Search results for: Reynolds number

Authors: Mohamed Elghorab, Vendra C. Madhav Rao, Jennifer X. Wen

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Turbulence modelling is still evolving, and efforts are on to improve and develop numerical methods to simulate the real turbulence structures by using the empirical and experimental information. The monotonically integrated large eddy simulation (MILES) is an attractive approach for modelling turbulence in high Re flows, which is based on the solving of the unfiltered flow equations with no explicit sub-grid scale (SGS) model. In the current work, this approach has been used, and the action of the SGS model has been included implicitly by intrinsic nonlinear high-frequency filters built into the convection discretization schemes. The MILES solver is developed using the opensource CFD OpenFOAM libraries. The role of flux limiters schemes namely, Gamma, superBee, van-Albada and van-Leer, is studied in predicting turbulent statistical quantities for a fully developed channel flow with a friction Reynolds number, Re_T = 180, and compared the numerical predictions with the well-established Direct Numerical Simulation (DNS) results for studying the wall generated turbulence. It is inferred from the numerical predictions that Gamma, van-Leer and van-Albada limiters produced more diffusion and overpredicted the velocity profiles, while superBee scheme reproduced velocity profiles and turbulence statistical quantities in good agreement with the reference DNS data in the streamwise direction although it deviated slightly in the spanwise and normal to the wall directions. The simulation results are further discussed in terms of the turbulence intensities and Reynolds stresses averaged in time and space to draw conclusion on the flux limiter schemes performance in OpenFOAM context.

Keywords: flux limiters, implicit SGS, MILES, OpenFOAM, turbulence statistics

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Authors: Nishitha Chowdary, Prabhav Dwivedi

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Solar radiation (or insolation) is responsible for 174 petawatts (PW) of energy reaching the Earth's atmosphere. About one-third of this is reflected in space. Solar energy is by far the most abundant source of energy on Earth. In this study to use solar energy to the fullest in a solar air heater, An analysis of a solar air heater duct roughened with fixed cylindrical ribs in 3-D has been done using CFD. These fixed cylindrical ribs have a uniform circular cross-section and are placed in transverse in-line and staggered arrangements. The orientation of ribs has been fixed and is perpendicular to the in-flow direction. Cylindrical ribs are arranged periodically with fixed pitch; therefore, one pitch length is only considered in the present study. Validation has been done with smooth as well as with roughened duct and is matched perfectly with the developed correlations. Geometric parameters, namely rib height (e), ranges from 1 to 2 mm and pitch ranges from 10 to 40 mm are used in the present investigation. Thermo-hydraulic performance parameters in terms of average Nusselt number and friction factor have been extracted for Reynolds number ranging 5000—18000 to optimize the performance of roughened duct.

Keywords: cylindrical ribs, solar air heater, thermo-hydraulic performance factor, roughened duct

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Authors: Deva Kanta Phukan

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An attempt is made where an electrically conducting fluid is injected from a fixed outer cylindrical casing onto an inner moving cylindrical rod. A magnetic field is applied parallel to the axis of the cylindrical rod. The basic governing set of partial differential equations for conservation of mass and momentum are reduced to a set of non-linear ordinary differential equation by introducing similarity transformation, which are integrated numerically. A perturbation solution for the case of large magnetic parameter is derived for constant Reynolds number.

Keywords: annular axi-symmetric stagnation flow, conducting fluid, magnetic field, moving cylinder

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Authors: Frederick Ferguson, Dehua Feng, Yang Gao

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No doubt, current CFD tools have a great many technical limitations, and active research is being done to overcome these limitations. Current areas of limitations include vortex-dominated flows, separated flows, and turbulent flows. In general, turbulent flows are unsteady solutions to the fluid dynamic equations, and instances of these solutions can be computed directly from the equations. One of the approaches commonly implemented is known as the ‘direct numerical simulation’, DNS. This approach requires a spatial grid that is fine enough to capture the smallest length scale of the turbulent fluid motion. This approach is called the ‘Kolmogorov scale’ model. It is of interest to note that the Kolmogorov scale model must be captured throughout the domain of interest and at a correspondingly small-time step. In typical problems of industrial interest, the ratio of the length scale of the domain to the Kolmogorov length scale is so great that the required grid set becomes prohibitively large. As a result, the available computational resources are usually inadequate for DNS related tasks. At this time in its development, DNS is not applicable to industrial problems. In this research, an attempt is made to develop a numerical technique that is capable of delivering DNS quality solutions at the scale required by the industry. To date, this technique has delivered preliminary results for both steady and unsteady, viscous and inviscid, compressible and incompressible, and for both high and low Reynolds number flow fields that are very accurate. Herein, it is proposed that the Integro-Differential Scheme (IDS) be applied to a set of vortex-shockwave interaction problems with the goal of investigating the nonstationary physics within the resulting interaction regions. In the proposed paper, the IDS formulation and its numerical error capability will be described. Further, the IDS will be used to solve the inviscid and viscous Burgers equation, with the goal of analyzing their solutions over a considerable length of time, thus demonstrating the unsteady capabilities of the IDS. Finally, the IDS will be used to solve a set of fluid dynamic problems related to flow that involves highly vortex interactions. Plans are to solve the following problems: the travelling wave and vortex problems over considerable lengths of time, the normal shockwave–vortex interaction problem for low supersonic conditions and the reflected oblique shock–vortex interaction problem. The IDS solutions obtained in each of these solutions will be explored further in efforts to determine the distributed density gradients and vorticity, as well as the Q-criterion. Parametric studies will be conducted to determine the effects of the Mach number on the intensity of vortex-shockwave interactions.

