Unsteady Water Flow Research Articles

Real-Time Analysis and Digital Twin Modeling for CFD-Based Air Valve Control During Filling Procedures

Air exchange in pressurized water pipelines is an essential but complex aspect of pipeline modeling and operation. Implementing effective air management strategies can yield numerous benefits, enhancing the system’s energy efficiency, reliability, and safety. This paper comprehensively evaluates an irregular profile pipeline filling procedure involving air-release through an air valve. The analysis includes real-time data tests and numerical simulations using Computational Fluid Dynamics (CFD). A Digital Twin model was proposed and applied to filling maneuvers in water installations. In particular, this research considers an often-overlooked aspect, such as filling a pipe with an irregular profile rather than a simple straight pipe. CFD simulations have proven to capture the main features of the transient event, which are suitable for tracking the air-water interface, the unsteady water flow, and the evolution of the trapped air pocket. Thus, they provide thorough and reliable information for real-time operational processes in the industry, focusing on the filling pressure and geometry of the air-valve hydraulic system. Additionally, this study provides details regarding the application of an efficient Digital Twin CFD approach, demonstrating its feasibility in optimizing the filling procedure in pipes with irregular profiles.

Development of runoff generation models in the former USSR and Russia: a historical overview

The paper presents a historical overview of the development of hydrological models in the former USSR and Russia since the 1930s. An overwhelming number of hydrological papers were published in Russian, and they are not sufficiently familiar to the world hydrological community. The purpose of the review is to fill the gap and present the main achievements, some of which were pioneering for their time. The period under consideration is divided into three sub-periods. Pre-computer 1930-1950s were associated, first of all, with the development of models of unsteady water flow in river channels and linear flood-routing models; in 1960-1980s, many theoretical and practical foundations for modelling the processes of the hydrological cycle and the formation of river runoff were developed; and the Russian era following 1991, when several notable advancements in the considered field were also made.

Оперативное диспетчерское управление водораспределением в оросительных системах по расчетному приращению объемов

Goal: to improve the methodological approach to developing an algorithm for operational dis-patch control of water distribution based on the calculated increment of water volumes in irri-gation canals. Materials and methods: the dispatch control methodology is described, which is based on the typification of flow conditions between two partitioning structures in technical and functional directions, as well as on the development of systems for unifying channels and their modes using similarity theory methods, which are widely used in hydromechanics and hydraulics. The basis for the implementation of the similarity theory is the principle of using similarity numbers, that is, combinations of dimensionless parameters that determine the char-acteristics of the unsteady motion of a heavy, incompressible, viscous fluid in channels. Re-sults: the general tasks of the dispatcher were determined to re-regulate the hydraulic regime of sections of the irrigation system, without tying them to specific types of hydraulic struc-tures. The main provisions of the method of dispatch control of water distribution based on the calculated increment of volumes, determination of the time of re-regulation between the main and compensating processes of re-regulation are substantiated. Four types of situations are identified when solving dispatch problems of water distribution, which are determined by comparing the volumes and flow rates installed on the site, for each of which the inherent re-regulation order is determined. Conclusion: the article outlines a new methodological ap-proach that ensures the joint use of the method of similarity theory and a simulation experi-ment with the Saint-Venant equations for steady and unsteady water flow in the canals of ir-rigation systems, to solve problems of operational dispatch control of water distribution ac-cording to the calculated increment of volumes.

Hyporheic exchange in a compound channel under unsteady flow: Numerical simulations

Hyporheic exchange (HE) within compound channels under unsteady surface water flow conditions plays an important role in the river-floodplain ecosystem. Numerical simulations were applied to investigate the HE in a compound channel under unsteady flow. High velocity regions were observed in the hyporheic zone near the banks of the floodplain and of the main channel, and the distribution of the pore water velocity in this region was seen to significantly change under the unsteady conditions. The velocity peaked during the rising and falling phases and had the smallest value when the inlet discharge of surface water had the maximum and minimum values. The changes in the relationship between surface groundwater recharge and discharge were observed in the context of a lateral water level threshold of approximately 1.2 m. About 75 % of the hyporheic exchange flux was due to the dynamic pressure. Comparing the hyporheic exchange in the compound channel driven by static pressure with that in a rectangular channel, it was found that the floodplain decreased the hyporheic exchange. These findings provide a better understanding of the HE driven by unsteady flow in a compound channel and may be applied in combined flood management and river ecological restoration.

