Unsteady Equations Research Articles

Aerodynamic Characteristics Analysis of Rectifier Drum of High-Speed Train Environmental Monitoring Devices

To study the aerodynamic characteristics of the convex structure of a surface-monitoring device on a high-speed train and to evaluate its impact on the aerodynamic performance of the high-speed train, numerical simulation research was conducted on three different layouts of the monitoring device. The computational fluid dynamics (CFD) method was used for the simulation study, and the unsteady compressible NS equation was used as the control equation. Hexagonal grid technology was used to reduce the demand for the grid quantity. The rationality of the grid size and layout was verified through grid independence research. To increase the accuracy of the numerical simulation, the γ-Reθ transition model and improved delayed detached eddy simulation (IDDES) method were coupled for the simulation research. The aerodynamic characteristics of the different operation directions and configurations were compared and analyzed. The research results showed that the windward side of the single pantograph detection device experienced positive pressure, and the sideline and leeward sides experienced negative pressure. Increasing the fillet radius of the sideline could appropriately reduce the aerodynamic resistance. When the speed was about 110 m/s, the drag force coefficient of the detection device was 210~410 N, and the lateral force was small, which means that it had little impact on the overall aerodynamic force of the train. According to the results of the unsteady analysis of the layout with a large space, the resistance during forward travel was greater than that during negative travel. The streamlined upwind surface was conducive to reducing the scope of the leeward separation zone and the amplitude of the pressure fluctuation in the leeward zone, and it thus reduced the resistance. For the running trains, a vortex was formed on their leeward surface. The pressure monitoring results showed that the separated airflow had no dominant frequency or energy peak. The possibility of the following train top and other components experiencing resonance damage is low.

Dynamics pattern of a radioactive rGO-magnetite-water flowed by a vibrated Riga plate sensor with ramped temperature and concentration

In recent times, the dynamics study of an electrically weak performing fluid stream regulated by Riga sensors has become an emerging research topic for scientists. Riga sensors’ utility for improving the effectiveness of heat and mass transport rates in industrial and engineering systems is diverse. This motivates us to inspect the stream pattern and heat-mass transmission mechanism of an electrically low-performing hybrid nanofluid (rGO-magnetite-water) near a vertically straightened Riga plate sensor embedding with absorbing materials under the guidance of thermal and concentration buoyancy and magnetization. The taken flow is being modelled by incorporating pertinent physical influences, namely radiation heat emission, chemical reaction, and ramped temperature and concentration at the boundary wall. The flow is presented mathematically in terms of unsteady partial differential equations. The compact-form expressions for model entities are founded by opting for the Laplace transform methodology. The Riga plate’s shear stress, heat and mass transfer rates are tabulated and graphed. The physical behaviours of substantial flow entities against model factors are conversed and judged graphically. The vital findings of this study demonstrate a swelling in the velocity distribution with an enhancement in modified Hartmann number and diminishing with an enlargement in the width of electrodes. The temperature and concentration are higher for constant plate temperature (CPT) and lower for ramped plate temperature (RPT). It is also motivating to note down that hybrid nanofluid containing reduced graphene nanomaterials will transmit extra heat in the flow regime. The heat flow across the Riga sensor elevates against the higher radiation parameter’s value. These novel findings will be extremely applicable in steam generators, chemical reactors, hybrid Riga plate electromagnetic devices, and phase transitions during material processing.

Self-oscillating jets in cooling applications

In the present computational study, an assessment of self-oscillating jets for use in cooling applications is investigated. The jet exits from a square nozzle into a narrow rectangular cavity at a Reynolds number of 54,000 based on nozzle hydraulic diameter and average jet exit velocity. The heated devices, such as electronic chips, are located externally on the surface of the cavity. A three-dimensional numerical simulation of the flow is conducted by solving the unsteady Reynolds-Averaged Navier-Stokes and energy equations to assess the thermal features of the flow field. The unsteady Elliptic Blending Reynolds Stress Model, which consists of transport equations for each of the stress tensor components, was used to model turbulence. The cooling performance of a self-oscillating jet is compared with that of a wall jet and a channel flow for the same flow conditions and the same arrangement of the hot devices. The cooling efficacy of two different arrangements of the heated devices is also evaluated. The self-oscillating jet provides a higher heat transfer for the heated blocks which are located farther from the central region, while the wall jet improves heat transfer around the central region. Self-oscillating jets can improve heat transfer over a larger area when the heated devices are aligned orthogonal to the axis of the nozzle. On a Nusselt number comparative basis, the channel flow provides the least desirable heat transfer performance.

