A discrete model for the apparent viscosity of polydisperse suspensions including maximum packing fraction

Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of spherical, non-colloidal particles is derived. The model connects the approaches by Bruggeman and Farris and is valid for large size ratios of consecutive particle classes during the construction process, appearing to be the first model consistently describing polydisperse volume fractions and maximum packing fraction within a single approach. In that context, the consistent inclusion of the maximum packing fraction into effective medium models is discussed. Furthermore, new generalized forms of the well-known Quemada and Krieger equations allowing for the choice of a second-order Taylor coefficient for the volume fraction ($\phi^2$-coefficient), found by asymptotic matching, are proposed. The model for the maximum packing fraction as well as the complete viscosity model are compared to experimental data from the literature showing good agreement. As a result, the new model is shown to replace the empirical Sudduth model for large diameter ratios. The extension of the model to the case of small size ratios is left for future work.Comment: 14 pages, 4 figure

Magnetohydrodynamics, natural convection and entropy generation of CuO-water nanofluid in an I-shape enclosure - a numerical study

This paper presents a numerical study of the magnetohydrodynamics, natural convection, and thermodynamic irreversibilities in an I-shape enclosure, filled with CuO-water nanofluid and subject to a uniform magnetic field. The lateral walls of the enclosure are maintained at different but constant temperatures, while the top and bottom surfaces are adiabatic. The Brownian motion of the nanoparticles is taken into account and an extensive parametric study is conducted. This involves the variation of Rayleigh and Hartmann numbers, and the concentration of nanoparticles and also the geometrical specifications of the enclosure. Further, the behaviors of streamlines and isotherms under varying parameters are visualized. Unlike that in other configurations, the rate of heat transfer in the I-shaped enclosure appears to be highly location dependent and convection from particular surfaces dominates the heat transfer process. It is shown that interactions between the magnetic field and natural convection currents in the investigated enclosure can lead to some peculiarities in the thermal behavior of the system. The results also demonstrate that different parts of the enclosure may feature significantly different levels of heat transfer sensitivity to the applied magnetic field. Further, the analysis of entropy generation indicates that the irreversibility of the system is a strong function of the geometrical parameters and that the variations in these parameters can minimize the total generation of entropy. This study clearly shows that ignoring the exact shape of the enclosure may result in major errors in the prediction of heat transfer and second law performances of the system

Effects of near wall modeling in the Improved-Delayed-Detached-Eddy-Simulation (IDDES) methodology

The present study aims to assess the effects of two different underlying RANS models on overall behavior of the IDDES methodology when applied to different flow configurations ranging from fully attached (plane channel flow) to separated flows (periodic hill flow). This includes investigating prediction accuracy of first and second order statistics, response to grid refinement, grey area dynamics and triggering mechanism. Further, several criteria have been investigated to assess reliability and quality of the methodology when operating in scale resolving mode. It turns out that irrespective of the near wall modeling strategy, the IDDES methodology does not satisfy all criteria required to make this methodology reliable when applied to various flow configurations at different Reynolds numbers with different grid resolutions. Further, it is found that using more advanced underlying RANS model to improve prediction accuracy of the near wall dynamics results in extension of the grey area, which may delay the transition to scale resolving mode. This systematic study for attached and separated flows suggests that the shortcomings of IDDES methodology mostly lie in inaccurate prediction of the dynamics inside the grey area and demands further investigation in this direction to make this methodology capable of dealing with different flow situations reliably

Analysis of transport from cylindrical surfaces subject to catalytic reactions and non-uniform impinging flows in porous media: a non-equilibrium thermodynamics approach