Experimental study of the stability of crescent barchan shape in subaqueous dune evolution in unsteady water flow

A water tunnel experiment adopting the frequency conversion technology is conducted to investigate the evolution of subaqueous barchan dune driven by the periodic water flow. The kinematic and morphological characteristics of the barchan dune evolution are derived through the imaging processing. Results exhibit a good correlation between the dune kinematics and the periodic variation of water flow, which indicates that the unsteadiness is transmitted from the fluid phase to the sand phase with nearly no inertia. The stable crescent barchan shape under unsteady flow is found. Meanwhile, this crescent barchan shape breaks and reconstructs periodically during the variation of unsteady flow, which implies a flexible compromise between the dune system and the propelling force. This study suggests that the stability of crescent barchan shape can be robust under unsteady flow, which brings new understandings of the morphological stability of sand dune evolution.

Hydraulic characteristics of the river flow and sediment transport conditions in the downstream pool of the hydroelectric complex

In this paper, the navigable section of the Svir River, located in the lower reaches of the Nizhne-Svirsky hydroelectric complex, is considered. Special in-situ observations were made in this section to study the hydraulic regime of the river flow under the conditions of unsteady water movement. The study has showed that the kinematic characteristics of the flow in the downstream pool vary with the distance from the site of the waterworks and depend on the regime of the discharge flows. The nature of the transformation of releases in the downstream under open channel and ice conditions has been studied. The values and intensity of changes in the main characteristics of the river flow during the propagation of the tail water wave in the lower reaches such as the nature of changes in the level regime and the slopes of the free surface on the hydraulic structures, the regime of water flow velocities, have been evaluated. The main hydraulic parameters of the river flow such as the values of the Froude number, the Chézy’s coefficient and the water flow modulus are determined. The character of changes in local and convective accelerations is studied and their contribution to the general value of energy losses along the stream length is evaluated. Numerical experiments make it possible to identify the peculiarities of sediment movement in conditions of unsteady water flow and to develop recommendations for modelling channel transformations in such conditions. It is found that during daily and weekly regulation of the river discharge, sediment transport is activated at the moment when a wave of daily water discharge is passing from the upstream reservoir of the hydroelectric power plant. At the same time, the basic parameters of sediment transport such as the speed of dune movement and sediment discharge increase in comparison with the stationary movement of the water.

POD-based ROM applied to unsteady free surface water flow

The numerical resolution of shallow water equations (SWE) is required in many environmental problems involving free surface flows. The upwind augmented Roe’s method [2] is widely used due to the robust and stable solutions it offers in realistic scenarios if properly corrected to deal with entropy fix and wet–dry fronts. On the other hand, reduced-order models (ROMs) are known to achieve more efficiency in terms of computational cost without losing accuracy. In this work, we analyse the properties and performance of a proper orthogonal decomposition (POD) based ROMs for this type of flows.

Pablo Solán - POD-based ROM applied to unsteady free surface water flow

Pablo Solán - POD-based ROM applied to unsteady free surface water flow

Diffusion‐thermo effect on convective MHD flow of Cu‐water nanofluid including ramped wall temperature, velocity and concentration

An unsteady convective MHD flow of water based Cu-nanofluid past an impulsively started infinite vertical plate embedded in porous medium including ramped velocity, temperature and concentration in the existence of diffusion-thermo effect, radiation and chemical reaction has been investigated. The non-dimensional domain equations are computed by adopting Laplace transform technique. The impact of various pertinent parameters that are associated with the fluid velocity, temperature, concentration and moreover on skin friction coefficient, Nusselt number and Sherwood number has been represented graphically. It is figured out that, increase of Dufour effect causes to rise in both the momentum and temperature boundary layer. Further, it is ascertained that increase in the volume fraction of nanoparticles causes fall of velocity whereas it increases temperature together with the rate of heat transfer at the walls.

