Hydraulic Equations Research Articles

On Singular Perturbation of Neutron Point Kinetics in the Dynamic Model of a PWR Nuclear Power Plant

This short communication makes use of the principle of singular perturbation to approximate the ordinary differential equation (ODE) of prompt neutron (in the point kinetics model) as an algebraic equation. This approximation is shown to yield a large gain in computational efficiency without compromising any significant accuracy in the numerical simulation of primary coolant system dynamics in a PWR nuclear power plant. The approximate (i.e., singularly perturbed) model has been validated with a numerical solution of the original set of neutron point-kinetic and thermal–hydraulic equations. Both models use variable-step Runge–Kutta numerical integration.

An integrated MILP model for optimal planning of multi-period onshore gas field gathering pipeline system

Onshore gas field gathering pipeline system (GPS) plays a key role in the onshore gas field production and is often constructed in stages due to the phased development of the gas field. However, the influence of phased development on the optimal design of GPS has been neglected in previous studies. Although some research on the optimization of gas field development strategy involves the multi-period construction of GPS, they simplify the characteristics of the gathering network and ignore some very important parameters.This study develops an integrated mixed-integer linear programming (MILP) model for optimizing multi-period GPS to determine the central processing facility (CPF) location, pipeline (routes and diameters) installation and expansions, well site-CPF connections, the flowrate of each pipeline, and the operating pressure of each node in each time period simultaneously. Taking minimum total construction cost as the objective function, the proposed model considers various operational and technical constraints related to multi-period construction and hydraulic characteristics, such as obstacles, three-dimensional terrain, pipeline topological structures, pipeline diameters, and wellhead pressure. Ant colony optimization is used for route optimization to provide parameters for the proposed model. A piecewise approximation method is employed to deal with the nonlinear terms of hydraulic equations. Therefore, the MILP model can be solved by the branch-and-bound algorithm to obtain the global optimal solution integrally. Finally, the model is successfully applied to three real-world gas fields. Compared with the actual construction scheme and other literature methods, the results prove the superiority of multi-period planning considering time.

CFD modeling of an industrial scale two-fluid nozzle fluidized bed granulator

A 3D computational fluid dynamic modeling of atomization and fluidization of urea was simulated in an external mixing, bottom spray, fluidized bed granulator. The Eulerian–Lagrangian approach was used to predict the mean diameter of melt urea droplets similar to the droplets produced by an industrial scale two-fluid nozzle under hot atomized air. Temperature changes and evaporation of water content from droplets were determined during simulations. Furthermore, three-phase fluidization was simulated in the Eulerian approach whereby the bed expansion of the granulator was predicted. The mean diameter of droplets and bed height were found in good agreement with the empirical correlation and the real bed height, as characterized by a level transmitter instrument in the industrial granulator, respectively. The important features of this study included solving mass, heat and hydraulic equations simultaneously, as well as simulating a real urea fluidized bed granulation unit.

On Singular Perturbation of Neutron Point Kinetics in the Dynamic Model of a PWR Nuclear Power Plant

This short communication makes use of the principle of singular perturbation to approximate the ordinary differential equation (ODE) of prompt neutron (in the point kinetics model) as an algebraic equation. This approximation is shown to yield a large gain in computational efficiency without compromising any significant accuracy in the numerical simulation of primary coolant system dynamics in a PWR nuclear power plant. The approximate (i.e., singularly perturbed) model has been validated with a numerical solution of the original set of neutron point-kinetic and thermal–hydraulic equations. Both models use variable-step Runge–Kutta numerical integration.

