant reduction in velocity upstream the barrage led to more sedimentation in the river reach.

Experimental study on the interfacial heat transfer of sessile droplet evaporation using temperature-sensitive paint

The present work is aimed at analyzing changes in the interfacial temperature distribution and interfacial heat flux distribution during sessile droplet evaporation. In particular, two kinds of nonintrusive measurement techniques, temperature-sensitive paint (TSP) and infrared imaging were used simultaneously. TSP was used to capture the interfacial temperature distribution, and then a one-dimensional unsteady transient model was established to obtain the heat flux distribution. An infrared camera was applied to observe the thermal patterns during droplet evaporation from the top view. Three kinds of liquids, pentane, HFE-7100 and hexane, were used during our experiments, and the experimental results show that the contact line profile captured by TSP was consistent with that captured by an infrared camera. Three stages could be observed during droplet evaporation: initial droplet heating, convection cell evaporation and thin film evaporation. Convection cells could be observed in the infrared images during the second stage, and an obvious temperature gradient at the contact surface could also be seen from the images captured by TSP. In addition, the heat flux at the contact line was higher than that at the centre. Finally, the heat dissipation due to droplet evaporation could also be obtained by double integration of interfacial heat flux data with contact area and evaporation time, which further demonstrated the soundness of the present experimental and calculated methods.

A novel non-linear one-dimensional unsteady model for thermoacoustic engine and its application on a looped traveling-wave thermoacoustic engine

A novel non-linear one-dimensional unsteady model (1DUM) for thermoacoustic engine is proposed to study on the working mechanism of thermoacoustic engines, with its focus on the unsteady onset process. Numerical simulation of a looped 3-stage traveling-wave thermoacoustic engine (TWTAE) is carried out based on this model. The complete self-excited onset process from static state to saturation is firstly realized in simulation without introducing any external disturbance. The simulation results indicate that the thermal conduction is a crucial factor to excite the oscillation in transient onset process. The onset mechanism and energy balance of thermoacoustic engine is then explained. Experimental work and calculation based on the linear thermoacoustic simulation platform, DeltaEC, are carried out to verify the model. It is shown that the calculated frequency and the proportion of the high-order harmonics by 1DUM agree well with the experiment, and 1DUM presents a reliable acoustic field distribution for the looped multi-stage TWTAE without empirical inputs like DeltaEC, which greatly simplifies the modeling process. Compared with computational fluid dynamics (CFD), 1DUM is more efficient at simulating the non-linear and unsteady onset process.

Testing of an Optimization-Simulation Model for Real-Time Flood Operation of River-Reservoir Systems

A new methodology was developed for the 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 MATLAB with 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 real-time 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 time t, rainfall is known and rainfall over the future time-period (Δt) to time t + Δt 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 river-reservoir 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.

Loop heat pipe dynamics modeling and analysis

The report presents mathematical model and computational analysis of dynamic processes in the loop heat pipe, as well as some ways of regulating its work. This is considered a one-dimensional unsteady model of the loop. For each element of loop the model contains the energy equation for flow of fluid and to the walls, and the equation of conservation of momentum of the working fluid. The joint solution of a system of such equations for all elements of the loop allows to calculate the temperature distribution and pressure contour at any point in time. The calculations showed that under certain conditions in the loop heat pipe can be auto-oscillations of different nature. Analysed methods of eliminating these auto-oscillations. One way to regulate the loop heat pipe is the use of a control valve on the additional bypass line. The analysis showed that this method can significantly improve the quality of temperature control and reduce energy consumption by regulation or do without energy consumption. Presents a model of the dynamics of loop heat pipe gives physically reasonable results of calculations and is consistent with the results of the tests.

Water Oscillation Modelling Inside OWC Chamber for Wave Energy Conversion

Among wave energy converters (WECs), the Oscillating Water Column (OWC) system is considered as one of the most promising converters; this system works on the principle of water oscillations in an enclosed air chamber due to incident sea waves. The amount of pneumatic power that can be harvested depends on the elevation level, the water oscillations' frequency inside the chamber, and the chamber's global damping. A one-dimensional (1-D) unsteady model has been elaborated to analyze the water elevation's dynamic behavior. Great attention has been paid to determining the natural frequency and the global damping for maximum wave energy capture. The model is based on a water mass block moving periodically upward and downward as a piston inside the chamber, inducing the enclosed air to flow alternately through a turbine. The Lagrangian formalism has been adopted to derive the governing differential equation for the piston water motion. Then the poincare-Lindstedt method has been used to deal with the non-linearity of the problem. The elaborated model has been adapted to an OWC system in the case of monochromatic waves. Results have been compared to another referenced paper for validation and pertinence. Fair agreements have been noted.