A High-Order Velocity-Based Discontinuous Galerkin Scheme for the Shallow Water Equations: Local Conservation, Entropy Stability, Well-Balanced Property, and Positivity Preservation

The nonlinear shallow water equations (SWEs) are widely used to model the unsteady water flows in rivers and coastal areas. In this work, we present a novel class of locally conservative, entropy stable and well-balanced discontinuous Galerkin (DG) methods for the nonlinear shallow water equation with a non-flat bottom topography. The major novelty of our work is the use of velocity field as an independent solution unknown in the DG scheme, which is closely related to the entropy variable approach to entropy stable schemes for system of conservation laws proposed by Tadmor (in: Tezduyar, Hughes T (eds) Proceedings of the winter annual meeting of the American Society of Mechanical Engineering 1986) back in 1986, where recall that velocity is part of the entropy variable for the shallow water equations. Due to the use of velocity as an independent solution unknown, no specific numerical quadrature rules are needed to achieve entropy stability of our scheme on general unstructured meshes in two dimensions. The proposed DG semi-discretization is then carefully combined with the classical explicit strong stability preserving Runge–Kutta (SSP–RK) time integrators (Gottlieb et al. in SIAM Rev. 43, 89–112, 2001) to yield a locally conservative, well-balanced, and positivity preserving fully discrete scheme. Here the positivity preservation property is enforced with the help of a simple scaling limiter. In the fully discrete scheme, we re-introduce discharge as an auxiliary unknown variable. In doing so, standard slope limiting procedures can be applied on the conservative variables (water height and discharge) without violating the local conservation property. Here we apply a characteristic-wise TVB limiter (Cockburn and Shu in J Comput Phys 141:199–224, 1998) on the conservative variables using the Fu-Shu troubled cell indicator (Fu and Shu in J Comput Phys 347:305–327, 2017) in each inner stage of the Runge–Kutta time stepping to suppress numerical oscillations. This fully discrete can be readily applied to various SWEs simulations without dry areas where the water height is close to zero. The case with dry areas need further special attention, where the velocity approximation can be unphysically large near cells with a small water height, which may eventually crashes the simulation if no special treatment is used near these cells. Here we propose a simple wetting/drying treatment for the velocity update without violating the local conservation property to enhance the robustness of the overall scheme. One- and two-dimensional numerical experiments are presented to demonstrate the performance of the proposed methods.

Parametric Study on Abutment Scour under Unsteady Flow

Experimental results on scour at abutments under unsteady clear water flow condition are presented. Three shapes of short abutments (abutment length/upstream flow depth < 1) were tested, namely, rectangular/vertical wall, semi-circular, and trapezoidal/45° wing-wall abutments embedded in uniform sands of two sizes having d50 = 0.52 mm and 0.712 mm. The unsteadiness of the flow is considered in the form flood hydrographs of three forms, namely: advanced flood hydrograph (Type I), symmetrical flood hydrograph (Type II), and delayed flood hydrograph (Type III) with the flow maintained at clear water condition in all cases. The experimental findings are used to represent the influence of various parameters on scour depth at bridge abutments. It was observed that the scour depth at rectangular abutments is greater than that at trapezoidal and semi-circular abutments. The scour depths at abutments embedded in finer sediments are greater than those in coarser sediments. In addition, based on the study of effect of three flood hydrographs, it was noticed that the delayed flood hydrograph yields greater scour depth as compared to the other two cases. Further, based on the method of superposition and the correction of shape factor, a semi-empirical model using dimensionless parameters is proposed to compute the temporal evolution of scour depth at abutments under unsteady clear water conditions. The parameters used in this model include flow shallowness, flow intensity, sediment coarseness, and time factor. It was found that the proposed model corresponds well with the data of time-dependent scour depth in uniform sediments obtained from the present experiments (unsteady flows) and reported by different investigators (steady flows).

