Dimensionless Operating Parameters Research Articles

Numerical Investigation of Double-Diffusive Convection in an Irregular Porous Cavity Subjected to Inclined Magnetic Field Using Finite Element Method

Purpose—This study aims to perform an in-depth analysis of double-diffusive natural convection (DDNC) in an irregularly shaped porous cavity. We investigate the convective heat transfer process induced by the lower wall treated as a heat source while the side walls of the enclosure are maintained at a lower temperature and concentration, and the remaining wall is adiabatic. Various factors, such as the Rayleigh number, Darcy effects, Hartmann number, Lewis number and effects of magnetic inclination are evaluated for their influence on flow dynamics and heat distribution. Design/methodology/approach—After validating the results, the FEM (finite element method) is used to simulate the flow pattern, temperature variations, and concentration by solving the nonlinear partial differential equations with the modified Rayleigh number (104 ≤ Ra ≤ 107), Darcy number (10−4 ≤ Da ≤ 10−1), Lewis number (0.1≤Le≤10), and Hartmann number 0≤Ha≤40 as the dimensionless operating parameters. Findings—The finding shows that the patterns of convection and the shape of the isotherms within porous enclosures are notably affected by the angle of the applied magnetic field. This study enhances our understanding of how double-diffusive natural convection (DDNC) operates in these enclosures, which helps improve heating and cooling technologies in various engineering fields. Research limitations/implications—Numerical and experimental extensions of the present study make it possible to investigate differences in thermal performance as a result of various curvatures, orientations, boundary conditions, and the use of three-dimensional analysis and other working fluids. Practical implications—The geometry configurations used in this study have wide-ranging applications in engineering fields, such as in heat exchangers, crystallization, microelectronics, energy storage, mixing, food processing, and biomedical systems. Originality/value—This study shows how an inclined magnetic field affects double-diffusive natural convection (DDNC) within a porous system featuring an irregularly shaped cavity, considering various multiphysical conditions.

Thermodynamic investigation of the secondary flow inside centrifugal compressor for compressed air energy storage based on local dissipation

Centrifugal compressors are critical components of compressed air energy storage (CAES) systems and are of great interest to understanding internal secondary flows and their resulting energy losses. While previous studies have primarily described these secondary flows using empirical correlation equations, this paper conducts numerical simulations of a high-loading centrifugal compressor after performing an experimental validation. The changes in the secondary flow structure in the impeller are analyzed for different operating conditions using a specific identification method based on the simulation results. The local dissipation coefficient is used as a weighting to analyze the enthalpy losses due to different sources during the impeller's thermodynamic process. The variations of the loss proportions from different sources with the dimensionless operating parameters (flow coefficient, impeller machine Mach number, and loading coefficient) are discussed. The reasons for the trends of different loss types correlate with the flow structure, and three different loss regions in the whole operation range are distinguished. The energy loss inside an optimized impeller is compared with the baseline, and the results demonstrate that different losses can be controlled by adjusting the secondary flow structure within the impeller. This study provides a reference for enhancing the understanding of thermodynamic processes within a centrifugal impeller and aims to further the development of advanced centrifugal compressors.

Hybridized nanofluidic convection in umbrella-shaped porous thermal systems with identical heating and cooling surfaces

PurposeThis study aims to investigate the impact of different heater geometries (flat, rectangular, semi-elliptical and triangular) on hybrid nanofluidic (Cu–Al2O3–H2O) convection in novel umbrella-shaped porous thermal systems. The system is top-cooled, and the identical heater surfaces are provided centrally at the bottom to identify the most enhanced configuration.Design/methodology/approachThe thermal-fluid flow analysis is performed using a finite volume-based indigenous code, solving the nonlinear coupled transport equations with the Darcy number (10–5 ≤ Da ≤ 10–1), modified Rayleigh number (10 ≤ Ram ≤ 104) and Hartmann number (0 ≤ Ha ≤ 70) as the dimensionless operating parameters. The semi-implicit method for pressure linked equations algorithm is used to solve the discretized transport equations over staggered nonuniform meshes.FindingsThe study demonstrates that altering the heater surface geometry improves heat transfer by up to 224% compared with a flat surface configuration. The triangular-shaped heating surface is the most effective in enhancing both heat transfer and flow strength. In general, flow strength and heat transfer increase with rising Ram and decrease with increasing Da and Ha. The study also proposes a mathematical correlation to predict thermal characteristics by integrating all geometric and flow control variables.Research limitations/implicationsThe present concept can be extended to further explore thermal performance with different curvature effects, orientations, boundary conditions, etc., numerically or experimentally.Practical implicationsThe present geometry configurations can be applied in various engineering applications such as heat exchangers, crystallization, micro-electronic devices, energy storage systems, mixing processes, food processing and different biomedical systems (blood flow control, cancer treatment, medical equipment, targeted drug delivery, etc.).Originality/valueThis investigation contributes by exploring the effect of various geometric shapes of the heated bottom on the hydromagnetic convection of Cu–Al2O3–H2O hybrid nanofluid flow in a complex umbrella-shaped porous thermal system involving curved surfaces and multiphysical conditions.

