Simplified Correlation Research Articles

Efficient propagation of suspended HL-60 cells in a disposable bioreactor supporting wave-induced agitation at various Reynolds number

Growth of human nonadherent HL-60 cell cultures performed in disposable bioreactor under various hydrodynamic conditions of 2-D wave-assisted agitation has been compared and discussed. Influence of Reynolds number for liquid (ReL) and the kLa coefficient, as key parameters characterized the bioprocessing of HL-60 cells in ReadyToProcess WAVETM 25 system, on reached values of the apparent maximal specific growth rate (μmax) and the specific yield of biomass (Y*X/S) has been identified. The values of ReL (i.e., 510–10,208), as well as kLa coefficient (i.e., 2.83–13.55 h−1), have been estimated for the cultures subjected to wave-induced mixing, based on simplified dimensionless correlation for various presents of WAVE 25 system. The highest values of apparent μmax = 0.038 h−1 and Y*X/S = 25.64 × 108 cells gglc−1 have been noted for cultures independently performed at wave-induced agitation characterized by ReL equaled to 5104 and 510, respectively. The presented results have high applicability potential in scale-up of bioprocesses focused on nonadherent animal cells, or in the case of any application of disposable bioreactors presenting similitude.

Thermodynamic Effects on Grade Transition of Polyethylene Polymerization in Fluidized Bed Reactors

AbstractAn off‐line dynamic optimization procedure is employed to optimize the transition between different grades of linear low density polyethylene in a fluidized bed reactor. This type of reactor is frequently operated under condensed mode, which consists of injecting induced condensing agents (ICA) to absorb part of the reaction heat. However, the presence of ICA affects the solubility of monomers in the polymer, so it is important to account for this effect in a grade transition optimization strategy. A kinetic model is combined with a thermodynamic model based on the Sanchez–Lacombe equation of state to describe the grade transitions. Simplified correlations are then suggested to predict the impact of ICA on ethylene and comonomer solubility in a quaternary system. The results highlight the importance of the thermodynamic model during grade transition.

Experimental study on flame propagation over horizontal electrical wires under varying pressure

Flame propagation behavior over the polymer insulation of electrical wires can ignite adjacent combustibles and increase the scale of the fire. In this study, the flame propagation behavior over polyethylene (PE)-insulated wires was investigated theoretically and experimentally under varying pressures. The experiments were conducted in three cities with different altitudes (64, 76, and 100 kPa) and in a newly designed hypobaric chamber (7.5–101.3 kPa) for the first time. The flame morphology, structure, and spread rate were examined and discussed. The results show that pressure significantly affects flame propagation behavior. With increasing pressure, the flame illumination increases, and the flame shape changes, while the average flame height increases monotonously with decreasing average flame width. The weaker reaction rate and reduced heat transfer are the essential factors that result in a decreasing flame spread rate at lower pressures. In addition, a simplified correlation between the flame spread rate, pressure, and wire configuration in the form of Vf∝(P2L3)0.65 is proposed to predict flame propagation along an electrical wire. Moreover, the influence of the metal core on the flame behavior was observed based on the different heat transfer mechanisms in the flame front zone. All results contribute to the safe operation of electrical wires.

On the development of a simplified model for thermal comfort control of split systems

Despite split-type systems for cooling purposes became popular in countries such as China, Japan. India, Indonesia and Brazil, their use commonly promote high gradients of both temperature and air velocity in rooms which may cause considerable thermal discomfort. Hence, this work aims at developing a simplified thermal comfort index, based on temperature and air speed, in order to develop controllers for those types of air conditioning systems, replacing the traditional on-off temperature set-point control by an effective and inexpensive thermal-comfort based control. The work is focused on the assessment of comfort in classrooms by carrying out measurements according to ISO 7730 and ASHRAE 55 Standards, which defines the thermal satisfaction in occupied environments based on the PMV index. Specifically, the speed, temperature and relative humidity of the air and the mean radiant temperature of the room were measured at eight positions within the space. The field experiments were performed considering two 10.5-kW cooling capacity appliances installed in different positions relatively to the layout of the room, considering three levels of supply airflow (high, medium and low) and three set-point temperatures (23, 24 and 25 °C). An analysis of uncertainties is presented for PMV measurements and a regression analysis was applied to the measured data to determine a simplified correlation between thermal comfort (by means of the PMV index) air temperature and air velocity, aiming at developing afterwards a control device based on thermal comfort instead of temperature setpoint only. Results are shown in terms of distribution of air speed, air temperature and PMV index for the two configurations of equipment installation, as well as the resulting empirical model correlating thermal comfort index with both temperature and air speed. In addition, thermal comfort opinions from a survey are contrasted with the simplified thermal comfort model.

