Steady-state Mathematical Model Research Articles

Exergy analysis and parameter optimization of sinter cooling process in vertical moving bed for waste heat recovery

A steady-state mathematical model is proposed to investigate the sinter cooling process in vertical moving bed, and the optimal parameter combination of vertical tank (VT) is obtained based on the maximum enthalpy exergy of cooling air (EECA) through the method of orthogonal experiment. The results show that, the air outlet temperature increases with increasing the air inlet temperature, bed inner diameter and height, and decreasing the air flow rate. The gas flow pressure drop basically increases linearly with increasing the air flow rate, air inlet temperature and bed height, and decreases exponentially with increasing the bed inner diameter. EECA can reach the maximum value with the increase of air flow rate and air inlet temperature. When the air flow rate exceeds a certain limit value, EECA also has a maximum value with the increase of bed height, while there is not a turning point for the change curve of EECA with the bed inner diameter. Taking the actual annual output of 360 m2 sintering machine as the research object, the optimal parameter combination of VT is 9 m for the bed inner diameter, 8 m for the bed height, 353 K for the air inlet temperature and 180 kg/s for the air flow rate, respectively.

A comprehensive improved coordinated control strategy for a STATCOM integrated HVDC system with enhanced steady/transient state behaviors

As a parallel type of reactive power compensation equipment, a static synchronous compensator (STATCOM) is often used to connect at the weak AC end of the inverter side of the high voltage direct current (HVDC) transmission system. In this paper, an improved coordinated control strategy of a STATCOM is investigated with three main contributions: 1) The operation modes of the STATCOM are analyzed and its steady-state mathematical model is established. The dynamic behaviors of the STATCOM under different operating conditions are studied; 2) A coordinated control strategy of the STATCOM, which takes both the steady-state and transient characteristics of the HVDC system into account, is proposed. The control strategy under steady states includes two control modes: constant AC voltage control and constant reactive power control. The control strategy under transient states also includes two control modes: fast reactive power droop control and active blocking control. Based on the operating conditions of both the HVDC system and the STATCOM, the decision criterion and the switching control of the STATCOM adopting the specific control strategy are proposed; 3) Aiming at the problem of slow reactive power response in the STATCOM using the traditional maximum reactive power control under transient conditions, a fast reactive power droop control strategy is proposed and a turn-off angle negative feedback control is added. This method can provide reactive power compensation more rapidly under transient conditions and mitigate the occurrence of commutation failures for the HVDC system. A simulation model of the STATCOM integrated HVDC system is established in PSCAD/EMTDC. The effectiveness of the proposed improved coordinated control strategy in enhancing the receiving AC system strength and reducing the probability of commutation failures under transient conditions, is verified by the simulation results.

Performance analysis of the sky radiative and thermoelectric hybrid cooling system

In this paper, the radiative sky cooler (RSC) and thermoelectric cooler (TEC) are integrated to form the RSC-TEC hybrid cooling system that can reduce the TEC required power consumption and increase the system’s cooling capacity over a standalone RSC. Specifically, a feasibility study is conducted to evaluate the design and working conditions that allow this system to have superior performance; For example, the TEC module type and number, RSC surface area and radiative emissivity value, solar absorption coefficient and air convective heat transfer coefficient have been parametrically swept to assess their effects on the system’s cooling capacity and the TEC power saving coefficient, a metric to define the degree of TEC power consumption reduction due to the RSC. The analyzes have been conducted through a non-dimensional steady-state mathematical model of the hybrid system that cools an enclosed space. Results demonstrate that a 0.1 m2 RSC could reduce the required power consumption of a TEC module (size 4 cm by 4 cm) by up to 10%. Moreover, increasing the RSC surface area further improved the TEC power saving coefficient, but the solar absorption coefficient had to be under 0.02 to maintain a reasonable TEC power saving coefficient.