Numerical simulations of air-assisted primary atomization at different air-to-liquid injection angles

Numerical simulations have been performed for a coaxial, twin-fluid nozzle to study the influence of the angle α between the central liquid jet and the annular airflow on the primary atomization process. A glycerol/water mixture with a high dynamic viscosity of 200 mPas is used and the gas-to-liquid ratio is 0.6. The simulations show good agreement with experiments for the breakup morphology. The liquid jet breaks up quickly and its core length LC decreases with α from 0° to 30°, which is attributable to a reinforced aerodynamic interaction. The flow velocity of the gas phase close to the liquid jet increases with α in this case, which is confirmed by corresponding PIV measurements. This is due to the formation of a high pressure zone at the base of the liquid jet, which results in a favorable pressure gradient in the bulk flow direction. However, further increase of α from 30° to 60° leads to a decreased gas flow velocity along the liquid jet and an increase of LC. The same behavior has been found for the integral specific kinetic energy kL in the liquid phase, which represents a measure for the momentum transfer between the gas and liquid phases. kL increases from α=0∘ to 30° and it decreases again with higher α. Moreover, kL yields a similar distribution compared with the turbulent kinetic energy (TKE) of a typical turbulent flow in the spectral domain. This is attributed to the local concentration of TKE of the liquid phase in a small region around the tip of the liquid jet. The results reveal that, in addition to the common dimensionless operating parameters, the flow direction has an essential impact on the atomization process. According to the current work, the best atomization performance is achieved at an angle of α=30∘. The spectral correlation of kL with TKE of the gas flow may be used to assess the dynamics of the liquid phase.

Enhancement of mass transfer performance by nanoparticles during the CO2 absorption with MDEA solution in a randomly packed tower

AbstractIn this study, the mass transfer enhancement by nanoparticles during CO2 absorption process with MDEA solution in a randomly packed tower was investigated. The mass transfer performance of MDEA solution with and without nanoparticles were quantified and analyzed in terms of the volumetric overall mass transfer coefficient (KGav). An enhancement factor (E), defined as the ratio of KGav with and without nanoparticles, was further introduced to evaluate the enhancement effect of the addition of nanoparticles. The effects of TiO2 nanoparticle concentration, MDEA concentration, liquid flow rate, liquid temperature, inert gas flow rate, and CO2 loading on KGav and E were systematically studied in the packed tower. It is found that the maximum value of E can reach 1.37, when the nanoparticle concentration is 0.09wt%, the liquid flow rate is 21.22 m3/m2·h, the liquid temperature is 27°C, the MDEA concentration is 30%, the gas flow rate is 7.58 kmol/m2·h and the CO2 loading is 0.2 mol CO2/mol MDEA. Usually, the KGav of the MDEA nanofluids can be increased by 10–37% in a randomly packed tower compared to that of the MDEA solution, which is consistent with the results from the bubbling reactors. However, when the CO2 loading of absorption exceeds 50%, E becomes less than 1.0, which means that high CO2 loading inhibits the enhancement effect of nanoparticles. In order to predict the mass transfer performance of MDEA nanofluid, a formula correlating E and various dimensionless operating parameters (i.e. , , and ) is proposed and fitted with an average absolute deviation of 14%. © 2022 Society of Chemical Industry and John Wiley & Sons, Ltd.

Using Transitional Points in the Optical Injection Locking Behavior of a Semiconductor Laser to Extract Its Dimensionless Operating Parameters

The complete set of intrinsic dimensionless parameters of a packaged and fiber-pigtailed distributed feedback (DFB) semiconductor laser are extracted from the non-linear operational stability boundaries of the optical-injection-locking (OIL) architecture. Specifically, this procedure is done by relating the intrinsic parameters to the injection ratios corresponding to the Hopf bifurcation points at zero detuning, as well as the detuning of the Hopf-Saddle-Node point. The bifurcation points of the injected laser's operational space are found by coupling its output into a high-resolution optical spectrum analyzer. This is enabled by establishing a 30 dB side mode suppression ratio between the central mode and Period 1 oscillations to define the boundaries of Stable Locking. Along with the laser's threshold current and free-running relaxation oscillation frequencies, performing these measurements over a range of pumping values allows for the calculation of the laser's linewidth enhancement factor, irrespective of the device packaging. Utilizing a high pump approximation, the remaining dimensionless parameters are extracted after obtaining the photon lifetime. Using this approach, the operational capabilities of an arbitrarily-packaged laser can be determined, allowing for the analysis of an injected laser's operational space for a variety high-frequency and dynamical applications.

