Simulation Analysis of New Energy Vehicle Engine Cooling System Based on K-E Turbulent Flow Mathematical Model

New energy vehicles have better clean and environmental protection characteristics than traditional fuel vehicles.The new energy engine cooling technology is critical in the design of new energy vehicles.This paper used oneand three-way joint simulation methods to simulate the refrigeration system of new energy vehicles.Firstly,a k-εturbulent flow model for the cooling pump flow field is established based on the principle of computational fluid dynamics.Then,the CFD commercial fluid analysis software FLUENT is used to simulate the flow field of the cooling pump under different inlet flow conditions.This paper proposes an optimization scheme for new energy vehicle engines’“boiling”phenomenon under high temperatures and long-time climbing conditions.The simulation results show that changing the radiator’s structure and adjusting the thermostat’s parameters can solve the problem of a“boiling pot.”The optimized new energy vehicle engine can maintain a better operating temperature range.The algorithm model can reference each cryogenic system component hardware selection and control strategy in the new energy vehicle’s engine.

Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Overtopping is one of the main reasons for the breaching of concrete-face sand-gravel dams(CFSGDs).In this study,a refined mathematical model was established based on the characteristics of the overtopping breaching of CFSGDs.The model characteristics were as follows:(1)Based on the Renormailzation Group(RNG)k-εturbulence theory and volume of fluid(VOF)method,the turbulent characteristics of the dam-break flow were simulated,and the erosion surface of the water and soil was tracked;(2)In consideration of the influence of the change in the sediment content on the dam-break flow,the dam material transport equation,which could reflect the characteristics of particle settlement and entrainment motion,was used to simulate the erosion process of the sand gravels;(3)Based on the bending moment balance method,a failure equation of the concrete face slab under dead weight and water load was established.The proposed model was verified through a case study on the failure of the Gouhou CFSGD.The results showed that the proposed model could well simulate the erosion mode of the special vortex flow of the CFSGD scouring the support body of the concrete face slab inward and reflect the mutual coupling relationship between the dam-break flow,sand gravels,and concrete face slabs.Compared with the measured values,the relative errors of the peak discharge,final breach average width,dam breaching duration,and maximum failure length of the face slab calculated using the proposed model were all less than 12%,thus verifying the rationality of the model.The proposed model was demonstrated to perform better and provide more detailed results than three selected parametric models and three simplified mathematical models.The study results can aid in establishing the risk level and devising early warning strategies for CFSGDs.

MATHEMATICAL MODELLING OF BUBBLE DRIVENFLOWS IN A NOVEL ALUMINUM ELECTROLYSIS CELL

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THE STUDY ON THREE-DIMENSIONAL MATHEMATICAL MODEL OF RIVER BED EROSION FOR WATER-SEDIMENT TWO-PHASE FLOW

Based on the tensor analysis of water-sediment two-phase how, the basic model equations for clear water flow and sediment-laden flow are deduced in the general curve coordinates for natural water variable-density turbulent how. Furthermore, corresponding boundary conditions are also presented in connection with the composition and movement of non-uniform bed material. The theoretical results are applied to the calculation of the float open caisson in the construction period and good results are obtained.

Development of Mathematical Model of Slag Flow Field and Temperature Field in ESR System

The heat transfer phenomena and driving forces of slag bath flow in ESR process were analyzed, and the mathematical models in ESR system were reviewed and evaluated. The electromagnetic force is the main driving force for the flow formation in the ESR slag pool, and the temperature difference in the pool creates a convective flow in the system. The shape of the electrode tip has an effect on electromagnetic field distribution in slag pool, thus affects the flow pattern. Finally an improved mathematical model of slag pool flow was proposed.

A mathematical model capable of describing the liquid flow mainly in a blast furnace

The molten liquid flow inside a packed bed is a familiar momentum transportation phenomenon in a blast furnace. With regard to the reported mathematical models describing the liquid flow within a packed bed, there are some obstacles for their application in engineering design, or some limitations in the model itself. To overcome these problems, the forces from the packed bed to the liquid flow were divided into appropriate body and surface forces on the basis of three assumptions. Consequently, a new mathematical model was built to present the liquid flow inside the coke bed in a blast furnace. The mathematical model can predict the distribution of liquid flowrate and the liquid flowing range inside the packed bed at any time. The predicted results of this model accord well with the experimental data. The model will be applied considerably better in the simulation on the ironmaking process compared with the existent models.