A one-dimensional semi-implicit finite volume modeling of non-inertia wave through rockfill dams

Abstract For hydraulic routing through coarse rockfill dams, there is still debate on whether the inertia terms might be neglected as a result of the drag force generated by the rock materials. In this study, a one-dimensional unsteady model for flow-through rockfill dams is built. For this purpose, inertia terms of Saint–Venant equations are disregarded. A semi-implicit scheme adopted for linearizing the nonlinear friction term within the time integration satisfies the Courant–Friedrich–Lewy stability criterion. The most challenging issue in the modeling of flows through rockfill dams is the appropriate definition of boundary conditions at the dam's exit zone. In addition to the analysis of different exit boundary conditions proposed in the literature, a Neumann-type boundary condition suitable for the non-inertia wave equation is also employed to estimate the exit boundary condition. This procedure is basically in appreciation of the nonlinear behavior of the water surface closer to the exit boundary. Due to the existence of the sloping edges in the trapezoidal-shaped dam, an effective length is considered for the solution domain. Finally, the model is compared with observed data and a dynamic wave model. A very good match is observed, which builds confidence in the presented modeling approach.

Study on NOx emission during corn straw/sewage sludge co-combustion: Experiments and modelling

The co-combustion of sewage sludge (SS) and biomass is promising for achieving energy recovery and compensating for individual feedstock disadvantages. However, the emission of nitric oxide (NOx) during this process is of concern, but no relevant study has focused on this. In this study, the release characteristics of NOx during co-combustion of SS and corn straw (CS) were investigated under different mixing ratios, heating rates, and SS moisture contents. The synergetic effect of SS and CS on NOx reduction was determined and quantified. An independently designed one-dimensional unsteady model with a fully implicit scheme was used. The results showed that with the increase in the SS mixing ratio to 20, 40, 60, and 80 wt%, the NOx emission peak values were reduced by 26%, 38%, 35%, and 40%, respectively. The case with a 60 wt% water content of SS was the best choice for NOx reduction. Furthermore, the model could describe the NOx emission trend accurately, especially for CS combustion and SS/CS co-combustion. This study showed effective NOx reduction during SS/CS co-combustion, thereby indicating that co-combustion is beneficial for the disposal of SS. In the future, the mechanism of the synergetic effect of SS and CS will be investigated from a micro point of view by more comprehensive experiments coupled with process parameter simulation.

Response characteristics of external receiver for concentrated solar power to disturbance during operation

The practical operation of the receiver for solar power tower plant is under unsteady conditions because of the variation of direct normal irradiation, as well as the output power load. A 100 MW external receiver was designed and selected as the object. The unsteady one-dimensional model was established for the receiver and validated by comparing the simulation results with the published experimental data, aiming to launch the thermal, hydraulic and mechanical analysis. The heat transfer characteristics, thermal efficiency, as well as the thermal stress in the flow direction, are demonstrated by the static analysis. By comparison of different panels, the harsh working condition of the first and the last panels is discovered, including that of the highest temperature difference and tangential thermal stress along tubes. The tangential thermal stress is prominent at the light spot. The molten salt at the last panel is most likely to decompose. Dynamic simulation is carried out to analyze the thermal inertia and heat transport characteristics. The response curves and time constants of the receiver under step and periodical disturbances of different factors from the environment and load side are acquired. The thermal inertia of the receiver and its effect to dampen weather fluctuation are illustrated. These security problems and thermal performance will make demands on the control strategy and control accuracy. The results can provide a reference for the control strategy development of the solar power tower plant.

Water diversion and allocation for typical confined polder river-net in Taihu Basin

AbstractHydraulic restoration in a confined polder river-net is a new issue under the concept of the Interconnected River System Network (IRSN) proposed by the Ministry of Water Resources (MWR) in China. This paper studies the typical hydrographic connection in the polder, and analyses the current situation of the hydrographic river-net in the typical area of Subaiwei in Changshu City by setting up a one-dimensional unsteady hydrodynamic model. The best water diversion-allocation schemes in the confined polder river-net are simulated and optimized in various scheduling rules. In order to recover the ability of hydro-connection and stream function, the effects of different scheduling rules and the duration time of water diversion under the ability of pump stations around polder boundary are compared. The results show that the optimized injects can enhance the total flow velocity and the exchange rate is more than 20% on average in various streams. This study is critical for the sustainable utilization of limited clean water in a confined river-net polder, and for quantifying the water ecological recharge for hydrodynamic connection.