Effect of moisture release on radiation behavior of burning coal bed between enclosed confined surfaces

In this study, a numerical analysis was performed to predict the radiation characteristics of burning coal layers heated on confined surfaces in an enclosed chamber. The one-dimensional (1D) unsteady energy balance equation and radiative transfer equation (RTE) were solved simultaneously using the semi-implicit Runge–Kutta method (SIRK) and discrete ordinate method (DOM). In addition to the 1D analysis, a commercial software was used to analyze the two-dimensional (2D) radiation behavior of the burning coal layers using the DOM.The heat generation rate (relevant to the combustion rate) and particle absorption coefficient were independently determined using combustion and thermal emission experiments. The gas absorption coefficient was calculated from gray gas models to account for the change of H2O vapor along coal and gas mixture with high moisture content. The dimensionless radiative heat flux and temperature distribution were determined for the three calculation cases. Two different predictions based on 1D and 2D geometries were validated against measured heat flux and temperature data. The effect of the moisture release inside the particle layer was particularly examined. The result indicates that the condensation of H2O is probably more responsible than the absorption of H2O vapor for a reduced heat flux observed in the combustion condition of high moisture coal burning at high pressure.

Velocity field and cavity dynamics in drop impact experiments.

Drop impact experiments allow to model a wide variety of natural processes, from raindrop impacts to planetary impact craters. In particular, interpreting the consequences of the planetary impacts requires an accurate description of the flow associated with the cratering process. In our experiments, we release a liquid drop above a deep liquid pool to investigate simultaneously the dynamics of the cavity and the velocity field produced around the air-liquid interface. Using particle image velocimetry, we analyse quantitatively the velocity field using a shifted Legendre polynomials decomposition. We show that the velocity field is more complex than considered in previous models, in relation to the non-hemispherical shape of the crater. In particular, the velocity field is dominated by the degrees 0 and 1, with contributions from the degree 2, and is independent of the Froude and the Weber number when these numbers are large enough. We then derive a semi-analytical model based on the Legendre polynomials expansion of an unsteady Bernoulli equation coupled with a kinematic boundary condition at the crater boundary. This model explains the experimental observations and can predict the time evolution of both the velocity field and the shape of the crater, including the initiation of the central jet.

Heat Transfer Coefficient Distribution—A Review of Calculation Methods

Determination of the heat transfer coefficient (HTC) distribution is important during the design and operation of many devices in microelectronics, construction, the car industry, drilling, the power industry and research on nuclear fusion. The first part of the manuscript shows works describing how a change in the coefficient affects the operation of devices. Next, various methods of determining the coefficient are presented. The most common method to determine the HTC is the use of Newton’s law of cooling. If this method cannot be applied directly, there are other methods that can be found in the open literature. They use analytical formulations, the lumped thermal capacity assumption, the 1D unsteady heat conduction equation for a semi-infinite wall, the fin model, energy conservation and the analogy between heat and mass transfer. The HTC distribution can also be calculated by means of computational fluid dynamics (CFD) modelling if all boundary conditions with fluid and solid properties are known. Often, the surface on which the HTC is to be determined is not accessible for any measuring sensors, or their installation might disturb the analysed phenomenon. It also happens that calculations using direct or CFD methods cannot be performed due to the lack of required boundary conditions or sufficiently proven models to analyse the considered physical phenomena. Too long a calculation time needed by CFD tools may also be problematic if the method should be used in the online mode. One way to solve the above problem is to assume an unknown boundary condition and include additional information from the sensors located at a certain distance from the investigated surface. The problem defined in this way can be solved by inverse methods. The aim of the paper is to show the current state of knowledge regarding the importance of the heat transfer coefficient and the variety of methods that can be used for its determination.

