Maximum Average Absolute Deviation Research Articles

Thermal full-field prediction of an air-cooled data center using a novel multi-scale approach based on POD and CFD coupling

A full-knowledge of the temperature distribution in a data center is crucial for the design and operation to avoid thermal failure. However, it is a great challenge to conduct full-field simulations using the computational fluid dynamics/heat transfer (CFD/HT) method due to the unacceptable computational cost caused by the multi-scale structure of data centers. In this paper, a novel multi-scale model based on POD and CFD coupling is proposed to predict the thermal and fluid characteristics in data centers from room scale to chip scale. The temperature and flow fields in an air-cooled data center are predicted and analyzed under the scales of room, server, IGBT and chip. Based on the CFD results of Room-Server level, 16 sets of design cases’ temperature fields for Server-IGBT level are compared using the POD and CFD methods, which shows that the maximum average absolute deviation and average relative deviation are 0.004 °C and 0.59%, respectively. Subsequently, three sets of off-design cases for Server-IGBT level and IGBT-Chip level are predicted using the aforementioned methods, yielding the maximum relative deviation 7.21% and 0.98%, respectively. The salient outcome is the remarkable 175-fold reduction in CPU processing time achieved with the POD model compared to traditional CFD simulations.

Isothermal Vapor–Liquid Equilibrium for the Tetrafluoromethane (R14) + Octafluoropropane (R218) Binary Mixture at Five Temperatures from 173.150 to 213.150 K

Tetrafluoromethane (R14) and octafluoropropane (R218) are essential nonflammable refrigerants for mixed-refrigerant Joule Thomson refrigerators. In this paper, the vapor–liquid equilibrium (VLE) data were acquired for the R14 + R218 binary mixture from 173.150 to 213.150 K by a vapor-phase single-cycle method. The VLE data were regressed by the Soave–Redlich–Kwong (SRK) equation of state plus van der Waals (vdW) mixing rule model (SRK-vdW) and the Soave–Redlich–Kwong (SRK) equation of state combined with modified Huron–Vidal first-order (MHV1) mixing rule plus non-random two liquids (NRTL) activity coefficient model (SRK-MHV1-NRTL). The maximum average absolute relative deviation of pressure (AARDp) and the maximum average absolute deviation of vapor-phase mole concentration (AADy) are 2.42% and 0.0019 for the SRK-vdW model, respectively. A better correlation result was obtained by the SRK-MHV1-NRTL model, and the maximum AARDp and AADy are 1.04% and 0.0019, respectively. Based on the experimental and calculated results, a strong non-azeotropic behavior was found.

Simultaneous Prediction of Equilibrium, Interfacial, and Transport Properties of CO2-Brine Systems Using Molecular Dynamics Simulation: Applications to CO2 Storage

This study aims to provide accurate simultaneous predictions of crucial properties affecting CO2 storage in saline aquifers with deep microstructural insights using comprehensive molecular dynamics (MD) simulations under actual operating conditions ranges. We investigated the effects of pressure, temperature, and salinity on mutual solubility, interfacial tension (IFT), density, and viscosity of a CO2-brine system over the temperature range of 323.15–393.15 K, pressures up to 30 MPa, and salinity range of 0.98–2.97 mol/kg. Brine was resembled by employing different brine systems like actual reservoirs, including mixed electrolyte solutions containing monovalent and divalent ions. MD model configurations and force fields were validated by experimental data of a CO2-water/NaCl aqueous solution. The maximum average absolute deviations for the solubility, density, and IFT were 5.50, 6.95, and 7.136%, respectively. The simulation results indicated that mutual solubilities of CO2 and water in the CO2-NaCl + KCl solution system are higher than those of CO2-NaCl + CaCl2, while for IFT, the opposite trend is observed. Unlike pressure, salt concentration variations result in considerable density and viscosity changes for all systems. The maximum density and viscosity values are obtained for the brine-containing divalent cations. This study gives insight into the storage process and relates the microstructure effects to solubility, IFT, and viscosity of CO2-brine systems using a single MD model.

