text:
\section{Introduction}
\label{sec:intro}

Multi-phase turbulent flows are ubiquitous in nature and several industrial applications such as cloud formation, plankton dispersion in sea, fuel sprays, emulsification, homogenisation and mixing in chemical reactors and drag reduction. In particular, two-phase flows which typically comprise a secondary phase dispersed into a primary carrier flow (e.g. droplets/bubbles dispersed into water or air) are prevalent in many applications involving drag reduction, heat transfer, liquid atomisation etc. Theoretical and numerical modelling of such flows is extremely challenging due to the wide range of length and time scales involved both in the dispersed and carrier phase. Among the many parameters that influence the global response and local statistics of two-phase systems, the shape and orientation of a non-spherical anisotropic dispersed phase plays a very important role.

In this work, we study the shape and orientation statistics of neutrally buoyant, sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette (TC) flow. TC flow is one of the paradigmatic systems to study turbulence in shear flows (see \citet{grossman2016high} for a recent review). It is a geometrically simple system where the flow is driven by two independently rotating co-axial cylinders. The driving in a TC flow can be quantified using $Re_i=r_i\omega_i(r_o-r_i)/\nu$ and $Re_o=r_o\omega_o(r_o-r_i)/\nu$ which are the inner and outer cylinder Reynolds number, respectively ($r_i$, $r_o$ and $\omega_i$, $\omega_o$ are the radii and angular velocities of the inner and outer cylinder, respectively while $\nu$ is the kinematic viscosity of the carrier fluid). When the driving in TC flow is beyond a critical value, the flow transitions from a purely azimuthal laminar flow to a turbulent flow, during which a wide range of coherent flow patterns develop in the gap width. The various regimes that can be observed in a single phase turbulent TC flow have been summarised by \citet{andereck1986flow} for the low Reynolds number regime and  recently extended for the highly turbulent case by \citet{ostilla2014exploring}. In the last decade, two-phase TC flow has also been of interest due to the massive reduction in drag achieved with the addition of a very small concentration  of dispersed phase ($\sim O(1)$\% of bubbles in water). Moreover, through several experimental and numerical studies in turbulent channel and TC flow, it has been shown that the deformability of the bubbles is of paramount importance to achieve strong drag reduction \citep{lu2008effect,dabiri2013transition,van2013importance}. Understanding the dynamics of deformation and orientation of an anisotropic dispersed phase (for e.g. ellipsoidal bubbles or drops) and its dependence on the underlying local flow topology can thus be useful for optimising several industrial and engineering applications.

The degree of deformation of the dispersed phase depends on many factors such as the size of the drops/bubbles, intensity of local inertial and viscous forces which tend to elongate or deform the drop from its initial spherical shape, surface tension forces which are responsible for restoring the drop back to its original spherical shape etc. \citep{rallison1984deformation,stone1994dynamics}. In his pioneering work, \citet{taylor1932viscosity,taylor1934formation} was one of the first to study theoretically the deformation of a viscous drop dispersed into a carrier fluid where he showed that the shape of a deformed drop in presence of a velocity gradient depends on the viscosity ratio of the droplet and the carrier phase $\hat \mu =\mu_d/\mu_c$ ($\mu_d$ and $\mu_c$ are the dynamic viscosities of the droplet and the carrier liquid respectively) and the capillary number $Ca=\mu_cRG/\sigma$ ($R$, $G$, and $\sigma$ are the drop radius, local shear rate, and surface tension, respectively) which is the ratio of viscous to surface tension forces. In flows where the range of velocity gradients experienced by the dispersed phase is limited and deviation of the drop shape from sphericity is small, analytical solutions to compute the shape of the drop exist \citep{chaffey1967second,cox1969deformation,frankel1970constitutive}. However, when the flow field becomes complex and deviation from sphericity is beyond a critical value, the constitutive equations become intractable.

In turbulent flows, when the dispersed phase is larger than the Kolmogorov length scale, inertial forces play a primary role in deforming the drops which may eventually lead to breakup.  \citet{kolmogorov1949disintegration} and \citet{hinze1955fundamentals} proposed one of the earliest models to study the process of deformation and breakup of such droplets dispersed into a turbulent carrier flow. The breakup of these droplets and its distribution in homogenous isotropic turbulence was further investigated by \citet{perlekar2012droplet} using a multicomponent lattice Boltzmann method. Through Lagrangian tracking of individual droplets, these simulations showed that the local Weber number at the droplet position is strongly correlated with the degree of deformation and thus eventual breakup. A series of studies used the front-tracking approach to investigate the influence of inertial size spherical and deformable bubbles on the wall drag in a turbulent channel flow \citep{lu2005effect,lu2008effect,dabiri2013transition,tryggvason2013multiscale}. While the process of breakup and coalescence of the droplets cannot be modelled yet using this approach, it provides useful insight into the effect of deformability on the dynamics of bubbles much larger than the Kolmogorov scale ($d_b\sim100\eta_k$) in wall bounded turbulence.

When the drops are smaller than Kolmogorov scale (sub-Kolmogorov), local viscous forces acting on the droplet are more dominant in the deformation process. In this situation \citet{cristini2003breakup} used the boundary integral formulation to study the deformation and breakup process of drops dispersed into an isotropic turbulent flow with $Re_\lambda \sim 50$ ($\lambda$ is the Taylor microscale). The process of drop deformation, elongation, neck formation and eventual breakup into satellite droplets was completely resolved and captured in these simulations. However, such fully resolved simulations come at an expense of the intensity of turbulence that can be achieved in the carrier flow field and also the number of droplets that can be simulated simultaneously.

Due to the huge computational costs involved, simulating millions of fully resolved droplets or bubbles which can deform, breakup and coalesce in highly turbulent flow fields is still beyond reach  \citep{tryggvason2013multiscale}. However, useful insights in such flows can still be attained with the use of sub-grid models that can capture the motion and deformation of the dispersed phase. Instead of fully resolving the interaction between the dispersed phase and carrier phase, semi-empirical or phenomenological models can be used to track, deform, breakup, or coalesce a large number of droplets or bubbles in highly turbulent environments. Such an approach has been adopted by \citet{biferale2014deformation}, where they study the deformation and orientation statistics of approximately $10^4$ sub-Kolmogorov neutrally buoyant drops in homogenous isotropic turbulence. The drops were assumed to be tri-axial ellipsoids and the shape and orientation of these passively advected drops was calculated using a phenomenological model proposed by \citet{maffettone1998equation}. More recently, \citet{babler2015numerical} studied the breakup of approximately $10^5$ colloidal aggregates in canonical setups like turbulent channel flow, developing boundary layer and homogenous isotropic turbulence. A similar work by \citet{marchioli2015turbulent} investigated the statistics of ductile rupture of colloidal aggregates tracked as massless particles in a turbulent channel flow. A simple criteria for aggregate breakup or rupture was adopted by both \citet{babler2015numerical} and \citet{marchioli2015turbulent} where the occurrence of a colloid breakup is directly related to the local hydrodynamic stress being higher than a critical threshold stress. The coupling of direct numerical simulations (DNS) of the carrier phase along with semi-empirical or phenomenological models for the deformation and breakup process makes it possible to simulate millions of droplets or colloidal aggregates in highly turbulent environments.

In this study we follow the same approach to simultaneously track approximately $10^5$ neutrally buoyant sub-Kolmogorov deformable drops in a turbulent Taylor-Couette flow. The drops are treated as passive inertialess particles while the deformation and orientation of these drops is computed based on the phenomenological model proposed by \citet{maffettone1998equation} (hereafter referred to as \lq MM\rq\ model). This approach is similar to the one adopted by \citet{biferale2014deformation} for drops dispersed in homogenous isotropic turbulence and also by \citet{de2012computational} to predict hemolysis by tracking several deformable red blood cells.

