Hydrodynamic Mathematical Model Research Articles

Data processing of field measurements of expedition research for mathematical modeling of hydrodynamic processes in the Azov Sea

This paper describes a three-dimensional mathematical hydrodynamic model capable of taking into account the processes of salt and heat transfer in the Azov Sea. The model allows obtaining three-dimensional fields of the vector of water flow rates, pressure, sea water density, salinity and temperature. The model is based on the equations of motion (Navier-Stokes), the continuity equation in the case of variable density, and the equations of heat and salt transport. The boundary and initial conditions are indicated. To approximate the equation of diffusion-convection-reaction in time, we analyzed the schemes with weights. The approximation of the problem of calculating the velocity field of the aquatic environment in terms of spatial variables was carried out on the basis of the balance method taking into account the occupancy ratios of the control areas. The stationary modes of the heat and salt transfer problem were investigated. The initial distribution of the salinity and temperature functions, which have a sufficient degree of smoothness at the points of setting the field values, was calculated using the Laplace equation. Using the interpolation algorithm and by superimposing the boundaries of the region, maps of salinity and temperature of the Sea of Azov were obtained. Based on the monitoring of the water area, three-dimensional mathematical models of the movement of the aquatic environment designed to predict possible scenarios for the development of the Azov Sea ecosystem were constructed in order to avoid the occurrence of anaerobic infection areas and take timely measures for their localization. The full-scale data obtained using different types of measuring instruments was used to develop observation models for prediction of the changes in hydrodynamic processes. A modified Kalman filter algorithm was applied to obtain unbiased minimum-variance state estimation for the dynamic system. A description is given of a software package that allows modeling hydrodynamic processes in shallow water bodies with complex spatial structures of currents, taking into account the transport of salts and heat.

Numerical study on influence of waterway regulation project, a case study of Minjiang

The waterway regulation project from Longxikou junction to Hejiangmen of Yibin, Minjiang River, is an urgent need for the construction of a comprehensive transportation hub in Western Sichuan Province. It plays a positive role in promoting the social and economic development of the economic region and has significant social benefits. A two-dimensional hydrodynamic mathematical model is established to study the variation characteristics of river water level and velocity before and after the implementation of waterway regulation project. The research ideas and results can provide reference for similar projects.

Design of a 1000 L pilot-scale airlift bioreactor for nitrification with application of a three-phase hydrodynamic mathematical model and prediction of a low liquid circulation velocity

In this study, a 1000L pilot scale internal loop airlift bioreactor was operated and compared to a mathematical model to determine the best design for optimal supply of oxygen for nitrification and sufficient air for biomass fluidization. The design model is based on parameters such as geometry, carrier density, and airflow of the 1000L pilot scale bioreactor. The model predicts a range of superficial air velocities (0.009–0.013m/s) under which the airlift bioreactor was fluidized. Three superficial air velocities (0.009m/s, 0.011m/s and 0.013m/s) were experimentally tested in the pilot plant and the obtained circulation velocities were compared with the predicted design scenarios. The predicted velocity was in agreement with the measured velocity. The aim of the mathematical model and the calculations of different geometry scenarios was to define the optimal geometry design for the physical model. The results show that the ratio of the cross-sectional area between the riser and the downcomer of 1.33 resulted in the lowest superficial liquid velocity of 0.076m/s in the riser at a relative low superficial air velocity of 0.011m/s and a carrier density of 1030kg/m3. This bioreactor design enabled longest retention time of particles in the oxygenated riser.

Development and Implementation of an Innovative Metal Receiver for a Slab CBCM Tundish

Features are considered for working conditions of slab CBCM tundishes on the example of the 27-ton unit of the oxygen-converter workshop of PAO Severstal’. Results are provided for mathematical modeling of hydrodynamics in a tundish with different turbulence dampers for the inlet stream. The designed, patented, and implemented metal receiver (brand REINSTREAM®) with a wavy inner surface is intended to improve continuously-cast billet quality, as well as providing increased stability and productivity due to the special design.