Thermodynamic analysis and multi-objective optimization of a novel power generation system driven by geothermal energy

A novel combined system integrated with a Kalina and a transcritical CO2 (T-CO2) cycle is proposed and investigated for making effective use of geothermal resources. Geothermal energy is first utilized by Kalina sub-cycle and then deeply recovered by T-CO2 sub-cycle. A steady-state mathematical model is developed to further study the novel combined system. The result shows that under the given conditions, the system net power output is up to 2808 kW, which is higher than both the single Kalina cycle and single T-CO2 cycle. The exergy analysis shows that the evaporator II is the component with the largest exergy destruction. The parametric analysis shows that increasing the basic ammonia-water solution concentration and turbine I inlet temperature, or decreasing the turbine I inlet pressure and condensation pressure of condenser I have significant effects on system performance. Furthermore, a multi-objective optimization considering both thermodynamic and economic aspects is carried out to obtain the Pareto frontier solutions, and the decision-making analysis shows that the two-stage recycling system could greatly improve the geothermal water utilization degree compared to the conventional system. The findings could provide a useful reference for system design and operation to make better use of geothermal energy.

A novel hybrid and interactive solar system consists of Stirling engine ̸vacuum evaporator ̸thermoelectric cooler for electricity generation and water distillation

This paper introduces a novel hybrid and interactive solar system to generate electricity and produce desalinated water. The system consists of a Stirling engine driven by concentrated solar radiation and cooled by saline water. Also, the system consists of an evacuated evaporator chamber to evaporate the saline water and thermoelectric cooler, driven by Stirling engine, to condensate the distilled water. The novelty of the system is in its positive interactivity since each component and product enhances the performance and productivity of others. The rejected heat from both the cold side of Stirling engine and the hot side of the TEC modules is used to heat the saline water before entering the evaporator. Also, the cold side of the TEC modules is used to enhance the condensation and hence the desalination rate. The importance of the second enhancement technique relays in the fact that many applications do not suffer from the absence of hot evaporative heating sources but suffer from the absence of condensation cool surfaces. A steady-state mathematical model has been proposed and validated by being compared with published data. The results show that at an optimized design point (solar radiation of 700 W/m2, wind speed of 5 m/s, swept volume of 210 cm3, dish diameter of 2.68 m, etc.), the overall efficiency of the system was 65.8% with a net output power of 506 W and desalinated water of 28 kg/day. Including the TEC system has enhanced the condensation rate from 2.93 kg/day to 34.14 kg/day and the efficiency from 22.84% to 54.87%. Also, the two preheating effects (rejected heat from Stirling engine and from TEC modules) enhance the desalination rate from 2.93 kg/day to 11.74 kg/day and efficiency from 22.84% to 34.53%. Combining both enhancement techniques increase the desalination rate from 2.93 kg/day to 40.96 kg/day and efficiency from 22.84% to 64.44%.

Steady-state modelling and performance of a rotary direct drive digital valve

A rotary direct drive digital valve driven by a stepper motor was proposed. By analysing its working principle, the steady-state mathematical model reflecting the relationship between the pressure, the flow and the angular displacement was deduced. Based on this mathematical model, the models of the null valve coefficients, the zero leakage flow and the steady-state flow torque were given. The simulation shows that the relationship between the pressure and the flow of the rotary valve is nonlinear; however, under a constant load pressure, the flow characteristics and the steady-state flow torque characteristics of the rotary valve with rectangular throttle orifices are linear. The experimental results show that the flow is directly proportional to the steps of the stepper motor, and the proposed mathematical models are valid.