As mentioned previously, the driving of the TC system can induce several transitions in the flow from a purely laminar state to a fully turbulent system. In this study the outer cylinder is kept stationary ($Re_o=0$) and only the inner cylinder is rotated until the system transitions into turbulence. We consider two different inner cylinder Reynolds numbers; one where there is a strong footprint of coherent structures i.e. the Taylor rolls and a higher $Re_i$ where the turbulence intensity is higher and the rolls lose its coherence. For each of these drivings, we vary the capillary number ($Ca$) and viscosity ratio ($\hat \mu$) of the droplets with the carrier fluid. Under these conditions, the questions we want to address in this paper are: Does the the degree of deformation of the droplets depend on their spatial position in the gap width? How do these drops deform in different regions of the flow like the Taylor rolls, plume ejection and plume impact regions, respectively ? \citep{ostilla2014boundary}. Are the drops more prolate or more oblate like and does the capillary number and viscosity ratio have an influence on the shape? What is the preferential direction of orientation of these drops in the boundary layers and bulk region? These are some questions we attempt to answer in this paper.

In the following section, we elaborate on the numerical schemes and methods employed to solve the equations of the carrier phase and the dispersed phase and also give a brief review on the MM model which is used to compute the deformation and orientation characteristics of the drops. In section 3 we discuss the results of our simulations where we analyse the averaged profiles of extent of deformation of the drops, probability distribution functions (p.d.f's) of the extent of anisotropy in the dispersed phase and their orientational preferences for different $Ca$ and $\hat \mu$. Finally, in section 4 we summarise the paper and give an outlook on future line of simulations.

\section{Governing Equations and Numerical Details}
\label{sec:num}
For the carrier flow, DNS was used to solve the Navier-Stokes equations in cylindrical coordinates using a second-order accurate finite-difference scheme with fractional time-stepping \citep{verzicco1996finite,van2015pencil}. This code has already been validated and tested extensively for a wide range of parameters to study the various spatio-temporal dynamics of high Reynolds number single phase TC turbulence for both rotating and stationary outer cylinder \citep{ostilla2013optimal,ostilla2014optimal,ostilla2014boundary,ostilla2014exploring}. The code for DNS coupled with two-way coupled Lagrangian tracking has also been validated and used previously for studying the effect of buoyant spherical bubbles on the net drag reduction in a turbulent Taylor-Couette flow \citep{spandan2016drag}.  For the purpose of this study the radius ratio and aspect ratio of the TC setup is fixed to $\eta=r_i/r_o=0.833$ and $\Gamma=L/d=4$, respectively. Periodic boundary conditions are employed in the azimuthal and axial directions and a non-uniform grid spacing (clipped Chebychev clustering) is employed only in the wall normal direction.
Since we employ periodic boundary conditions in the axial direction, we have ensured through additional test simulations that the mean profiles and other relevant statistics discussed in section 3 are not influenced by increasing the aspect ratio \citep{ostilla2015computational,spandan2016drag}.

The dispersed phase is composed of neutrally buoyant sub-Kolmogorov drops which are treated as passive tracers \citep{biferale2014deformation}. The dispersed phase is advected based on the local velocity of the carrier phase at the exact location of each drop. Since the dispersed phase is treated in a Lagrangian manner, the position of each droplet does not necessarily coincide with the location of grid nodes on the carrier phase mesh. This limitation is overcome with the use of a tri-linear interpolation scheme to compute the velocity of the carrier phase at the exact droplet position.

\begin{equation}
\frac{d \textbf x_p}{dt}=\textbf v.
\label{eqn:ppos}
\end{equation}

The droplet position is updated after every time step according to equation \ref{eqn:ppos} using a second order Runge-Kutta scheme ($\textbf v$ is the interpolated carrier phase velocity at the droplet position and $\textbf x_p$ is the droplet position vector). In order to couple the tracking of the droplets with deformation, the droplets are assumed to be tri-axial ellipsoids. Under this assumption, the drop shape and orientation can be easily described in the form of a second-order positive-definite symmetric tensor $\pmb S$ (shape tensor). This tensor satisfies the condition $\pmb S^{-1}:\textbf {xx}=1$, where $\textbf x$ is the position vector of any point on the ellipsoid surface relative to its origin. For any known tensor $\pmb S$, the eigenvalues of the shape tensor give the square of semi-axes of the ellipsoid while the eigenvectors give the orientation of the semi-axes of the ellipsoid. In case of ellipsoidal drops, the MM model proposes a phenomenological evolution equation of the shape tensor $\pmb S$ based on the competing actions of drag which tends to elongate the droplet and surface tension which tends to recover the spherical shape corresponding to minimum surface energy. In dimensional form this equation reads:

\begin{equation}
\frac{d\pmb S}{dt} - (\pmb \Omega\cdot \pmb S-\pmb S\cdot \pmb \Omega)=-\frac{f_1}{\tau}(\pmb S-g(\pmb S)\pmb I)+f_2(\pmb E\cdot \pmb S+\pmb S \cdot \pmb E).
\label{eqn:deqn_dim}
\end{equation}

We now non-dimensionalise as follows: $\pmb S^* = \pmb S/R^2$ where $R$ is the radius of the undistorted spherical drop. $\pmb E^*=\pmb E/G$ and $\pmb \Omega^*=\pmb \Omega/G$ are the non-dimensional strain rate and vorticity rate tensors; $\pmb E = 0.5[\nabla \pmb u + \nabla \pmb u^T ]$, $\pmb \Omega = 0.5[\nabla \pmb u - \nabla \pmb u^T]$, and $G=1/\tau_\eta$ is the inverse Kolmogorov turbulent time scale. $Ca$ is the capillary number which is the ratio of the viscous forces to the interfacial forces or can also be defined as the ratio of the interfacial relaxation time ($\tau=\mu_cR/\sigma$) to the characteristic flow time ($\tau_\eta$) i.e. $Ca=\tau/\tau_\eta$ ; $\mu_c$ is viscosity of the carrier phase and $\sigma$ the interfacial tension.

In non-dimensional form the evolution equation for the shape tensor ($\pmb S^*$) can be written as follows:

\begin{equation}
\frac{d\pmb S^*}{dt} - Ca(\pmb \Omega^*\cdot \pmb S^*-\pmb S^*\cdot \pmb \Omega^*)=-f_1(\pmb S^*-g(\pmb S^*)\pmb I)+f_2Ca(\pmb E^*\cdot \pmb S^*+\pmb S^* \cdot \pmb E^*).
\label{eqn:deqn}
\end{equation}

Since we consider both fluids to be incompressible and no occurrence of droplet breakup or coalescence, the volume of each droplet must be conserved. This implies that the third invariant or the determinant of the tensor $\pmb S$ must be constant and the function $g(\pmb S^*)=3III_s/II_s$ embedded into the evolution equation ensures volume conservation ($II_s$ and $III_s$ are the second and third invariant of the shape tensor, respectively). The parameters $f_1$ and $f_2$ depend only on the viscosity ratio ($\hat \mu$) and are chosen to make the MM model recover the asymptotic limits for small $Ca$, viscosity ratio $1/\hat \mu \rightarrow 1$ and $\hat \mu =1$ and is given by \citet{maffettone1998equation} as follows:

\begin{equation}
f_1=\frac{40(\hat \mu+1)}{(2\hat \mu+3)(19\hat \mu+16)} \qquad f_2=\frac{5}{2\hat \mu+3},
\label{eqn:pfact}
\end{equation}

The expression for $f_2$ under predicts the net deformation when the $Ca$ and $\hat \mu$ are large and this can be corrected by including an additional dependence of $f_2$ on $Ca$ \citep{maffettone1998equation,biferale2014deformation}. However, for the sake of brevity we use equation (\ref{eqn:pfact}) in this work. The constitutive equation for the evolution of the shape tensor (equation \ref{eqn:deqn}) has terms which would require the evaluation of the local strain rate and rotation rate tensor at the location of the droplet. An interpolation scheme similar to the one used for computing the velocity in equation (\ref{eqn:ppos}) is implemented for this purpose. Analogous to the carrier phase, azimuthal and axial periodicity is adopted for the dispersed phase, i.e. when the droplets exit an azimuthal or axial boundary they are re-entered at the opposite boundary with the same velocity, shape and orientation. The entire simulation for a single case consists of two parts. First the carrier phase is simulated without any dispersed phase until it reaches a statistically stationary state. At this point the simulation is stopped, and $10^5$ sub-Kolmogorov spherical drops are introduced in the gap width at random positions and the simulation is allowed to develop. The trajectories and the information on the shape tensor of every droplet is recorded at a frequency of approximately 20 snapshots every $\tau_\eta$ for almost 100 full inner cylinder rotations. Two different Reynolds numbers for the inner cylinder ($Re_i$=2500, 5000) are studied and in each system four different capillary numbers $Ca$ = 0.05, 0.1, 0.2 and 0.3 and two different viscosity ratios $\hat \mu$=1 and 100 are considered.

\begin{figure}
\centerline{\includegraphics[scale=0.375]{./figures/fig1.pdf}}
\caption{Azimuthally, axially and time averaged radial profiles of deformation parameters ($D$) for four different $Ca$; (a) $Re_i$=2500 (b) $Re_i$=5000. The viscosity ratio $\mu$=1. The direction of the arrow indicates increasing $Ca$. The grey shaded areas near the left and right extremes of the $\tilde r$ axis represent the inner and outer cylinder boundary layer thickness, respectively.}
\label{fig:radprofd}
\end{figure}

\section{Results}
\label{sec:res}

In this section we analyse the statistics of the shape and orientation of the droplets for different Reynolds $Re_i$ and capillary numbers $Ca$ while keeping the viscosity ratio fixed at $\hat \mu=1$. Since we consider the droplets to be triaxial ellipsoidal, we denote the lengths of the three semi-axes by $d_1$, $d_2$ and $d_3$ ($d_1<d_2<d_3$); i.e. $d_1$ and $d_3$ are the lengths of the minor and major semi-axes, respectively.