Keywords: vortex dominated flows, shockwave interactions, high Reynolds number, integro-differential scheme

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Authors: Masood Otarod, Ronald M. Supkowski

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This abstract discusses a method that reduces the general dispersion model in cylindrical coordinates to a second order linear ordinary differential equation with constant coefficients so that it can be utilized to conduct kinetic studies in packed bed tubular catalytic reactors at a broad range of Reynolds numbers. The model was tested by 13CO isotope transient tracing of the CO adsorption of Boudouard reaction in a differential reactor at an average Reynolds number of 0.2 over Pd-Al2O3 catalyst. Detailed experimental results have provided evidence for the validity of the theoretical framing of the model and the estimated parameters are consistent with the literature. The solution of the general dispersion model requires the knowledge of the radial distribution of axial velocity. This is not always known. Hence, up until now, the implementation of the dispersion model has been largely restricted to the plug-flow regime. But, ideal plug-flow is impossible to achieve and flow regimes approximating plug-flow leave much room for debate as to the validity of the results. The reduction of the general dispersion model transpires as a result of the application of a factorization theorem. Factorization theorem is derived from the observation that a cross section of a catalytic bed consists of a solid phase across which the reaction takes place and a void or porous phase across which no significant measure of reaction occurs. The disparity in flow and the heterogeneity of the catalytic bed cause the concentration of reacting compounds to fluctuate radially. These variabilities signify the existence of radial positions at which the radial gradient of concentration is zero. Succinctly, factorization theorem states that a concentration function of axial and radial coordinates in a catalytic bed is factorable as the product of the mean radial cup-mixing function and a contingent dimensionless function. The concentration of adsorbed compounds are also factorable since they are piecewise continuous functions and suffer the same variability but in the reverse order of the concentration of mobile phase compounds. Factorability is a property of packed beds which transforms the general dispersion model to an equation in terms of the measurable mean radial cup-mixing concentration of the mobile phase compounds and mean cross-sectional concentration of adsorbed species. The reduced model does not require the knowledge of the radial distribution of the axial velocity. Instead, it is characterized by new transport parameters so denoted by Ωc, Ωa, Ωc, and which are respectively denominated convection coefficient cofactor, axial dispersion coefficient cofactor, and radial dispersion coefficient cofactor. These cofactors adjust the dispersion equation as compensation for the unavailability of the radial distribution of the axial velocity. Together with the rest of the kinetic parameters they can be determined from experimental data via an optimization procedure. Our data showed that the estimated parameters Ωc, Ωa Ωr, are monotonically correlated with the Reynolds number. This is expected to be the case based on the theoretical construct of the model. Computer generated simulations of methanation reaction on nickel provide additional support for the utility of the newly conceptualized dispersion model.

Keywords: factorization, general dispersion model, isotope transient kinetic, partial differential equations

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Authors: Li Chen

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For an aerofoil or hydrofoil in high Reynolds number flows, broadband noise is generated efficiently as the result of the turbulence convecting over the trailing edge. This noise can be related to the surface pressure fluctuations, which can be predicted by either CFD or empirical models. However, in reality, the aerofoil or hydrofoil often operates at an angle of attack. Under this situation, the flow is subjected to an Adverse-Pressure-Gradient (APG), and as a result, a flow separation may occur. This study is to assess trailing-edge noise models for such flows. In the present work, the trailing-edge noise from a 2D airfoil at 6 degree of angle of attach is investigated. Under this condition, the flow is experiencing a strong APG, and the flow separation occurs. The flow over the airfoil with a chord of 300 mm, equivalent to a Reynold Number 4x10⁵, is simulated using RANS with the SST k-ɛ turbulent model. The predicted surface pressure fluctuations are compared with the published experimental data and empirical models, and show a good agreement with the experimental data. The effect of the APG on the trailing edge noise is discussed, and the associated trailing edge noise is calculated.

Keywords: aero-acoustics, adverse-pressure gradient, computational fluid dynamics, trailing-edge noise

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Authors: I. Behroyan, P. Ganesan, S. He, S. Sivasankaran

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This study compares the predictions of five types of Computational Fluid Dynamics (CFD) models, including two single-phase models (i.e. Newtonian and non-Newtonian) and three two-phase models (Eulerian-Eulerian, mixture and Eulerian-Lagrangian), to investigate turbulent forced convection of Cu-water nanofluid in a tube with a constant heat flux on the tube wall. The Reynolds (Re) number of the flow is between 10,000 and 25,000, while the volume fraction of Cu particles used is in the range of 0 to 2%. The commercial CFD package of ANSYS-Fluent is used. The results from the CFD models are compared with results from experimental investigations from literature. According to the results of this study, non-Newtonian single-phase model, in general, does not show a good agreement with Xuan and Li correlation in prediction of Nu number. Eulerian-Eulerian model gives inaccurate results expect for φ=0.5%. Mixture model gives a maximum error of 15%. Newtonian single-phase model and Eulerian-Lagrangian model, in overall, are the recommended models. This work can be used as a reference for selecting an appreciate model for future investigation. The study also gives a proper insight about the important factors such as Brownian motion, fluid behavior parameters and effective nanoparticle conductivity which should be considered or changed by the each model.