Study of a steering model for 4-axle 8·8 off road vehicles

The purpose of this study is to establish a steering model for a 4-axle 8×8 vehicle, which provides the design of the assisted steering system. To obtain the best steering performance, this system aims to minimise the turning radius. In this study, the steady-state mathematical steering model of this vehicle is established and the actual physical parameters are added to this model. By actually driving the vehicle, the model is verified and the results show that the model can accurately predict the steering behaviour of the vehicle. After correction, the model is added to assist the steering of the fourth axle and find the optimal steering mode. To evaluate the design, this model inputs the functions of time and steering wheel angle and outputs the tracks of driving this vehicle. We verify the steering assistance design of this vehicle by comparing the driving tracks with and without it.

Simulation of Multi-Stage Flash with Brine Circulating Desalination Plant

Multi-stage flash (MSF) desalination is the main process to solve the problem of limited freshwater resources in the world. This work describes the developed steady-state mathematical model for analysing and evaluating the performance of Multistage flashing with brine circulation desalination process (MSF-BC). It is based on the laws of energy balance, material balance, and heat transfer equations with physical properties correlations equations. The nonlinear equations are linearized and arranged into a tridiagonal matrix form. The model solution is obtained by a computer code written by MATLAB program software. It can predict the productivity of the plant with temperature profiles and flow rates for all stages in the unit. The model results were compared with some previous results presented in literature. The comparison shows good agreement with these available data. An MSF desalination plant in Ayoun Mousa, Egypt of capacity 5000 m 3 /day was presented as a case study.

Numerical Analysis on Performance of COREX CGD Shaft Furnace with Top Gas Recycling

A three-dimensional steady state mathematical model, considering the chemical reactions and the transfers of momentum, heat and mass between the gas and solid phases, is developed to investigate the performance of COREX central-gas-distribution (CGD) shaft furnace with top gas recycling (TGR). The model is validated first by data from practical measurement and then is used to study the performance of CGD shaft furnace with TGR. The results reveal that, compared with the process of 15% CGD gas input without TGR, the TGR can reduce the fresh gas consumption from 1058 Nm3/tBurden to 392 Nm3/tBurden. The reduction potential of top gas with TGR increases from 0.5755 to 0.6293, the utilization rate of top gas decreases from 34.18% to 28.03%, the metallization rate of solid product increases from 61.80% to 70.05%, and the standard deviation of metallization rate decreases from 0.8% to 0.4%.

Study on a novel spray-evaporation multi-effect distillation desalination system

As the negative environmental impacts associated with disposal of brine concentrate become increasingly recognized and attracting public attention, zero liquid discharge (ZLD) is emerging as a technique for desalination plants to minimize waste and recover resources. In this study, an innovative concept of a spray-evaporation multi-effect distillation (SE-MED) system is proposed to achieve ZLD, in which a spray evaporation tank (SET) is used to fully split brine disposal for water and salts. A steady-state mathematical model for the SE-MED process is developed under several simplification assumptions. A five-effect forward SE-MED system with a bleed fraction of 20% is designed based on the mathematical model. A simplified vaporization model is also developed to describe the motion and evaporation behavior of a single water droplet in the SET. The calculated trajectories of the droplet provide guidance to the SET design. Two-phase simulations are performed to provide further insight into spray evaporation performance inside the SET. Results indicate that a high evaporation efficiency of 99.86% is achievable by the modified SET. In addition, the application of the Reaction Engineering Approach in the hindered spray evaporation simulation is discussed and validated for future study.

One-dimensional steady-state mathematical model of a novel loop heat pipe with liquid line capillary wick

A novel loop heat pipe used for data center with a liquid line wick is designed, and its one-dimensional steady-state mathematical model is developed based on the energy and thermodynamic equilibrium of each component and the simulation results were validated by comparing with the experimental data in this work. The compensation chamber of the loop heat pipe was removed, and a section of capillary wick was added in the end of liquid line in order to reduce heat leakage and vapor backflow and increase working medium circulation power. The mathematical model of the novel loop heat pipe can be used to predict the operating temperature of each characteristic point with small relative errors of <13%. A parametric study of the steady-state performance characteristics including the effects of material, diameter, length, and porosity of liquid line wick are conducted, which provides a powerful basis for the design of novel loop heat pipe experiment.