\subsection{Droplet shape distribution}

\begin{comment}
We will first analyse how the semi-axes of the droplets vary with time and their corresponding position in the gap-width of the TC cell. In figure \ref{fig:timeser}a we plot a time series of the three semi-axes ($d_1$, $d_2$, $d_3$) of a randomly chosen droplet for a inner cylinder Reynolds number $Re_i=2500$, $Ca=0.05$ and $\hat \mu =1$. From the evolution of the semi-axes it can be clearly observed that the droplet goes through several phases where there is almost no difference in the semi-axes ($d_1\sim d_2\sim d_3$) i.e. droplet is almost spherical (for example $50<t/\tau_\eta<100$), to phases where there is large deviation from sphericity ($150<t/\tau_\eta<200$). The corresponding normalised radial position $\tilde r= (r-r_i)/(r_o-r_i)$ of the droplet is plotted in figure \ref{fig:timeser}b and it can be clearly noticed that large deviation from sphericity occurs when the droplet is close to the inner cylinder i.e. $\tilde r \sim 0$. Although this plot contains the time series of only a single droplet similar characteristics are observed also for other  droplets as we will see later in the mean deformation profiles. Large deformation of an initially spherical droplet can be attributed to the large velocity gradients in the inner boundary layer resulting in the shear forces overcoming the surface tension forces.  Deviation from sphericity can also be observed when the droplet reaches positions close to the outer cylinder ($\tilde r \sim 1$, approximately $225<t/\tau_\eta<250$). However, the degree of deformation here is relatively smaller as compared to near the inner cylinder and this is due to the relatively thicker boundary layer and thus the weaker shear near the outer cylinder wall \citep{ostilla2013optimal}.
\end{comment}
\begin{figure}
\centerline{\includegraphics[scale=0.80]{./figures/fig2.pdf}}
\caption{Zoomed in plot of figure \ref{fig:radprofd}a. The schematic on the right shows interaction of a highly deformed drop (top) and a relatively less deformed drop (bottom) with the wall. The centre of mass of a less deformed drop can approach more closer to the wall as compared to a highly deformed drop.}
\label{fig:radprofd_in}
\end{figure}

In order to quantify the degree of deformation in the droplet shape, we make use of a non-dimensional deformation parameter defined as $D=(d_3-d_1)/(d_3+d_1)$ \citep{taylor1932viscosity,taylor1934formation,maffettone1998equation,guido1998three,guido2000drop,biferale2014deformation}. When $D\sim0$, the droplet is close to spherical, while $D\gg0$ implies the droplet is highly deformed. In order to properly quantify the correlation between the spatial position of the droplets and the degree of deformation, we plot the radial profiles of azimuthally, axially and time averaged deformation parameter for four different $Ca$ in figure \ref{fig:radprofd}. The radial position of the drops are normalised using $\tilde r=(r-r_i)/(r_o-r_i)$; the drop is close to the inner cylinder when $\tilde r \sim 0$ and close to the outer cylinder when $\tilde r \sim 1$. Along with the averaged profiles we show the inner boundary layer (IBL) and outer boundary layer (OBL) thickness using grey shaded areas which has been computed following the approach of \citet{ostilla2013optimal,ostilla2014boundary} which we describe here briefly. To compute the thickness of the IBL and OBL, a straight line is first fit through three computational nodes nearest to both walls while in the bulk a line is fit through the point of inflection and the two nearest computational nodes. The intersection of the line in the bulk along with the lines fitted near the inner and outer cylinder gives the inner boundary layer (IBL) and outer boundary layer (OBL) thickness, respectively \citep{ostilla2013optimal,spandan2016drag}.

We can clearly observe in figure \ref{fig:radprofd} that capillary number $Ca$ has a strong influence on the mean deformation parameter $D$. As expected, owing to relatively weaker surface tension forces $D$ increases with increasing $Ca$. Additionally, as noted from figure \ref{fig:radprofd} a clear indication of the spatial dependence of the deformation parameter $D$ is visible. $D$ is higher near the boundary layers (marked by grey shaded areas) for both Reynolds numbers as compared to the bulk where it is almost three times lower. Additionally, we also observe that when $Ca=0.2$ and $Ca=0.3$, the peak of the deformation parameter $D$ lies away from the inner cylinder. To observe this deviation more clearly, in figure \ref{fig:radprofd_in} we show a zoomed-in plot of figure \ref{fig:radprofd}a and it can be clearly seen that for $Ca=0.2$ and $Ca=0.3$ there is a slight increase in $D$ away from the wall and the occurrence of this peak moves away from the wall with increasing $Ca$. This is just a consequence of the modelling of interaction of the droplet with the wall. Since we assume elastic collision between a droplet and the wall, the centre of mass of a highly deformed droplet lies farther away from the wall as compared to a less deformed droplet as shown in the schematic of figure \ref{fig:radprofd_in}). Indeed, this also depends on the relative orientation of the droplets with the wall and we will analyse this in detail in later sections.

\begin{figure}
\centerline{\includegraphics[scale=0.4]{./figures/fig3.pdf}}
\caption{Azimuthally, radially and time averaged axial profiles of the deformation parameter ($D$) for four different $Ca$; (a) $Re_i$=2500 (b) $Re_i$=5000. The viscosity ratio $\mu$=1. The direction of the arrow indicates increasing $Ca$ (refer to figure \ref{fig:radprofd} for description of the markers). Instantaneous snapshots of the azimuthal velocity of the corresponding $Re_i$ are shown on the top of each panel to better visualise the plume ejections and the Taylor rolls.}
\label{fig:axprofd}
\end{figure}

Similar to figure \ref{fig:radprofd} we plot axial profiles of the azimuthally, radially and time averaged deformation parameter $D$ as a function of the normalised axial position $\tilde z =z/d$ for $Re_i$ = 2500 and 5000 and for different $Ca$ in figure \ref{fig:axprofd}. When $Re_i$ = 2500 (c.f. figure \ref{fig:axprofd}a), we observe that regardless of the capillary number, $D$ is higher near the plume ejection regions of the inner cylinder i.e $\tilde z \sim$ 1 and 3 (also refer to the top panel in figure \ref{fig:axprofd}a which shows an instantaneous snapshot of the carrier phase azimuthal velocity). This is again a result of relatively high strain rates stretching the ellipsoidal drops in the plume ejection region near the inner cylinder; an effect likely to be produced by the Taylor rolls which make locally thinner or thicker the boundary layer produced by the cylinder rotation. A similar observation is made even for $Re_i$=5000 in figure \ref{fig:axprofd}b where the plume ejection regions near the inner cylinder are at approximately $\tilde {z}$ = 1.75 and 3.75. Although relatively high strain rates are observed in the plume ejection regions, the plumes themselves which extend from the inner cylinder into the bulk have a relatively lower strain rate owing to a strong azimuthal velocity component. This causes a sudden drop in $D$ at the exact axial position where the plumes extend into the bulk, an effect which is seen more clearly for $Re_i$=2500 due to the more coherent nature of the plumes. However, when the Reynolds number is increased the plumes are more erratic and turbulent and the sudden drop in $D$ is not clearly observed. The differences in plume structure in the bulk of the flow for both Reynolds number is clearly visible in the instantaneous snapshots of the azimuthal velocity in figure \ref{fig:axprofd}.