Safety parameters for oxygen-enriched flames

The utilization of low-quality gaseous fuel from biomass gasification and the abundance of oxygen-rich streams obtained as a by-product of nitrogen-air separation by membrane technology has incentivized the development of sustainable oxygen-enriched combustion technologies in the last decades. However, a dearth of experimental and numerical analysis addressing the reactivity and safety aspects of these mixtures at initial low temperatures can be observed in the current literature.In this work, the heat flux burner was adopted for the measurement of the laminar burning velocity of methane in oxygen enriched air at different equivalence ratios. Results were compared with numerical data obtained by means of detailed kinetic mechanisms developed at the University of Bologna and the Gas Research Institute (GriMech3.0). Simplified correlations for the estimation of the laminar burning velocity with respect to the oxygen content at any equivalence ratio were developed, tested and evaluated.An elemental reaction-based function was found appropriate for the estimation of the overall reactivity of the investigated mixtures. Besides, numerical analyses were performed to characterize the flame structures in terms of temperature and product distribution under several initial conditions. These results gave further insights into the reaction mechanisms of gaseous fuels in the case of oxygen-enriched air, highlighting potential bottlenecks for kinetic model refinements. Eventually, relevant safety parameters were estimated, in particular the flammability range of the fuel/oxidant mixture, in terms of lower and upper flammability limits.

Steady state relative permeability experiments with capillary end effects: Analytical solutions including derivation of the intercept method

Steady state relative permeability experiments are performed by coinjection of two (or more) immiscible fluids. The relative permeabilities can be calculated directly from the stabilized pressure drop and saturation of the core if capillary end effects and transient effects are negligible. In most cases such conditions are difficult to obtain.This work presents an analytical solution in form of explicit expressions for the spatial profiles of pressure gradients and saturation, average saturation and pressure drop for a core being injected simultaneously with two phases at steady state when capillary end effects are significant. When arbitrary saturation functions are applied, such parameters and distributions can only by obtained by numerical integration.By assumption of simplified saturation function correlations the differential equation describing steady state can be integrated. A new dimensionless capillary number N is obtained which contains the fluid and rock parameters, but also the saturation function parameters (relative permeability and capillary pressure), fluid viscosities, injected flow fraction, total flow rate and more. It is shown that when this number is of magnitude 1, end effects cover parts of the core, but parts of the core are also unaffected. For N>10 the end effects are negligible, while for N<10 end effects are dominant.This paper gives the first formal proof of the intercept method from basic assumptions. It is shown that when the inlet saturation is sufficiently close to that of a no capillary pressure situation; the average saturation changes linearly with the inverse of total rate towards the saturation corresponding to no capillary forces; also, the pressure drop divided by the pressure drop of a no end effect situation goes linearly towards 1 with the inverse of total rate.

A fast prediction method for maximum APF of heat pump type air conditioners based on a single group of experimental data

The annual performance factor (APF) is a new performance index of heat pump type air conditioners (HPACs) based on multiple testing conditions which may result in orders of magnitude larger workload in the product development for enhancing the APF to be close to the maximal value. The development process can be accelerated if the maximum APF can be predicted. The purpose of this study is to present a fast prediction method with a high precision for the maximum APF of HPACs based on a single group of experimental data. The idea of achieving fast prediction is to establish a simplified lumped parameter model for the calculation of capacities and efficiencies of HPACs, and to present a simplified approximate APF correlation by eliminating all the intermediate parameters from the complicated APF equations defined in standards of HPACs. A group of experimental data is applied in the prediction model to improve the precision of the fast prediction method. Application of this method for a typical HPAC shows that the predicted maximum APF of the HPAC agrees well with the tested maximum APF, the maximum deviation of predicted capacities and efficiencies from the experimental data is within ±1.4%; and the duration of prediction for maximum APF is within 12 s on a typical personal computer, significantly saving the time of HPAC development.

DEM simulation of dense granular flows in a vane shear cell: Kinematics and rheological laws

The rheology of dense granular flows is investigated through discrete element method (DEM) simulation of a vane shear cell. From the simulation, profiles of shear stress, shear rate, and velocity are obtained, which demonstrates that the flow features in the vane shear cell are equivalent to those in the classic annular Couette cell. A novel correlation for the apparent viscosity is formulated and leads to a new expression for μKT in the kinetic theory analysis. The μKT formulation is able to qualitatively capture the μ-I relation in the shear cell. A correlation length is added in the energy dissipation term to account for the effects of the particle motion correlation. A simplified correlation length model is derived based on DEM results and is compared with the literature. The modified granular kinetic energy equation is able to correctly predict the granular temperature profiles in the shear cell.

