Main Dimensionless Groups Research Articles

Data-informed characterization of spatio-temporal scales in experiments of microconfined high-pressure transcritical turbulence

The spatio-temporal scales of microconfined high-pressure transcritical turbulence are characterized in relation to the resolution capabilities of present time-resolved two-dimensional μPIV technology. Utilizing CO2 as the working fluid, the physical scales are examined by considering the main dimensionless groups of the problem, which correspond to the Reynolds, Brinkman, and Stokes numbers and the mass fraction of particles in the fluid. In detail, the methodology employed leverages direct numerical simulation data to inform the estimation of hydrodynamic, thermophysical, and particle-related scales, and selects a state-of-the-art μPIV setup to describe the optical performance of the current technology. The results indicate that the temporal scales can be experimentally captured for a wide range of operating conditions. However, the scenario becomes much more complex when trying to capture the spatial scales of microconfined high-pressure transcritical turbulent flow. Particularly, the Kolmogorov and Batchelor spatial scales can be captured for bulk Reynolds numbers below O(103). Otherwise, the spatial scales can only be partially captured and/or remain completely masked due to insufficient resolution, like for example in the case of boundary layer viscous scales and fluid density variations. This limitation is not imposed by the tracer behavior of microparticles, as the Stokes number remains significantly low for all the system configurations studied. Instead, the limitation is mainly a result of the optical capabilities of present μPIV systems. Finally, given the generalizable properties of dimensionless numbers, the results and insight obtained can be extended to other experiments of μPIV-based visualization/quantification of microconfined multiscale flows involving large thermophysical variations.

Dimensional analysis and calibration of a power model for compressive strength of solid-clay-brick masonry

In the present work, the power model adopted to predict compressive strength of masonry as a function of brick and mortar strengths was studied by means of Dimensional Analysis, identifying the main dimensionless groups ruling the problem. The approach was applied on a dataset of solid-clay-brick masonry tests collected from the literature. Data were represented in a novel way that permitted to display the importance of the main dimensionless parameters. The dataset was filtered distinguishing these parameters and used to propose a new calibration of the power model considering mortar type and geometry of the specimens. Results show an interesting improvement in terms of indicators of regression quality with respect to the power models proposed in the literature. Both Dimensional Analysis and regressions confirm that the power models are specific for the type of specimens, i.e. dimensionless parameters, used for their calibration and direct comparisons among them should be done with great caution.

Analysis of Dynamics in Multiphysics Modelling of Active Faults

Instabilities in Geomechanics appear on multiple scales involving multiple physical processes. They appear often as planar features of localised deformation (faults), which can be relatively stable creep or display rich dynamics, sometimes culminating in earthquakes. To study those features, we propose a fundamental physics-based approach that overcomes the current limitations of statistical rule-based methods and allows a physical understanding of the nucleation and temporal evolution of such faults. In particular, we formulate the coupling between temperature and pressure evolution in the faults through their multiphysics energetic process(es). We analyse their multiple steady states using numerical continuation methods and characterise their transient dynamics by studying the time-dependent problem near the critical Hopf points. We find that the global system can be characterised by a homoclinic bifurcation that depends on the two main dimensionless groups of the underlying physical system. The Gruntfest number determines the onset of the localisation phenomenon, while the dynamics are mainly controlled by the Lewis number, which is the ratio of energy diffusion over mass diffusion. Here, we show that the Lewis number is the critical parameter for dynamics of the system as it controls the time evolution of the system for a given energy supply (Gruntfest number).

Linear dynamics modelling of droplet deformation in a pulsatile electric field

A linear dynamic model of water droplet deformation in the presence of an electric field has been developed. Analytical solutions of the differential equation of motion are provided with different waveforms as forcing terms, namely in the case of half-sinusoidal, square and sawtooth waves. The main dimensionless groups are identified as a result of this analysis. The predictions of the model are compared with some data of droplet deformation available in the literature. The calculations based on this model show that the waveform affects the response of the droplet to the electric field stimulus. Resonance is possible only when the droplets are sufficiently large (i.e. for Ohnesorge number less than 1). The oscillation amplitude decreases rapidly with the electric field frequency. A qualitative comparison with some experiments of droplet-interface coalescence available in the literature has also been addressed, suggesting a correlation between the formation of secondary droplets and the amplitude of oscillation of the mother droplet. The outcomes of this analysis can be useful for the selection of the best operating conditions to improve the electrocoalescence process efficiency, as they can provide guidelines to the choice of the most suitable electric field parameters.