\begin{figure}
\centerline{\includegraphics[scale=0.38]{./figures/fig4.pdf}}
\caption{Probability distribution function (pdf) of the ratio of semi-axes ($d_1<d_2<d_3$) for $Re_i$=2500 and $\hat \mu=1$ (a) $Ca=0.05$ (b) $Ca=0.2$. The three panels for each $Ca$ correspond to droplets in the inner boundary layer (IBL), bulk and outer boundary layer region (OBL).}
\label{fig:semrat}
\end{figure}

Until now we have looked at the variation of the deformation parameter $D$ with the radial and axial distance in the TC domain. Although $D$ can be used to study whether the droplet is close to spherical or highly deformed, it cannot be used to distinguish between oblate (disk-like) and prolate (cigar-like) droplets. In order to make this distinction, \citet{biferale2014deformation} used the $s^*$ parameter which was introduced by \citet{lund1994improved} to quantify the probability distribution of strain rate tensor eigen-values in turbulent flows. The shapes of the droplets can also be categorised based on simple ratios of the semi-axes i.e. $d_2/d_1$ and $d_3/d_1$ (where $d_1<d_2<d_3$). When the droplet is close to spherical $d_2/d_1 \sim d_3/d_1 \sim 1$, while for deformed droplets both $d_2/d_1>1$ and $d_3/d_1>1$. When the droplets are deformed they can additionally be categorised into oblate (disk-like) ellipsoids when $d_2/d_1 \sim d_3/d_1$ and prolate (cigar-like) ellipsoids when $d_2/d_1 \ll d_3/d_1$.

In figure \ref{fig:semrat}, we plot the probability distribution functions (p.d.f's) of the ratio of semi-axes ($d_2/d_1$ and $d_3/d_1$) of droplets for two different capillary numbers $Ca=0.05$ and 0.2 while $Re_i=2500$ and $\hat \mu=1$. The three different panels for each capillary number correspond to the position of the droplet in the inner boundary layer (IBL), bulk region (BULK), and the outer boundary layer (OBL). When $Ca=0.05$, the droplets are almost spheroidal or in other words axis-symmetric (i.e. $d_2/d_1 \sim 1$). In the bulk region where the strain rates are relatively weaker as compared to the boundary layer region, the droplet is close to being spherical with minimum deformation (i.e. $d_2/d_1\sim d_3/d_1 \sim 1$). Additionally, the p.d.f's of $d_3/d_1$ in the IBL and OBL have much wider tails indicating that the droplets are more prolate in comparison to the bulk region.  \citet{biferale2014deformation} found that with increasing capillary number ellipsoidal drops in homogenous isotropic turbulence tend to be more cigar-like or prolate where the major axis ($d_3$) is relatively much larger than the other two axes ($d_1$, $d_2$). A similar behaviour can be observed in the bottom panels of figure \ref{fig:semrat} when the capillary number is increased to $Ca=0.2$. The tails of $d_3/d_1$ become much wider in the IBL and OBL regions as compared to $Ca=0.05$ which is a consequence of the weaker surface tension forces for higher capillary number drops. An additional consequence is that the droplets now tend to become less spheroidal and more tri-axial.

\subsection{Orientational behaviour of the drops}

\begin{figure}
\centerline{\includegraphics[scale=0.4]{./figures/fig5.pdf}}
\caption{Probability distribution functions of the stream-wise orientation of the major axis of droplets for $Ca=0.05$ and $Ca=0.2$ (a) $Re_i=2500$ (b) $Re_i=5000$. The three panels for each $Re_i$ correspond to droplets in the inner boundary layer (IBL), bulk and outer boundary layer region (OBL).}
\label{fig:ang_pdf}
\end{figure}

In addition to the shape and size of the ellipsoidal droplets it would also be interesting to understand their orientational preference. A number of studies \citep{mortensen2008orientation,marchioli2010orientation,njobuenwu2015dynamics} investigating the orientation behaviour of axis-symmetric solid ellipsoidal particles in wall bounded turbulent flows found that the major axis of the particles tend to align with the stream-wise direction near the wall. The shape and size of solid ellipsoidal particles does not depend on their spatial position and underlying flow conditions. However, for deforming droplets the orientation dynamics can be strongly coupled to the shape evolution which would in turn depend on the local flow conditions. \citet{biferale2014deformation} found that neutrally buoyant ellipsoidal droplets dispersed into a homogenous isotropic turbulent flow aligned with the most extensional strain-rate eigen direction and the vorticity. With an increase in the capillary number $Ca$ the alignment is lost due to an increase in the interfacial relaxation time.

\begin{figure}
\centerline{\includegraphics[scale=0.4]{./figures/fig7.pdf}}
\caption{Probability distribution functions of the cosine of the angle between the eigen-vector of the major axis ($\bf e^3$) of the ellipsoid and three strain-rate eigen-directions ($\bf e_s^1, e_s^2, e_s^3$) $Re_i=2500$ $\hat \mu=1$ for (a) $Ca=0.05$ and (b) $Ca=0.2$.}
\label{fig:strang_pdf}
\end{figure}

\begin{figure}
\centerline{\includegraphics[scale=0.4]{./figures/fig8.pdf}}
\caption{Probability distribution functions of the cosine of the angle between the eigen-vector of the semi-major axis ($\bf e^3$) of the ellipsoid and the vorticity ($\pmb \Omega$) $\hat \mu=1$ for (a) $Re_i=2500$ and (b) $Re_i=5000$.}
\label{fig:vor_pdf}
\end{figure}

Here we describe the relative orientation of the major axis of the ellipsoidal droplets with respect to the coordinate system in the form of direction cosines of the angle between them i.e. $l=\mbox{cos} \theta_{\hat\theta}$, $m=\mbox{cos} \theta_{\hat r}$, $n=\mbox{cos} \theta_{\hat z}$, where $l$, $m$, $n$ are the direction cosine of the orientation with $\hat \theta$  (stream-wise), $\hat r$ (wall-normal), and $\hat z$ (span-wise) directions, respectively. In order to study the statistics of droplet orientation in detail, we plot the p.d.f's of the cosine of the angle between the droplet major axis and the stream-wise direction in figure \ref{fig:ang_pdf}. We observe that the droplets tend to be strongly aligned with the stream-wise direction (i.e. $l \sim 1.0$) in the IBL and OBL. As can be seen from the left-most panels of figure \ref{fig:ang_pdf}, the alignment is more pronounced in the case of $Re_i=2500$ as compared to $Re_i=5000$. This may be possible due to the more erratic and time dependent nature of the boundary layer region and plume ejections from the inner cylinder in the case of $Re_i=5000$ as was also seen in the contour plots of figure \ref{fig:axprofd}b. A similar behaviour is also seen in the case of solid ellipsoidal particles in the vicinity of a wall in a turbulent channel flow \citep{mortensen2008orientation,marchioli2010orientation,njobuenwu2015dynamics}.
In the bulk, the orientation of the droplets is highly isotropic showing no specific preference in alignment with the stream-wise direction which is a consequence of the efficient mixing provided by the Taylor rolls. The capillary number $Ca$ seems to have minimal influence on the orientational behaviour of drops suggesting that it is only dominant in the deformation process and not in the effective orientation of the drops.