Keywords: heat transfer, nanofluid, single-phase models, two-phase models

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Authors: Harish Aryal, Roger Hague, Daniel Sotelo, Felipe Astete Salinas

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This paper presents a comparative study of different coolants, materials, and temperatures that can affect the effectiveness of heat exchangers that are used in small modular reactors. The corrugated plate heat exchangers were chosen out of different plate options for testing purposes because of their ease of access and better performance than other existing heat exchangers in recent years. SolidWorks enables us to see various results between water coolants and helium coolants acting upon different types of conducting metals, which were selected from different fluids that ultimately satisfied accessibility requirements and were compatible with the software. Though not every element, material, fluid, or method was used in the testing phase, their purpose is to help further research that is to come since the innovation of nuclear power is the future. The tests that were performed are to help better understand the constant necessities that are seen in heat exchangers and through every adjustment see what the breaking points or improvements in the machine are. Depending on consumers and researchers, the results may give further feedback as to show why different types of materials and fluids would be preferred and why it is necessary to keep failures to improve future research.

Keywords: heat exchangers, Solidworks, coolants, small modular reactors, nuclear power, nanofluids, Nusselt number, friction factor, Reynolds number

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Authors: Carlos Teodoro, Oscar Bautista

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In this work, we analyze theoretically the mass transport in a time-periodic electroosmotic flow through a parallel flat plate microchannel under different periodic functions of the applied external electric field. The microchannel connects two reservoirs having different constant concentrations of an electro-neutral solute, and the zeta potential of the microchannel walls are assumed to be uniform. The governing equations that allow determining the mass transport in the microchannel are given by the Poisson-Boltzmann equation, the modified Navier-Stokes equations, where the Debye-Hückel approximation is considered (the zeta potential is less than 25 mV), and the species conservation. These equations are nondimensionalized and four dimensionless parameters appear which control the mass transport phenomenon. In this sense, these parameters are an angular Reynolds, the Schmidt and the Péclet numbers, and an electrokinetic parameter representing the ratio of the half-height of the microchannel to the Debye length. To solve the mathematical model, first, the electric potential is determined from the Poisson-Boltzmann equation, which allows determining the electric force for various periodic functions of the external electric field expressed as Fourier series. In particular, three different excitation wave forms of the external electric field are assumed, a) sawteeth, b) step, and c) a periodic irregular functions. The periodic electric forces are substituted in the modified Navier-Stokes equations, and the hydrodynamic field is derived for each case of the electric force. From the obtained velocity fields, the species conservation equation is solved and the concentration fields are found. Numerical calculations were done by considering several binary systems where two dilute species are transported in the presence of a carrier. It is observed that there are different angular frequencies of the imposed external electric signal where the total mass transport of each species is the same, independently of the molecular diffusion coefficient. These frequencies are called crossover frequencies and are obtained graphically at the intersection when the total mass transport is plotted against the imposed frequency. The crossover frequencies are different depending on the Schmidt number, the electrokinetic parameter, the angular Reynolds number, and on the type of signal of the external electric field. It is demonstrated that the mass transport through the microchannel is strongly dependent on the modulation frequency of the applied particular alternating electric field. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.

Keywords: electroosmotic flow, mass transport, oscillatory flow, species separation

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Authors: Boualem Chetti

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The dynamic characteristics of a three-lobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory and the finite difference technique has been used to solve it. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show compared with Newtonian fluids, that micropolar fluid exhibits better stability.

Keywords: three-lobe bearings, micropolar fluid, dynamic characteristics, stability analysis

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Authors: Ramy H. Mohammed

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In heat sinks, the flow within the core exhibits separation and hence does not lend itself to simple analytical boundary layer or duct flow analysis of the wall friction. In this paper, I present some findings from an experimental and numerical study aimed to obtain physical insight into the influence of the presence of the shield and its position on the hydraulic and thermal performance of square pin fin heat sink without top by-pass. The variations of the Nusselt number and friction factor are obtained under varied parameters, such as the Reynolds number and the shield position. The numerical code is validated by comparing the numerical results with the available experimental data. It is shown that, there is a good agreement between the temperature predictions based on the model and the experimental data. Results show that, as the presence of the shield, the heat transfer of fin array is enhanced and the flow resistance increased. The surface temperature distribution of the heat sink base is more uniform when the dimensionless shield position equals to 1/3 or 2/3. The comprehensive performance evaluation approach based on identical pumping power criteria is adopted and shows that the optimum shield position is at x/l=0.43 where energy is saved.