The development of TM2-RIA code for TRIGA type research reactors

This work presents the development of indigenous code TM2-RIA for steady-state and transient analyses of TRIGA type research reactor at Istanbul Technical University Energy Institute. The 2-dimensional code adapts piecewise constant function for solving point kinetics equation linked with thermal–hydraulic equations for cylindrical fuel type. TM2-RIA provides flexibility of implementing different delayed neutron parameters, it also offers different thermal-hydraulics structure options (number of channels and control volumes). The code is tested against the experimental data and calculations of EUREKA-2/RR code. Considering many experimental uncertainties, the TM2-RIA 5-channels model agrees acceptably with the steady-state experimental results. In the transient analyses, three pulsing scenarios are investigated, based on the results, the code has performed differently with different neutronic sets and thermal-hydraulics structures. That indicates how the reactor kinetics is being influenced by the differences in the recorded thermal history, and it shouldn’t be neglected even for small deviation. Besides, the constant overestimation of the fuel temperatures implies the need for modelling the heat sink induced by central Zirconium rod in fuel element and investigating its effect. That being said, the code agrees fairly well in many cases corresponding to those changes, when it predicts the peak power and fuel centerline temperature. Moreover, the gap between the experimental and the numerical results for the fuel temperature gets smaller with the increase of the pulsing reactivity. Another promising aspect is that the adapted point kinetics approach shows similar performance, in comparison with the common Cohen’s approach used by EUREKA-2/RR, while providing relative simplicity in developing and implementing the TM2-RIA code.

A new method for determining the hydraulic aperture of rough rock fractures using the support vector regression

Understanding fluid flow in rock fractures is relevant to many engineering applications, including underground nuclear waste disposition, oil and gas exploitation, dam and slope design, as well as contaminant transport. Rough rock fracture is usually idealized as two parallel plates separated by the hydraulic aperture, the determination of which is key to solving seepage problems in fractured rock using the cubic law. The mechanical aperture and fracture morphology are the main aspects affecting the hydraulic aperture. Here, an innovative hydraulic aperture prediction equation for two-dimensional fractures is established based on the mechanical aperture and fracture morphology. Six parameters were firstly selected to predict the hydraulic aperture, including three mechanical aperture parameters and three fracture morphology parameters. A training database was then established from numerical experiments of 300 fracture models, which were built based on Barton's 10 standard profiles and their combinations. The numerical experiments were conducted with FLUENT software. Based on the database, a hydraulic aperture prediction model was established using the support vector machine theory and the particle swarm optimization algorithm, which was transformed into an explicit equation. Finally, 20 natural fractures were used to validate the performance of this equation, with the comparisons of four existing empirical equations. The results show that this method worked well in predicting the hydraulic aperture. This method provides an alternative and effective way to directly determine the hydraulic aperture using the geometry information of rough rock fractures.

Development of the formulas for estimating the travel time of rainwater slope runoff and channel flow for the anthropogenic territories of small catchment basins

The article presents developed formulas for estimating the travel time of rainwater slope runoff and channel flow based on a unified schematization of mixed catchment basins with wide anthropogenic territories together with diversion channels. The estimation of common travel time for the rainwater overland flow on the adjacent watershed and further along the diversion channel is derived by modeling the catchment basins preserving their natural configurations. The necessary hydrological and hydraulic equations for describing the unsteady rainwater slope runoff and channel flow formation are chosen and proposed taking into consideration the proper factors affecting the flow. When developing a general formula for calculating the preliminary total travel time of the slope and channel flow have been taken into consideration the proper patterns of rainwater runoff on the inclined surfaces and stepped sectors applicable for estimation of the unsteady slope runoff and channel discharge (flow rate) in case of using the differential equations of one-dimensional hydraulics. The developed formula can be used for determining the travel time in predicting rainwater runoff for designing the system of road surface drainage and culverts facilities in mixed catchment basins with terraced paddy fields and other slope areas. Authors have proposed some recommendations and drawn the relevant conclusions.

New dynamic two-layer model for predicting depth-averaged velocity in open channel flows with rigid submerged canopies of different densities

The depth-averaged velocity is the commonly used engineering quantity in natural rivers, and it needs to be predicted in advance, especially in flood seasons. A model that can provide a unified physical foundation for open channel flows with different canopy densities remains lacking despite ongoing researches. Here, we use the concept of the auxiliary bed to describe the influence of momentum exchange on rigid canopy elements with varying density and submergence. The auxiliary bed divides the vegetated flow into a basal layer and a suspension layer to predict average velocity in each layer separately. In the basal layer, the velocity profile is assumed to be uniform. In the suspension layer, a parameter called “penetration depth” is applied to present the variations in velocity distribution. We also apply a data-driven method, called genetic programming (GP), to derive Chezy-like predictors for average velocity in the suspension layer. Compared to the hydraulic resistance equation for rough-wall flows, the new formulae calculated by the weighted combination method show sound physical meanings. In addition, comparison with other models shows that the new dynamic two-layer model achieves high accuracy in flow rate estimation, especially for vegetated flow with sparse canopies.