\begin{comment}
\begin{figure}
\centerline{\includegraphics[scale=0.425]{./figures/fig6.pdf}}
\caption{Schematics of two different arrangements of an ellipsoidal drop in the vicinity of a wall (a) towards the wall where $l\cdot m<0$ (b) away from the wall where $l\cdot m>0$. Pdf's of the relative orientation with the wall are shown in (c) $Re_i=2500$ and (d) $Re_i=5000$ for three different capillary numbers and $\hat \mu=1$.}
\label{fig:ang_chpdf}
\end{figure}
Although the p.d.f's shown in figure \ref{fig:ang_pdf} give us a good understanding of the alignment preference of the ellipsoids with the stream-wise direction, it is not useful to understand their relative orientation with the wall. To depict this more clearly, we show schematics of two ellipsoids close to a wall in figure \ref{fig:ang_chpdf} a,b. It is not possible to make the distinction between these two arrangements of the ellipsoids solely based on the pdf of $l$ since in both cases $l_1>0$ and $l_2<0$ ($l_1$, $l_2$ are the direction cosines of the angle of the ends of the major axis with the stream-wise direction). In figure \ref{fig:ang_chpdf} c,d we plot the pdf's of the product $l\cdot m$, i.e. ($l_1\cdot m_1$ or $l_2\cdot m_2$) for three different capillary numbers $Ca=0.05,0.1,0.2$ and two different $Re_i=2500,5000$. If the ellipsoid is oriented towards the wall as shown in figure \ref{fig:ang_chpdf}a, the product $l\cdot m<0$ while in the case of figure \ref{fig:ang_chpdf}b the product $l\cdot m>0$.
[Do not show lm product but cos(l1)*sin(l1)]
As can be seen from the pdf's, the ellipsoids prefer to orient themselves towards the wall in the IBL i.e. $lm<0$  regardless of the Reynolds number $Re_i$ or the capillary number $Ca$. The alignment preference is similar to what is seen when a droplet is immersed in a simple two-dimensional shear flow \citep{maffettone1998equation,guido1998three}. The distribution is more uniform in the OBL where the ellipsoids show almost no preference in arrangement. This can be briefly explained as follows. We can see from equation \ref{eqn:deqn} that the rotation of the drop is strongly linked to the vorticity term which is weaker in the OBL as compared to IBL. This causes the arrangement of the ellipsoids to be relatively more uniform in the OBL. We will look into this in more detail in section 3.3 where we vary the viscosity ratio $\hat \mu$.
\end{comment}

Now we look at the orientation statistics of the major axis with respect to the local strain-rate eigen directions and vorticity. In figure \ref{fig:strang_pdf} and figure \ref{fig:vor_pdf} we plot the pdf's of the cosine of the angle between the eigen-vector of the major axis ($\bf e^3$), the three strain-rate eigen directions ($\bf e_s^1, e_s^2, e_s^3$, where $\bf e_s^1$ and $\bf e_s^3$ are the compressive and extensional strain-rates, respectively) and vorticity ($\pmb \omega$), respectively. In homogenous isotropic turbulence, \citet{biferale2014deformation} found that the major axis of neutrally buoyant ellipsoidal droplets align with both the most extensional strain-rate eigen direction and vorticity. In figures \ref{fig:strang_pdf} and \ref{fig:vor_pdf} we find that the preference of alignment with the strain rate eigen directions and vorticity depends strongly on its relative spatial location.

In figure \ref{fig:strang_pdf}, we consider two different configurations with capillary numbers $Ca=0.05$ and $Ca=0.2$ for a fixed Reynolds number $Re_i=2500$. In the boundary layer regions the ellipsoid major axis has a strong preference to align with the extensional strain-rate eigen direction (here the extensional strain-rate direction in the boundary layers is the azimuthal direction). In the bulk, the preference is relatively more uniform while some traces of droplets aligning with $e_s^3$ can still be found, an indication that there seems to be a competition between the extensional strain-rates trying to align itself with the droplet major axis and the homogenising nature of the Taylor rolls. This effect is clearly seen when $Ca=0.2$ given the prolate nature of the droplets (c.f. figure \ref{fig:semrat}). While the ellipsoidal droplets tend to align with the most extensional strain-rate direction in the inner boundary layer (IBL) region (left panels of figure \ref{fig:strang_pdf}) they prefer to be aligned orthogonally with the vorticity (left panel in figure \ref{fig:vor_pdf}). This is different from the behaviour of solid axis-symmetric ellipsoidal particles in an isotropic turbulent flow where rod-like particles tend to align with the vorticity \citep{shin2005rotational,parsa2012rotation,chevillard2013orientation}. The difference in behaviour is a consequence of the inhomogeneity and anisotropy of the carrier flow along with the ellipsoidal droplets continuously deforming based to the underlying flow conditions unlike solid ellipsoidal particles which are fixed in shape. With increase in Reynolds number $Re_i$, the preference of alignment with the vorticity stays qualitatively similar. Additionally, from figures \ref{fig:ang_pdf}, \ref{fig:strang_pdf} and \ref{fig:vor_pdf} we find that the capillary number $Ca$ seems to play an important role only in deforming the drops but has negligible influence on the relative orientation of the major axis of the ellipsoid while the spatial position of the droplet is crucial in the orientational preference owing to the strong inhomogeneity and anisotropy in the field.

Until now we have looked at the effect of capillary number $Ca$ and Reynolds number $Re_i$ on the droplet deformation and orientation statistics and in the next subsection we will study the effect of viscosity ratio $\hat \mu$.

\subsection{Effect of viscosity ratio}

\begin{figure}
\centerline{\includegraphics[scale=0.41]{./figures/fig9.pdf}}
\caption{Azimuthally, axially and time averaged radial profiles of deformation parameters ($D$) for four different $Ca$; (a) $Re_i$=2500 (b) $Re_i$=5000. The viscosity ratio is $\hat \mu$=100. The direction of the arrow indicates increasing $Ca$. The grey shaded areas near the left and right extremes of the x-axis represent the inner and outer cylinder boundary layer thickness, respectively.}
\label{fig:radprofd_m100}
\end{figure}

In figure \ref{fig:radprofd_m100} we plot the averaged radial profiles of the deformation parameter $D$ for different $Ca$ in a high viscosity ratio system $\hat \mu=100$. On comparison with $\hat \mu=1$ (c.f. figure \ref{fig:radprofd}) the degree of deformation is at least 5 times smaller for all capillary numbers. This behaviour can be intuitively expected as for the same strain rates the stretching is lower for more viscous drops. Additionally, due to the relatively smaller deformations the peaks in the deformation parameter $D$ lie close to the wall for all $Ca$. While it is clear from figure \ref{fig:radprofd_m100} that there is a reduction in the overall deformation of the droplets, it would be interesting to look at the shape of the droplets as we did in figure \ref{fig:semrat}; in the case of $\hat \mu=1$ the droplets were more prolate (cigar-like). In figure \ref{fig:semrat_m100} we plot the pdf's of the ratio of semi-axes in the IBL, bulk region and OBL (similar to figure \ref{fig:semrat}). It can be seen that the semi-axes ratios $d_2/d_1 \sim d_3/d_1>1$ which is a clear indication that the droplets tend to be more oblate (disk-like) when $\hat \mu=100$. A similar behaviour is observed when the capillary number of the drops is increased. While we found previously that the capillary number plays an important role in the degree of deformation of the droplets, here we find that the droplet shape also depends strongly on the the viscosity ratio $\hat \mu$.

\begin{figure}
\centerline{\includegraphics[scale=0.425]{./figures/fig10.pdf}}
\caption{Probability distribution function (pdf) of the ratio of semi-axes ($d_1<d_2<d_3$) for $Re_i$=2500 and $\hat \mu=100$ (a) $Ca=0.05$ (b) $Ca=0.2$.}
\label{fig:semrat_m100}
\end{figure}

\begin{figure}
\centerline{\includegraphics[scale=0.415]{./figures/fig11.pdf}}
\caption{Probability distribution functions of the stream-wise orientation of the major axis of droplets for $Ca=0.05$ and $Ca=0.2$ and $\hat \mu=100$ (a) $Re_i=2500$ (b) $Re_i=5000$.}
\label{fig:ang_pdf_m100}
\end{figure}

\begin{figure}
\centerline{\includegraphics[scale=0.425]{./figures/fig12.pdf}}
\caption{Probability distribution functions of the cosine of the angle between the eigen-vector of the semi-major axis ($\bf e^3$) of the ellipsoid and three strain-rate eigen-directions ($\bf e_s^1, e_s^2, e_s^3$) $Re_i=2500$ $\hat \mu=100$ for (a) $Ca=0.05$ and (b) $Ca=0.2$.}
\label{fig:strang_pdf_m100}
\end{figure}
\begin{comment}
\begin{figure}
\centerline{\includegraphics[scale=0.415]{./figures/fig13.pdf}}
\caption{Probability distribution functions of the cosine of the angle between the eigen-vector of the semi-major axis ($\bf e^3$) of the ellipsoid and the vorticity vector ($\pmb \omega$) for $\hat \mu=100$ for (a) $Re_i=2500$ and (b) $Re_i=5000$.}
\label{fig:vor_pdf_m100}
\end{figure}
\end{comment}