Liquid–liquid gravity displacement in a vertical fracture during drilling: Experimental study and mathematical model

Gravity displacement often occurs when drilling a vertical fractured formation, causing a downhole complexity with risk of blowout and reservoir damage, well control difficulty, drilling cycle prolongation, and increased costs. Based on an experimental device created for simulating the gravity displacement, various factors affecting the displacement quantity were quantitatively evaluated by simulating the fracture width, asphalt viscosity, drilling fluid density, and viscosity under different working conditions, and a liquid–liquid displacement law was obtained. Using the theories of rock mechanics, fluid mechanics, and seepage mechanics, based on conformal mapping, as well as a fracture-pore double substrate fluid flow model, we established a steady-state mathematical model of fractured formation liquid–liquid gravity displacement by optimizing the shape factors and using a combination of gravity displacement experiments to verify the feasibility of the mathematical model. We analyzed the influence of drilling fluid density, fracture height and length, and asphalt viscosity on displacement rate, and obtained the corresponding laws. The results show that when the oil–fluid interface is stable, the fracture width is the most important factor affecting the gravity displacement, and plugging is the most effective means of managing gravity displacement.

Dynamic WPT system for EV charging with integrated energy storage

Wireless power transfer (WPT) can be used to charge electric vehicles (EVs) safely and efficiently. Dynamic wireless EV charging systems to charge EVs while moving has been developed but this technology is not yet widespread. One of the key challenges of dynamic charging is the pulsed nature of the transferred power, which may negatively impact battery life and the utility grid. Hybrid energy storage systems have been demonstrated as a potential solution, at the expense of a dedicated converter to interface with the energy storage element. This study presents a possible solution to the problem of adsorption and conditioning of high-power pulses, in the form of a novel converter topology that combines inductive WPT and super capacitor energy storage without the need for an additional converter stage. A suitable switching pattern is presented along with a steady-state mathematical model based on inductive power transfer, providing insight into the operation of the system. Experimental results of a prototype bi-directional WPT system are shown to validate the model and demonstrate the applicability of the proposed converter topology.

Numerical investigation of an evaporating meniscus in a heated capillary slot

This paper numerically studies heat transfer and fluid flow from an evaporating meniscus of a wetting fluid within a heated capillary. A simplified steady state mathematical model is developed for predicting the wicking height of the meniscus and the evaporation mass flow rate which includes: (1) one-dimensional flow and energy equations for the liquid and vapor regions, (2) one-dimensional model for the evaporating meniscus region, and (3) two-dimensional energy equation for the capillary wall. Three parameters, namely, apparent contact angle, cumulative heat transfer, and evaporating meniscus height characterize the evaporating meniscus region. In this paper, the apparent contact angle in the evaporating meniscus is uniquely deduced from the meniscus curvature at the centre of the capillary using the thickness profile obtained from standard extended meniscus theory (which includes the evaporating thin film and bulk meniscus regions). Correlations are obtained for the cumulative heat transfer, apparent contact angle and evaporating meniscus height as a function of the difference between the wall and saturation temperatures from the evaporating thin film theory for the meniscus region, which is called as micromodel. The macroscopic model accounts for wall heat conduction and heat transfer with fluid flow in the liquid and vapor regions. The micromodel deals with heat transfer and fluid flow in the evaporating meniscus region. In this paper, a novel scheme to link the “macroscopic” momentum and energy equations in the capillary slot and the evaporating meniscus through the correlations developed above is proposed. Using this numerical model, the wicking height and the evaporation mass flow rate are estimated and the results are compared with previously conducted experiments. The trends in the numerical results of the mathematical model correlate reasonably well with the experimental data.