Keywords: shield, fin array, performance evaluation, heat transfer, energy

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Authors: C. S. Sona, Makrand A. Khanwale, Channamallikarjun S. Mathpati

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New generation nuclear power plants are currently being developed to be highly economical, to be passive safe, to produce hydrogen. An important feature of these reactors will be the use of coolants at temperature higher than that being used in current nuclear reactors. The molten fluoride salt with a eutectic composition of 46.5% LiF - 11.5% NaF - 42% KF (mol %) commonly known as FLiNaK is a leading candidate for heat transfer coolant for these nuclear reactors. CFD simulations were carried out using large eddy simulations to investigate the flow characteristics of molten FLiNaK at 850°C at a Reynolds number of 10,500 in a cylindrical pipe. Simulation results have been validated with the help of mean velocity profile using direct numerical simulation data. Transient velocity information was used to identify and characterise turbulent structures which are important for transfer of heat across solid-fluid interface. A wavelet transform based methodology called wavelet transform modulus maxima was used to identify and characterise the singularities. This analysis was also used for flow visualisation, and also to calculate the heat transfer coefficient using small eddy model. The predicted Nusselt number showed good agreement with the available experimental data.

Keywords: FLiNaK, heat transfer, molten salt, turbulent structures

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Authors: Imdat Taymaz, Erman Aslan, Kemal Cakir

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The Lattice Boltzmann Method (LBM) is performed to computationally investigate the laminar flow and heat transfer of an incompressible fluid with constant material properties in a 2D channel with a built-in triangular prism. Both momentum and energy transport is modelled by the LBM. A uniform lattice structure with a single time relaxation rule is used. Interpolation methods are applied for obtaining a higher flexibility on the computational grid, where the information is transferred from the lattice structure to the computational grid by Lagrange interpolation. The flow is researched on for different Reynolds number, while Prandtl number is keeping constant as a 0.7. The results show how the presence of a triangular prism effects the flow and heat transfer patterns for the steady-state and unsteady-periodic flow regimes. As an evaluation of the accuracy of the developed LBM code, the results are compared with those obtained by a commercial CFD code. It is observed that the present LBM code produces results that have similar accuracy with the well-established CFD code, as an additionally, LBM needs much smaller CPU time for the prediction of the unsteady phonema.

Keywords: laminar forced convection, lbm, triangular prism

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Authors: Mohammadreza Nezamirad, Sepideh Amirahmadian, Nasim Sabetpour, Azadeh Yazdi, Amirmasoud Hamedi

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Cavitation inside diesel injector nozzle is investigated using Reynolds-Stress-Navier Stokes equations. Schnerr-Sauer cavitation model is used for modeling cavitation inside diesel injector nozzle. The carrying fluid utilized in the current study is diesel fuel. The flow is verified at the beginning by comparing with the previous experimental data, and it was found that K-Epsilon turbulent model could lead to a better accuracy comparing to K-Omega turbulent model. Moreover, the mass flow rate obtained numerically is compared with the experimental value, and the discrepancy was found to be less than 5 percent which shows the accuracy of the current results. Finally, a real-size four-hole nozzle is investigated, and the flow inside it is visualized based on velocity profile, discharge coefficient, and cavitation number. It was found that the mesh density could be reduced significantly by utilizing periodic boundary conditions. Velocity contour at the mid nozzle showed that the maximum value of velocity occurs at the end of the needle before entering the orifice area. Last but not least, at the same boundary conditions, when different needle heights were utilized, it was found that as needle height increases with an increase in cavitation number, discharge coefficient increases, while the mentioned increases are more tangible at smaller values of needle heights.

Keywords: cavitation, diesel fuel, CFD, real size nozzle, mass flow rate

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Authors: Zbigniew Czyz, Krzysztof Skiba, Miroslaw Wendeker

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This paper discusses the results of aerodynamic investigation of the Tajfun gyroplane body designed by a Polish company, Aviation Artur Trendak. This gyroplane has been studied as a 1:8 scale model. Scaling objects for aerodynamic investigation is an inherent procedure in any kind of designing. If scaling, the criteria of similarity need to be satisfied. The basic criteria of similarity are geometric, kinematic and dynamic. Despite the results of aerodynamic research are often reduced to aerodynamic coefficients, one should pay attention to how values of coefficients behave if certain criteria are to be satisfied. To satisfy the dynamic criterion, for example, the Reynolds number should be focused on. This is the correlation of inertial to viscous forces. With the multiplied flow speed by the specific dimension as a numerator (with a constant kinematic viscosity coefficient), flow speed in a wind tunnel research should be increased as many times as an object is decreased. The aerodynamic coefficients specified in this research depend on the real forces that act on an object, its specific dimension, medium speed and variations in its density. Rapid prototyping with a 3D printer was applied to create the research object. The research was performed with a T-1 low-speed wind tunnel (its diameter of the measurement volume is 1.5 m) and a six-element aerodynamic internal scales, WDP1, at the Institute of Aviation in Warsaw. This T-1 wind tunnel is low-speed continuous operation with open space measurement. The research covered a number of the selected speeds of undisturbed flow, i.e. V = 20, 30 and 40 m/s, corresponding to the Reynolds numbers (as referred to 1 m) Re = 1.31∙106, 1.96∙106, 2.62∙106 for the angles of attack ranging -15° ≤ α ≤ 20°. Our research resulted in basic aerodynamic characteristics and observing the impact of undisturbed flow speed on the correlation of aerodynamic coefficients as a function of the angle of attack of the gyroplane body. If the speed of undisturbed flow in the wind tunnel changes, the aerodynamic coefficients are significantly impacted. At speed from 20 m/s to 30 m/s, drag coefficient, Cx, changes by 2.4% up to 9.9%, whereas lift coefficient, Cz, changes by -25.5% up to 15.7% if the angle of attack of 0° excluded or by -25.5% up to 236.9% if the angle of attack of 0° included. Within the same speed range, the coefficient of a pitching moment, Cmy, changes by -21.1% up to 7.3% if the angles of attack -15° and -10° excluded or by -142.8% up to 618.4% if the angle of attack -15° and -10° included. These discrepancies in the coefficients of aerodynamic forces definitely need to consider while designing the aircraft. For example, if load of certain aircraft surfaces is calculated, additional correction factors definitely need to be applied. This study allows us to estimate the discrepancies in the aerodynamic forces while scaling the aircraft. This work has been financed by the Polish Ministry of Science and Higher Education.