Mathematical Modeling,Field Calibration and Numerical Simulation of Low-Speed Mixed Traffic Flow in Cities

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Modeling Tracer Flow Characteristics in Different Types of Pores: Visualization and Mathematical Modeling

Structure of porous media and fluid distribution in rocks can significantly affect the transport characteristics during the process of microscale tracer flow.To clarify the effect of micro heterogeneity on aqueous tracer transport,this paper demonstrates microscopic experiments at pore level and proposes an improved mathematical model for tracer transport.The visualization results show a faster tracer movement into movable water than it into bound water,and quicker occupancy in flowing pores than in storage pores caused by the difference of tracer velocity.Moreover,the proposed mathematical model includes the effects of bound water and flowing porosity by applying interstitial flow velocity expression.The new model also distinguishes flowing and storage pores,accounting for different tracer transport mechanisms(dispersion,diffusion and adsorption)in different types of pores.The resulting analytical solution better matches with tracer production data than the standard model.The residual sum of squares(RSS)from the new model is 0.0005,which is 100 times smaller than the RSS from the standard model.The sensitivity analysis indicates that the dispersion coefficient and flowing porosity shows a negative correlation with the tracer breakthrough time and the increasing slope,whereas the superficial velocity and bound water saturation show a positive correlation.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived.The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool,such as mass flow rates,flow coefficients,efflux angles and steady state flow forces under different operating conditions.At last,the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test.It is presented that the bottom arc of sloping U-shape notch(ABU) should not be omitted when it is required to accurately calculate the orifice area of ABU.Although the theoretical flow area of plain bottom sloping U-shape notch(PBU) is larger than that of ABU at the same opening,the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening,while the simulated flow force of PBU is larger than that of ABU at the same opening.Therefore,it should be prior to adapt the ABU when designing the spool with proportional character.

Mathematical model of flow characteristic in multi-strand continuous casting tundishes

In this paper, the subject of mathematical model is a series of math expressions, which is used to calculate different regions＇ volume fraction and analyze flow characterization in multi-strand tundish. But research about mathematical model for multi-strand tundish is few, and so far, there has been no acknowledged math model for multi- strand tundish to describe its flow characteristic. If Sahai＇s model, which is originally proposed for the case of single-strand tundish （proposed in reference, and this model is widely used in the world）, is applied to describe flow feature in multi-strand tundish, the calculation results would be unreasonable. Based on the data of watermodel experiment results, the sum of each strand＇s dead region＇s volume fraction is bigger than 100%, and this obviously doesn＇T agree with reality; and the value of dead region＇s volume fraction is calculated to be minus according to mathematical simulation results data in another case. What＇s more, Sahai＇s model does not propose the standard of plotting the RTD-curve, and this makes scholars around the world can＇t achieve consensus of views about plotting RTD-curve. And the model doesn＇t consider the bypass flow and can＇t calculate its volume fraction, but bypass flow is critical to tundish metallurgy. And through Sahai＇s model, the calculation result of plug flow region＇s volume fraction is also not reasonable, because the model doesn＇t well describe the essence of plug flow. So these suggest that it is not reliable to apply Sahai＇s single-strand tundish model to multi-strand tundish case. Then a new model is attempted to propose in this paper for your discussion. In the new model, the standard of plotting RTD curve is definitely proposed, and relative calculation method is also proposed; and the feature of dead region is carefully studied and the model proposes a new method to calculate its volume fraction, and the calculation formula about its volume fraction can be adjustable according the actual demand; what＇s more, the new model considers the bypass flow and proposes a method to calculate its volume fraction for the first time, and then volume fraction of plug flow region, backmix flow region, dead region and bypass flow can be calculated and obtained at the same time; and this new model can better capture the deviation of reality flow pattern from ideal plug flow pattern, and reflects the feature of plug flow.

Mathematical Model and Theoretical Research of Flow Shear Constitutive Relation during Rheo-rolling of Semisolid Alloy

The mathematical model of flow shear constitutive relation during rheo-rolling process has been established. The distribution of velocity and shear stress in rolling cavity was investigated, and the effects of process parameters on shear stress of Sn-15 Pb alloy during rheo-rolling process were studied. In rolling cavity, the nearer the roll is, the bigger the velocity and shear stress are. The shear stress increases with the increment of the roll speed and the roll radius during rheo-rolling process, but deceases with the increment of the thickness of the strip. When the solid fraction of Sn-15 Pb alloy increases from 0.3 to 0.5, the shear stress increases slowly, but when the solid fraction increases from 0.5 to 0.6, the shear stress rapidly.

MATHEMATICAL MODELLING OF FLOW PHENOMENA IN METAL BATH COVERED WITH MOLTEN SLAG

By use of the two-component LDA and high speed camera,the water model of the flow field in metal bath under molten slag layer has been tested.On the basis of experimental results,the flow boundary conditions of liquid metal at the slag-metal interface of a gas injecting bath were deduced.The flow field and the turbulent parameters of the metal bath covered with slag were solved by the vorticity-stream function method.The results reveal that the flow velocity, turbulent energy and circulating rate of the melt under slag are lower than that of without slagcover.Another one “dead zone” of the lowest turbulent energy is formed in the top layer under cover of slag near the ladle linning.