In order to understand these dependencies we need to go back to the equation governing the droplet shape (i.e. equation \ref{eqn:deqn}). By changing the viscosity ratio we influence the values of the parameters $f_1$ and $f_2$ which are calculated according to equation (\ref{eqn:pfact}). $f_1$ and $f_2$ are monotonically decreasing functions of $\hat \mu$ and while the ratio $f_1/f_2$ is almost constant (see also figure 11 of \citet{biferale2014deformation}), $f_1$ and $f_2$ decrease by up to a factor of almost 50 by increasing the viscosity ratio from $\hat \mu=1$ to $\hat \mu=100$. This has a strong influence on the effective strengths of droplet stretching, relaxation, and rotation of the ellipsoidal droplets. More importantly, in comparison to low-viscosity ratio systems the influence of rotation becomes more dominant when the viscosity ratio is high \citep{biferale2014deformation}. Additionally, reducing $f_1$ results in an increase in the effective interfacial relaxation time (i.e. $\tau/f_1$) or in other words the surface tension force acting on the ellipsoidal droplet has lesser time to adjust to the local flow conditions resulting in some highly stretched drops. The increased influence of rotation can also result in the loss of a preferential stretching axis for the ellipsoid thus resulting in more oblate or disk-like droplets.

To understand the influence of rotation on the relative orientation we plot p.d.f's of the direction cosine of the major axis with the stream-wise direction in figure \ref{fig:ang_pdf_m100} for two different Reynolds numbers and $\hat \mu=100$. It can be immediately observed that similar to $\hat \mu=1$ the orientation is highly isotropic in the bulk region even for $\hat \mu=100$. In the IBL and OBL, while there is a tendency for the major axis to align with the stream-wise direction which is similar to what we observed for $\hat \mu=1$, the distribution of the orientation for $\hat \mu=100$ is more uniform than $\hat \mu=1$ which can be explained from earlier discussions about the increased influence of rotation. A similar behaviour is also observed in the p.d.f's of orientation of the major-axis with the eigen directions of the strain-rate tensor which are shown in figure \ref{fig:strang_pdf_m100}. In the IBL and OBL the droplets tend to align with the most extensional strain-rate eigen direction which is similar to $\hat \mu=1$ while the distribution is relatively more uniform. This is in contrast to the behaviour of oblate disk-like solid ellipsoids in an isotropic turbulent flow \citep{chevillard2013orientation} the droplets do not tend to align orthogonally to the most contracting eigen direction. These effects are connected to the anisotropy and continuously deforming nature of the drops as discussed previously.

From figures \ref{fig:strang_pdf}, \ref{fig:vor_pdf} and \ref{fig:strang_pdf_m100} it is clear that the orientational behaviour of continuously deforming ellipsoidal droplets is completely different from that of solid axis-symmetric ellipsoids. For both viscosity ratios, the capillary number has negligible influence on the rotational behaviour of the droplets, suggesting that the droplets adjust to the underlying flow conditions regardless of the degree of deformation.

\section{Summary and Outlook}
\label{sec:summ}

In this work we study the influence of capillary number $Ca$ and viscosity ratio $\hat \mu$ on the deformation and orientation statistics of neutrally buoyant sub-Kolmogorov drops dispersed into a turbulent Taylor-Couette (TC) flow. The drops are considered to be triaxial ellipsoids which allows us to mathematically represent the surface of the drop using a symmetric second-order positive definite tensor. By coupling the phenomenological model proposed by \citet{maffettone1998equation} for ellipsoidal drops with Lagrangian tracking and DNS for the carrier flow, we solve the time dependent evolution equation of the shape tensor of approximately $10^5$ drops dispersed into a turbulent TC flow. We find that increasing the capillary number results in large deformations of the ellipsoidal droplets due to weakening surface tension forces. Additionally, the drops deform more when they are in the inner and outer boundary layer as compared to the bulk region. Due to increased influence of rotation with increase in viscosity ratio, the droplets tend to be more oblate or disk-like as compared to more prolate or cigar-like droplets for low viscosity ratio systems. Regardless of the capillary number $Ca$ and viscosity ratio $\hat \mu$, the major axis of the drop tends to align with the stream-wise direction in the inner and outer boundary layer while the orientation is highly isotropic in the bulk; a behaviour similar to solid ellipsoidal particles in a turbulent channel flow. However, the preference of orientation with the eigen directions of strain rate tensor of these drops is very different from those exhibited by axis-symmetric ellipsoids in a isotropic turbulent flow. This is a result of the continuously deforming nature of the ellipsoidal drops dispersed into a highly inhomogeneous anisotropic flow.

In our next line of simulations we focus on tracking continuously deforming ellipsoids with relevant hydrodynamic forces acting on them along with two-way coupling onto the carrier phase which will help us understand the influence of deformability of bubbles or drops on the dynamics of the carrier phase and consequently drag reduction. However it needs to be remembered that the bubbles/drops being sub-Kolmogorov is a limitation of the current approach and to explore the physics behind the experiments of \citet{van2013importance} where the bubbles are much larger than Kolmogorov scale, more advanced techniques such as immersed boundaries and front tracking are being implemented.

We would like to thank R. Ostilla-M{\'o}nico for various stimulating discussions during the development of the code. This work was supported by the Netherlands Center for Multiscale Catalytic Energy Conversion (MCEC), an NWO Gravitation programme funded by the Ministry of Education, Culture and Science of the government of the Netherlands and the FOM-CSER program. We acknowledge PRACE for awarding us access to FERMI based in Italy at CINECA under PRACE project number 2015133124 and NWO for granting us computational time on Cartesius cluster from the Dutch Supercomputing Consortium SURFsara.