Keywords: aerodynamics, criteria of similarity, gyroplane, research tunnel

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Authors: Gokturk Memduh Ozkan, Huseyin Akilli

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The aim of present study is to control the unsteady flow structure downstream of a circular cylinder by use of attached permeable plates. Particle image velocimetry (PIV) technique and dye visualization experiments were performed in deep water and the flow characteristics were evaluated by means of time-averaged streamlines, Reynolds Shear Stress and Turbulent Kinetic Energy concentrations. The permeable plate was made of a chrome-nickel screen having a porosity value of β=0.6 and it was attached on the cylinder surface along its midspan. Five different angles were given to the plate (θ=0°, 15°, 30°, 45°, 60°) with respect to the centerline of the cylinder in order to examine its effect on the flow control. It was shown that the permeable plate is effective on elongating the vortex formation length and reducing the fluctuations in the wake region. Compared to the plain cylinder, the reductions in the values of maximum Reynolds shear stress and Turbulent Kinetic Energy were evaluated as 72.5% and 66%, respectively for the plate angles of θ=45° and 60° which were also found to be suggested for applications concerning the vortex shedding and consequent Vortex-Induced Vibrations.

Keywords: bluff body, flow control, permeable plate, PIV, VIV, vortex shedding

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Authors: Shamik Hazra, Sushanta Mitra, Ashis Sen

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Despite growing interest of microparticle manipulation in non-Newtonian fluids, combined effect of viscoelasticity and shear thinning on particle lateral position is not well understood. We performed experiments with rigid microparticles of 15 µm diamater in popular Shear thinning viscoelastic (STVE) liquid poyethylene oxide (PEO) of different molecular weights (MW) and concentrations (c), for Reynolds number (Re) < 1. Microparticles in an STVE liquid revealed four different migration regimes: original streamline (OS), bimodal (BM), centre migration (CM) and defocusing (DF), depending upon the Re and c and interplay of different forces is also elucidated. Our investigation will be helpful to select proper polymer concentration to achieve desired particle focusing inside microchannel.

Keywords: lateral migration, microparticle, polyethylene oxide, shear thinning, viscoelasticity

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Authors: B. Chetti, W. A. Crosby

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The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: two-lobe bearing, thermal effect, static, dynamic characteristics

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Authors: Sylvana A. Vega, Cesar E. Huilinir, Carlos J. Gonzalez

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Co-digestion in anaerobic biodigesters is a technology improving hydrolysis by increasing methane generation. In the present study, the dimensional computational fluid dynamics (CFD) is numerically analyzed using Ansys Fluent software for agitation in a full-scale Continuous Stirred Tank Reactor (CSTR) biodigester during the co-digestion process. For this, a rheological study of the substrate is carried out, establishing rotation speeds of the stirrers depending on the microbial activity and energy ranges. The substrate is organic waste from industrial sources of sanitary water, butcher, fishmonger, and dairy. Once the rheological behavior curves have been obtained, it is obtained that it is a non-Newtonian fluid of the pseudoplastic type, with a solids rate of 12%. In the simulation, the rheological results of the fluid are considered, and the full-scale CSTR biodigester is modeled. It was coupling the second-order continuity differential equations, the three-dimensional Navier Stokes, the power-law model for non-Newtonian fluids, and three turbulence models: k-ε RNG, k-ε Realizable, and RMS (Reynolds Stress Model), for a 45° tilt vane impeller. It is simulated for three minutes since it is desired to study an intermittent mixture with a saving benefit of energy consumed. The results show that the absolute errors of the power number associated with the k-ε RNG, k-ε Realizable, and RMS models were 7.62%, 1.85%, and 5.05%, respectively, the numbers of power obtained from the analytical-experimental equation of Nagata. The results of the generalized Reynolds number show that the fluid dynamics have a transition-turbulent flow regime. Concerning the Froude number, the result indicates there is no need to implement baffles in the biodigester design, and the power number provides a steady trend close to 1.5. It is observed that the levels of design speeds within the biodigester are approximately 0.1 m/s, which are speeds suitable for the microbial community, where they can coexist and feed on the substrate in co-digestion. It is concluded that the model that more accurately predicts the behavior of fluid dynamics within the reactor is the k-ε Realizable model. The flow paths obtained are consistent with what is stated in the referenced literature, where the 45° inclination PBT impeller is the right type of agitator to keep particles in suspension and, in turn, increase the dispersion of gas in the liquid phase. If a 24/7 complete mix is considered under stirred agitation, with a plant factor of 80%, 51,840 kWh/year are estimated. On the contrary, if intermittent agitations of 3 min every 15 min are used under the same design conditions, reduce almost 80% of energy costs. It is a feasible solution to predict the energy expenditure of an anaerobic biodigester CSTR. It is recommended to use high mixing intensities, at the beginning and end of the joint phase acetogenesis/methanogenesis. This high intensity of mixing, in the beginning, produces the activation of the bacteria, and once reaching the end of the Hydraulic Retention Time period, it produces another increase in the mixing agitations, favoring the final dispersion of the biogas that may be trapped in the biodigester bottom.