Intermittent recycle-integrated reactor-separator for production of well-defined non-digestible oligosaccharides from oat β-glucan

A recycle-integrated reactor-separator system was studied experimentally and based on simulations for the acid-catalyzed depolymerization of oat beta-glucan polysaccharide. The aim was to produce oligosaccharides with degree of polymerization in a narrow range (DP = 15–30). The reactor was operated intermittently at 80 °C. Batch chromatography with Sephadex G-25 size-exclusion gel was found suitable for the separation of product from reactants and impurities. Part of the reaction mixture was periodically withdrawn and fed to the separation column. Molar mass distributions in four chromatographic fractions (waste, recycle, product, impurities) were monitored with SEC-MALLS. Experiments with 4 h mean residence time showed that the reactor-separator achieved approximately 2.0 and 2.5 times higher yield and purity of target DP than a batch reactor. Dimensionless operating parameters and equipment design parameters were introduced for analyzing performance of intermittent reactor-separators. The simulations show that intermittent operation offers higher yield and product purity than continuous operation (CSTR and chromatographic separation) when mean residence time in the reactor is long. Continuous operation is better when productivity is maximized by using short mean residence time and low yield.

Speedy standing wave design and simulated moving bed splitting strategies for the separation of ternary mixtures with linear isotherms

Simulated Moving Bed (SMB) has advantages over batch chromatography in terms of productivity and solvent efficiency. However, SMB applications in large scale production are still limited because of the many design parameters that must be specified and the multiple splitting strategies that can be implemented. To overcome these barriers, this study extends the Speedy Standing Wave Design (SSWD) method of Weeden and Wang for binary linear systems to ternary linear adsorption systems. The dimensionless operating parameters, sorbent productivity, and solvent efficiency can be quickly calculated without process simulations. SSWD also gives an overview of the productivity and solvent efficiency as a function of two key dimensionless groups. This overview can be used for optimization of separation costs and for comparison of splitting strategies. The SSWD method was verified using rate model simulations for the separation of three amino acids. The simulated yields agree with the SSWD target yields within 1% for all components. The example was also used to illustrate the key design rules for ternary separations. High productivity and solvent efficiency can be achieved with a large difference in the retention factors of the heavy key and light key, which are the components that define the split of the feed between extract and raffinate products. For ternary ideal systems, solvent efficiency is inversely proportional to the largest difference in retention factors. For this reason, minimizing the overall range of retention factors can significantly improve the solvent efficiency and product concentration without sacrificing productivity. If more than one SMB is needed, the easiest split should be done first for higher productivity, solvent efficiency, and product concentration. In the example case study, both the productivity and solvent efficiency were about an order of magnitude higher when the easiest split was done in the first ring. The SSWD method can be used to design a wide array of multi-component separations with high yield, productivity, and solvent efficiency.

Modelling and experimental validation for off-design performance of the helical heat exchanger with LMTD correction taken into account

Today the helical coil heat exchanger is being employed widely due to its dominant advantages. In this study, a mathematical model was established to predict off-design works of the helical heat exchanger. The model was based on the LMTD and e-NTU methods, where a LMTD correction factor was taken into account to increase accuracy. An experimental apparatus was set-up to validate the model. Results showed that errors of thermal duty, outlet hot fluid temperature, outlet cold fluid temperature, shell-side pressure drop, and tube-side pressure drop were respectively ±5%, ±1%, ±1%, ±5% and ±2%. Diagrams of dimensionless operating parameters and a regression function were also presented as design-maps, a fast calculator for usage in design and operation of the exchanger. The study is expected to be a good tool to estimate off-design conditions of the single-phase helical heat exchangers.

