scholarly journals An optimal control framework to determine diffusivity versus concentration surfaces in ternary systems of two gases and a non volatile phase

2021 ◽  
Author(s):  
Amir Jalal Sani
Keyword(s):  
Carbon Dioxide ◽  
Optimal Control ◽  
Diffusion Coefficient ◽  
Mass Fraction ◽  
Transfer Model ◽  
Cross Diffusion ◽  
Control Framework ◽  
Mass Fractions ◽  
Volatile Phase ◽  
The Cross

Diffusivity is a strong function of concentration and an important transport property. Diffusion of multiple species is far more frequent than the diffusion of one species. However, there are limited experimental data available on multi-component diffusivity. The objective of this study is to develop an optimal control framework to determine multi-component concentration-dependent diffusivities of two gases in a non-volatile phase such as polymer. In Part 1 of this study, we derived a detailed mass-transfer model of the experimental diffusion process for the non-volatile phase to provide the temporal masses of gases in the polymer. The determination of diffusivities is an inverse problem involving principles of optimal control. Necessary conditions are determined to solve this problem. In Part 2 of this study, we utilized the results of Part 1 to determine the concentration-dependent, multi-component diffusivities of nitrogen and carbon dioxide in polystyrene. To that end, solubility and diffusion experiments are conducted to obtain necessary data. In the ternary system of nitrogen (1), carbon dioxide (2), and polystyrene (3), the diffusivities and D11, D12, D21, and D22 versus the gas mass fractions are two-dimensional surfaces. The diffusivity of carbon dioxide was found to be greater than that of nitrogen. The value of the main diffusion coefficient D11 was found to increase as the concentration of carbon dioxide increased. The highest value of D11 obtained was 2.2 X 10^-8m^2s^-1 for nitrogen mass fraction of 3.14 X10^-4 and for a carbon dioxide mass fraction of 5.67 X 10^-4 . The cross-diffusion coefficient increased as the concentrations of nitrogen and carbon dioxide increased. The diffusivity reached its maximum value when the concentrations of nitrogen and carbon dioxide were at their maximum values. The diffusivity was of the order of 10^-9m^2s^-1. The diffusivity of the cross-diffusion coefficient D21 was found to be increased for the mass The diffusivity of the cross-diffusion coefficient was found to be increased for the mass fractions of carbon dioxide ranging from 0 to 1.70 X 10^-3 . The diffusivity was found to be of the order of . The diffusion coefficient, D22, was found to increase with the concentrations of nitrogen and carbon dioxide, D22 remained high with low concentrations of carbon dioxide. The diffusivity was found to be of the order of 10^-7m^2s^-1

scholarly journals An optimal control framework to determine diffusivity versus concentration surfaces in ternary systems of two gases and a non volatile phase

2021 ◽  
Author(s):  
Amir Jalal Sani
Keyword(s):  
Carbon Dioxide ◽  
Optimal Control ◽  
Diffusion Coefficient ◽  
Mass Fraction ◽  
Transfer Model ◽  
Cross Diffusion ◽  
Control Framework ◽  
Mass Fractions ◽  
Volatile Phase ◽  
The Cross

Diffusivity is a strong function of concentration and an important transport property. Diffusion of multiple species is far more frequent than the diffusion of one species. However, there are limited experimental data available on multi-component diffusivity. The objective of this study is to develop an optimal control framework to determine multi-component concentration-dependent diffusivities of two gases in a non-volatile phase such as polymer. In Part 1 of this study, we derived a detailed mass-transfer model of the experimental diffusion process for the non-volatile phase to provide the temporal masses of gases in the polymer. The determination of diffusivities is an inverse problem involving principles of optimal control. Necessary conditions are determined to solve this problem. In Part 2 of this study, we utilized the results of Part 1 to determine the concentration-dependent, multi-component diffusivities of nitrogen and carbon dioxide in polystyrene. To that end, solubility and diffusion experiments are conducted to obtain necessary data. In the ternary system of nitrogen (1), carbon dioxide (2), and polystyrene (3), the diffusivities and D11, D12, D21, and D22 versus the gas mass fractions are two-dimensional surfaces. The diffusivity of carbon dioxide was found to be greater than that of nitrogen. The value of the main diffusion coefficient D11 was found to increase as the concentration of carbon dioxide increased. The highest value of D11 obtained was 2.2 X 10^-8m^2s^-1 for nitrogen mass fraction of 3.14 X10^-4 and for a carbon dioxide mass fraction of 5.67 X 10^-4 . The cross-diffusion coefficient increased as the concentrations of nitrogen and carbon dioxide increased. The diffusivity reached its maximum value when the concentrations of nitrogen and carbon dioxide were at their maximum values. The diffusivity was of the order of 10^-9m^2s^-1. The diffusivity of the cross-diffusion coefficient D21 was found to be increased for the mass The diffusivity of the cross-diffusion coefficient was found to be increased for the mass fractions of carbon dioxide ranging from 0 to 1.70 X 10^-3 . The diffusivity was found to be of the order of . The diffusion coefficient, D22, was found to increase with the concentrations of nitrogen and carbon dioxide, D22 remained high with low concentrations of carbon dioxide. The diffusivity was found to be of the order of 10^-7m^2s^-1