Comparison on Mathematical Models for Description of Flow Curves of Stable Austenitic Steels

The flow curves were measured for the stable austenitic steels 304L and 304LN by means of tensile test at room temperature,which are described by the models σ=K1εn1 + exp(K2 + n2ε), σ=Kεn1+n2lnε and σ=σ0+Kεn (where, K1, K2, n1 andn2; K, n1 and n2; σ0, K and n are constant). The comparison of the maximum deviations and the consideration of thevariation of the work hardening rate with true strain show that the flow curves for the austenitic steels 304L and 304LN canbe described by the model σ=Kεn1+n2 lnε at higher precision.The derivatives of the models σ=K1εn1 + exp(K2 + n2ε) and σ=Kεn1+n2lnε with respect to true strain, exhibit theextreme at low true strain. This inherent character indicates that both models are unsuitable to describe the part of the workhardening rate curve at low true strain.

Mathematical Models for Flow of Chyme during Gastrointestinal Endoscopy

Intestinal infection has become a common disease in human and endoscopy can be a powerful means in diagnosis of intestinal illnesses. Mathematical models are developed for an inserted endoscope on the flow of chyme in the small intestine considering a Newtonian incompressible fluid flow, under an axisymmetric condition, in a cylindrical annulus between the small intestine and the endoscope. We obtain novel mathematical expressions for the pressure drop, forces exerted by the endoscope on the flow of chyme, and the force exerted by the chyme on the intestine for one wave length of the peristaltic rush wave. We also investigate and calculate the flow velocity and pressure for different flow rates and the wave lengths. The results are presented, and discussed for the cases and conditions under which pressure, pressure drop can be positive or negative and the forces can be acted either by the intestine or endoscope on the flow or vice-versa.

The Mathematical Model for Particle Suspension Flow through Porous Medium

Transport of suspensions and emulsions in porous media occurs in numerous processes of environmental, chemical, petroleum and civil engineering. In this work, a mass balance particle transport equation which includes filtration has been developed. The steady-state transport equation is presented and the solution to the complete advective-dispersion equation for particulate suspension flow has been derived for the case of a constant filter coefficient. This model in-cludes transport parameters which are particle advective velocity, particle longitudinal dispersion coefficient and filter coefficient. This work recommends to be investigated by particle longitudinal dispersion calculation from experimental data, directly. Besides, the numerical model needs to be developed for general case of a transition filter coefficient.

AN EXPLORATION TO THE MODELLING OF TWO-DIMENSIONAL COMPLEX TURBULENT SHEAR FLOWS

The regions with shear stress and mean velocity gradient of opposite sign often existin complex turbulent shear flows.In these cases,the eddy viscosity hypothesis breaksdown.Hinze regards the,departure from eddy viscosity hypothesis as a result from transportationof mean momentum over distance by the large structures and arrives at a shearstress expression including the second order derivatives of the mean velocity.However,hisexpression greatly overestimates the shear stress.This implies that the flow particles areunlikely to have enough memory of the mean momentum over distance.By assuming thedeparture from eddy viscosity hypothesis as a result from transportation of the shear stresscontained in smaller eddies over distance by the large structures,the present author hasarrived at a new shear stress expression.The shear stress estimated so far is in goodagreement with the experiments.

Experimental Research and Mathematical Model of Drag Torque in Single-plate Wet Clutch

Reduction of drag torque is one of important potentials to improve transmission efficiency.Existing mathematical model of drag torque was not accurate to predict the decrease after oil film shrinking because of the difficulty in modeling the flow pattern between two plates.Flow pattern was considered as laminar flow and full oil film in the gap between two plates in traditional model.Subsequent equivalent circumferential degree model presented an improvement in oil film shrinking due to centrifugal force,but was also based on full oil film in the gap,which resulted difference between model prediction and experimental data.The objective of this paper is to develop an accurate mathematical model for the above problem by using experimental verification.An experimental apparatus was set up to test drag torque of disengaged wet clutch consisting of single friction and separate plate.A high speed camera was used to record the flow pattern through transparent quartz disk plate.The visualization of flow pattern in the clearance was investigated to evaluate the characteristics of oil film shrinking.Visual test results reveal that the oil film begins to shrink from outer radius to inner radius at the stationary plate and only flows along the rotating plate after shrinking.Meanwhile,drag torque decreases sharply due to little contact area between the stationary plate and the oil.A three-dimensional Navier-Stokes （N-S） equation based on laminar flow is presented to model the drag torque.Pressure distributions in radial and circumferential directions as well as speed distributions are deduced.The model analysis reveals that the acceleration of flow in radial direction caused by centrifugal force is the key reason for the shrinking at the constant feeding flow rate.An approach to descript flow pattern was presented on the basis of visual observation.The drag torque predicted by the model agrees well with test data for non-grooved wet clutch.The proposed model enhances the precision for predicting drag torque,and lays down a framework on which some subsequent models are developed.