Unified Design of chromatographic processes with timed events: Separation of ternary mixtures

An important unifying property of single and multicolumn chromatographic processes, whether discontinuous or continuous, is that they are based on timed events. The Unified Design method was revised by defining three kinds of events (cut event, fixed-bed event, SMB event). Binary and multicomponent separations in various process configurations, from single column batch to complex multicolumn units, can readily be described as combinations of such events. New dimensionless parameters were introduced to describe these events, and their combinations were used as operating parameters for different processes. Transformations between physical and dimensionless operating parameters were introduced. Regions of feasible operating parameters for complete separation of ternary mixtures with linear isotherms were derived for batch chromatography and two SMB-type processes (Japan Organo, 3W−ISMB) using the equilibrium theory. It was shown that these can be visualized and overlaid on the Unified Design operating parameter plane, which enables their direct comparison. It was found that in many cases the complete separation regions of apparently very different process schemes are identical or exhibit strong similarities. This indicates that it should be possible to transfer the operating point from one process mode to another without affecting the product purity if column efficiency is very high.

Thermal characteristics of a skutterudite thermoelectric generator: influence of device pin length on efficiency and output power

Thermodynamic analysis is presented in terms of dimensionless operating parameters, which includes temperature and load resistance ratios, and dimensionless device pin length for a skutterudite thermoelectric generator. To obtain the device geometric configuration maximising the thermal efficiency, the device characteristics are computed for various values of operating and pin geometric parameters. It is found that the device maximum efficiency does not coincide with the optimum dimensionless device pin length corresponding to the maximum thermal efficiency. Altering load resistance from its optimum value lowers the thermal efficiency considerably and the thermal efficiency variation becomes gradual for the reduced external load resistance. In addition, electrical resistance of the thermoelectric generator beyond its optimum value has an adverse effect on the thermal efficiency.

Unified design of chromatographic separation processes

A unified method is developed for the designing preparative chromatographic processes of various types. The method allows, for example, generalizing the established triangle theory of counter-current simulated moving bed technique for other single and multi-column chromatographic schemes including (1) classical batch chromatography, (2) mixed-recycle steady state recycling chromatography, (3) cross-current chromatography, and (4) mixed-recycle cross-current recycling chromatography. The approach allows direct prediction of the range of feasible dimensionless operating parameters that lead to complete separation of a binary feed mixture. By using the equilibrium theory of chromatography, explicit design equations are derived for systems that follow linear or competitive Langmuir isotherm model. It is shown that under ideal conditions the boundaries of the dimensionless operating parameters are identical for all studied process concepts, except for the upper limit of a parameter that is related to the regeneration of the fluid phase in the case of Langmuir isotherm. The practical relevance of the unified design method is demonstrated with numerical simulations. It is shown that even under non-ideal conditions the counter-current SMB can be designed with good accuracy based on a single pulse injection to a batch column, especially for relatively low purity requirements.

Limiting current density in the electrodialysis of multi-ionic solutions

The aim of this work was the development of an explicit model to estimate the limiting current density in the electrodialysis of dilute multi-ionic solutions. The model assumes that the ionic transport occurs in a film layer adjacent to an ion exchange membrane and it is quantified by a linearized form of the Nernst–Planck (NP) equations together with the electroneutrality requirement at the solution/ion exchange membrane interface. An explicit expression for the limiting current density of a dilute multi-ionic solution was derived, involving a mass-transfer coefficient based on an effective diffusivity of the multi-ionic solution. The model further assumes that the steric exclusion of the ions by the membrane is negligible, and thereby the limiting current density is attained when the concentration of each and every ion is null at the solution/membrane interface. The model predictions for the limiting current density were compared with experimental data of single salt solutions (MgCl 2) and multi-ionic solutions (MgSO 4 + MgCl 2) in a bench-scale electrodialysis unit (EUR2C-7P18, Eurodia, France) for various Reynolds numbers and salts concentrations. The average relative deviations between the model predictions and the experimental data were lower than 13% for MgCl 2 solutions (10, 20 equiv./m 3) and solutions of MgSO 4 + MgCl 2 (5 + 5, 10 + 10 equiv./m 3). The dimensionless limiting current density and the counterions transport numbers predicted by the linearized and non-linear Nernst–Planck equations were also compared for a broad range of dimensionless operating parameters and a fair to good agreement was observed between the two approaches.