Numerical investigation of one-dimensional unsteady detonation wave characteristics of magnesium particle-air mixture

In this paper, a one-dimensional unsteady model is established for the detonation of magnesium particle-air mixture. Through numerical simulation, the influences of the loss caused by the side wall of the detonation tube, the diameter of the magnesium particles, the initial equivalent ratio of the magnesium particles, and the deposition process on the surface of the particles, and the ignition energy on the structure and development of the detonation wave and the distribution of the flow field parameters inside the detonation wave are obtained. The studies show that there appear oscillations during the propagation of the fully developed one-dimensional unsteady detonation wave of magnesium particle-air mixture, but the amplitude is less than 1 m/s. Considering the loss of the wall, the pressure and temperature inside the detonation wave decrease with the inner diameter of the detonation tube decreasing, thus leading the propagation velocity and the thickness of the detonation wave decreasing. In the case without the wall loss, as the initial particle size increases, the detonation wave velocity remains unchanged, and the detonation wave thickness monotonically increases. With the wall loss taken into consideration, the stable velocity and thickness of detonation wave are lower than without considering the wall loss under the same initial conditions. Both the difference between the velocities and the difference between thickness values under the conditions with and without considering the wall loss increase as initial particle size increases. The detonation wave thickness with a double-size-distribution initial particle size is more than that with an equivalent single-size-distribution. Meanwhile the stable propagation velocity of the former is less than that of the latter. In the range of initial particle equivalent ratio of 0.5–2, as the initial equivalent ratio increases, the stable velocity of ideal detonation wave first increases and then decreases, and the thickness of the detonation wave first decreases and then increases. Considering the loss of the wall, with the increase of the initial equivalence ratio, the stable velocity of detonation wave first decreases and then increases and the thickness of the detonation wave monotonically decreases. When the initial equivalence ratio of the initial particles is in a lower range (0.337–0.382), the melting of MgO occurs near the CJ plane. As a result, the melting process of MgO has no significant effect on the stability of the detonation wave propagation, but has a greater influence on the structure of the detonation wave: when the initial equivalence ratio is lower in the above range, MgO in the detonation wave is partially melted and then re-solidified. When the initial equivalence ratio is higher in the above range, the MgO at the CJ plane is still in the melting process, and there is a low-strength secondary compression process in the detonation wave. Considering the fact that the combustion products are deposited on the particle surface, the detonation wave velocity increases while the corresponding thickness of the detonation wave remains almost unchanged with the increase of the deposition rate. The parameters of the ignition region have no influence on the final stable propagation state of the detonation wave, but will affect the development process of the detonation wave. Selecting appropriate paraneters of ignition zone can shorten the distance of denotation wave reaching to the steady propagation.

Thermal Analysis of a Volumetric Solar Receiver

The volumetric receiver has received wide attention due to its high thermal efficiency. This paper studied a new type of a solid-liquid composite volumetric receiver. The heat transfer in a solid-liquid composite volumetric solar receiver was analyzed using a one-dimensional unsteady simulation model of the solid-liquid receiver. The model included absorption of the incident solar radiation by the glass window, the silicon carbide porous ceramic heat absorber panel and the water. The results were verified against experimental data for a volumetric receiver and the error did not exceed 10%. It can be used to predict the heat transfer in solid-liquid composite volumetric receivers.

Modeling of gasification process of Indian coal in perspective of underground coal gasification (UCG)

In the present study, the steam gasification of Indian coal and its demineralized coal were investigated in a specially designed fixed-bed reactor, to determine the intrinsic kinetics parameters with optimum operating temperature and partial pressures of steam in the perspective of underground coal gasification (UCG). The gasification reactivity of a chosen coal was higher compared to the demineralized coal and the reason could be mineral content of ash present in the coal. A one-dimensional unsteady kinetic model was developed for the steam gasification process in a fixed-bed reactor. The intrinsic kinetic parameters for steam gasification and water–gas shift reaction are estimated by fitting the developed models with the experimental data.