Simulation of two-dimensional interior ballistics model of solid propellant electrothermal-chem ical launch with discharge rod plasma generator

Instead of the capillary plasma generator(CPG),a discharge rod plasma generator(DRPG)is used in the30 mm electrothermal-chemical(ETC)gun to improve the ignition uniformity of the solid propellant.An axisymmetric two-dimensional interior ballistics model of the solid propellant ETC gun(2D-IB-SPETCG)is presented to describe the process of the ETC launch.Both calculated pressure and projectile muzzle velocity accord well with the experimental results.The feasibility of the 2D-IB-SPETCG model is proved.Depending on the experimental data and initial parameters,detailed distribution of the ballistics parameters can be simulated.With the distribution of pressure and temperature of the gas phase and the propellant,the influence of plasma during the ignition process can be analyzed.Because of the radial flowing plasma,the propellant in the area of the DRPG is ignited within 0.01 ms,while all propellant in the chamber is ignited within 0.09 ms.The radial ignition delay time is much less than the axial delay time.During the ignition process,the radial pressure difference is less than 5 MPa at the place 0.025 m away from the breech.The radial ignition uniformity is proved.The temperature of the gas increases from several thousand K(conventional ignition)to several ten thousand K(plasma ignition).Compare the distribution of the density and temperature of the gas,we know that low density and high temperature gas appears near the exits of the DRPG,while high density and low temperature gas appears at the wall near the breech.The simulation of the 2D-IB-SPETCG model is an effective way to investigate the interior ballistics process of the ETC launch.The 2D-IB-SPETC model can be used for prediction and improvement of experiments.

Mathematical Modelling of Particle Movement Ahead of the Solid-liquid Interface in Continuous Casting

Whether the particle will be trapped by the solid-liquid interface or not is dependent on its moving behavior ahead of the interface, so a mathematical model has been developed to investigate the movement of the particle ahead of the solid-liquid interface. Based on the theory for the boundary layer, the fluid velocity field near the solid-liquid interface was obtained, and the trajectories of particles were calculated by the equations of motion for particles. In this model, the drag force, the added mass force, the buoyance force, the gravitational force, the Saffman force and the Basset history force are considered. The results show that the behavior of the particle ahead of the solid-liquid interface is affected by the physical property of the particle and fluid flow. And in the continuous casting process, if it moves in the stream directed upward or downward near vertical solid-liquid interface or in the horizontal flow under the solid-liquid interface, the particle with the diameter from 5 um to 60um can reach the solid-liquid interface. But if it moves in horizontal flow above the solid-liquid interface, only the particle with the diameter from 5 um to 10 um can reach the solid-liquid interface.

Physical and Mathematical Modeling of the Argon-Oxygen Decarburization Refining Process of Stainless Steel

The available studies in the literature on physical and mathematical modeling of the argon oxygen decarburization (AOD) process of stainless steel have briefly been reviewed. The latest advances made by the author with his research group have been summarized. Water modeling was used to investigate the fluid flow and mixing characteristics in the bath of an 18 t AOD vessel, as well as the 'back attack' action of gas jets and its effects on the erosion and wear of the refractory lining, with sufficiently full kinematic similarity. The non rotating and rotating gas jets blown through two annular tuyeres, respectively of straight tube and spiral flat tube type, were employed in the experiments. The geometric similarity ratio between the model and its prototype (including the straight tube type tuyeres) was 1:3. The influences of the gas flow rate, the angle included between the two tuyeres and other operating parameters, and the suitability of the spiral tuyere as a practical application, were examined. These latest studies have clearly and successfully brought to light the fluid flow and mixing characteristics in the bath and the overall features of the back attack phenomena of gas jets during the blowing, and have offered a better understanding of the refining process. Besides, mathematical modeling for the refining process of stainless steel was carried out and a new mathematical model of the process was proposed and developed. The model performs the rate calculations of the refining and the mass and heat balances of the system. Also, the effects of the operating factors, including adding the slag materials, crop ends, and scrap, and alloy agents; the non isothermal conditions; the changes in the amounts of metal and slag during the refining; and other factors were all considered. The model was used to deal with and analyze the austenitic stainless steel making (including ultra low carbon steel) and was tested on data of 32 heats obtained in producing 304 grade steel in an 18 t AOD vessel. The changes in the bath composition and temperature during the refining process with time can be accurately predicted using this model. The model can provide some very useful information and a reliable basis for optimizing the process practice of the refining of stainless steel and control of the process in real time and online.