A framework to introduce urban flood resilience into the design of flood control alternatives

Urban flooding is still frequently treated as a direct consequence of excess rainfall, without considering the watershed as an interdependent system connected with the development of its territory. The traditional flood control approach implies in continuous corrective interventions, usually of local character, and resulting from post-events responses. This process requires increasingly large investments to implement (or retrofit) structures capable to accommodate the runoff generated by new urbanized areas. These efforts have not prevented floods from continuing to cause high damages worldwide. Thus, there is a need to change stormwater management strategies, shifting to a risk management approach, not only considering cost-benefit analysis, but also internalizing the residual risk accounting for inherent uncertainties, such as climate change and fast and uncontrolled urban growth. This paper proposes a multi-criteria index, the Urban Flood Resilience index-UFRI, to measure quantitatively urban resilience to floods, supported by a hydrodynamic mathematical model and socio-economic indicators, resulting in spatialized maps as a communicating tool. A case study of an urban watershed in Rio de Janeiro/Brazil is used to demonstrate UFRI potential.

Development and implementation of an innovative metal receiver for the intermediate ladles of caster slab

The features of the working conditions of intermediate ladles of caster slab are considered on the example of the 27-ton units of the oxygen-converter workshop of PJSC «Severstal». The results of mathematical modeling of hydrodynamics in an intermediate ladle with different turbulence dampers of the incoming jet are given. Designed, patented and implemented metal receiver (brand REYNSTREAM / REINSTREAM®) with a wave-like inner surface, designed to improve the quality of continuously cast billets, as well as providing increased stability and processability of the continuous casting process through a special design.. Ill. 6. Ref. 7.

Mathematical modeling of hydrodynamics and heat exchange in liquid channels of the thermoelectric cooling module

The article presents the results of the synthesis of the mathematical model of hydrodynamics of nonisothermic flow of heat-transfer fluid in channels bordering on the heat-absorbing surface of the thermoelectric cooler (TEC), based on the ANSYS CFX toolkit. The lengths of the unstabilized flow regions at the inlet and outlet of the channels were determined. The parameters of the non-uniform distribution of the coolant through the individual fluid channels were determined. A physical experiment was planned on the model of a local thermal stabilization system to determine the integral parameters of convective heat emission on the heat-absorbing and heat-generating surfaces of the TEC of a liquid-air circuit. The regression dependence of the heat-transfer coefficient on the heat-absorbing surface of the TEC on the determining parameters was found.

Simulation of induction heating technology for the production of seamless large diameter tees

The article is dedicated to nonstationary simulation of induction heating technology for the production of seamless large diameter tees. A mathematical model of induction heating process representing a multi-physical (heat transfer and electromagnetism) task for technology of tees production is developed. Numerical simulation was carried out for a flat spiral inductor. The developed model was verified according to the results of experimental studies. The hydrodynamic 3D mathematical model is developed for the design of the inductor cooling system. Optimal operating modes are determined by simulation results and confirmed by experimental data. The calculation results are presented for pipes with wall thicknesses: 15 mm, 40 mm, 60 mm, 70 mm.

Spectral Problem for a Mathematical Model of Hydrodynamics

Spectral Problem for a Mathematical Model of Hydrodynamics

Oil spill at sea based on non-hydrostatic three-dimensional hydrodynamic mathematical model

Oil spill at sea based on non-hydrostatic three-dimensional hydrodynamic mathematical model

PECULIARITIES OF MATHEMATICAL MODELING OF THE FLOW WHEN SELECTING THE GENERAL SIZES OF A BRIDGE CROSSING WITH GROUP HOLES

The problems of mathematical modeling of hydrodynamics of open flows are analyzed in the article when general sizes of bridge crossings with group holes are assigned. Most of the existing methods for calculating branched flows are based on the use of one-dimensional models, it does not allow to describe sufficiently the hydrodynamic processes occurring in zones with separated flows. Therefore, in the calculation of bridge crossings with group holes, two-dimensional models that take into account the features of the morphology of natural watercourses, the uneven distribution of the average velocities along the vertical, the phenomenon of flow separation, as well as the change in rate along the flow due to the separation of the flow is suggested. The existing experimental and theoretical studies are analyzed, the flow structure and the physical model of the flow branching process in the zone of influence of bridge crossings with group holes are considered. Based on the fundamental equations of flow transfer, a mathematical two-dimensional model of the flow of open flows is presented, which takes into account the influence of secondary currents. To substantiate the zone of influence of bridge crossings with group holes, an equation for vorticity is proposed that reflects the distribution of vortex structures. For the closure of the equations of motion and continuity, algebraic relations for the Reynolds stresses in conjunction with the two-parameter k-ε model for depth-averaged values are used, which is modified to take into account the effect of the curvature of the flow. The method of numerical realization of the proposed mathematical model is based on the predictor-corrector method using the McCormack scheme, modified by splitting the model equations with respect to spatial coordinates and time. The method of successive upper relaxation based on the Gauss-Seidel iterative method is used to realize the algebraic relations of turbulent stress transfer. The conclusion is made about the expediency of practical application of this model