Numerical assessment of stability behaviour in supercritical CO2 based NCLS configured with heater, heat exchanger and isothermal wall as heat source

Three-dimensional numerical analysis is presented in this study to assess the transient and stability behaviour of supercritical CO2 (sCO2) based NCLs configured with three different types of heat sources, i.e., heater, a hot heat exchanger (HHX) and isothermal wall (ISO) at the source, and a cold heat exchanger (CHX) at the sink in all three NCLs. Unsteady threedimensional conservation equations (mass, momentum and energy equations) are solved to assess the transient and stability behaviour of sCO2 mass flow rate, temperature and velocity as a function of time. Further, the effect of pressure on sCO2 mass flow rate is also assessed to compare the loops performance. Performance of the loop has been studied for various heat inputs at the source by keeping constant mass flow rate and temperature at the sink. It is observed that for any boundary condition at the source, the loop experiences some initial disturbances or instabilities before reaching the steady-state. However, the time needed to attain a steady-state varies with the nature of heat input employed at the source. Results show a higher magnitude of instabilities in the Heater-CHX loop than HHX-CHX and ISO-CHX loops, and these instabilities mitigate at a faster rate in the ISO- CHX loop at all levels of heat input and operating pressure of the loop. It is also observed that as loop fluid operating pressure increases, the instability of the system decreases and the loop fluid mass flow rate increases. Further, the Nusselt number in the Heater-CHX loop is more than other loops because of its high turbulent kinetic energy. The findings of this study are validated with the published experimental and numerical data and found a good agreement.

Experimental Study and Modelling of the Sublimation and Desorption Periods for Freeze Drying of Apple, Banana and Strawberry

Slices of fresh apple, banana and strawberry were frozen at -20 oC and freeze-dried using a shelf temperature of 40 oC. Theoretical expressions were proposed to predict vapor transfer kinetics during the primary and secondary drying stages. In the former, a model that predicts the sublimation rate as a function of time, considering the increasing dried layer thickness, was used, which improves greatly the sublimation time equation offered in several textbooks without adding much complexity. In the latter, an analytical solution of the unsteady state diffusion equation was applied. Permeabilities were determined for the primary drying model at an absolute pressure of about 30 Pa, though the relevant kinetic coefficient combines permeability and the mass of ice to sublime relative to the dry matter (sublimation kinetic coefficient). In the secondary drying stage, diffusion coefficients of vapor in the dried layer were in the order of 10−09 m2s−1 for pressures of about 3-5 Pa. In both periods, agreement of predicted and experimental values was more than satisfactory. A minimum freeze-drying time of 12, 6.8 and 8.7 h, considering a final moisture content of 4% w/w, was calculated for apple, banana and strawberry, respectively. Normalized drying curves showed a faster sublimation rate for banana, intermediate for strawberry and slowest for apple. On the other hand, desorption curves showed a faster desorption rate for apple, intermediate for banana and slower for strawberry. In each period, the ordering of the relevant kinetic coefficients (sublimation and diffusion coefficients, respectively) represented the ordering of experimental curves.

Treatment of the Unsteady Heat Equation Subject to Heat Flux Boundary Conditions: The Method of Discretization in Time Complemented With Regression Analysis

Treatment of the Unsteady Heat Equation Subject to Heat Flux Boundary Conditions: The Method of Discretization in Time Complemented With Regression Analysis

Comparison of the Power Extraction Performance of an Oscillating Hydrofoil Turbine with Different Deflector Designs

The unsteady RANS equations for a two-dimensional hydrofoil were solved using ANSYS Fluent to model and simulate the hydrofoil at a constant Reynolds number, Re, of 2 × 105 and a fixed reduced frequency, f*, of 0.14. The simulations were performed by varying parameters, such as the number of deflectors N, tilt angle of the deflectors β, and vertical spacing of the deflectors J* = J/c, to determine the effect of the upstream deflector’s position on the hydrofoil’s performance. The results demonstrated that the deflector was effective at redirecting the separated flow away from the edges, which was then amplified downstream before colliding with the leading edge of the oscillating hydrofoil to increase power extraction. The performance of the oscillating hydrofoil was highly reliant on all three studied parameters. The hydrofoil with two deflectors (N = 2) displayed marginally superior power extraction capability compared to the hydrofoil with a single deflector (N = 1). Furthermore, the hydrofoil with the rightward inclined deflector at a low tilt angle (−5° ≥ β ≥ −10°) exhibited relatively better power extraction performance than the others. The best deflector design increased the hydrofoil’s cycle-averaged power coefficient by approximately 32% compared to a hydrofoil without a deflector. The vortex structures revealed that the flow evolution and power extraction performance were dependent on the size, robustness, and growth rate of the leading edge vortex (LEV) as well as the timing of LEV separation. The power extraction efficiency of an oscillating hydrofoil increased in the mid downstroke and upstroke due to the formation of a more robust LEV when the hydrofoil–deflector interaction was advantageous, but it dropped in the wing reversal due to the early separation of the LEV when the hydrofoil–deflector interaction was counterproductive.