Numerical study and correlations for heat and mass transfer coefficients in indirect evaporative coolers with condensation based on orthogonal test and CFD approach

Previous studies obtained the heat and mass transfer coefficients of Indirect evaporative coolers (IECs) with condensation based on the following assumptions: (1) empirical equations in the dry channel without water evaporation or condensation, or the boundary condition is assumed to be a constant surface heat flux or temperature so that constant values of Nusselt number can be employed for evaluating the heat transfer coefficient; and (2) Lewis number is assumed to be unity so that the mass transfer coefficients can be then calculated via the heat and mass transfer analogy. Thus far, the heat and mass transfer coefficients of IECs with condensation under naturally formed boundary condition are lacking. In this paper, an experimental-validated computational fluid dynamics (CFD) model has been established to investigate the heat and mass transfer processes of IECs incorporating the phenomenon of condensation. A single factor analysis and a multiple factor analysis are concurrently carried out to evaluate the effects of the nine parameters on the heat and mass transfer processes of IECs. Key findings revealed that both mean Nusselt and Sherwood numbers under the presented conditions are larger than those obtained under constant surface temperature and heat flux conditions; and the respective values of the primary and secondary Lewis numbers are observed to change from 0.37 to 0.75 and 0.70 to 0.85 which severely deviate from the conventional assumed value of unity. Finally, empirical correlations are developed for the mean heat and mass transfer coefficients based on an orthogonal test method. The simplified linear correlations can serve as new fundamental references to account for IEC that are consistently experiencing with condensation.

A simplified ICA-based local similarity stereo matching

Since the existing stereo matching methods may fail in the regions of non-textures, boundaries and tiny details, a simplified independent component correlation algorithm (ICA)-based local similarity stereo matching algorithm is proposed. In order to improve the DispNetC, the proposed algorithm first offers the simplified independent component correlation algorithm (SICA) cost aggregation. Then, the algorithm introduces the matching cost volume pyramid, which simplifies the pre-processing process for the ICA. Also, the SICA loss function is defined. Next, the region-wise loss function combined with the pixel-wise loss function is defined as a local similarity loss function to improve the spatial structure of the disparity map. Finally, the SICA loss function is combined with the local similarity loss function, which is defined to estimate the disparity map and to compensate the edge information of the disparity map. Experimental results on KITTI dataset show that the average absolute error of the proposed algorithm is about 37% lower than that of the DispNetC, and its runtime consuming is about 0.6 s lower than that of GC-Net.

Frictional Factor Correlation for Laminar High-Viscosity Oil/Gas Flow in Horizontal Pipes

Summary Pressure drop prediction of high-viscosity oil/gas flow is an important issue in several industries, and it has a great interest for many researchers. This paper presents a simplified correlation for two-phase high-viscosity oil/gas flow friction factor in horizontal pipes. The developed friction factor is a sole function of Reynolds number on the basis of the mixture velocity and liquid properties. The recently developed friction factor correlation for laminar and turbulent gas/liquid flow is not suitable for the high-viscosity liquid/gas flow for which Reynolds number is less than 2,000. The validation of the proposed correlation against experimental data and the newly developed correlation showed accurate results for the two-phase friction factor for the cases matching gas/heavy oil flow with liquid holdup greater than 0.5 and mixture Reynolds number on the basis of liquid properties less than 2,000. The proposed correlation accuracy is better than the generalized correlation developed for all viscosities and Reynolds numbers and liquid holdup greater than 0.5. The less the Reynolds number, the more accurate the results.

Far field radiation properties of gaseous modelled wind-blown pool fires: An experimental investigation and simplified geometrical analysis

This paper presents an experimental study on the far-field radiation properties of modelled gaseous pool fires in cross winds, which have not been previously discussed in the literature. Bench scale experiments were conducted to quantify the evolution of radiation emission of pool fires using square porous burners (stainless-steel boxes filled with quartz sand) of different sizes (8, 10, 15 and 20 cm), employing propane as the fuel. The radiation heat flux as well as the radiation fraction were measured by a single-point method. For all pool fires employed, it was found that the radiation heat flux, as well as the radiation fraction, declined with increasing wind speed from ~0.5 m/s up to ~5 m/s. Based on an assumed triangular geometric approximation of flame projection area of wind-blown pool fires, a simplified correlation related to the flame surface area exposed to the radiometer was proposed to interpret the changing radiation fraction of pool fires of different sizes and heat release rates (HRR) in cross winds. The proposed function correlates the experimental data well under relative strong wind conditions (Fr > 1). This work provides new basic data revealing the radiation evolution behaviour of gaseous pool fires with respect to wind speed.