Theoretical Foundations for Calculating the Erosion of Soil Dams during Overflow of Water over the Ridge

Large-scale hydraulic engineering construction associated with the erection and operation of large dams and reservoirs has an impact on the ecosystem and physical and geographical characteristics of the construction area. In addition, during the passage of catastrophic floods and high waters, the danger of a hydrodynamic accident increases, i. e. overflow of reservoirs, overflow of masses over the ridge of an earthen dam and its destruction, accompanied by the formation of a closure channel and the outflow of an unsteady water flow through it into the lower reaches in the form of a breakthrough wave. The process of erosion of an underground dam due to the overflow of water over the ridge can be divided into two stages. During the first one, the lower slope is eroded, along which the water moves as if by a rapid current. The profile of the dam, initially trapezoidal, by the end of the erosion takes a shape close to triangular, and the ridge mark on the side of the upper slope remains constant. The second stage is characterized by an intensive reduction of the ridge; the dam quickly takes the form of a practical profile spillway, which persists until the end of erosion. At the same time, there is an intensive expansion of the closure channel. As the analysis showed, the existing mathematical models used to calculate the dynamics of the erosion of the dam, especially its first stage before the expansion of the closure channel, are not perfect. The article presents a refined methodology developed by the authors for modeling the process of erosion of ground dams during water overflow over the ridge. The calculations made in accordance with this methodology make it possible to construct a flow hydrograph in the location of the eroded dam. The methodology can be used in the development of project documentation at the first stage of dam design, as well as in determining the forecast quantitative and qualitative characteristics of the water regime of reservoirs.

Two-phase Flow Model and Productivity Evaluation of Gas and Water for Dual-Medium Carbonate Gas Reservoirs

Fluid flow in the dual-medium carbonate gas reservoir is characterized by stress sensitivity and non-Darcy flow effect. In order to accurately describe the unsteady flow of gas and water in the dual-medium gas reservoir, a two-phase flow model of gas and water is built. First, reservoir space and fluid flow characteristics of carbonate gas reservoirs are investigated, and the flow model that considers both the stress sensitivity and non-Darcy flow is built based on the fundamental flow theory, after fully investigating the reservoir space and fluid flow characteristics of carbonate gas reservoirs. Then, the perturbation theory is introduced, and the model is solved in the Laplace space, after which the obtained Laplace space analytical solution is converted into the real-space solution. Finally, the productivity evaluation model for the dual-medium gas reservoir with the gas-water two-phase flow is built, based on the flowing material balance method and Newton iteration. The presented productivity evaluation model is applied to analyze the effects of stress sensitivity and non-Darcy flow on the two-phase flow model of gas and water for the dual-medium gas reservoir and the reservoir productivity. The results indicate that a higher stress sensitivity coefficient is demonstrated to indicate higher stress sensitivity and accelerated production decline of the reservoir, while a lower non-Darcy flow effect coefficient represents a stronger non-Darcy effect and boosted drop of initial production of the reservoir. Hence, it is not reasonable to neglect the effects of stress sensitivity and non-Darcy flow during the evaluation of the productivity of a dual-medium carbonate gas reservoir. The model presented in this research provides important references for improving the recovery performance of dual-medium gas reservoirs.

Numerical Analysis of a New Type of Dishwasher Pump for Different Rotation Speeds of the Volute

The interaction between impeller and volute produces a complex and unsteady water flow. It involves the interference of the non-uniform flow (such as the impeller’s jet wake and a secondary flow). In this paper, the transient flow in a new type of dishwasher pump is investigated numerically. In addition, pressure measurements are used to validate the numerical method, and the simulation results agree well with the experiment. Three schemes, 0 rpm (revolutions per minute)/30 rpm/60 rpm, of volute speeds are investigated. Multiple monitoring points are set at different positions of the new dishwasher pump to record pressure-pulse signals. In addition, frequency signals are obtained using a Fast Fourier Transform, which is then used to analyze the effect of the volute tongue and the outflow of the impeller. The radial force on the principal axis is recorded, and the schemes with different rotation speeds of volute are compared. The results show that the volute speed has only a small effect on the pump performance. In addition, the speed of the volute mainly affects the flow field in the transition section located between impeller and volute. The difference of the flow field in the impeller depends on the relative position between the impeller and the volute. The time domain curve for the pressure pulse is periodic, and there is a deviation between the peak for the schemes in the outflow region. In the frequency domain, the characteristic frequency equals the blade passing frequency. In the outflow region, the effect of the volute speeds increases with increasing volute speed. For the radial force, the rotating volute strengthens the fluctuation of the radial force, which affects the operational stability of the pump. The shape of the vector distribution is most regular for the 30 rpm scheme, which indicates that the stability of the pump is the highest. This paper can be used to improve both the control and selection of volute speeds.