Numerical Study of Heat Transfer and Fluid Flow over Circular Cylinders in 2D Cross Flow

Among the many experiments Which deals with the study of the characteristics of flow, a numerical study of flow air (Pr=0.71) crosses a circular cylinder is conducted. Variations in flow and thermal characteristics such as average Nusselt number, local pressure coefficient and drag coefficient are presented around the cylinders for Reynold numbers ranging from 100 to 5000 by solving the incompressible two-dimensional unsteady Navier-Stokes and energy equations. Commercial software package FLUENT 19 is applied to solve the equations. The diameter of the circle is D = 20 mm, the width is 20 times the diameter of the cylinder. The results obtained are compared with data of previous study for Nusselt Number values showed acceptable agreement. The results of the drag coefficient confirm a noticeable decrease in the transition from low values of Reynolds numbers to the high values.

Numerical analysis of aerodynamic regime near tailings storage facility

Tailings formed during the mining and beneficiation of iron ore are sources of intensive dust generation. In order to assess the intensity of dust formation and determine the effectiveness of methods of its reduction, it is necessary to know the local velocity of the air flow near the various surfaces of the tailings storage facility. For the theoretical solution of this problem, a CFD model was developed, which allows determining the velocity field of the air flow when flowing around the tailings storage facility. The model allows you to obtain the value of the wind speed near the surfaces of the structure and, based on this information, to make a forecast of possible dust formation. The constructed CFD model is based on the use of an aerodynamic model of potential motion. The modeling equation is the Laplace equation for the velocity potential. To build a numerical model, the idea of establishing a solution in time is used, therefore numerical integration of the “unsteady equation” for the velocity potential is carried out. Numerical integration is carried out using the finite-difference method of total approximation. The results of the computational experiment are presented.

Mechanistic-mathematical modeling of intracranial pressure (ICP) profiles over a single heart cycle. The fundament of the ICP curve form

The intracranial pressure (ICP) curve with its different peaks has been comprehensively studied, but the exact physiological mechanisms behind its morphology has not been revealed. If the pathophysiology behind deviations from the normal ICP curve form could be identified, it could be vital information to diagnose and treat each single patient. A mathematical model of the hydrodynamics in the intracranial cavity over single heart cycles was developed. A Windkessel model approach was generalized but the unsteady Bernoulli equation was utilized for blood flow and CSF flow. This is a modification of earlier models using the extended and simplified classical Windkessel analogies to a model that is based on mechanisms rooted in the laws of physics. The improved model was calibrated with patient data for cerebral arterial inflow, venous outflow, cerebrospinal fluid (CSF), and ICP over one heart cycle from 10 neuro-intensive care unit patients. A priori model parameter values were obtained by considering patient data and values taken from earlier studies. These values were used as an initial guess for an iterated constrained-ODE (ordinary differential equation) optimization problem with cerebral arterial inflow data as input into the system of ODEs. The optimization routine found patient-specific model parameter values that produced model ICP curves that showed excellent agreement with clinical measurements while model venous and CSF flow were within a physiologically acceptable range. The improved model and the automated optimization routine gave better model calibration results compared to previous studies. Moreover, patient-specific values of physiologically important parameters like intracranial compliance, arterial and venous elastance, and venous outflow resistance were determined. The model was used to simulate intracranial hydrodynamics and to explain the underlying mechanisms of the ICP curve morphology. Sensitivity analysis showed that the order of the three main peaks of the ICP curve was affected by a decrease in arterial elastance, a large increase in resistance to arteriovenous flow, an increase in venous elastance, or a decrease in resistance to CSF flow in the foramen magnum; and the frequency of oscillations were notably affected by intracranial elastance. In particular, certain pathological peak patterns were caused by these changes in physiological parameters. To the best of our knowledge, there are no other mechanism-based models associating the pathological peak patterns to variation of the physiological parameters.