Modeling sediment transport with an integrated view of the biofilm effects

AbstractMost natural sediment is invariably covered by biofilms in reservoirs and lakes, which have significant influence on bed form dynamics and sediment transport, and also play a crucial role in natural river evolution, pollutant transport, and habitat changes. However, most models for sediment transport are based on experiments using clean sediments without biological materials. In this study, a three‐dimensional mathematical model of hydrodynamics and sediment transport is presented with a comprehensive consideration of the biofilm effects. The changes of the bed resistance mainly due to the different bed form dynamics of the biofilm‐coated sediment (biosediment), which affect the hydrodynamic characteristics, are considered. Moreover, the variations of parameters related to sediment transport after the biofilm growth are integrated, including the significant changes of the incipient velocity, settling velocity, reference concentration, and equilibrium bed load transport rate. The proposed model is applied to evaluate the effects of biofilms on the hydrodynamic characteristics and sediment transport in laboratory experiments. Results indicate that the mean velocity increases after the biofilm growth, and the turbulence intensity near the river bed decreases under the same flow condition. Meanwhile, biofilm inhibits sediment from moving independently. Thus, the moderate erosion is observed for biosediment resulting in smaller suspended sediment concentrations. The proposed model can reasonably reflect these sediment transport characteristics with biofilms, and the approach to integration of the biological impact could also be used in other modeling of sediment transport, which can be further applied to provide references for the integrated management of natural aqueous systems.

Modeling of the process of oilseed meat cooking in a multi-vat cooker during processing of oil raw materials

A new method for determining design and technological parameters and the number of cooker vats for the moisture-thermal oilseed meat treatment has been proposed. The peculiarity of this technique is that the set values of the mean and mean-square oilseed meat moisture were taken as the criteria for the validity of the calculated data. A mathematical model of hydrodynamics of motion of the oilseed meat particles in the cooker vat was developed as a single process of motion of the oilseed meat fluxes along the horizontal concentric circles and along the vertical (meridian) ones traversing the vat axis. The basis of the model is the differential equation of particle motion along the blade rotating around the axis over the heated bottom of the cooker vat. The equation takes into account the design features of the stirrer, speed of blade rotation, length of the blades and physical characteristics of the oilseed meat expressed in terms of friction coefficients. Solution of the equation makes it possible to determine velocity of the particle in the direction of the blade and the circumferential velocity, the time of motion along the blade. This is the initial data for the axial movement of the oilseed meat. The time of passage of the oilseed meat along the agitator blade makes it possible to justify conditions of conductive heat exchange. The time of passage along the vat axis makes it possible to justify the conditions of convective heat exchange. A discrete model of the moving contact layer of the oilseed meat at the hot surface of the vat bottom was developed. Moisture content of the oilseed meat was described by a matrix in which the number of rows is equal to the number of elementary layers and the number of columns is equal to the number of elementary time intervals. The mass of the dry oilseed meat substance is determined by the row vector of the matter mass in the thick layer. Thermal balance of conductive and convective heat and mass transfer of the oilseed meat drying process has been compiled taking into account the heat spent for removal of the bound moisture from the solid phase which will ensure more accurate calculation of the technological conditions of cooking.

Spectral Problems for One Mathematical Model of Hydrodynamics

Spectral problems of the form $ (T + P) u = \lambda u $ have a huge range of applications: hydrodynamic stability problems, elastic vibrations of a membrane, a set of possible states of systems in quantum mechanics, and so forth. The self-adjoint operators perturbed by bounded operators are most thoroughly studied. In applications, the perturbed operator is usually represented by the Sturm~--~Liouville or Schrodinger operator. At present moment, the researchers are very interested in the equations not solved with respect to the highest derivative $ L \dot {u} = T u + f $, which are known as Sobolev type equations. The study of Sobolev type equations leads to spectral problems of the form $ T u = \lambda L u $. In many cases, the~operator~$ T $ can be perturbed by an operator $ P $, and then the spectral problem takes the~form \mbox{$ (T + P) u = \lambda L u $.} The study of such problems allows to construct a solution of the equation, as well as to investigate various parameters of mathematical models. Previously, such spectral problems with the perturbed operator were not studied. In this paper, we propose the method for investigating and solving the direct spectral problem for a hydrodynamic model.