Novel mathematical correlation for accurate prediction of gas compressibility factor

Gas compressibility factor is a critical thermodynamic property that is a required input in the estimation of many reservoir fluid properties and reservoir engineering calculations. Experimentally derived values are considered the best, but these are very expensive and time-consuming. In this work, we have developed a new simplified explicit compressibility factor correlation based on a large dataset using a hybrid nonlinear optimization technique. The new model has a correlation coefficient of 0.9997 and very low average relative error and root-mean-square errors. Statistical analysis shows that this new correlation outperforms all of the existing correlations within the range of 0.2 < Ppr <15 and 1.05 < Tpr < 2).

Energy efficiency analysis for a kilo-watt class vanadium redox flow battery system

A new methodology for estimation of the key characteristics of commercial scale Vanadium Redox Flow Battery (VRFB) at different operating conditions is proposed. The method is based on a set of simplified correlations that allow estimating VRFB rated power, capacity and operation time directly from the geometry of stack and tank without detailed numerical simulation of the battery. The study is focused on investigation of a kilo-watt class VRFB system (5 kW/15kWh) considering a wide range of current densities (40–100 mA cm−2). The proposed simplified approach is validated considering the most representative cases of battery operation strategies related to slow and fast modes. It demonstrated high accuracy for the estimation of rated power and operation time (average error below 3%) as well as stored energy (average error below 6%) compare to results of detailed numerical simulation. As a result, the proposed methodology can be used as a simple tool for development of proper battery usage protocol (a schedule for battery usage), which could allow avoiding over/underestimation of committed battery energy and power during battery operation. In addition, the obtained results can be also used in order to improve the accuracy of techno-economic studies determining the most economically attractive cases for application of VRFB systems.

Assessment of a Simplified Correlation Between Wettability Measurement and Dispersion/Coagulation Potency of Oxide Particles in Ferrous Alloy Melt

This article seeks to demonstrate a direct and simplified correlation between the measurement of the wettability and the agglomeration potency of the inclusion particles in liquid ferrous alloy. The established methodology has been validated by the agreement between the calculated coagulation coefficient of Al2O3 particles and the experimental data in the open literature. Subsequently, the coagulation coefficient of Al2O3, MgO, and Ti2O3 particles in ferrous alloy melts was evaluated quantitatively by the proposed method using the actual experimental data of contact angle and surface tension. Meanwhile, the effect of the matrix composition has been investigated by comparing the Hamaker constant and coagulation coefficient between Ti2O3/pure iron and Ti2O3/low-carbon steel systems. It is noted that the change of coagulation coefficient associated with the contact angle is caused by the formation of a new phase at the oxide/metal interface at the high temperature. The present work aims to provide a deep understanding of the connection between inclusion motion behavior in the liquid alloy and the high temperature interfacial phenomenon.

Improving a thermal conductivity model of unsaturated soils based on multivariate distribution analysis

Soil thermal conductivity (k) is a key parameter for the design of energy geo-structures, and it depends on many soil properties such as saturation degree, porosity, mineralogical composition, soil type and others. Capturing these diversified influencing factors in a soil thermal conductivity model is a challenging task for engineers due to the nonlinear dependencies. In this study, a multivariate distribution approach was utilized to improve an existing soil thermal conductivity model, Cote and Konrad model, by quantitatively considering the impacts of dry density (ρd), porosity (n), saturation degree (Sr), quartz content (mq), sand content (ms) and clay content (mc) on thermal conductivity of unsaturated soils. A large database containing these seven soil parameters was compiled from the literature to support the multivariate analysis. Simplified bivariate and multivariate correlations for improving the Cote and Konrad model were derived analytically and numerically to consider different influencing factors. By incorporating these simplified correlations, the predicted k values were more concentrated around the measured values with the coefficient of determination (R2) increased from 0.83 to 0.95. It is concluded that the developed correlations with the information of different soil properties provide an efficient, rational and simple way to predict soil thermal conductivity more accurately. Moreover, the quartz content is a more important factor than the porosity that shall be considered in the establishment of thermal conductivity models for unsaturated soils with high quartz content.