Simple Direct Relationship between Scaled Viscosity and a Dimensionless Calorimetric Parameter for Saturated Liquids

The relationship between the transport property and thermodynamic property was explored in this paper. More specifically, a dimensionless calorimetric parameter (DCP) was employed in order to predict the viscosity of different fluids for the first time. It was found that a strong linear correlation between the macroscopically scaled viscosity and the DCP of different fluids in saturated liquid states takes place. Additionally, the values of linearly correlated slopes K for each fluid were found to be in a narrow range (0.411 ± 0.034). Based on this, a quasi-universal viscosity prediction model was proposed. Fourteen fluids representing different molecular structures were selected, and the reliability of the theoretical framework was verified through comparison with experimental data. The results indicated that the correlation approach was very satisfactory with a maximum average absolute deviation (AAD) of 4.40%. Furthermore, by correlating the slopes with the fluid-specific parameters, a generalized function with no adjusting parameters was finally established. Compared with experimental data, the AADs were all located within 7.23%, except those for R125 and R143a. This work provides a convenient calculation method for the estimation of the transport property (viscosity) of different fluids only from the respective thermodynamic properties.

Phase equilibrium for the binary mixture of 1,1,2,3,3,3-hexafluoro-1-propene (R1216) + propane (R290) at temperatures from 283.15 to 313.15 K

Based on the study of the mixture containing 1,1,2,3,3,3-hexafluoro-1-propene (R1216) and propane (R290) by a set of static-analytical type experimental apparatus, this paper presents a series of vapour-liquid equilibrium data at the temperature from 283.15 K to 313.15 K. It is the first time to report the VLE data at a temperature below 313.15 K. Moreover, the uncertainties of pressure, temperature, and mole fraction in this experiment were determinate. The PR equation of state (EoS) combined with the following two models respectively, the van der Waals (vdWs) mixing rule and the Huron-Vidal (HV) mixing rule relating to the non-random two-liquid (NRTL) activity coefficient model were used to correlate the experimental VLE data of the binary system. Two models all presented an extremely content correlation of the experimental data for the R290 + R1216 mixtures, and the second model is more suitable as the pressure's maximum average relative and absolute deviation are 0.003 and 0.0026, respectively, and the maximum average absolute deviation of the vapor phase mole fraction AAD(y) is 0.0045. Near azeotropic phenomenon occurred within the temperature range of the experiment when the proportion of R290 is about 0.6 to 0.7.

A robust approach to establish tolerance limits for the gamma passing rate-based patient-specific quality assurance using the heuristic control charts.

Establishing the tolerance limits of patient-specific quality assurance (PSQA) processes based on the gamma passing rate (GPR) by using normal statistical process control (SPC) methods involves certain problems. The aim of this study was threefold: (a) to show that the heuristic SPC method can replace the quantile method for establishing tolerance limits in PSQA processes and is more robust, (b) to introduce an iterative procedure of "Identify-Eliminate-Recalculate" for establishing the tolerance limits in PSQA processes with unknown states based on retrospective GPRs, and (c) to recommend a workflow to define tolerance limits based on actual clinical retrospective GPRs. A total of 1671 volumetric-modulated arc therapy (VMAT) pretreatment plans were measured on four linear accelerators (linacs) and analyzed by treatment sites using the GPRs under the 2%/2mm, 3%/2mm, and 3%/3mm criteria. Normality testing was performed using the Anderson-Darling (AD) statistic and the optimal distributions of GPRs were determined using the Fitter Python package. The iterative "Identify-Eliminate-Recalculate" procedure was used to identify the PSQA outliers. The tolerance limits of the initial PSQAs, remaining PSQAs after elimination, and in-control PSQAs after correction were calculated using the conventional Shewhart method, two transformation methods, three heuristic methods, and two quantile methods. The tolerance limits of PSQA processes with different states for the respective methods, linacs, and treatment sites were comprehensively compared and analyzed. It was found that 75% of the initial PSQA processes and 63% of the in-control processes were non-normal (AD test, p<0.05). The optimal distributions of GPRs for the initial and in-control PSQAs varied with different linacs and treatment sites. In the implementation of the "Identify-Eliminate-Recalculate" procedure, the quantile methods could not identify the out-of-control PSQAs effectively due to the influence of outliers. The tolerance limits of the in-control PSQAs, calculated using the quantile of optimal fitting distributions, represented the ground truth. The tolerance limits of the in-control PSQAs and remaining PSQAs after elimination calculated using the heuristic methods were considerably close to the ground truth (the maximum average absolute deviations were 0.50 and 1.03%, respectively). Some transformation failures occurred under both transformation methods. For the in-control PSQAs at 3%/2mm gamma criteria, the maximum differences in the tolerance limits for four linacs and different treatment sites were 3.10 and 5.02%, respectively. The GPR distributions of PSQA processes vary with different linacs and treatment sites but most are skewed. In applying SPC methodologies to PSQA processes, heuristic methods are robust. For in-control PSQA processes, the tolerance limits calculated by heuristic methods are in good agreement with the ground truth. For unknown PSQA processes, the tolerance limits calculated by the heuristic methods after the iterative "Identify-Eliminate-Recalculate" procedure are closest to the ground truth. Setting linac- and treatment site-specific tolerance limits for PSQA processes is necessary for clinical applications.