Simulation of Unsteady Movement in the Downstream of a Hydroelectric Complex During the Destruction of a Soil Dam

153 reservoirs have been created in the Republic of Belarus. During the period of passing catastrophic floods and high waters along the river, there is a risk of overflowing reservoirs, overflow of water masses through the crest of an earthen dam and flooding of significantly large areas. The destruction of the dam is accompanied by the formation of a breach and the outflow through it of an unsteady flow of water in the form of a breakthrough wave into the downstream. A breakthrough wave and catastrophic flooding of the area are the main destructive factors of hydrodynamic accidents. Calculations to determine parameters of the wave and to assess the possible consequences of flooding are necessary when drawing up operational-and-tactical plans for the prevention and elimination of emergencies in case of accidents at retaining structures, determining the probable damage from flooding of the territory in the downstream of a hydraulic structure as a result of the passage of a breakthrough wave. It is necessary to assess the flooding zone and the hydrodynamic parameters of the flow, viz. the maximum values of the depth and velocity of the flow in the zone of catastrophic flooding, the time from the beginning of the accident to the arrival of a breakthrough wave at the particular point of the terrain, the duration of flooding, the boundaries of the zone of catastrophic flooding, the hydrographic flow rate in the section of the eroded dam and the graph of the fall headwater level. The degree of reliability of predictive calculations is determined by the accuracy of the two applied mathematical models, viz.: 1) erosion of the dam; 2) the movement of the breakout wave. The analysis of the applied mathematical models shows that in all cases the hydrodynamic models based on the oneand two-dimensional equations of Boussinesq – Saint-Venant are used to calculate the movement of the breakthrough wave. Wave parameters, i. e. wave height and speed of its propagation, completely depend on the hydrograph of the discharge in the section of the eroded dam, which, in its turn, is determined by the dynamics of its erosion. The aim of the work is to develop a methodology for calculating the flooding of the downstream as a result of the destruction of a soil dam.

A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation

In hydrodynamics (hydraulics), there are numerous approaches to solving the problem of water flow dynamics control in river beds and channels, while the results of each methods differ, and estimates of their reliability do not always exist. The shallow water equation (or Saint-Venant's equations in one-dimensional form) is often used by hydraulic engineers in their practice.  Its apparent simplicity and ability to describe well enough the behavior of rivers and flows make it a useful tool for many applications, such as the regulation of navigable rivers and irrigation networks in agriculture. The main direction of research in the field of numeric problems described by Saint-Venant equations is the development of numerical methods of computation implemented on super-powerful computers. Development of numerical models of surface water dynamics in the shallow water approximation is actively advancing during the recent years. The article is devoted to a review of mathematical studies of the dynamics of processes in unsteady water flows using differential equations, as well as an assessment of these approaches from the point of view of the model's reflection of real processes. The work is aimed at analyzing different approaches to modeling the dynamics of processes in non-stationary water flows. The objectives of the study include the analysis of scientific publications with different approaches to modeling the shallow water equation, taking into account factors, parameters, and modeling methods.

On Thermodynamically Compatible Finite Volume Methods and Path-Conservative ADER Discontinuous Galerkin Schemes for Turbulent Shallow Water Flows