\bibliographystyle{jfm}

redpajama_set_name: RedPajamaArXiv


text:
How To Build a Remarkable & Fully Functional Data Center?
Before we understand the basic layout of the components in a Data Center, we should go through Downtime and Its Consequences:
Google's 5 minute downtime in 2013 was reported to have cost over 500,000 USD and caused a 40% network traffic drop.
Amazon lost USD 1,104.00 per second when it went down due to an unusually strong thunderstorm in Northern Virginia and generators failed to operate properly.
Amadeus flight reservation system downtime caused over 400 flight delays in Australia.
"hosting.com" downtime affected 1,100 customers because of a human error during preventive maintenance of the UPS systems.
Keeping all these issues in mind, we should have a fully functional Data center. The key Components of a data Center are:
1. Location of Data Center :
The choice of location for installation of the Data Center should be made taking into account the region, consistent with the Code of the City zoning, land size, easy access for delivery of equipment, high areas without flooding, existence of infrastructure basic sanitation, water, telephone and electricity.
Criteria For Site Selection of Data Center:
Being close to points of presence to access networks of optical fiber enabling the connection of two different trunks.
Availability of energy with the possibility of obtaining two power inputs
Scalability, to allow increased building area over time.
2. Architecture of Data Center :
Data Center is usually divided into three areas of physical security in increasing order of restriction of access:
Zone I: Public areas including the Lobby, the area for visitors and administrative areas.
Zone II: Areas of Data Center Operation.
Zone III: Equipment rooms, the heart of the Data Center, where the servers are located, the "shaft" of cables, power distribution units (PDUs), batteries and air conditioning machines
3. Construction of Data Center :
The construction should provide a solid structure composing secure facilities that complement and protect equipment and information residing in the Data Center.
The Electrical segment consists of the Uninterrupted Power System (UPS) and the Emergency Power System and Power Distribution Units (PDU). The UPS has the function of providing energy for all data center equipment including safety equipment, fire detection and alarm. It consists of sets of compounds by UPS batteries, rectifiers and inverter. These UPS's are redundant and are connected in parallel to ensure a continuous supply of power even in case of power transformer failure. The banks of batteries are sized to feed the loads for a period of 15 minutes. This time is sufficient for starting a connection of diesel generators in case of power failure of the Concessionaire.
The power system consists of a group emergency diesel generator which will come into operation and connect to the electrical system of the Data Center automatically.
Generators are rated to withstand all the loads necessary for the operation of all the Equipment and Data Center during a power failure of the Concessionaire. The goal is to assist the operation 24×7, considering the conditions for preventive maintenance, adding new components and replacement operation after unplanned outages.
The power distribution units (PDU) are responsible for conditioning the signal that is used to feed multiple devices at Data Center.
4. Air conditioning in Data Center :
The segment of Air Conditioning has the function of maintaining a controlled temperature and humidity in the premises of Data Center. The segment includes the air conditioning system for cooling units and air handling system Distribution of Air Conditioning. It should be connected to emergency power generators.
The Cooling System provides heating, cooling, humidification and de-humidification of the building.
The Air Treatment System must be separated into three types of area: Room Facilities: Data Center area offices, equipment rooms Air Conditioning and Electrical. The separation is due to differences in sensible heat and latent heat of each area, the temperature conditions and humidity.
The Distribution System of Air Conditioning Equipment Room to the Data Center will use the system to supply air for the full set beneath the raised floor. This system involves inflating the raised floor at a minimum height of 60 cm., That depending on the amount of conduit, tubing, mats, etc., should have its height adjusted so as to allow air to circulate throughout the room Data Center. The goal is to operate 24×7.
An adequate cooling is essential for maintaining performance and safety of operation of data center services.
5. Fire Protection System in Data Center :
The Data Center is a facility for electronics essentials such as servers and other types of computers and telecommunications equipment. In addition to meeting standards of the local fire department, the fire protection system should seek to avoid damage to the equipment in case of fire.
One of the best solutions for the firefighting equipment rooms is a combination of the Combat System with Pre Action Sprinkler (with dry pipe) above the raised floor system and Fire Fighting for Gas FM 200 below the raised floor.
The combat system with gas will be connected to a sensitive detection system and be the first to be fired. The gas is spread throughout the area, leaving no residue to damage sensitive equipment or to order a cleanup cost of the equipment.
The system of pre-action when triggered, discharges water only in the sprinklers that have been operated by heat over the fire.
6. Supervision and Control System in Data Center :
The control and supervision system continuously monitors the various segments of Data Center tracking items such as:
Control of loading and parallelism of the generating sets
Supervision and control of medium voltage panels
Integration with system of generators
Integration with system rectifiers
Supervision and control panels for low-voltage
The system consists of computers with the latest technology capable of withstanding continuous use, appropriate systems for supervision and control. The same are redundant to each other, allowing high flexibility and performance system.
The Data Center also has a system of closed circuit television and access control that controls the entry and exit in various rooms and areas of physical security at Data Center.
With increased role of data center for business operation, the organization must be able to maintain high standards, integrity, and functionality. Fortunately, not many companies have their own data center IT professionals to design, plan, and maintain the needs of a data center. With this high demand for data center services, especially in conventional data centers, NTIPL supplies their skilled expert team to handle our clients needs for their successful data center operations.
For more information visit www.netlabindia.com
You can also tweet to us : @ntipl_netlab
Do leave a like and comment if you have anything to share with us.
Hello, How are you doing today? Ask us more information about https://www.netlabindia.com/solutions/how-to-build-a-remarkable-fully-functional-data-center i.e How To Build a Remarkable & Fully Functional Data Center?. Click the button below to continue on whats app.

redpajama_set_name: RedPajamaCommonCrawl


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Here's a story of how four sinless dogs fight it out to withstand the consequences of a hit-and-run not so illicit!
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Full, natural-looking eyelashes can now be achieved through a prescription treatment called Latisse™. Women who want eyelash extensions in New Jersey use Latisse, the first and only eyelash treatment approved by the FDA to help grow longer, fuller and darker eyelashes and treat hypotrichosis, a condition that includes having inadequate or not enough eyelashes.
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LATISSE® can grow thinning lashes. In the US Phase III LATISSE® clinical trial, 91% of women participating (n=134) were 35 or older, and results show that LATISSE® more than doubled lash fullness after 16 weeks of treatment for these patients.
Dr. Schrader has 10 years experience, over 6 years in private practice in the Pennsylvania area and performed hundreds of LATISSE® and other cosmetic procedures.


text:
package sqlite.gr7.compumovil.udea.edu.co.sqlite;

import android.content.ContentValues;
import android.content.Context;
import android.database.Cursor;
import android.database.sqlite.SQLiteDatabase;

/**
 * Created by santiago on 3/7/16.
 */
public class DataBaseManager {

    public static final String TABLE_NAME = "contacts";
    public static final String CN_ID = "_id";
    public static final String CN_NAME = "name";
    public static final String CN_PHONE = "phone";

    public static final String CREATE_TABLE = "create table " + TABLE_NAME + " ("
            + CN_ID + " integer primary key autoincrement,"
            + CN_NAME + " text not null,"
            + CN_PHONE + " text );";

    private DBHelper helper;
    private SQLiteDatabase db;

    public DataBaseManager(Context context) {
        helper = new DBHelper(context);

        db = helper.getWritableDatabase();
    }

    private ContentValues generateContentValues(String name, String phone) {
        ContentValues values = new ContentValues();

        values.put(CN_NAME, name);
        values.put(CN_PHONE, phone);

        return values;
    }

    public void create(String name, String phone) {
        db.insert(TABLE_NAME, null, generateContentValues(name, phone));
    }

    public void create_string(String name, String phone) {
        db.execSQL("insert into " + TABLE_NAME + " values (null, '" + name + "', '" + phone + "');");
    }

    public void delete(String name) {
        db.delete(TABLE_NAME, CN_NAME + "=?", new String[]{name});
    }

    public void delete(String name1, String name2) {
        db.delete(TABLE_NAME, CN_NAME + " IN (?, ?)", new String[]{name1, name2});
    }

    public void update_phone(String name, String phone) {
        db.update(TABLE_NAME, generateContentValues(name, phone), CN_NAME + "=?", new String[]{name});
    }

    public Cursor load_contacts() {
        String[] columns = new String[]{CN_ID, CN_NAME, CN_PHONE};

        return db.query(TABLE_NAME, columns, null, null, null, null, null);
    }

    public Cursor find_contact(String name) {
        String[] columns = new String[]{CN_ID, CN_NAME, CN_PHONE};

        return db.query(TABLE_NAME, columns, CN_NAME + "=?", new String[]{name}, null, null, null);
    }

}

redpajama_set_name: RedPajamaGithub


text:
Tag: Pastries
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I toured the new Nosh that opened in Telus Garden in downtown Vancouver, this new dining concept from the Global Group features a one-of-a-kind grab n' go eatery and pâtisserie. Transitioning from a bakery in the morning, to a salad and panini…
LIBERTY BAKERY
3699 Main Street, Vancouver Tel: (604) 709-9999 Web: https://www.facebook.com/Libertyyvr Twitter: @Libertyyvr Advice: Closed Monday. In the heart of bustling Main Street sits a wonderful café and bakery on the corner, all white on the outside, on the inside it's cute…
DOUGHGIRLS BAKE SHOP
3322 Shrum Lane, Vancouver Tel: (604) 333-5474 Web: http://www.doughgirlsbakeshop.com/ Twitter: @DoughgirlsBake Advice: Join the line-up for delicious treats. Take 'n Bake selection of entries for takeout. Located in the Wesbrook Village neighborhood close to the UBC campus is a star studded…
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SATE BAKERY
2879 Commercial Drive, Vancouver Tel: 604-725-8400 Web: www.bakerysate.com Twitter: @BakerySate Advice: Go early for the breakfast pastries as they come out of the oven. Patisseries have been opening in many neighborhoods around the city, now foodies need not look further on…
CAFÉ AL MERCATO
2215 Marine Drive, West Vancouver Tel: 604-922-4334 Web: n/a Twitter: @CaffeAlMercato Advice: Sit at the communal table. This Italian style café and market is filled with a large selection of fresh baked goods, such as breads, muffins, scones, cakes and…
MOLLI CAFÉ
1225 Burrard Street, Vancouver Tel: 604-336-6554 Web: not yet Twitter: @MolliCafe Advice: No reservations. One of my favourite cuisines is Mexican, I love the flavours of the varied types of dishes from the many different regions that make up their…
Afternoon Tasting at Temper Pastry
Last week I revisited one of my favourite chocolatiers and pastry shop in West Vancouver. Chef Steve Hodge is a creative wizard concocting new pastries, chocolates and desserts that fill his pastry case. My friend Chef Felix Yau joined me…
2409 Marine Drive, West Vancouver Tel: 604-281-1152 Web: http://www.temperpastry.com/ Twitter: @Temperpastry Advice: Join the line-up for delicious treats. Closed Monday. Every neighborhood needs an amazing patisserie café, Pastry Chef/Owner Steven Hodge recently opened the spot. Not only is it already…
CHEZ CHRISTOPHE
4712 Hastings Street, Burnaby Tel: 604-428-4200 Web: www.christophe-chocolat.com Twitter: @Chez_Christophe Advice: Closed Sunday and Monday Having had a sweet tooth since childhood, I have always searched out the patisseries and pastry chefs who run them as I've travelled around the…
BEAUCOUP BAKERY & CAFÉ
2150 Fir Street, Vancouver Tel: (604) 732-4222 Web: http://www.beaucoupbakery.com Twitter: @beaucoupbakery Advice: Go early as some of the pastries sell out within minutes. From the get go, even before the bakery café had opened, I was a fan of Jackie…
UPDATED 4/15/15 BUSINESS HAS CLOSED 1055 Canada Place, Vancouver Phone: 604-647-7559 Web: http://www.leonidaswaterfront.com/ Twitter: @LeonidasChocola Advice: Located on the wharf towards the water, outside of the new Vancouver Convention Centre. As a chocolate enthusiast, I am always searching out…
1262 Homer Street, Vancouver Tel: 604-899-1098 Web: http://www.ganacheyaletown.com/ Advice: Come by after 11am daily for the fresh baked from the oven Almond and other Croissants. Known for their pastries and spectacular wedding cakes, they are also a morning stop for…
LA BAGUETTE & L' ECHALOTE
UPDATED 7/30/14 BUSINESS HAS CLOSED 1689 Johnston Street, Vancouver Tel: 604-684-1351 Web: http://www.labaguette.ca Advice: Get their between 10:30-11:30 am to get your choice of sandwich before they are all gone. I have been coming to this bakery to pick up…