Slow Continuous Ultrafiltration with Bound Solute Dialysis

Bound solute dialysis (BSD), often referred to as "albumin dialysis" (practiced clinically as the molecular adsorbents recirculating system, MARS, or single-pass albumin dialysis, SPAD) or "sorbent dialysis" (practiced clinically as the charcoal-based Biologic-DT), is based upon the thermodynamic principle that the driving force for solute mass transfer across a dialysis membrane is the difference in free solute concentration across the membrane. The clinically relevant practice of slow continuous ultrafiltration (SCUF) for maintenance of patients with liver failure is analyzed in conjunction with BSD. The primary dimensionless operating parameters that describe SCUF-BSD include (1) beta, the dialysate/blood binder concentration ratio; (2) kappa, the dialyzer mass transfer/blood flow rate ratio; (3) alpha, the dialysate/blood flow rate ratio; and, (4) gamma, the ultrafiltration/blood flow rate ratio. Results from mathematical modeling of solute removal during a single pass through a dialyzer and solute removal from a one-compartment model indicate that solute removal is remarkably insensitive to gamma. Solute removal approaches an asymptote (improvement in theoretical clearance over that obtainable with no binder in the dialysate) with increasing beta that is dependent on kappa and independent of alpha. The amount of binder required to approach the asymptote decreases with increasing solute-binder equilibrium constant, i.e., more strongly bound solutes require less binder in the dialysate. The results of experimental observations over a range of blood flow rates, 100 to 180 mL/min, dialysate flow rates, 600 to 2150 mL/h, ultrafiltration rates, 0 to 220 mL/h, and dialysate/blood albumin concentration ratios, beta = 0.01 to 0.04, were independently predicted remarkably well by the one-compartment model (with no adjustable parameters) based on BSD principles.

Theoretical Analysis and Experimental Verification of Ozone Mass Transfer in Bubble Columns

Modeling the performance of ozone bubble columns for water and wastewater treatment was carried out using two models: the axial dispersion model and the back flow cell model (BFCM). Expressing these two models in terms of dimensionless operating parameters allowed the examination of their predictions of dissolved ozone, gaseous ozone, and superficial gas velocity profiles along the bubble column height. Pilot-scale experimental data from the literature were used to test the models' predictions of the dissolved ozone profiles for water treatment applications. The models have demonstrated reliable predictions of the dissolved ozone concentration profiles along the bubble column for water treatment conditions in the co-current and the counter-current flow modes. The axial dispersion model and the back flow cell model have proved to be adequate for describing the performance of ozone bubble columns, however, the BFCM was easier to formulate and solve.

Regimes of Contact in Spline Couplings

The contact between the male and female teeth of involute spline couplings connecting misaligned transmission shafts has been studied using an elastostatic contact model with stick-slip friction based on the boundary integral element method. The effect on the distribution of pressure and on the slip path during shaft rotation, of a wide range of design parameters and of applied torque and misalignment has been explored. The predicted behavior is classified according to the regime of friction (cyclic stick-slip or gross slip) and to that of the pressure history (uniform, cyclic, discontinuous, or toppled). The magnitude of the maximum tooth load, the axial skewness of the distribution of pressure and a maximum wear depth parameter are presented in terms of dimensionless design and operating parameters. The effect of tooth crowning is briefly examined. The results show a number of previously unreported features including a cyclic tooth load—which declines to zero for certain conditions—and an effective slip amplitude of around half the rigid-body value. This may affect the interpretation of laboratory fretting tests.

Designing Ozone Bubble Columns: A Spreadsheet Approach to Axial Dispersion Model

When designing ozone bubble columns, two major sources of uncertainties usually exist: (1) the measurement techniques and the estimation methods of the various operating parameters; and (2) the application of the pertinent design model. This paper presents a simple and easy-to-use, yet accurate and reliable design model for describing the performance of ozone bubble columns for water and wastewater treatment applications. This mode! is a modified non-isobaric steady-sate one-phase axial dispersion model (1P-ADM). The 1P-ADM is different from the complete axial dispersion model, or referred to as the two-phase axial dispersion model (2P-ADM), in its simple use for practical design and process control of full-scale contacting chambers. The 2P-ADM is represented by a system of two non-linear partial differential equations. In order to solve that system of equations, an elaborate numerical solving technique is needed. On the other hand, die 1P-ADM is composed of a single non-homogeneous linear second-order ordinary differential equation representing the liquid phase. Yet, this liquid-phase differential equation accounts for the countering effects of die gas bubbles' shrinkage and expansion caused by gas depletion and absorption and reduced liquid hydrostatic head. The differential equation was solved analytically by the method of variation of parameters. Expressing the 1P-ADM in terms of dimensionless operating parameters and with the available analytical solution of the differential equation, the model predictions of the dissolved and the gaseous ozone profiles along the column height were examined using a simple spreadsheet approach. Therefore, describing mat analytical solution in terms of a simple spreadsheet program facilitated obtaining the model predictions for any operating conditions represented by the model parameters entered into die spreadsheet program. Consequently, using die 1P-ADM for process design and/or on-line process control becomes very feasible. The 1P-ADM was initially tested to evaluate its predictions of the dissolved ozone profiles for water treatment conditions. The model provided excellent predictions of the dissolved ozone profiles along the bubble column for die counter-current and the co-current flow modes.