Binary mixture isothermal vapour-liquid equilibrium: Trifluoromethane (R23) + octafluoropropane (R218) at the temperature from 223.150 K to 263.150 K

The mixed-refrigerant Joule-Thomson refrigerator (MJTR) is simple in structure, safe and reliable, and is suitable for temperatures from 80 to 230 K. Trifluoromethane (R23) and octafluoropropane (R218) are satisfactory as non-flammable refrigerants in MJTR. In this paper, the gas-phase single-cycle method was used to conduct a vapor–liquid equilibrium (VLE) experiment on the R23 + R218 binary system in the temperature range from 223.150 K to 263.150 K. The VLE experimental data were correlated using the Peng-Robinson (PR) equation of state and the Huron-Vidal (HV) mixing rule combined with non-random two-liquid (NRTL) activity coefficient model. The maximum average absolute relative deviation of pressure (AARDp) and the maximum average absolute deviation of vapor phase composition (AADy) are 0.67% and 0.005, respectively.

Helmholtz Scaling: An Alternative Approach to Calculate Viscosity with the PCP-SAFT Equation of State

We propose an alternative approach to calculate viscosity, based on the Rosenfeld scaling theory, which can be applied to pure components and their mixtures in a wide range of temperatures, pressures, and compositions. The Helmholtz scaling (A-scaling) applies the Chapman–Enskog relation, an Ansatz function, and the PCP-SAFT equation of state to predict the viscosity. Although it was implemented with the PCP-SAFT EoS, A-scaling has potential to be coupled with other EoS. Substances from n-alkanes, alcohols, aromatics, ethers, chlorofluorocarbons, carbon dioxide, and nitrogen were used to obtain five parameters to better correlate the experimental viscosity data. We tested the A-scaling performance of predicting the viscosity of 33 binary mixtures at different temperature and pressure conditions. For pure components, the minimum and maximum average absolute deviations (AADs) were 1.51 and 6.53%, respectively. Meanwhile, for mixtures, 0.70 and 23.95% were the lowest and highest values. By comparing this method with the successful and consolidated entropy scaling, it was found that AADs in most of the pure substances and mixtures were lower for A-scaling. Thus, since it is suitable for polar, nonpolar, and hydrogen-bonding substances, A-scaling covers many substances for industry applications, with no usage of adjustable parameters to predict viscosity for mixtures.

Thermodynamic investigation of hydrate-based CO2 capture from simulated flue gas with new mixed promoters

Abstract CO2 hydrate-based desalination (CHBD) has been developing for decades to meet the global demands of decreasing carbon dioxide (CO2) emissions. In this work, the CO2 was captured from the simulated flue gas which consists of 18.30 mol% carbon dioxide and 81.70 mol% nitrogen in the presence of tetra-n-butyl ammonium bromide (TBAB) + cyclopentane (CP) + glucoamylase. Then the phase equilibrium data of CO2 hydrate were measured by the method of isochoric pressure-search. Among the seven cases with same concentration of TBAB (0.29 mol%) and CP (5.00 vol%) and different glucoamylase proportions (ranging from 0.00 to 20.00 wt%), the optimum concentration of glucoamylase in the mixed promoters was 3.00 wt%. The phase equilibrium data was calculated by the modified van der Waals–Platteeuw (vdW–P) model with a modification of vapor pressure of water in the empty hydrate lattice. The Peng–Robinson equation of state was used to calculate the fugacity of gas. The maximum average absolute deviation was 4.09% between the calculated results and the experimental results. It revealed that the calculated results were in good agreement with the experimental results.