This paper investigates forced convection of heat and mass from the catalytic surface of a cylinder featuring non-uniform transpiration and impinging flows in porous media. The non-equilibrium thermodynamics including Soret and Dufour effects and local thermal non-equilibrium are considered. Through employing appropriate change of variables, the governing equations in cylindrical coordinate are reduced to nonlinear ordinary differential equations and solved using a finite difference scheme. This results in the calculation of the temperature and concentration fields as well as the local and surface-averaged Nusselt and Sherwood numbers. The conducted analyses further include evaluation of the rate of entropy generation within the porous medium. It is shown that internal heat exchanges inside the porous medium, represented by Biot number, dominate the temperature fields and Nusselt number. This indicates that consideration of local thermal non-equilibrium is of highly important. It is also demonstrated that Dufour and Soret effects can significantly influence the development of thermal and concentration boundary layers and hence modify the values of Nusselt and Sherwood numbers. In particular, it is shown that small variations in Soret and Dufour numbers can lead to noticeable changes in the average Nusselt and Sherwood numbers. Such modifications are strongly dependent upon the type of transpiration and characteristics of the impinging flow. The present work is the first analysis of non-equilibrium effects upon transport by stagnation flows around the curved surfaces embedded in porous media

Entropy generation assessment for wall-bounded turbulent shear flows based on the Reynolds Analogy assumptions

Heat transfer modeling plays a major role in design and optimization of modern and efficient thermal-fluid systems. Further, turbulent flows are thermodynamic processes, and thus, the second law of thermodynamics can be used for critical evaluations of such heat transfer models. However, currently available heat transfer models suffer from a fundamental shortcoming: their development is based on the general notion that accurate prediction of the flow field will guarantee an appropriate prediction of the thermal field, known as the . In this work, an assessment of the capability of the in predicting turbulent heat transfer when applied to shear flows of fluids of different Prandtl numbers will be given. Towards this, a detailed analysis of the predictive capabilities of the concerning entropy generation is presented for steady and unsteady state simulations. It turns out that the provides acceptable results only for mean entropy generation, while fails to predict entropy generation at small/sub-grid scales

Two-dimensional heat and mass transfer and thermodynamic analyses of porous microreactors with Soret and thermal radiation effects: An analytical approach

Transport of heat and mass and the thermodynamics of porous microreactors with thermal diffusion and radiation effects are investigated analytically. The examined configuration includes an axisymmetric, thick-wall microchannel with an iso-flux thermal boundary condition imposed on the external surfaces. The microchannel is filled with porous materials and accommodates a zeroth order homogenous chemical reaction. Internal radiative heat transfer is modelled in addition to heat convection and conduction, while the local thermal non-equilibrium approach is taken within the porous section of the system. The transport of species is coupled with that of heat via the inclusion of thermodiffusion or Soret effect. Two-dimensional heat and mass transfer differential equations are solved analytically. The results are subsequently used to predict the thermodynamic irreversibilities inside the reactor and a thorough analysis of local and total entropy generation rates is performed. Also, the changes in Nusselt number, calculated on the internal walls of the microreactor, versus various parameters are reported. It is shown that the radiation effects can impact the temperature of the solid phase of the porous medium and lead to alteration of Nusselt number. It is further observed that the transfer of mass is the main source of irreversibility in the system. The findings are of particular use for the design and analysis of the microreactors with homogenous chemical reactions and can be also used for the validation of computational models

Assessment of predictive capability of hybrid URANS/LES methods in residence time calculation

The present study aims to assess capability of mostly used hybrid URANS/LES methods in dealing with a complex swirled configuration/reactor when the residence time characteristics need to be predicted at acceptable level of accuracy and fidelity. The configuration is quite complex and out of reach of the classical RANS turbulence models as it consists of different, partly swirled inlet channels and a large variety of time and length scales. In this work only the flow field is considered and is investigated using three different hybrid URANS/LES simulation methods. The models: the Scale Adaptive Simulation (SAS), the Improved Delayed Detached Eddy Simulation(SA-IDDES) and the k-ω-DES, use different triggering mechanisms and underlying RANS models. The results of the flow field, the residence time characteristics and all related quantities are compared with both the Large Eddy Simulation (LES) and experimental data reported in Doost et al. (2016). It turns out that none of the considered hybrid methods is able to predict the residence time characteristics as well as LES does mainly due to the inaccurate prediction of the flow field. It was found that there is a need to improve the hybrid approaches by addressing the shortcomings, particularly those regarding triggering mechanism to make hybrid approaches a reliable computational tool for study complex turbulent flows inside full scale configurations where LES can be prohibitively expensive

Double-diffusive transport and thermodynamic analysis of a magnetic microreactor with non-Newtonian biofuel flow