Analytical solution for ultimate embedment depth and potential holding capacity of plate anchors

This paper proposes an analytical approach to evaluate the ultimate embedment depth and holding capacity that plate anchors can potentially achieve. Based on a plasticity model for anchor–soil interaction and compatible chain solution, detailed derivations are presented that allow the main dimensionless groups of input parameters to be identified. For typical cases where the weight of the anchor is negligible relative to its holding capacity, explicit expressions are provided in non-dimensional form for ultimate embedment and anchor capacity. A thorough parametric sensitivity study highlights the major factors affecting these quantities. Two practical examples are considered that demonstrate the proposed analytical approach for different types of anchors, in one case revealing significant scope for improved design of plate anchors in order to optimise performance.

Transport modeling of convection-enhanced hollow fiber membrane bioreactors for therapeutic applications

In this paper, a theoretical framework is presented for the design of hollow fiber membrane bioreactors (HFMBs) operated in closed-shell mode in the presence of high recirculation flows in the cell compartment. Navier–Stokes and Brinkman equations were used to describe fluid transport, and the convection-diffusion-reaction equations to describe transport of dissolved oxygen and glucose to cells. Numerical solutions were sought with the finite element method for the high permeability typical of new medical membranes, and operating conditions typical of therapeutic applications. Generalized charts intended to help the bioreactor designer were obtained giving the non-hypoxic (or well-nourished) fractional shell volume as a function of the main dimensionless groups influencing the magnitude of the recirculation flow. Results indicate that designs and operations promoting moderate-to-high recirculation flows in the bioreactor shell markedly enhance solute transport and permit much better cell oxygenation and nourishment, and control of the pericellular environment, than diffusion-limited bioreactors. With these charts, bioreactor design may be optimized for a given therapeutic treatment, or operation adjusted to the properties of the cell aggregate as tissue forms in tissue engineering applications, so as to provide cells with a physiological supply of oxygen and nutrients and a physiological pericellular environment.

Comparison between CFD calculations of the flow in a rotating disk cell and the Cochran/Levich equations

Three CFD (Computational Fluid Dynamics) models (single-phase, VOF and Euler–Euler) are employed to simulate the flow in a finite, rotating electrode cell under different operative conditions. The main dimensionless groups are derived and their effect on the flow is investigated. Except very close to the rotating electrode (i.e. in the hydrodynamic layer), the results show a flow pattern considerably different from Cochran’s approximate analytical solution often used in electrochemistry. Historically, the Cochran equation was used to derive the Levich equation, which permits the calculation of the limiting current density on a rotating electrode. Despite the general inadequacy of Cochran’s analytical solution, however, we show that the Levich equation often retains its validity because, in many practical situations, the concentration boundary layer is considerably smaller than the hydrodynamic boundary layer. When bubbles are generated on the electrode and a certain critical void fraction is exceeded, however, the Levich equation also becomes inaccurate. We propose, therefore, an amended version of this equation, which provides results closer to the CFD calculations.