Numerical investigation on hydraulic performance of backward bend duct buoy

A 3-D mathematical hydrodynamic model was conducted to investigate the regular wave motion on the backward bend duct buoy (BBDB), and it was validated with the theoretical wave surface well. It was used to compute the wave heights in the gas chamber and after the BBDB. It was found that the wave transmission coefficient in the gas chamber increased firstly and then decreased with increasing horizontal duct height or the gas chamber length respectively. However, it after the BBDB decreased firstly and then increased with increasing horizontal duct height or the gas chamber length respectively. The gas chamber length plays a more important role in wave transmission coefficient in the gas chamber than horizontal duct height does. The flow rate per unit width increased firstly and then decreased with the increasing horizontal duct height or gas chamber length respectively.

A hydrogeological model of the open-cast mine Tamnava-West Field (Kolubara Coal Basin, Serbia)

The Kolubara Coal Basin is the largest coal-producing area in Serbia. It is administratively comprised of several open-cast mines: Field A, Field B, Field C, Field D, Field E, Field F, Field G, Veliki Crljeni, Sopic-Lazarevac, Tamnava - West Field, Tamnava - East Field, Radljevo, Zvizdar, Ruklade, and Trlic. The paper focuses on the largest active open-cast mine: Tamnava - West Field. A study and conclusions about the hydrogeologic functions of the lithologic strata, and insight into their spatial interactions, are extremely important for hydrogeologic modeling of a given area. The main purpose of a hydrogeologic model is to derive conclusions about the spread of the aquifers in the study area, their interactions, and groundwater flow conditions. Based on geologic and hydrogeologic exploration, and analysis and synthesis of the collected data, the paper describes hydrogeologic modeling of the open-cast mine Tamnava - West Field. The software used in the research provides a portrayal of the 3D distribution of the aquifers present in the study area. As such, the hydrogeologic model constitutes a basis for developing a hydrodynamic (mathematical) model of the groundwater regime.

Математические модели гидродинамики одно и двухфазных сред с внешним тепломассобменом

Математические модели гидродинамики одно и двухфазных сред с внешним тепломассобменом

Heat transfer and thermohydrodynamic fluctuations in aluminum–air fuel cell

Numerical simulation and experimental investigation of processes of conjugate heat transfer, hydrodynamics, and electrochemical kinetics in an alkaline aluminum–air fuel cell are performed. A mathematical model of hydrodynamics, heat and mass transfer, and electrochemical kinetics in an alkaline aluminum–air fuel cell with regard to the temperature dependence of electrochemical kinetics of electrodes, the ohmic heat losses, the thermogravimetric convection in electrolyte, and water evaporation from the cathode surface is proposed. Three-dimensional nonstationary vortex structures producing temperature fluctuations of the hydrodynamic nature are developed in the region of the electrolyte chamber with unstable electrolyte stratification, which is above the heated electrodes. It is shown that the thermohydrodynamic temperature fluctuations cause fluctuations of net power of the fuel cell during discharge.

Dynamics Modeling and Control Simulation of an Autonomous Underwater Vehicle

ABSTRACT Liu, G.; Chen, G.; Jiao, J., and Jiang, R., 2015. Dynamics modeling and control simulation of an autonomous underwater vehicle. A dynamics model of an open-shelf Autonomous underwater vehicle (AUV) is described in this paper. The virtual prototype technology and the control simulation software are used to build the virtual prototype model of AUV, and AUV dynamic location control arithmetic is simulated based on analyzing motion and hydrodynamic mathematical model of the virtual prototype. The simulation results indicate that the virtual prototype system has the function of simulation demo and performance validation, and can provide one kind of new method for AUV graphic simulation, and has very important practical meaning on AUV design and control research.

The Mathematical Model of Hydrodynamics and Heat and Mass Transfer at Formation of Steel Ingots and Castings

Abstract The generic mathematical model and computational algorithm considering hydrodynamics, heat and mass transfer processes during casting and forming steel ingots and castings are offered. Usage domains for turbulent, convective and non-convective models are determined depending on ingot geometry and thermal overheating of the poured melt. The expert system is developed, enabling to choose a mathematical model depending on the physical statement of a problem.