Keywords: anaerobic co-digestion, computational fluid dynamics, CFD, net power, organic waste

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Authors: Azzedine Abdedou, Khedidja Bouhadef

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The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: forced convection, porous media, oriented confined jet, fluid mechanics

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Authors: Hany Elsaid Fawaz Abdallah

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This study presents a new artificial neural network(ANN) model to predict the Nusselt Number and pressure drop for the turbulent flow in a triangular corrugated plate heat exchanger for forced air and turbulent water flow. An experimental investigation was performed to create a new dataset for the Nusselt Number and pressure drop values in the following range of dimensionless parameters: The plate corrugation angles (from 0° to 60°), the Reynolds number (from 10000 to 40000), pitch to height ratio (from 1 to 4), and Prandtl number (from 0.7 to 200). Based on the ANN performance graph, the three-layer structure with {12-8-6} hidden neurons has been chosen. The training procedure includes back-propagation with the biases and weight adjustment, the evaluation of the loss function for the training and validation dataset and feed-forward propagation of the input parameters. The linear function was used at the output layer as the activation function, while for the hidden layers, the rectified linear unit activation function was utilized. In order to accelerate the ANN training, the loss function minimization may be achieved by the adaptive moment estimation algorithm (ADAM). The ‘‘MinMax’’ normalization approach was utilized to avoid the increase in the training time due to drastic differences in the loss function gradients with respect to the values of weights. Since the test dataset is not being used for the ANN training, a cross-validation technique is applied to the ANN network using the new data. Such procedure was repeated until loss function convergence was achieved or for 4000 epochs with a batch size of 200 points. The program code was written in Python 3.0 using open-source ANN libraries such as Scikit learn, TensorFlow and Keras libraries. The mean average percent error values of 9.4% for the Nusselt number and 8.2% for pressure drop for the ANN model have been achieved. Therefore, higher accuracy compared to the generalized correlations was achieved. The performance validation of the obtained model was based on a comparison of predicted data with the experimental results yielding excellent accuracy.

Keywords: artificial neural networks, corrugated channel, heat transfer enhancement, Nusselt number, pressure drop, generalized correlations

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Authors: Ehan Sabah Shukri, Wirachman Wisnoe

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Temperature distribution investigation in a conical diffuser fitted with helical screw-tape with and without center-rod is studied numerically. A helical screw-tape is inserted in the diffuser to create swirl flow that helps to enhance the temperature distribution rate with inlet Reynolds number 4.3 x 104. Three pitch lengths ratios (Y/L = 0.153, 0.23 and 0.307) for the helical screw-tape with and without center-rod are simulated and compared. The geometry of the conical diffuser and the inlet condition for both arrangements are kept constant. Numerical findings show that the helical screw-tape inserts without center-rod perform significantly better than the helical tape inserts with center-rod in the conical diffuser.

Keywords: diffuser, temperature distribution, CFD, pitch ratio

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Authors: Iryna Shevchenko

Abstract:

The science of mathematics was originated at the order of count of objects and subsequently for the measurement of size and quality of objects using the logical or abstract means. The laws of mathematics are based on the study of absolute values. The number 0 or "nothing" is the purely logical (as the opposite to absolute) value as the "nothing" should always assume the space for the something that had existed there; otherwise the "something" would never come to existence. In this work we are going to prove that the number "0" is the abstract (logical) and not an absolute number and it has the absolute value of “∞” (infinity). Therefore, the number "0" might not stand in the row of numbers that symbolically represents the absolute values, as it would be the mathematically incorrect. The symbolical value of number "0" in the row of numbers could be represented with symbol "∞" (infinity). As a result, we have the mathematical row of numbers: epsilon, ...4, 3, 2, 1, ∞. As the conclusions of the theory of number “0” we presented the statements: multiplication and division by fractions of numbers is illegal operation and the mathematical division by number “0” is allowed.