Simplified correlations for free convection from a horizontal isothermal cylinder

Heat transfer by buoyancy-driven convection from a heated horizontal cylinder is present in many situations. Applications occur in nuclear reactor safety, solar energy systems, computer cooling, and many heat exchangers. A number of experimental and numerical studies exist for such flow situations and often provide correlating equations to calculate the heat transfer. The existing studies, most of which are for the case where Prandtl number is approximately 0.7, show a considerable variation in their average Nusselt number predictions. Some studies have addressed the variation in Prandtl number with reasonably accurate and consistent correlations but these are often complex and cumbersome to use. To address these issues, the current paper proposes simplified sets of correlating equations using results from prior numerical and experimental studies.

Fully Integrated Low-Power Energy Harvesting System With Simplified Ripple Correlation Control for System-on-a-Chip Applications

This paper presents a fully integrated energy harvesting (EH) system that even includes an input capacitor and a simplified ripple correlation control (RCC) maximum power point tracking (MPPT) method for low-power system-on-a-chip applications. The proposed system implements the RCC block with a charge pump (CP) that can be integrated into the chip, instead of the inductive switching converter that is commonly used for conventional RCC methods. The CP changes the input impedance by changing the size of the flying capacitor to ensure system reliability. The simplified RCC method is implemented using a low-power analog divider operated in a subthreshold region. A test chip fabricated in a 180 nm CMOS process achieves over 95% MPPT accuracy with a very small input capacitor of 5 nF and a low quiescent current of 2.6 μA. The chip size of the entire system is 8 mm2, and the harvested power range is from 6 μ W to 1.4 mW.

Thermal losses evaluation of an external rectangular receiver in a windy environment

The efficiency of a CSP plant heavily depends on the performance of the receiver. The receiver is responsible for light-heat conversion in a power generation system. With the objective of numerical evaluation of the thermal losses of an external receiver, a method was developed in the present study. Solar flux was obtained on a north-facing receiver using the “SolarPilot” software, through Monte-Carlo ray tracing technique. Apposite boiling heat transfer coefficients were selected and then applied to obtain the temperature at the surface of the boiling tubes. Numerical simulations were performed to quantify the heat losses in the receiver at different wind velocities. Maximum heat flux and temperature were obtained at the center of the receiver. The results indicated that wind direction and wind velocity have a significant impact on the extent of heat losses. Maximum heat losses occur in the side-on wind direction (i.e., west bound) while losses are minimum in the head-on wind direction (i.e., north bound). Thermal losses through the receiver contribute a sizeable portion to overall energy losses in power tower systems, hence, to attenuate the heat losses a new, yet simple, design is proposed with the addition of wind-blocking walls at the receiver’s periphery. The walls achieve noticeable heat retention in all wind directions, but their role is more prominent in the head-on wind direction. In best case scenario, attaching 1 m wide wind blocking walls resulted in a diminution of about 33 percent of losses in the head-on wind direction at 9 m/s wind velocity. Results obtained are then employed to derive a simplified correlation model to evaluate convective heat losses as a function of wind direction, wind velocity, receiver’s surface area and wind blocking wall width.

Analysis of flow pattern transition from segregated to slug flow in upward inclined pipes

Segregated and slug flows are two of the most common flow patterns encountered in two-phase upward inclined pipe flow. However, the transition between them is ambiguous. Coherent and distinctive structures have been observed within the transition. These structures have been classified as pseudo-slug flow. The nature of pseudo-slug flow is not well understood due to the complexity of the structure. At low liquid loading conditions, this flow pattern can occupy a large operating region and cannot be neglected. This paper presents a detailed experimental work conducted in a facility with a valley configuration, focusing on the transition region between segregated and slug flows. Wire-mesh sensors were employed to investigate the liquid phase distribution within the flow structure.The current paper investigates the flow patterns and their transition in upward inclined pipe from different perspectives. The investigation includes analysis of images from high-speed videos, evaluation of 2-D liquid holdup axial evolution, 2-D liquid holdup distribution at pipe cross-section, 3-D interfacial structure evolution, and analysis of pressure gradient and liquid holdup measurement, flow characteristics, etc. Differences between slug and pseudo-slug flows are also presented.Three superficial liquid velocities (0.001, 0.005 and 0.01 m/s) and five inclination angles (2°, 5°, 10°, 15°, and 20°) are studied. Simplified correlations are proposed for pseudo-slug structural velocity, showing fair agreement.