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text:
active 48 minutes ago Sande Kennedy
@saocv
Points balance: 4,399,071
Member since May 4, 2016
Total Reads: 31,123
Total Points: 4,399,071
Kenya is a country of many talents. From great footballers to actors to innovators, the country is indeed a hotbed of smart people who have not only put their names and the country on the map but also made lots and lots of money while at it. Well,with that said,two Kenyan men have become an instant online sensation thanks to their incredible […] View
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Sande Kennedy posted an update 2 months, 2 weeks ago
Kenya is a country of many talents. From great footballers to actors to innovators, the country is indeed a hotbed of smart people who have not only put their names and the country on the map but also made lots and lots of money while at it. Well,with that said,two Kenyan men have become an instant online sensation thanks to their incredible…[Read more]
Nandwa Muyuka's profile was updated 2 months, 2 weeks ago
Nandwa Muyuka became a registered member 2 months, 2 weeks ago
Sande Kennedy wrote a new post, Qatar Working hours announced for Ramadan 2019 2 months, 2 weeks ago
Her Excellency Minister of Justice and Acting Minister of State for Cabinet Affairs Dr. Issa bin Saad Al Jafali Al Nuaimi, issued a circular on Sunday defining the working hours during the holy month of Ramadan […]
Sande Kennedy wrote a new post, List of best Hotels in Doha Qatar 2 months, 2 weeks ago
Doha is a compact city with a wide variety of hotels. Check out the hotels listing below.
Alwadi Hotel Doha MGallery by AccorHotels
Alwadi Hotel Doha is the first MGallery boutique hotel by AccorHotels in […]
Sande Kennedy wrote a new post, Why DP William Ruto will never be President – Hon. Weston Wanjohi Patron- GEMA-K 2 months, 2 weeks ago
Reality slowly sinking in….this guy William Ruto is campaigning for a position which will not be there in 2022. OVERRATED!
As a common voter, how will you vote for overrated William Ruto in a p […]
Sande Kennedy wrote a new post, Confirmed : UoN student leader Ann Mwangi Mvurya dating Govonor Mike Sonko 2 months, 2 weeks ago
Ms Mvurya visited Sonko at his City Hall office shortly after she won UNSA election. [PHOTO/COURTESY]
University of Nairobi students' president, Ann Mwangi Mvurya, has rubbished rumours suggesting she could b […]
Sande Kennedy wrote a new post, China Is Slaughtering Millions Of Donkeys In Africa – Here's Why 2 months, 2 weeks ago
In the crime-ridden borderlands where Zimbabwe and South Africa meet, donkeys have been sought-after by smuggling syndicates since late 2015 because they are silent and can transport heavy cargo across the rough […]
Sande Kennedy wrote a new post, TOP 10 LARGEST CITIES AND TOWNS IN KENYA BY POPULATION 2 months, 2 weeks ago
Been wondering which are the largest cities and towns in Kenya as of 2018? Well, it's evident that the country's population is growing at an alarming rate. Today, we take a close look at top 10 largest cities and […]
Sande Kennedy wrote a new post, Idris Elba secretly marries girlfriend Sabrina Dhowre in 3-day lavish wedding in Morocco (photos) 2 months, 3 weeks ago
Idris Elba and Sabrina Dhowre are married. The couple, who got engaged in 2018, exchanged vows on April 26 at the Ksar Char Bagh hotel in Marrakesh. Dhowre wore two custom dresses by Vera Wang; while Elba wore a […]
Sande Kennedy wrote a new post, The revolution Kenyans have been waiting for is here. 2 months, 3 weeks ago
Are you feeling the pain of Economic sabotage and helplessness?
Kenyans in the capital city Nairobi have organized a peaceful protest scheduled for 30th April, 2019.
The protests which are known as 'Red V […]
Sande Kennedy wrote a new post, HOW TO APPLY FOR A WORK PERMIT IN KENYA 2 months, 3 weeks ago
This is a guide on how to apply for a work permit in Kenya. Foreign nationals who wish to work in Kenya are required by the law to obtain a work permit. A work permit is a document issued by the director of […]
Sande Kennedy wrote a new post, New Whip Alert – Regina Daniels Buys Mercedes BrabusBy Aanu Damilare On Apr 24, 2019 2 months, 3 weeks ago
Nollywood teen actress, Regina Daniels, has taken to social media to show off her new Mercedes Brabus, and she is no doubt a Benz lover.
Taking to her social media page, Regina shared im […]
Sande Kennedy wrote a new post, Did you know this facts about Africa? 2 months, 4 weeks ago
Africa has a population of 1. 3 billionEquatorial Guinea is Africa's only
spanish speaking country.South Africa is the most visited
African country.Nigeria has the richest Black people in A […]
Sande Kennedy wrote a new post, A Message to all Africans let Me Just remind you that .. 2 months, 4 weeks ago
Africans must know all this information
More than $ 5 trillion in gold and oil were stolen in the invasion of Iraq.
Remember that Saddam did not have weapons of mass destruction and was not involved in […]
Sande Kennedy wrote a new post, Qatar 2022 World Cup stadiums Progress : All you need to know 2 months, 4 weeks ago
A look at the progress of the tournament venues as Qatar prepares to host Middle East's first football World Cup.
Months after the completion of the 2018 FIFA World Cup in Russia, all eyes are on Qatar as it […]
Sande Kennedy wrote a new post, Why Africans Should not Donate anything towards the rebuilding of satanic Notre Dame which is a case of misplaced empathy 3 months ago
Why is it that a Catholic cathedral in flames provokes more public grieving than the mass suffering and death of humans?
People gather on the banks for the River Seine near Notre-Dame Cathedral after a […]
Sande Kennedy wrote a new post, This is Why Europe is the monster to African Progress 3 months ago
France since 1957 controls 85% of the national reserves of 14 African countries. All are FORCED to pay colonial taxes to France. The 14 countries (Benin, Burkina Faso, Guinea Bissau, Côte d'Ivoire, Mali, Niger, […]
Sande Kennedy wrote a new post, Employers lobby says housing levy Gazette notice illegal 3 months ago
From FKE
Dear Member,
Our attention has been drawn to the Public Notice published in today's Daily Nation Newspaper under the headline Housing Fund Levy.
The notice by the Ministry of Transport, I […]
Sande Kennedy wrote a new post, Confirmed Kenyans to pay Ksh 2000 from their salaries for Uhuru's cheap homes 3 months ago
• The employers are require to deduct and remit the levy together with other statutory levies
The government will start deducting 1.5 per cent housing levy from all employees effective this month.
The f […]