Evaluation on Excess Entropy Scaling Method Predicting Thermal Transport Properties of Liquid HFC/HFO Refrigerants

The application of the excess entropy scaling (EES) method to predict the viscosity, thermal conductivity and thermal diffusivity of HFC/HFO refrigerants is evaluated in this paper. The universal coefficients of the EES model were firstly obtained from the properties of HFC refrigerants, and the accuracy of the model was further investigated with HFO properties. It was suggested that the EES model correlated the viscosity very well with the average absolute deviations (AADs) of most HFC refrigerants lower than 6.55% except R32. The correlations also provided very good prediction on the viscosity for R1234yf and R1234ze(E), but not for R1336mzz(Z). The prediction of thermal conductivity for both HFC and HFO refrigerants was generally well with the maximum AAD of 11.44%. However, the paper also indicated that there were no universal thermal diffusivity coefficients for even HFC refrigerants, and the linear function could not fit the thermal diffusivity curve very well. Therefore, the exclusively two-order polynomial correlations based on the EES model were presented for each HFC/HFO refrigerant.

Experimental measurements and modelling of viscosity and density of calcium and potassium chlorides ternary solutions

Measured viscosity and density data for ternary aqueous solutions of CaCl2 and KCl are presented at temperatures between 293 and 323 K with 5 K increment. A modified Jones–Dole was introduced by adding extra terms and proved to be suitable for modelling of the viscosity data. Goldsack and Franchetto, Hu and Exponential models are used to correlate the viscosity data, too. Al models are correlated as a function of temperature and concentration. All models had successfully predicted the viscosity with high precision reaching a maximum average absolute deviation (AAD) of less than 2.3%. The modified Jones–Dole showed the best results among other models. Viscosity of the ternary solution is higher than the viscosity of water by about 15% at low concentrations and reaches about 270% at the highest concentrations. The amount of CaCl2 has more significant effect on the ternary mixture viscosity compared to KCl. This has created difficulty in measuring the viscosity and consequently the challenge in finding the different models parameters. Ternary solution densities were successfully correlate with Kumar’s model with AAD of less than 0.4%. Comparison of the ternary solution density and viscosity with the few available data literature showed a good agreement.

Efficient bivariate EWMA charts for monitoring process dispersion

AbstractTo ensure high quality standards of a process, the application of control charts to monitor process performance has become a regular routine. Multivariate charts are a preferred choice in the presence of more than one process variable. In this article, we proposed a set of bivariate exponentially weighted moving average (EWMA) charts for monitoring the process dispersion. These charts are formulated based on a variety of dispersion statistics considering normal and non‐normal bivariate parent distributions. The performance of the different bivariate EWMA dispersion charts is evaluated and compared using the average run length and extra quadratic loss criteria. For the bivariate normal process, the comparisons revealed that the EWMA chart based on the maximum standard deviation (SMAXE) was the most efficient chart when the shift occurred in one quality variable. It also performed well when the sample size is small and the shift occurred in both quality variables. The EWMA chart based on the maximum average absolute deviation from median (MDMAXE) performed better than the other charts in most situations when the shift occurred in the covariance matrix for the bivariate non‐normal processes. An illustrative example is also presented to show the working of the charts.

Measurements of isothermal vapor-liquid equilibrium for 2,3,3,3-tetrafluoroprop-1-ene + 1,1,1,2-tetrafluoroethane + propane system at temperatures from 283.15 to 323.15 K

Isothermal vapor liquid equilibrium (VLE) data of the alternative 2,3,3,3-tetrafluoroprop-1-ene + 1,1,1,2-tetrafluoroethane + propane ternary mixture over the temperature range of 283.15–323.15 K at 10 K intervals were measured using a circulation type apparatus. The experimental VLE data were correlated by Wilson-RK model, NRTL-RK model and PR-WS-MUNIFAC model. All of the models can well present the experimental data. The average absolute relative deviation (AARD) of pressure are within 0.60% and the maximum average absolute deviation (AAD) of vapor mass fraction is 0.0154 for the PR-WS-MUNIFAC model. Based on the UNIFAC (Dortmund) method, the two new functional groups of C2H2F and CH2F were divided and the relevant group parameters were obtained by fitting the experimental data.