Numerical study of liquid/liquid slug flow in a capillary microreactor

AbstractThe great advantage of microreactors is associated with an extremely large surface‐to‐volume ratio. Hence, microreactors permit promising operating conditions, such as almost‐perfect heat or mass transfer. This, of course, requires that the hydrodynamics is well understood. The hydrodynamics of a liquid/liquid slug flow in a micro‐capillary is characterized by a complex vortex structure in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persist between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner.Apparently, several effects influence the hydrodynamics. The main dimensionless groups are a Reynolds number, a Capillary number, and the ratio of viscosities and densities of both phases. To study the physics of this complex two‐liquid system, a modified level‐set method in conjunction with an immersed‐boundary formulation is engaged. Presently, the simulations are time‐dependent and axially‐symmetric in nature. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mathematical Model for Calculating Oxygen Mass Transfer Coefficient in Diffused Air Systems

The key element in developing an analytical or mathematical procedure is to determine the main factors that possess potential importance in oxygen transfer process. In this paper, the factors that affect the oxygen mass transfer coefficient (KLa) in activated sludge units are determined. A dimensional analysis procedure is adopted to develop a mathematical model, which can be used for calculating these factors. A very high accurate model with a correlation factor of (98.889 %) is obtained from this analysis. The solution of the model shows that: The main dimensionless groups which controlling the oxygen mass transfer in this units are: Reynolds number, Froude number, the ratio of bubbles diameter to length of its bath in water, the ratio of water depth in the tank to tank length, and the ratio of diffusers area to tank area. Each of the Reynolds number and the ratio of area of diffusers to the area of tank have positive effect on the oxygen mass transfer coefficient. Increasing any of airflow rates, the area of diffusers coverage in the tank and the length of the path of bubbles in water significantly increase the oxygen mass flow rate while this ability can also be increased by decreasing the diameter of bubbles in the system.

Design optimization by numerical characterization of fluid flow through the valveless diffuser micropumps

Valveless piezoelectric micropumps are in wide practical use due to their ability to conduct particles with absence of interior moving mechanical parts. In this paper, an extended numerical study on fluid flow through micropump chamber and diffuser valves is conducted to find out the optimum working conditions of micropump. In order to obtain maximum generality of the reported results, an analytical study along with a dimensional analysis is presented primarily, to investigate the main dimensionless groups of parameters affecting the micropump net flux. Consequently, the parameters appeared in the main dimensionless groups have been changed in order to understand how the pump rectification efficiency and optimum diffuser angle depend on these parameters. A set of characteristic curves are constructed which show these dependencies. The application of these curves would have far reaching implications for valveless micropumps design and selection purposes.

Pressure Drop Across a Double-Outlet Vortex Chamber

The properties of the pressure drop in a medium-aspect-ratio vortex chamber with double outlets are examined both experimentally and theoretically. Dimensional analysis provides the functional relationships between the main dimensionless groups. Application of the integral equations of continuity and energy over the control volume, along with the minimum-pressure-drop principle, furnish the required formulas that relate the predominant nondimensionalparameters. In the vortex-dominatedregime, the theoretical results, given in terms of the pressure drop across the chamber, are found to agree with the experimental observations. The larger outlet has been shown to control the  ow. A considerable reduction in static pressure drop across the chamber can be gained by adding an extra outlet at the opposite end-plate.

Penetrative convection in a horizontal layer of seawater near its freezing point

A series of numerical experiments are performed to investigate steady thermosolutal convection induced by the partial freezing of a horizontal pool of seawater from the top. This study is aimed at achieving a better understanding of the role of convection in transporting oceanic heat into the atmosphere during the formation of a polynya. The mathematical model considered accounts for the density anomaly of seawater and for the dependence of the freezing point on salinity. A new solutal regime is isolated wherein solutal convection is present even though the solutal expansion coefficient is set to zero. This convection process arises as a result of the coupling between the fluctuations of temperature and salinity at the ice–water interface. A parametric study is undertaken as function of the main dimensionless groups characterizing the problem, namely the thermal Rayleigh number, the density ratio and an extremum parameter which quantifies the effect of the nonlinear equation of state. Several indicators of the convection process, such as the Nusselt and Sherwood numbers, the kinetic energy in the fluid layer and the buoyancy are calculated. It is found that a two-layer convection regime generally predominates for relatively large Rayleigh numbers. These results imply that the penetrative convection which results from the coupling between the nonlinear equation of state and the freezing process acts in such a way as to delay the release of heat to the atmosphere during the formation of a polynya.