A novel PVT/PTC/ORC solar power system with PV totally immersed in transparent organic fluid

A novel hybrid PVT/parabolic trough concentrator (PTC)/organic Rankine cycle (ORC) solar power system integrated with underground heat exchanger has been proposed. The evaporator unit consists of a transparent flat PVT solar collector and a PTC connected in series. The first transparent solar collector has transparent covers and consists of solar cells totally immersed within a pressurized transparent organic fluid that allows the solar radiation to reach the solar cells, cools them effectively, and captures all thermal losses from the solar cells. The second concentrator is a conventional one with opaque black receiver used to reheat the transparent organic fluid to higher temperatures. Both solar collectors (the PVT and PTC) perform as the boiler and superheater for the ORC. The performance of the proposed system is investigated by a steady-state mathematical model. The results show that, at design conditions, the efficiency of the PV modules stabilizes around 12%, absorber efficiency varies within 64% to 75%, and the ORC efficiency varies within 7% to 17%.

Numerical simulation on characteristics of COREX shaft furnace with central gas distribution

A three-dimensional steady-state mathematical model, considering the chemical reactions and transfers of momentum, heat and mass between the gas and solid phases, was developed to investigate the characteristics of the shaft furnace with the central gas distribution (CGD) device. The model was verified by the practical production data of a COREX-3000 shaft furnace, and then, it was used to study the inner characteristics of the shaft furnace with CGD. The results show that, compared with the COREX shaft furnace without CGD, the gas utilization rate (UR) and solid metallization rate (MR) increase from 33.66% to 34.18% and 60.4% to 61.8%, respectively. Especially, the standard deviation of solid MR decreases from 6.9% to 0.8%, which means that the MR of direct reduced iron from the furnace with CGD is more uniform than that without CGD. Additionally, the effects of operational conditions and CGD design on gas UR, solid MR and direct reduced iron uniformity were further discussed and the optimized conditions were suggested.

Development of system of automatic control of robotic arm drive

Currently, the scope of application of robotic systems and complexes is expanding significantly. The introduction of industrial robots is one of the most promising areas of complex automation of production processes, which will significantly increase labor productivity and save people from monotonous, difficult and harmful work. Many tasks are solved by facilitating robotic manipulators to facilitate human performance and to achieve higher quality and accuracy of production. Thus, thanks to the development of automatic control systems, information technologies and their application in the creation of modern robotic systems, the opportunity has emerged to release a person from work that poses a threat to his life and health. When using manipulator robots, an important task is to develop a control system that provides positioned movement of the links of the manipulator. The main task of the automatic drive control system is to form and implement a set of control effects, in accordance with technological requirements. In this work we propose a system of automatic control of the actuator of the manipulator, which provides positioned movement of the manipulator link along a given trajectory. Using the tables of originals and images of typical functions for which continuous Laplace transforms and Z-transforms are calculated, a discrete linear steady-state mathematical model of the robot-manipulator automatic control system is constructed. The parameters of the corrective devices of the system of automatic control of the electric actuator of the robot manipulator were made, which allowed to improve the characteristics of the transient process, namely: to reduce the time of over-regulation and the duration of the transient. The obtained results of the simulation of transients allow to confirm that the synthesized parameters of the corrective devices for the analog automatic control system can be used in the digital automatic control system of the electric actuator of the robot manipulator.

Thermodynamic analysis of three ejector based organic flash cycles for low grade waste heat recovery