Keywords: illegal operation of division and multiplication by fractions of number, infinity, mathematical row of numbers, theory of number “0”

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Authors: S. Kida

Abstract:

We consider the flow of an incompressible viscous fluid in a precessing sphere whose spin and precession axes are orthogonal to each other. The flow is characterized by two non-dimensional parameters, the Reynolds number Re and the Poincare number Po. For which values of (Re, Po) will the flow approach a steady state from an arbitrary initial condition? To answer it we are searching the instability boundary of the steady states in the whole (Re, Po) plane. Here, we focus the rapidly rotating and weakly precessing limit, i.e., Re >> 1 and Po << 1. The steady flow was obtained by the asymptotic expansion for small ε=Po Re¹/² << 1. The flow exhibits nearly a solid-body rotation in the whole sphere except for a thin boundary layer which develops over the sphere surface. The thickness of this boundary layer is of O(δ), where δ=Re⁻¹/², except where two circular critical bands of thickness of O(δ⁴/⁵) and of width of O(δ²/⁵) which are located away from the spin axis by about 60°. We perform the linear stability analysis of the steady flow. We assume that the disturbances are localized in the critical bands and make an expansion analysis in terms of ε to derive the eigenvalue problem for the growth rate of the disturbance, which is solved numerically. As the solution, we obtain an asymptote of the stability boundary as Po=28.36Re⁻⁰.⁸. This agrees excellently with the corresponding laboratory experiments and numerical simulations. One of the most popular instability mechanisms so far is the parametric instability, which turns out, however, not to give the correct stability boundary. The present instability is different from the parametric instability.

Keywords: boundary layer, critical band, instability, precessing sphere

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Authors: Muhammad Abdullah, Asma Rashid Butt, Nauman Raza

Abstract:

Biomagnetic fluids like blood play key role in different applications of medical science and bioengineering. In this paper, the magnetohydrodynamic flow of a viscous fluid with magnetic particles through a cylindrical tube is investigated. The fluid is electrically charged in the presence of a uniform external magnetic field. The movement in the fluid is produced due to the cylindrical tube. Initially, the fluid and tube are at rest and at time t=0⁺, the tube starts to move along its axis. To obtain the mathematical model of flow with fractional derivatives fractional calculus approach is used. The solution of the flow model is obtained by using Laplace transformation. The Simon's numerical algorithm is employed to obtain inverse Laplace transform. The hybrid technique, we are employing has less computational effort as compared to other methods. The numerical calculations have been performed with Mathcad software. As the special cases of our problem, the solution of flow model with ordinary derivatives and flow without magnetic particles has been procured. Finally, the impact of non-integer fractional parameter alpha, Hartmann number Ha, and Reynolds number Re on flow and magnetic particles velocity is analyzed and depicted by graphs.

Keywords: viscous fluid, magnetic particles, fractional calculus, laplace transformation

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Authors: Oscar Bautista, Jose Arcos

Abstract:

In this work, we conduct a theoretical analysis of an oscillatory electroosmotic flow in a parallel-plate microchannel taking into account slippage at the microchannel walls. The governing equations given by the Poisson-Boltzmann (with the Debye-Huckel approximation) and momentum equations are nondimensionalized from which four dimensionless parameters appear; a Reynolds angular number, the ratio between the zeta potentials of the microchannel walls, the electrokinetic parameter and the dimensionless slip length which measures the competition between the Navier slip length and the half height microchannel. The principal results indicate that the slippage has a strong influence on the magnitude of the oscillatory electroosmotic flow increasing the velocity magnitude up to 50% for the numerical values used in this work.

Keywords: electroosmotic flows, oscillatory flow, slippage, microchannel

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Authors: C. F. Alegretti, F. R. Cunha, R. G. Gontijo

Abstract:

This work investigates the effects of an applied magnetic field on the geometry-driven boundary layer detachment flow of a ferrofluid over a sudden expansion. Both constitutive equation and global magnetization equation for a ferrofluid are considered. Therefore, the proposed formulation consists in a coupled magnetic-hydrodynamic problem. Computational simulations are carried out in order to explore, not only the viability to control flow instabilities, but also to evaluate the consistency of theoretical aspects. The unidirectional sudden expansion in a ferrofluid flow is investigated numerically under the perspective of Ferrohydrodynamics in a two-dimensional domain using a Finite Differences Method. The boundary layer detachment induced by the sudden expansion results in a recirculating zone, which has been extensively studied in non-magnetic hydrodynamic problems for a wide range of Reynolds numbers. Similar investigations can be found in literature regarding the sudden expansion under the magnetohydrodynamics framework, but none considering a colloidal suspension of magnetic particles out of the superparamagnetic regime. The vorticity-stream function formulation is implemented and results in a clear coupling between the flow vorticity and its magnetization field. Our simulations indicate a systematic decay on the length of the recirculation zone as increasing physical parameters of the flow, such as the intensity of the applied field and the volume fraction of particles. The results all are discussed from a physical point of view in terms of the dynamical non-dimensional parameters. We argue that the decrease/reduction in the recirculation region of the flow is a direct consequence of the magnetic torque balancing the action of the torque produced by viscous and inertial forces of the flow. For the limit of small Reynolds and magnetic Reynolds parameters, the diffusion of vorticity balances the diffusion of the magnetic torque on the flow. These mechanics control the growth of the recirculation region.

Keywords: boundary layer detachment, ferrofluid, ferrohydrodynamics, magnetization, sudden expansion

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Authors: Serebryanaya Fatima, Essaih Hind

Abstract:

The Rosa damascena (Rosa damascena Mill.) is an interesting medicinal plant; it is famous in different countries and has medicinal use in many cultures. The main groups of pharmacological actions of rose oil are connected with anti-inflammatory, antifungal activity, also antioxidant and antibacterial, and antiparasitic properties. We have prepared the quality indicators analysis of the Damascus rose oil. An iodine number, acid number, and oil peroxide number were determined. The following indicators of the quality of rose oil have been studied. The determination was carried out according to the pharmacopoeic methods of analysis of essential oils, the definition of peroxide number (1,971%), iodine number (3,365%), and acid number (0,0526%).