Research on three kinds of splitting finite element schemes for 2D/3D unsteady incompressible thermomicropolar fluid equations

AbstractIn this article, three kinds of splitting finite element schemes are proposed for the 2D/3D unsteady incompressible thermomicropolar fluid equations, which are named as the standard splitting scheme, the consistent splitting schemes (I and II) and the splitting Oseen scheme. The unconditionally energy stable of all the schemes and error estimation of the standard splitting scheme are proved. Furthermore, numerical experiments are carried out on the last two kinds of schemes based on different selection of finite element pairs, numerical results show that the presented schemes are reliable, especially some not inf‐sup stable finite element pairs can also be applied for the consistent splitting scheme II. In addition, for moderate Reynolds number problems, the splitting Oseen scheme exhibit the better performance of numerical stability than the consistent splitting schemes.

A new hypothesis on the intrusion of the Loop Current

The unsteady and inviscid shallow water equations of motion and continuity for a northward moving Loop Current (LC) on the f-plane were integrated to derive an equation for the rate of LC area increase. The dA/dt, where A is the LC surface area, is a function of kinetic energy change across the LC and absolute vorticity. This equation agrees with previous results and is proposed as a new hyphothesis to explain the LC intrusion: a reduction in kinetic energy from west to east across the LC causes mass to be stored inside the Gulf of Mexico (GOM) because the outflow is smaller than the inflow and is manifested as a positive dA/dt indicating a growing and intruding LC into the GOM. The necessary kinetic energy reduction for driving the LC intrusion is caused by relative vorticity and dissipative energy mechanisms. Observations from the intruding LC showed a horizontal reduction of kinetic energy as suggested herein. We discussed that relative vorticity, dissipative forces, and baroclinic and baratropic instabilities induce a kinetic energy reduction across the LC causing an intrusion. Because of the possibility of several kinetic and potential energy-changing mechanisms acting jointly, finding a single mechanism or “trigger” to explain the LC intrusion seems difficult. Additionally, it seems that the relative vorticity values within the LC act to keep dA/dt close to its steady state value. The proposed hypothesis sheds light on the correlation between the LC intrusion and relative vorticity found by Candela et al. (2002). This hypothesis is diagnostic in the sense that it suggests a mechanism or mechanisms that induce a kinetic energy reduction across the LC and the intrusion. Numerical models are ideally suited to evaluate such mechanism(s), to verify the hypothesis, and help design field experiments to test it in the real ocean.

Analysis of solidification and physical behavior of nanomaterial during unsteady process

Alumina nanoparticles with various shapes have been loaded into water to accelerate the freezing phenomena within closed cavity. The mathematical model contains unsteady conduction equation in the existence of unsteady source terms for phase changing. In this model, three properties of NEPCM are involved and for calculating those parameters, single phase approximation has been utilized. By using FEM, outputs for impact of shape and volume of nanoparticles have been reported. Also, the method was verified by comparing the outputs with the previous data. Increasing the volume of nanoparticles to twice the range makes the needed time decrease by about 13.82%. When [Formula: see text], replacing nanoparticles with [Formula: see text] instead of [Formula: see text] makes freezing time decrease by about 3.92%.

A comprehensive pyrolysis model for lignocellulosic biomass particles with a special emphasis on the anisotropic characteristics

The porous and fibrous structural tissue of lignocellulosic biomass serves as a transport channel for water and nutrients along the growth direction, indicating a highly anisotropic nature of biomass. The anisotropies of the thermal and structural properties of biomass have substantial influences on particle-scale reactions, transport processes, and morphological evolution during thermal conversions. An in-depth investigation of the anisotropic characteristics of these physicochemical phenomena in pyrolysis benefits in the understanding of biomass gasification and combustion processes. In this study, a comprehensive 2D axisymmetric mathematical model is developed to quantitatively analyze the pyrolysis behaviors of a cylindrical wood particle with or without anisotropy. Correlative unsteady energy and mass conservation equations are combined with a multistep kinetic model of biomass devolatilization. To improve the numerical descriptions of volatiles flowing in a porous biomass matrix, the constitutive equations of the Brinkman equation and dusty gas model are adopted. Moreover, a binary differential equation is used to calculate the simultaneous changes in the pore structure and shrinkage of the wood particles. When considering anisotropy, validations of the model against literature data demonstrate that it can reliably predict the intraparticle temperature profiles, weight loss, and particle shrinking degree of lignocellulosic biomass. Using this model, the coupling effects of multi-physical fields and reactions inside pyrolyzing wood particles are explored. It is revealed that the anisotropic characteristics of biomass influence not only the orientations of intraparticle heat and mass transport processes but also their mechanisms, resulting in varying degrees of secondary reactions and particle shrinkage.