Water Irrigation Decision Support System for Practical Weir Adjustment Using Artificial Intelligence and Machine Learning Techniques

This research proposes a decision support system for weir sluice gate level adjusting. The proposed system, named AWARD (Appropriate Weir Adjustment with Water Requirement Deliberation), is composed of three modules, which are (1) water level prediction, (2) sluice gates setting period estimation, and (3) sluice gates level adjusting calculation. The AWARD system applies an artificial neural network technique for water level prediction, a fuzzy logic control algorithm for sluice gate setting period estimation, and hydraulics equations for sluice gate level adjusting. The water requirements and supplies are deducted from the field-survey and telemetry stations in Chiang Rai Province, Thailand. The results show that the proposed system can accurately estimate the water volume. Water level prediction shows high accuracy. The standard error of prediction (SEP) is 2.58 cm and the mean absolute percentage error (MAPE) is 7.38%. The sluice gate setting period is practically adjusted. The sluice gate level is adjusted according to the water requirement.

COMPARISON OF ENERGY CONSUMPTION OF VARIOUS ELECTRICAL MOTORS OPERATING IN A PUMPING UNIT

Purpose. Comparative analysis of energy consumption of various types electric motors in fixed speed centrifugal industrial pump applications is carried out. The purpose of the analysis is to choose the most efficient motor in the considered application. It is assumed that hydraulic flow of the pump is adjusted by throttling. The rated power of the pump unit is 2.2 kW. Direct on line motors of various energy efficiency classes from various manufacturers are considered: induction motors with permanent magnets on the rotor of IE4 class and squirrel cage induction motors of IE3 and IE4 classes. Methodology. Assessment of energy consumption of the motors is carried out based on the catalogue data from manufacturers of the pump and the motors. Pump hydraulic equations, interpolation of motor catalogue data and statistical data are also used. Results. The following values have been obtained: annual and daily energy consumption of the motors and electricity cost savings comparing with the least effective motor considered. Practical value. The following practical consideration are presented based on the theoretical results: choosing the motor based only on its IE efficiency class according to IEC 60034-30-1 is not enough to ensure the minimum energy consumption of pump units with variable flow during the load cycle. In addition, the energy consumption may be higher in the case of permanent magnet motors of IE4 class in comparison with induction motors of IE4 or even IE3 class. Therefore, it is necessary to take into account efficiency of the motors at underload and it is needed to calculate the energy consumption during the actual load cycle. It should be noted, that the existing approach based on the Energy Efficiency Index (EEI) calculation does not provide information about absolute values of energy savings and cost savings, in contrast to the described approach. While choosing motors to run in the considered application it is also important to take into account that the motors with permanent magnets on the rotor have significantly higher price and very restricted starting capabilities comparing with induction motors. In addition, the production of rare earth magnets causes a significant environmental damage.

Downstream hydraulic geometry across headwater channels in Upper Ogun River Basin, Southwestern Nigeria

ABSTRACT Hydraulic geometry is widely applicable in different environments and is quite essential across different channel units. In this study, downstream hydraulic geometry was used to ascertain differences in exponents across headwater channels within a Basement Complex in a humid tropical region. This study was conducted within the Upper Ogun River Basin, Southwestern Nigeria. The basin is approximately 200 km in length and 140 km wide. Eighty-three (83) reaches were sampled across third-order basins within the Upper Ogun River Basin. Hydraulic geometry variables were measured and derived at bankfull using appropriate techniques and basic hydraulic equations, respectively. For the six-individual basins covered, it was found that the exponents (b, f and m) of the downstream hydraulic geometry relations for Qbf covered a range of: b = −0.12–0.51; f = 0.44–0.67; m = 0.04–0.46. The channels of four basins out of six becomes progressively narrowed and deepened downstream while that of the remaining two becomes progressively wider and shallower downstream.