Measurement of critical properties for binary and ternary mixtures containing potential gasoline additive diethyl carbonate (DEC)

The critical temperatures (Tc) and critical pressures (pc) of five binary mixtures (DEC + hexane, DEC + heptane, DEC + octane, DEC + cyclohexane, DEC + ethanol) and a ternary mixture (DEC + ethanol + heptane) were determined over the whole range of concentration using an accurate experimental apparatus based on flow method. The combined standard uncertainty of temperature is 0.2 K while that of pressure is 5.2 kPa. The critical temperatures of DEC + octane and DEC + cyclohexane mixtures present a non-ideal behavior. The maximum average absolute deviations of Redlich–Kister equations for Tc and pc of five binary mixtures are 0.08% and 0.41%, respectively. Cibulka's equations and Singh−Sharma's equations were used to correlate the critical parameters of ternary mixture. The critical surfaces of ternary mixture were plot using Cibulka's equations.

Experimental determination of critical data of multi-component mixtures containing potential gasoline additives 2-butanol by a flow-type apparatus

In this work, we used a flow method for measurement of critical properties of six binary mixtures (2-butanol+cyclohexane, 2-butanol+hexane, 2-butanol+heptane, 2-butanol+octane, 2-butanol+nonane and 2-butanol+decane) and two ternary mixtures (2-butanol+hexane+heptane and 2-butanol+octane+decane). The critical properties were determined by observing the disappearance and reappearance of the gas–liquid phase meniscus in a quartz glass tube. The standard uncertainties of temperatures and pressures for both binary and ternary mixtures were estimated to be less than 0.2K and 5.2kPa, respectively. These critical data provide the boundaries of the two-phase regions of the related mixture systems. Six binary systems show non-ideal behaviors in the loci of critical temperatures. We used the Redlich–Kister equations to correlate the critical temperatures and pressures of these systems and listed the binary interaction parameters. The maximum average absolute deviation (AAD) of each binary system between experimental data and calculated results from Redlich–Kister equations is 0.038% for critical temperatures, and 0.244% for critical pressures. Moreover, the two ternary systems were newly reported and correlated by Cibulka’s and Singh’s expressions. The maximum AAD of critical temperatures and critical pressures are 0.103% and 0.433%, respectively.

Determination of critical properties for binary and ternary mixtures containing propanol and alkanes using a flow view-type apparatus

The critical temperatures and pressures of eight binary systems and two ternary systems (1-propanol+cyclohexane, 1-propanol+n-hexane, 1-propanol+n-heptane, 1-propanol+n-octane, 1-propanol+n-decane, 2-propanol+cyclohexane, cyclohexane+n-hexane, cyclohexane+n-heptane, 1-propanol+cyclohexane+n-heptane and 1-propanol+n-octane+n-decane) were measured using an efficient and accurate low residence time flow apparatus. The uncertainties of the critical temperature and the pressure were estimated to be less than 0.4K and 0.01MPa, respectively. All the critical loci of binary systems belong to the type I or type II as defined by Scott and van Konynenburg. The curves of critical temperatures for the six binary mixtures containing 1-propanol or 2-propanol are non-ideal. Maximum average absolute deviations of the Redlich–Kister equations from the experimental results for the critical temperatures and the critical pressures of all the binary systems are 0.05% and 0.07%, respectively. Moreover, the two ternary systems were correlated by Cibulka's and Singh's expressions with maximum average absolute deviations 0.06% for critical temperatures and 0.83% for critical pressures.