Systems based on Organic Flash Cycle (OFC) are promising technologies for waste heat recovery application due to a better match of the hot and cold heat transfer curves. However, the large amount of exergy lost during the throttling process, results in a low thermal efficiency for OFC. In this work, ejectors are introduced in basic OFC to replace the low pressure throttle valve, high pressure throttle valve and both two throttle valves, which namely Single Ejector and Single Flash evaporator based OFC (SESF-OFC), Single Ejector and Double Flash evaporators based OFC (SEDF-OFC) and Double Ejectors and Double Flash evaporators based OFC (DEDF-OFC), respectively. The thermodynamic analysis including energy analysis, exergy analysis, the parametric analysis and comparison analysis are evaluated by using steady-state mathematical model and thermodynamic laws. The ejector allows a high pressure fluid to entrain and compress a low pressure fluid to a medium pressure. Hence, the mass flow rate or expansion ratio of turbine can be enhanced, results in all of three ejector based OFCs are more efficient than the basic OFC. When the high temperature fluid with temperature of 453.15 K is set as heat source, the maximum global second law efficiency (ηII,G) of 38.95% belongs to DEDF-OFC followed SEDF-OFC (37.92%), SESF-OFC (33.68%) and basic OFC (31.43%). The SEDF-OFC is more efficient than SESF-OFC, which indicates that the high pressure throttle valve replaced by ejector is a more effective method than the low pressure throttle valve done. Moreover, the four OFCs have been compared with conventional Organic Rankine Cycle (ORC), and the comparison results show that the ηII,G of basic OFC and SESF-OFC are lower than that of ORC, while SEDF-OFC and DEDF-OFC are more efficient than ORC, and the average increment of SEDF-OFC and DEDF-OFC are 10.37% and 15.01%, respectively. Hence, the ejector based OFCs are alternative methods for waste heat recovery application with a high efficiency.

Performance simulation and optimization of COREX shaft furnace with central gas distribution

To improve the distribution of the reducing gas inside the shaft furnace, recently, a central gas distribution (CGD) device is installed at the bottom of the shaft furnace in Bayi Steel. In this work, a two-dimensional steady-state mathematical model, including momentum, heat and mass transfers and chemical reaction, is developed to study the performance of the furnace with CGD. The model is validated by industrial production data of COREX-3000, and then it is used to study the detailed phenomena in the furnace with CGD. The results show that, compared with the traditional COREX shaft furnace without CGD, the CGD device has a positive effect on improving the solid metallization rate (MR) and gas utilization rate (UR). The solid metallization rate (MR) increases from 0.601 to 0.628, the gas utilization rate (UR) increases from 0.3437 to 0.3519 and the standard deviation (STDEV) of solid MR decreases from 0.0820 to 0.0037, which means that the MR of the DRI from the furnace with CGD is more uniform than that without CGD. In addition, the effects of operation conditions and the CGD design on the solid MR, gas UR and STDEV of MR are discussed and the optimized conditions are suggested.

Numerical simulation of a new electroslag remelting technology with current conductive stationary mold

Based on a new electroslag remelting technology with current conductive stationary mold (ESR-CCSM), a two-dimensional axisymmetric steady-state mathematical model is established to first research the situation that the current totally flows out of the mold to power. With different boundary conditions of electromagnetic phenomena, the coupled electromagnetic field, flow field and temperature field are calculated to study distribution characteristics for traditional ESR and ESR-CCSM respectively. The results show that the magnetic field intensity of ESR-CCSM increases from the side of the symmetry axis and the baseplate to the side of the lateral surface of electrode and the free surface of slag. The current density and Joule heating between the electrode corner and the mold wall for ESR-CCSM are obviously higher than that for traditional ESR, and the temperature distribution of slag pool is more uniform. Compared to traditional ESR, the cylindrical section height of metal pool for ESR-CCSM is bigger, helping to gain smoother surface. Moreover, the metal pool of ESR-CCSM becomes shallower and the columnar crystal angle is smaller, propitious to obtain crystallization structure with a tendency to axial direction. Through comprehensive analysis, the optimal current parameter for a 350 mm diameter ingot of H13 die steel with ESR-CCSM is 5500 A. The in-situ experiment illustrates that the ingot surface is smooth. The columnar crystal growth is quite developed and the columnar crystal angle is mainly between 20° and 25°, tending to axial direction, much smaller than that for traditional ESR, which indicates that the H13 ingot produced by ESR-CCSM owns both good surface quality and solidification quality.