Microscale Mass Diffusion Sensing of Polymer Solutions Using Soret Forced Rayleigh Scattering

2008 ◽  
Author(s):  
Yuji Nagasaka
Keyword(s):  
Diffusion Coefficient ◽  
Polymer Films ◽  
Diffusion Coefficients ◽  
Rayleigh Scattering ◽  
Casting Process ◽  
Scattering Method ◽  
Binary Solutions ◽  
Forced Rayleigh Scattering Method ◽  
Cross Diffusion ◽  
The Cross

In the casting process of highly functional films, the control of complex micro and nano structures inside the polymer films is one of the most critical factors. The control requires the cross diffusion coefficients in multicomponent solutions because it has a direct influence on the formation of fine structures inside polymer films during the casting process [1]. However, most studies on diffusion in polymer solutions concentrate on measuring diffusion coefficients in binary solutions and only a few measurement techniques of the cross diffusion coefficient can be found. We have developed a measurement technique for the mutual diffusion coefficient in binary solutions, namely Soret forced Rayleigh scattering method [2–4]. In the present paper, we have applied Soret forced Rayleigh scattering method to measure the binary mass diffusion coefficient for the clarification of the cross diffusion phenomena in multicomponent diffusion.

A technique for uranium and plutonium determination using coulometric potentiostatic facility UPK-19 for analysis of mixed-oxide fuel

2020 ◽  
Vol 86 (12) ◽  
pp. 15-22
Author(s):  
N. A. Bulayev ◽  
E. V. Chukhlantseva ◽  
O. V. Starovoytova ◽  
A. A. Tarasenko
Keyword(s):  
Acid Solution ◽  
Mass Fraction ◽  
Background Electrolyte ◽  
Stable State ◽  
Sulfamic Acid ◽  
Oxide Fuel ◽  
Oxidation Current ◽  
Mox Fuel ◽  
Mass Fractions ◽  
Uranium Plutonium

The content of uranium and plutonium is the main characteristic of mixed uranium-plutonium oxide fuel, which is strictly controlled and has a very narrow range of the permissible values. We focused on developing a technique for measuring mass fractions of uranium and plutonium by controlled potential coulometry using a coulometric unit UPK-19 in set with a R-40Kh potentiostat-galvanostat. Under conditions of sealed enclosures, a special design of the support stand which minimized the effect of fluctuations in ambient conditions on the signal stability was developed. Optimal conditions for coulometric determination of plutonium and uranium mass fractions were specified. The sulfuric acid solution with a molar concentration of 0.5 mol/dm3 was used as a medium. Lead ions were introduced into the background electrolyte to decrease the minimum voltage of hydrogen reduction to –190 mV. The addition of aluminum nitride reduced the effect of fluoride ions participating as a catalyst in dissolving MOX fuel samples, and the interfering effect of nitrite ions was eliminated by introducing a sulfamic acid solution into the cell. The total content of uranium and plutonium was determined by evaluation of the amount of electricity consumed at the stage of uranium and plutonium co-oxidation. Plutonium content was measured at the potentials, at which uranium remains in the stable state, which makes it possible to subtract the contribution of plutonium oxidation current from the total oxidation current. The error characteristics of the developed measurement technique were evaluated using the standard sample method and the real MOX fuel pellets. The error limits match the requirements set out in the specifications for MOX fuel. The technique for measuring mass fractions of uranium and plutonium in uranium-plutonium oxide nuclear fuel was certified. The relative measurement error of the mass fraction of plutonium and uranium was ±0.0070 and ±0.0095, respectively. The relative error of the ratio of the plutonium mass fraction to the sum of mass fractions of uranium and plutonium was ±0.0085.