(Vapour + liquid) equilibrium data for the {1,1-difluoroethane (R152a) + 1,1,1,3,3-pentafluoropropane (R245fa)} system at temperatures from (323.150 to 353.150) K

In this paper, (vapour+liquid) equilibrium (VLE) for the {1,1-difluoroethane (R152a)+1,1,1,3,3-pentafluoropropane (R245fa)} system was determined by a static-analytical method at T=(323.150 to 353.150)K. Values of the VLE were correlated by the Peng–Robison equation of state (PR EoS) using two different models, the van der Waals (vdWs) mixing rule and the Huron–Vidal (HV) mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. The correlated results show good agreement with the experimental values. For the two models, the maximum average absolute deviations of the vapour phase mole fraction are 0.0034 and 0.0035, respectively.

Formula calculation methods of water content in sweet natural gas and their adaptability analysis

Estimation of water content is the foundation of natural gas processing and designing, and a formula calculation method provides a solution simple and easy to be programmed by computers. In this regard, several main formula calculation methods of water content in sweet natural gas were reviewed and evaluated individually. There are formulas fitted with nomographic data (e.g. Sloan formula, Ning Yingnan formula, Khaled formula and Bahadori formula), empirical formulas fitted with experimental data (e.g. Zhu Lin formula, Behr formula and Kazim formula) and formulas generated based on water-hydrocarbon phases equilibrium (e.g. Saturated Vapor Pressure Model, Modified Ideal Model, Simplified Thermodynamic Model and Bukacek formula). The comparison of calculated and experimental values of each above formula calculation method indicates that, the Khaled formula provided the minimum average absolute deviation (AAD) – 2.524 0%, while the Behr method achieved the maximum AAD – 19.255%. After the analysis of the AAD results calculated by the methods at different temperature ranges, the Zhu Lin formula is recommended for −50 to −40 °C, the Sloan formula for −40 to 0 °C, the Simplified Thermodynamic Model for 0 to 37.78 °C, the Khaled formula for 37.78 to 171.11 °C, and the Bukacek formula for 171.11 to 237.78 °C.

(Vapor + liquid) phase equilibrium measurements for {trifluoroiodomethane (R13I1) + propane (R290)} from T = (258.150 to 283.150) K

In this paper, the (vapor+liquid) equilibrium data for (R13I1+R290) were measured by a vapor-recirculation apparatus at temperatures from (258.150 to 283.150)K. The VLE data were correlated by the Peng–Robinson equation of state with two different models, the van der Waals mixing rule, and the Huron–Vidal mixing rule involving the NRTL activity coefficient model. Good agreements were found between the calculated data and the experimental data. The maximum average absolute relative deviation of pressure (AARD p) was 0.48%, while the maximum average absolute deviation of composition (AAD y) was 0.0040. Meanwhile, zeotropic behavior can be found for the measured system in this study. The total combined standard uncertainties for temperature, pressure and composition measurements were ±5mK, ±0.0005MPa and ±0.005, respectively.

Process Simulation of Sulfuric Acid Recovery by Azeotropic Distillation: Vapor–Liquid Equilibria and Thermodynamic Modeling

For development of the new process for the recovery of dilute sulfuric acid by azeotropic distillation proposed in our earlier publication [Li et al., Ind. Eng. Chem. Res., 2013, 52, 3481–3489], in this paper, the vapor–liquid equilibria (VLE) for the FeSO4 + H2O and H2SO4 + FeSO4 + H2O systems were first determined by the quasi-static ebulliometric method. The azeotropic temperatures of the H2SO4 + H2O + entrainer (cyclohexane and octane) systems were also measured. The corresponding electrolyte nonrandom two-liquid interaction parameters were obtained by regressing the experimental data with a maximum average absolute deviation of boiling points of 0.83 K. The model with newly obtained parameters was verified by comparing its prediction with the experimental azeotropic temperature for the H2SO4 + FeSO4 + H2O + C6H12 quaternary system. The temperature and sulfuric acid concentration ranges of the study were 305.9–396.9 K and 0–86.1 wt %, respectively. Following from the experimental results, semicontinuous distillation experiments for the sulfuric acid recovery were performed with cyclohexane as the entrainer. Equipped with the new parameters, Aspen Plus was adopted to carry out the process simulation for the recovery of dilute sulfuric acid by azeotropic distillation. The simulation results show that when cyclohexane was employed as the entrainer, the dilute sulfuric acid can be concentrated to 68% by a packed column containing 4 theoretical stages and with a reboiler temperature of only 361 K.