Back Analysis of the Initial Geo-Stress Field of Rock Masses in High Geo-Temperature and High Geo-Stress

In a high geo-temperature environment, it is rarely reported that geo-temperature has been considered during a back analysis. This may cause the initial geo-stress field that is obtained by a back analysis to be wrong. In this study, according to the theory of elasticity, the theoretical solution of the hydraulic fracturing equation is obtained in a high geo-temperature environment. Since the vertical stress that is obtained by the hydraulic fracturing method is calculated using the density of overlying strata, this vertical stress lacks the thermal stress that is caused by geothermal gradients. Therefore, in a high geo-temperature environment, inverting the initial geo-stress field of rock masses directly using the stress that is measured by the hydraulic fracturing method can cause serious errors. We propose that the regression coefficient of a gravitational stress field should be set to one during a back analysis if stresses are measured by the hydraulic fracturing method, and this regression coefficient should not be equal to one if stresses are measured by overcoring methods. We also propose a workflow for the back analysis of the initial geo-stress field of rock masses that considers geo-temperature, and this workflow is applied to the Sangzhuling tunnel in China.

Optimization of water distribution networks using a deterministic approach

Water distribution networks (WDNs) are the main component of industrial and urban water distribution systems and are currently formed by pipes, nodes and loops. In this article, a deterministic mathematical programming approach is proposed, aiming to minimize the cost of looped WDNs, considering known pipe lengths and a discrete set of commercially available diameters. The optimization model constraints are mass balances in nodes, energy balances in loops and hydraulic equations, in such a way that no additional software is needed to find the appropriate pressure drops and water velocities. Generalized disjunctive programming is used to reformulate the discrete optimization problem to a mixed-integer nonlinear programming (MINLP) problem. The GAMS (General Algebraic Modeling System) environment is used to solve the problem. Four cases are studied to test the applicability of the model and the results show compatibility with the literature.

Morphology of Dune-Like Relief in Rivers

Linearized equations of two-dimensional hydraulics have been analyzed by the method of small perturbations within a wide range of alluvial features sizes at large values of Froude numbers and hydraulic resistance. The preservation of three-dimensional effects in depth-averaged equations of motion, continuity, and deformation enabled the authors to identify domains with combinations of flow hydraulic characteristics that correspond to alluvial features of different size and morphology. The study confirmed the results of the earlier analysis for subcritical flows with small hydraulic resistance and showed new types of relationships between alluvial features morphology and the hydraulic characteristics of flow for flows with large Froude numbers and high hydraulic resistance. In addition, a relationship between the length of two-dimensional ultramicroforms and hydraulic resistance has been established. A new class of macroforms—two-dimensional macroforms—have been identified. The verification of the results of theoretical analysis by measurements data on the morphology of channel formations and hydraulic characteristics of the flow has shown that the analysis of linearized equations of two-dimensional hydrodynamics by small-perturbation method can be used to determine the morphology and dimensions of channel forms in both subcritical and supercritical streams. The step–pool systems in torrential streams in mountain rivers are analogues of antidunes (in supercritical flows) and ripples (in subcritical flows), obtained in large flumes with sand alluvium. Three-dimensional macroforms are most common in rivers. If such macroforms are well developed in wide channels (at flow width greater than the half-width of the macroform), their length is determined by channel depth. Macroforms in narrower channels cannot develop completely, and their lengths are limited by channel width and can be calculated only through this width.

Pipelines Designing By Using Hydraulic Criteria Equations

This work intend an original methodology, newly established by the authors, to design typical pipe systems by using hydraulic criteria equations, excluding the determination of the relevant Darcy factor. Therefore, it can be eliminated the necessity for searching iterative solutions of such problems. The established equations are easy to use, in terms of mathematical processing, which guarantees their proper application in solving engineering problems. It is considered for the proposed physical relations (equations) concerning the determination of the pipe system resistance characteristics to be highly useful in engineering practice, as for example: in determining a hydraulic machine work regime, used in a system transporting fluids, as well as in performing a synthesis and analysis of such systems or in accomplishing an energy analysis of pipe systems. A comparative analysis between the results found after applying the classical methods of calculations and by using a licensed specialized software product indicates that a highly sufficient (for engineering calculations) overlapping is achieved.

Determination of Contours of Flooded Areas Due to Possible Accident of Zhinvali (Georgia) Earth Dam and Calculation of the Hydrodynamic Parameters of a Destructive Wave at a Dam

Using theoretical and field studies, computer software programs (VOLNA-4, and MIKE-21, ) and GIS technology, and taking into account the possible accident (destruction) of the Earth Dam with a height of 102 meters, the contours of the riverbed of flooded territories in riverbeds for rivers Aragvi and Mtkvari have been defined in the given article considering the configuration of the water-catchment basins of rivers. By means of basic differential equations of hydraulics, geometrical dimensions of Zhinvali Earth Dam, hydrological basic parameters of the reservoir, and computer software, the basic hydrodynamic parameters of the destructive wave at the Zhinvali Earth Dam are calculated taking into account the time of flow movement.