Keywords: Rosa damascene, Rosa damascena Mill., iodine number, acid number, oil peroxide number

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Authors: C. D. Ellis, H. Xia, X. Chen

Abstract:

Experimental and computational studies investigating heat transfer in separated flows have been of increasing importance over the last 60 years, as efforts are being made to understand and improve the efficiency of components such as combustors, turbines, heat exchangers, nuclear reactors and cooling channels. Understanding of not only the time-mean heat transfer properties but also the unsteady properties is vital for design of these components. As computational power increases, more sophisticated methods of modelling these flows become available for use. The hybrid LES-RANS approach has been applied to a blunt leading edge flat plate, utilising a structured grid at a moderate Reynolds number of 20300 based on the plate thickness. In the region close to the wall, the RANS method is implemented for two turbulence models; the one equation Spalart-Allmaras model and Menter’s two equation SST k-ω model. The LES region occupies the flow away from the wall and is formulated without any explicit subgrid scale LES modelling. Hybridisation is achieved between the two methods by the blending of the nearest wall distance. Validation of the flow was obtained by assessing the mean velocity profiles in comparison to similar studies. Identifying the vortex structures of the flow was obtained by utilising the λ2 criterion to identify vortex cores. The qualitative structure of the flow compared with experiments of similar Reynolds number. This identified the 2D roll up of the shear layer, breaking down via the Kelvin-Helmholtz instability. Through this instability the flow progressed into hairpin like structures, elongating as they advanced downstream. Proper Orthogonal Decomposition (POD) analysis has been performed on the full flow field and upon the surface temperature of the plate. As expected, the breakdown of POD modes for the full field revealed a relatively slow decay compared to the surface temperature field. Both POD fields identified the most energetic fluctuations occurred in the separated and recirculation region of the flow. Latter modes of the surface temperature identified these levels of fluctuations to dominate the time-mean region of maximum heat transfer and flow reattachment. In addition to the current research, work will be conducted in tracking the movement of the vortex cores and the location and magnitude of temperature hot spots upon the plate. This information will support the POD and statistical analysis performed to further identify qualitative relationships between the vortex dynamics and the response of the surface heat transfer.

Keywords: heat transfer, hybrid LES-RANS, separated and reattached flow, vortex dynamics

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Authors: Mohammad Afkhami, Ali Hassanpour, Michael Fairweather

Abstract:

The work described in this paper was undertaken to gain insight into fundamental aspects of turbulent gas-particle flows with relevance to processes employed in a wide range of applications, such as oil and gas flow assurance in pipes, powder dispersion from dry powder inhalers, and particle resuspension in nuclear waste ponds, to name but a few. In particular, the influence of particle interaction and fluid phase behavior in turbulent flow on particle dispersion in a horizontal channel is investigated. The mathematical modeling technique used is based on the large eddy simulation (LES) methodology embodied in the commercial CFD code FLUENT, with flow solutions provided by this approach coupled to a second commercial code, EDEM, based on the discrete element method (DEM) which is used for the prediction of particle motion and interaction. The results generated by LES for the fluid phase have been validated against direct numerical simulations (DNS) for three different channel flows with shear Reynolds numbers, Reτ = 150, 300 and 590. Overall, the LES shows good agreement, with mean velocities and normal and shear stresses matching those of the DNS in both magnitude and position. The research work has focused on the prediction of those conditions favoring particle aggregation and deposition within turbulent flows. Simulations have been carried out to investigate the effects of particle size, density and concentration on particle agglomeration. Furthermore, particles with different surface properties have been simulated in three channel flows with different levels of flow turbulence, achieved by increasing the Reynolds number of the flow. The simulations mimic the conditions of two-phase, fluid-solid flows frequently encountered in domestic, commercial and industrial applications, for example, air conditioning and refrigeration units, heat exchangers, oil and gas suction and pressure lines. The particle size, density, surface energy and volume fractions selected are 45.6, 102 and 150 µm, 250, 1000 and 2159 kg m-3, 50, 500, and 5000 mJ m-2 and 7.84 × 10-6, 2.8 × 10-5, and 1 × 10-4, respectively; such particle properties are associated with particles found in soil, as well as metals and oxides prevalent in turbulent bounded fluid-solid flows due to erosion and corrosion of inner pipe walls. It has been found that the turbulence structure of the flow dominates the motion of the particles, creating particle-particle interactions, with most of these interactions taking place at locations close to the channel walls and in regions of high turbulence where their agglomeration is aided both by the high levels of turbulence and the high concentration of particles. A positive relationship between particle surface energy, concentration, size and density, and agglomeration was observed. Moreover, the results derived for the three Reynolds numbers considered show that the rate of agglomeration is strongly influenced for high surface energy particles by, and increases with, the intensity of the flow turbulence. In contrast, for lower surface energy particles, the rate of agglomeration diminishes with an increase in flow turbulence intensity.

Keywords: agglomeration, channel flow, DEM, LES, turbulence

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