Numerical and experimental investigation into effects of winglet shape on flow and noise performances of axial-flow fans for outdoor unit of air conditioner

In this study, the effects of winglet shape on the flow performance, efficiency, and aerodynamic noise of axial-flow fans, used as cooling fans in an outdoor unit of split-type air-conditioners, are numerically and experimentally investigated. Especially, a focus is placed on the coherent flow structures of the tip and leakage vortices: the former is generated from the fan blade tip near the leading edge, and the latter forms in the gap between the blade tip and the shroud. Two types of axial-flow fans are considered: one is with a blade-tip winglet, and the other is without the blade-tip winglet. The flow fields around the fans are simulated by numerically solving the three-dimensional unsteady incompressible RANS equations, and the radiated acoustic pressure is predicted using the Ffowcs-Williams and Hawkings equation. The validity of the numerical methods is confirmed through the predicted results with the measured ones. The flow field characteristics driven by the fans with and without the winglet are analyzed by comparing the detailed structure of the tip and leakage vortices in the gap flow region. In addition, the flow performance, efficiency, and sound pressure of the axial fans are characterized in association with the vortex structures. These results reveal that the winglet shape in the gap flow region has an adverse effect on the flow and acoustic performances of axial-flow fans by increasing the gap-vortex strength.

Dynamic simulation of a solar-autothermal hybridized gasifier: Model principle, experimental validation and parametric study

Solar thermochemical fuel production technologies, such as biomass gasification, are confronted to the intermittency of solar irradiance. The development of dynamic simulation tools is thus required to design around-the-clock control strategies. An innovative model was developed here, based on unsteady mass and energy conservation equations, considering gas-phase thermodynamic equilibrium and heterogeneous char oxidation kinetics. The char accumulation and gas species production rates were therefore tracked throughout operation, giving insight into the reactor dynamics with optimized computational cost. The model was validated via a comparison with experimental results, regarding both thermal and chemical reactor performances. Simulations reliably predicted the evolution of reactor temperatures and syngas production rates, under both solar-only and hybridized (solar-autothermal) operation. Parametric studies regarding the impact of reactants injection rates on steady-state performances were finally proposed. Steam addition (0.22 to 0.60 g/min) increased the syngas H2:CO molar ratio significantly (1.13 to 1.47). Biomass addition (1 to 3 g/min) boosted the solar-to-fuel efficiency (0.22 to 0.47), but altered the reactor temperature. Finally, oxygen addition kept the reactor running despite fluctuations of solar power, while decreasing the total H2 + CO production and cold-gas efficiency linearly. A constant H2 + CO production (2.17 NL/min) could however be achieved by feeding additional biomass and oxygen during hybridization, thus limiting the cold-gas efficiency decrease and improving the reactor energy efficiency (0.29 to 0.40). Such a dynamic reactor model can be further applied to hybridized gasification process optimization and dynamic control under real fluctuating solar irradiation conditions.

New DY-HS hybrid conjugate gradient algorithm for solving optimization problem of unsteady partial differential equations with convection term

This paper studies an optimization problem for the unsteady partial differential equations (PDEs) with convection term, widely used in continuous casting process. Considering the change of casting speed, a dynamic optimization method based on new DY-HS hybrid conjugate gradient algorithm (DY-HSHCGA) is proposed. In the DY-HSHCGA, the Dai–Yuan and the Hestenes–Stiefel conjugate gradient algorithms are convex combined, and a new conjugate parameter θk is obtained through the condition of quasi-Newton direction. Moreover, Lipschitz continuity of the gradient of cost function, as an important conditions for convergence, is analyzed in this paper. On the basis on this condition, the global convergence of DY-HSHCGA is proved. Finally, the effectiveness of DY-HSHCGA is verified by some instances from the steel plant. Comparing with other algorithms DY-HSHCGA obviously accelerates the convergence rate and reduces the number of iteration. The optimizer based on the DY-HSHCGA shows a more stable results.