Pipe roughness identification of water distribution networks: The full turbulent case

This paper proposes a technique to identify individual pipe roughness parameters in a water distribution network by means of the inversion of the steady-state hydraulic network equations. By enabling the reconstruction of these hydraulic friction parameters to be reliable, this technique improves the conventional model’s accuracy and thereby promises to enhance model-based leakage detection and localization. As it is the case in so-called fireflow tests, this methodology is founded on the premise to measure the pressure distributed at a subset of nodes in the network’s graph while assuming the nodal consumption to be known. Beside of the proposed problem formulation, which is restricted to only allow turbulent flow in each of the network’s pipes initially, developed algorithms are presented and evaluated using simulation examples.

Simulation-Based Analysis of a Real Water Distribution Network to Support Emergency Management

Water distribution systems have a safety-critical role and are vulnerable to a range of intentional threats. Committing to emergency preparedness, critical and missing metrics are the residual water storage in tanks and the estimated operative autonomy (in hours). This article presents a high-fidelity simulator developed to calculate the mentioned metrics and to evaluate the impact of adverse events, such as faults and/or cyber-attacks on a real water distribution system. This simulator utilizes a refined model of the network for accurate results; a commercial simulator to trustworthily solve the hydraulic equations; and an ad-hoc module to follow the evolution in time of the event. A large real water distribution network has been modeled thanks to real data provided by an operator and used as a case study. A comprehensive impact analysis of the single failure has been carried out. Results show that the simulator has been able to elicit unforeseen use cases and correctly quantify the required metrics. This article has been implemented in the framework of the European project ATENA.

An integrated MILP method for gathering pipeline networks considering hydraulic characteristics

High investment highlights the importance of optimizing gathering pipeline networks. In view of the problem of ignoring hydraulic characteristics in previous studies, an integrated mixed-integer linear programming (MILP) model for gathering pipeline networks is developed in this study. Taking the minimum total construction cost as the objective function, the proposed model considers the economic and technical constraints such as obstacles, three-dimensional terrain, pipeline topological structures, pipe diameters, wellhead back pressure, and pressure equipment. The ant colony optimization algorithm is used for route optimization to provide parameters for the proposed model. Moreover, a piecewise method is employed to linearize the nonlinear hydraulic equations. Then, the model is solved by the CPLEX solver to obtain the optimal solution integrally, including the optimal connection topology, the location of the central processing facility, the position of pressure equipment, the diameter and detailed route of each pipeline, the pipeline flowrate and the node pressure. Finally, two real-world gas fields and a virtual oil field are taken as examples to demonstrate the feasibility and practicality of the model. The optimal results illustrate that this model can be implemented as a decision-support tool to optimize gathering pipeline networks in the actual design process.

Numerical Research of Flow Heat Transfer through Micro Channel of Mems Device

Micro-channel has been increasingly applied in MEMS devices and electronics devices due to its higher efficiently heat dissipation rate, more compact size and lower cost. The present work demonstrates that the theoretical analysis of single phase micro channel has been investigated. To predict the behavior of micro-channel, the non-linear thermal hydraulic equations are developed namely mass, momentum and energy conservation, these equations are solved to predict the thermal physical properties and hydrodynamic behavior of the fluid in micro-channel. The configuration geometry of the problem has been made in design modular of commercial software ANSYS 15.0 Workbench and meshing of it has been done in ANSYS 15.0 Workbench fluent. Water is used as the working fluid in the micro-channel and the problem has been solved in ANSYS 15.0. To analyze the thermal behavior of micro-channel in force convection for various input power. Numerical simulation is carried out to calculate the wall temperature of the micro-channel, heat transfer coefficient (HTC) values etc. Next more simulation have been performed to investigate the parametric effect on the circular micro channel in terms of different diameter and length, and optimize the geometric parameters and coolant flow rate to maintain the critical temperature of the MEMS device (geometry and thermodynamic performance of micro-channel).