Magnetic microfuel-reforming is a promising method of biofuel processing in diesel engines. However, the complex interactions amongst the non-Newtonian biofuel flow, magnetic field and reactor have hindered understanding of their influences upon the transport phenomena in the system. To resolve this issue, the transport of heat and mass in a porous microreactor containing a Casson rheological fluid and subject to a magnetic field is investigated analytically. The system is assumed to host a homogenous and uniformly distributed endothermic/exothermic chemical reaction. Two-dimensional analytical solutions are developed for the temperature and concentration fields as well as the Nusselt number and local entropy generations, and the results are rigorously validated. It is demonstrated that changes in the non-Newtonian characteristics of the fluid and altering the magnetic and thermal radiation properties can lead to bifurcation of temperature gradient on the surface of the porous medium. The general behaviour of such bifurcation is dominated by the exothermicity (or endothermicity) of the chemical reaction in the fluid phase. It is also shown that variations in the Casson fluid parameter and changes in the intensity and incident angle of the magnetic field can modify the Nusselt number considerably. The extent of these modifications is found to be heavily dependent upon the wall thickness and diminishes as the walls become thicker. Further, the total entropy generation is shown to be highly sensitive to the wall thickness and increases by intensifying the magnetic field, provided that the microreactor walls are thin

Effects of Near Wall Modeling in the Improved-Delayed-Detached-Eddy-Simulation (IDDES) Methodology

The present study aims to assess the effects of two different underlying RANS models on overall behavior of the IDDES methodology when applied to different flow configurations ranging from fully attached (plane channel flow) to separated flows (periodic hill flow). This includes investigating prediction accuracy of first and second order statistics, response to grid refinement, grey area dynamics and triggering mechanism. Further, several criteria have been investigated to assess reliability and quality of the methodology when operating in scale resolving mode. It turns out that irrespective of the near wall modeling strategy, the IDDES methodology does not satisfy all criteria required to make this methodology reliable when applied to various flow configurations at different Reynolds numbers with different grid resolutions. Further, it is found that using more advanced underlying RANS model to improve prediction accuracy of the near wall dynamics results in extension of the grey area, which may delay the transition to scale resolving mode. This systematic study for attached and separated flows suggests that the shortcomings of IDDES methodology mostly lie in inaccurate prediction of the dynamics inside the grey area and demands further investigation in this direction to make this methodology capable of dealing with different flow situations reliably

Direct Numerical Simulation, Lie Group Analysis and Modeling of a Turbulent Channel Flow with Wall-normal Rotation

In this thesis laminar and turbulent channel flows with wall-normal rotation have been investigated by means of numerical and analytical approaches. Contrary to the streamwise and the spanwise rotating channel flow, channel flows with wall-normal rotation has been rarely studied. Since there is no possible experimental approach to the investigation of this flow, they can be studied only numerically and analytically. However, an analytical approach is only possible in the laminar case. In order to establish the effects of the wall-normal rotation on the turbulent channel flow and also to provide reference data for the turbulence case, direct numerical simulations at Re =180, 360 based on the friction velocity in the non-rotating case for various rotation rates (from very small to relatively high) have been performed. It has been found that the both flow states are very sensitive to the wall-normal rotation and are highly affected even with a very small rotation rate. In the turbulent case due to the induction of the spanwise velocity the flow is three-dimensional and as a result all of the Reynolds stress tensor components are non-zero. By increase in the rotation rate relamonarization effects have been observed and finally at very high rotation rates the flow reaches a fully laminar steady state. Further, the Lie symmetry approach has been applied to the Reynolds averaged Navier-Stokes equations describing a turbulent wall-normal rotating channel flow at very high Reynolds numbers to study the ability of this method to predicting the flow. Based on the results, one can conclude that Lie symmetry approach can not deal with the system of differential equations with unclosed terms. Finally the DNS results have been used to investigate the capability of relatively simple turbulence models to predict the flow. In other words we have used the DNS data to validate the simple RANS turbulence models. For weak rotation rates the convincing results indicate that in contrast to the streamwise and the spanwise rotating channel flows, the present flow could be predicted by this simple turbulence model. However, predicting of the flow at higher rotation numbers requires obviously advanced RANS models including relaminarization effect