scholarly journals Numerical Investigation of the Effect of Air Leaking into the Working Fluid on the Performance of a Steam Ejector

2021 ◽  
Vol 11 (13) ◽  
pp. 6111
Author(s):  
He Li ◽  
Xiaodong Wang ◽  
Jiuxin Ning ◽  
Pengfei Zhang ◽  
Hailong Huang
Keyword(s):  
Flow Structure ◽  
Mass Fraction ◽  
Internal Flow ◽  
Working Fluid ◽  
Physical Parameters ◽  
Entrainment Ratio ◽  
Air Mass ◽  
Steam Ejector ◽  
Primary Fluid ◽  
Mass Fractions

This paper investigated the effect of air leaking into the working fluid on the performance of a steam ejector. A simulation of the mixing of air into the primary and secondary fluids was performed using CFD. The effects of air with a 0, 0.1, 0.3 and 0.5 mass fraction on the entrainment ratio and internal flow structure of the steam ejector were studied, and the coefficient distortion rates for the entrainment ratios under these air mass fractions were calculated. The results demonstrated that the air modified the physical parameters of the working fluid, which is the main reason for changes in the entrainment ratio and internal flow structure. The calculation of the coefficient distortion rate of the entrainment ratio illustrated that the air in the primary fluid has a more significant impact on the change in the entrainment ratio than that in the secondary fluid under the same air mass fraction. Therefore, the air mass fraction in the working fluid must be minimized to acquire a precise entrainment ratio. Furthermore, this paper provided a method of inspecting air leakage in the experimental steam ejector refrigeration system.

Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion

2019 ◽  
Vol 29 (03) ◽  
pp. 1950036 ◽  
Author(s):  
R. Sivasamy ◽  
M. Sivakumar ◽  
K. Balachandran ◽  
K. Sathiyanathan
Keyword(s):  
Temporal Dynamics ◽  
Intake Rate ◽  
Diffusion Term ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Nonlinear Harvesting ◽  
Ratio Dependent ◽  
The Cross

This study focuses on the spatial-temporal dynamics of predator–prey model with cross-diffusion where the intake rate of prey is per capita predator according to ratio-dependent functional response and the prey is harvested through nonlinear harvesting strategy. The permanence analysis and local stability analysis of the proposed model without cross-diffusion are analyzed. We derive the conditions for the appearance of diffusion-driven instability and global stability of the considered model. Also the parameter space for Turing region is specified by keeping the cross-diffusion coefficient as one of the crucial parameters. Numerical simulations are given to justify the proposed theoretical results and to show that the cross-diffusion term plays a significant role in the pattern formation.

scholarly journals A Hida–Malliavin white noise calculus approach to optimal control

2018 ◽  
Vol 21 (03) ◽  
pp. 1850014
Author(s):  
Nacira Agram ◽  
Bernt Øksendal
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
White Noise ◽  
Backward Stochastic Differential Equation ◽  
Second Order ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Alternative Approach ◽  
Quadratic Optimal Control ◽  
White Noise Calculus

The classical maximum principle for optimal stochastic control states that if a control [Formula: see text] is optimal, then the corresponding Hamiltonian has a maximum at [Formula: see text]. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida–Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.