In this paper we propose a new reformulation of the first order hyperbolic model for unsteady turbulent shallow water flows recently proposed in Gavrilyuk et al. (J Comput Phys 366:252–280, 2018). The novelty of the formulation forwarded here is the use of a new evolution variable that guarantees the trace of the discrete Reynolds stress tensor to be always non-negative. The mathematical model is particularly challenging because one important subset of evolution equations is nonconservative and the nonconservative products also act across genuinely nonlinear fields. Therefore, in this paper we first consider a thermodynamically compatible viscous extension of the model that is necessary to define a proper vanishing viscosity limit of the inviscid model and that is absolutely fundamental for the subsequent construction of a thermodynamically compatible numerical scheme. We then introduce two different, but related, families of numerical methods for its solution. The first scheme is a provably thermodynamically compatible semi-discrete finite volume scheme that makes direct use of the Godunov form of the equations and can therefore be called a discrete Godunov formalism. The new method mimics the underlying continuous viscous system exactly at the semi-discrete level and is thus consistent with the conservation of total energy, with the entropy inequality and with the vanishing viscosity limit of the model. The second scheme is a general purpose high order path-conservative ADER discontinuous Galerkin finite element method with a posteriori subcell finite volume limiter that can be applied to the inviscid as well as to the viscous form of the model. Both schemes have in common that they make use of path integrals to define the jump terms at the element interfaces. The different numerical methods are applied to the inviscid system and are compared with each other and with the scheme proposed in Gavrilyuk et al. (2018) on the example of three Riemann problems. Moreover, we make the comparison with a fully resolved solution of the underlying viscous system with small viscosity parameter (vanishing viscosity limit). In all cases an excellent agreement between the different schemes is achieved. We furthermore show numerical convergence rates of ADER-DG schemes up to sixth order in space and time and also present two challenging test problems for the model where we also compare with available experimental data.

Two-dimensional (2D) numerical modelling of rainfall induced overland flow, infiltration and soil erosion: comparison with laboratory rainfall-runoff simulations on a two-directional slope soil flume

Abstract This paper presents a two-dimensional (2D) numerical model of soil erosion and sediment transport resulting from rainfall induced overland flow. It is a spatial and temporal dynamic model combining physical and empirical laws and comprises: i) An overland flow module that solves the two-dimensional unsteady water flow equations on an infiltrating surface; ii) A soil infiltration module that uses a combined Horton-SCS scheme; and iii) A soil erosion and sediment transport module that solves the two-dimensional sediment transport equation, distinguishing between rill erosion, interrill erosion and sediment deposition. The performance of the model was evaluated by comparing its results with observed data from laboratory rainfall-runoff experiments on a two-directional 2.00 × 2.00 m2 soil flume set at 1% and 10% slopes in the x- and y-directions, respectively. The x-direction produced remarkably lower runoff and transported sediments than the y-direction. The numerical model significantly underestimated x-direction lower values of runoff and transported sediments. However, in the y-direction the model presented very good performance. Overall, in total terms (x- plus y-direction), the numerically simulated graphs of runoff and sediment transport were in very good agreement with corresponding experimental measurements, demonstrating the laboratory proof-of-concept of the model.

Modelling of Thin CNTs Nanoliquid Film Flow Over a Bi-directional Stretching Surface

Unsteady flow of water and ethylene-glycol based carbon nanotubes (CNTs) nanoliquid film is examined on a bi-directional stretching surface under influence of transverse magnetic field and thermal radiation. Single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) are considered within the base liquid for investigation. Guiding full Navier–Stokes and energy equations were simplified using the thin film approximations and solved using the method of the asymptotic expansion. The result shows that nanoliquid thinning rate diminishes with rising values of CNTs volume fraction, Hartmann number and Biot number. The result also indicates that the thinning rate is more for MWCNTs with reference to the SWCNTs. It is seen that film thinning rate enhances for water-MWCNTs nanoliquid but reverse scenario is found for ethylene-glycol MWCNTs nanoliquid. The effect of various physical parameters on temperature profile has been discussed.

Propulsive forces on water polo players’ feet from eggbeater kicking estimated by pressure distribution analysis

ABSTRACT The purpose of this study was to characterise the unsteady propulsive force during eggbeater kicking by a fluid force estimation method based on pressure distribution analysis. The eggbeater kick was performed by six male water polo players. The participants’ eggbeater kicking motions were recorded by three cameras, and the kinematic foot variables were analysed. The pressure distributions around the foot were measured by four pairs of pressure sensors attached to the dorsal and plantar surfaces of the participants’ right foot. The resultant fluid force acting on the foot was estimated from the measured pressure and area of the foot. The calculated propulsive force increased with the pressure difference between the plantar and dorsal sides of the foot, which was mainly related to the decrease in pressure on the dorsal side, and peaked when the foot passed its maximum velocity and began to decelerate. These results cannot be elucidated only by conventional biomechanical theories of swimming propulsion (Newton’s laws of motion and the quasi-steady approach) but instead indicate a high possibility that the exerted propulsive force is induced by the effects of unsteady water flow.