Numerical and Experimental Investigation Into the Effects of Nanoparticle Mass Fraction and Bubble Size on Boiling Heat Transfer of TiO2–Water Nanofluid

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Cong Qi ◽  
Yongliang Wan ◽  
Lin Liang ◽  
Zhonghao Rao ◽  
Yimin Li
Keyword(s):  
Heat Transfer ◽  
Bubble Size ◽  
Boiling Heat Transfer ◽  
Mass Fraction ◽  
Experimental Methods ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Mass Fractions ◽  
Boiling Heat Transfer Coefficient ◽  
Bubble Sizes

Considering mass transfer and energy transfer between liquid phase and vapor phase, a mixture model for boiling heat transfer of nanofluid is established. In addition, an experimental installation of boiling heat transfer is built. The boiling heat transfer of TiO2–water nanofluid is investigated by numerical and experimental methods, respectively. Thermal conductivity, viscosity, and boiling bubble size of TiO2–water nanofluid are experimentally investigated, and the effects of different nanoparticle mass fractions, bubble sizes and superheat on boiling heat transfer are also discussed. It is found that the boiling bubble size in TiO2–water nanofluid is only one-third of that in de-ionized water. It is also found that there is a critical nanoparticle mass fraction (wt.% = 2%) between enhancement and degradation for TiO2–water nanofluid. Compared with water, nanofluid enhances the boiling heat transfer coefficient by 77.7% when the nanoparticle mass fraction is lower than 2%, while it reduces the boiling heat transfer by 30.3% when the nanoparticle mass fraction is higher than 2%. The boiling heat transfer coefficients increase with the superheat for water and nanofluid. A mathematic correlation between heat flux and superheat is obtained in this paper.

Effect of CeO2 addition on microstructure and tribological characteristics of laser cladded Cu10Al–MoS2 coating under oil lubrication

2021 ◽  
pp. 146442072110309
Author(s):  
Shao Lifan ◽  
Ge Yuan ◽  
Kong Dejun
Keyword(s):  
Abrasive Wear ◽  
Wear Mechanism ◽  
Mass Fraction ◽  
Friction Reduction ◽  
Depth Of Field ◽  
Oil Lubrication ◽  
Wear Properties ◽  
Fatigue Wear ◽  
Wear Rates ◽  
Mass Fractions

In order to improve the friction and wear properties of Cu10Al–MoS2 coating, the addition of CeO2 is one of the present research hot spots. In this work, Cu10Al–MoS2 coatings with different CeO2 mass fractions were successfully fabricated on Q235 steel using a laser cladding. The microstructure and phase compositions of obtained coatings were analyzed using an ultra-depth of field microscope and X-ray diffraction, respectively. The friction-wear test was carried out under oil lubrication using a ball-on-disk wear tester, and the effects of CeO2 mass fraction on the microstructure, hardness, and friction-wear properties were studied, and the wear mechanism was also discussed. The results show that the laser cladded Cu10Al–MoS2 coatings with the different CeO2 mass fractions were mainly composed of Cu9Al4, Cu, AlFe3, Ni, MoS2, and CeO2 phases. The Vickers-hardness (HV) of Cu10Al–8MoS2–3CeO2, Cu10Al–8MoS2–6CeO2, and Cu10Al–8MoS2–9CeO2 coatings was 418, 445, and 457 HV0.3, respectively, which indicates an increase in hardness with the increase of CeO2 mass fraction. The average coefficients of friction (COF) and wear rates decrease with the increase of CeO2 mass fraction, presenting the outstanding friction reduction and wear resistance performances. The wear mechanism of Cu10Al–MoS2 coatings is changed from abrasive wear with slight fatigue wear to abrasive wear with the increase of CeO2 mass fraction.

An Economic Model Predictive Control Approach for Wind Power Smoothing and Tower Load Mitigation

2018 ◽  
Author(s):  
Mohamed M. Alhneaish ◽  
Mohamed L. Shaltout ◽  
Sayed M. Metwalli
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Model Predictive Control ◽  
Wind Power ◽  
Predictive Control ◽  
Economic Model ◽  
Control Algorithm ◽  
Fatigue Load ◽  
Economic Model Predictive Control ◽  
Control Framework

An economic model predictive control framework is presented in this study for an integrated wind turbine and flywheel energy storage system. The control objective is to smooth wind power output and mitigate tower fatigue load. The optimal control problem within the model predictive control framework has been formulated as a convex optimal control problem with linear dynamics and convex constraints that can be solved globally. The performance of the proposed control algorithm is compared to that of a standard wind turbine controller. The effect of the proposed control actions on the fatigue loads acting on the tower and blades is studied. The simulation results, with various wind scenarios, showed the ability of the proposed control algorithm to achieve the aforementioned objectives in terms of smoothing output power and mitigating tower fatigue load at the cost of a minimal reduction of the wind energy harvested.

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