Discrete Cell Model Research Articles

Cellular Statistical Models of Broken Cloud Fields. Part II: Comparison with a Dynamical Model and Statistics of Diverse Ensembles

Abstract Cellular statistical models are designed to provide a simple two-parameter characterization of the structure of broken cloud fields described through distributions of cloud fraction and of chord lengths for clouds and clear gaps. In these analytical models cloud fields are assumed to occur on a semiregular grid of cells (which can be vaguely interpreted as atmospheric convective cells). In a simple, discrete cell model, cell size is fixed and each cell can either be completely filled with cloud with some probability or remain empty. Extending the discrete model to a continuous case provides more realism by allowing arbitrary cloud and gap sizes. Here the continuous cellular model is tested by comparing its statistics with those from large-eddy simulations (LES) of marine boundary layer clouds based on case studies from three trade-cumulus field projects. The statistics largely agree with some differences in small sizes approaching the LES model grid spacing. Exponential chord-length distributions follow from the assumption that the probability of any cell being cloudy is constant, appropriate for a given meteorological state (narrow sampling). Relaxing that assumption, and instead allowing this probability to have its own distribution, leads to a power-law distribution of chord lengths, appropriate to a broader sample of meteorological states (diverse sampling).

Calculations of oxygen transport by red blood cells and hemoglobin solutions in capillaries.

A theoretical model is developed to investigate the influence of hemoglobin-based oxygen carriers (HBOCs) on oxygen transport in capillary-size vessels. A discrete cell model is presented with red blood cells (RBCs) represented in their realistic parachute shape flowing in a single file through a capillary. The model includes the free and Hb-facilitated transport of O2 and Hb-O2 kinetics in the RBC and plasma, diffusion of free O2 in the suspending phase, capillary wall, interstitium and tissue. A constant tissue consumption rate is specified that drives the simultaneous release of O2 from RBC and plasma as the cells traverse the capillary. The model mainly focuses on low capillary hematocrits and studies the effect of free hemoglobin affinity, cooperativity and concentration. The results are expressed in the form of cell and capillary mass transfer coefficients, or inverse transport resistances, that relate the spatially averaged flux of O2 coming out of the RBC and capillary to a driving force for O2 diffusion. The results show that HBOCs at a concentration of 7 g/dl reduce the intracapillary transport resistance by as much as 60% when capillary hematocrit is 0.2. HBOCs with high O2 affinity unload most O2 at the venular end, while those with low affinity supply O2 at the arteriolar end. A higher cooperativity did not favor O2 delivery due to the large variation in the mass transfer coefficient values during O2 unloading. The mass transfer coefficients obtained will be used in simulations of O2 transport in complex capillary networks.

A Chemotactic Model for the Advance and Retreat of the Primitive Streak in Avian Development

The formation of the primitive streak in early avian development marks the onset of gastrulation, during which large scale cell movement leads to a trilaminar blastoderm comprising prospective endodermal, mesodermal and ectodermal tissue. During streak formation a specialized group of cells first moves anteriorly as a coherent column, beginning from the posterior end of the prospective anterior–posterior axis (a process called progression), and then reverses course and returns to the most posterior point on the axis (a process called regression). To date little is known concerning the mechanisms controlling either progression or regression. Here we develop a model in which chemotaxis directs the cell movement and which is capable of reproducing the principal features connected with progression and regression of the primitive streak. We show that this model exhibits a number of experimentally-observed features of normal and abnormal streak development, and we propose a number of experimental tests which may serve to illuminate the mechanisms. This paper represents the first attempt to model the global features of primitive streak formation, and provides an initial stage in the development of a more biologically-realistic discrete cell model that will allow for variation of properties between cells and control over movement of individual cells.

Single phase flow modeling in packed beds: discrete cell approach revisited

A discrete cell model (DCM), based on the minimization of the total rate of energy dissipation, is applied to compute the fluid velocity field in two-dimensional packed beds. The analysis of the individual terms of the energy dissipation rate equation is also presented. The results obtained by DCM are validated both by comparing them with the solutions of ensemble-averaged momentum and mass conservation equations (CFDLIB code) and by available experimental results. The differences between DCM and CFD simulations were found to be confined to within a 10% band over a wide range of Reynolds numbers ( Re′=5–171). Thus, a reasonable agreement between the predictions of the two methods can be claimed for engineering applications. An acceptable agreement of DCM/CFD predictions and the available experimental data in the literature is also achieved. The presented case studies justify the use of DCM for predicting the fluid velocity fields in packed beds with complex internal structures and with irregular distributed gas feeding points.

Two-phase flow distribution in 2D trickle-bed reactors

An extended discrete cell model (DCM), based on minimization of energy dissipation rate, is applied to predict two-phase flow distribution in the two-dimensional trickle-bed reactors. The main advantages of DCM are that it can qualitatively capture the experimental observations, and readily distinguish between flow distribution in prewetted and non-prewetted beds, as well as reflect the effects of bed structure and inlet liquid distributor on two phase flow distribution. For comparison purpose, the results of liquid distribution obtained by DCM are compared with both computational fluid dynamics (CFD) simulations and experimental observations in a 2D bed. The achieved qualitative and quantitative agreement justifies the use of DCM in predicting two phase flow distribution in packed beds. A particle wetting factor ( f) has been introduced into DCM to account for the influence of particle surface wetting on liquid flow distribution. Analysis of DCM simulations presented based on maldistribution factor (mf ) provides a convenient way of quantifying the effects of particle surface wetting, distributor design and bed depth on the two-phase flow field.

Modelling and measurement of gas flow distribution in corrugated sheet structured packings

A mathematical model and calculation procedure are developed for the gas flow distribution in channels formed between tightly packed, corrugated, unperforated metal sheets. The model is a discrete cell model based on averaged mass, momentum and energy balance equations for each of numerous crossings of gas flow channels, with characteristic friction factors for gas inlet, bulk zone and wall zone as model parameters, which can be easily obtained from pressure drop measurements for each type and size of structured packing. The model enables prediction of velocity profiles leaving an element or packing layer consisting of segments of unperforated, structured packing. It is also suited for perforated packings which under operating (wetted) conditions function as a closed surface packing.

Discrete cell model of fixed‐bed adsorbers with rectangular adsorption isotherms

AbstractAdsorption of organics inot activated carbon particles within a fixed‐bed adsorber is modeled using the concept of mixing cells. The adsorption isotherm of these organics is taken to be rectangular because of the commonly observed strong affinity of organics into activated carbons. The model equations are solved by a singular perturbation method, and this results in a graphical procedure similar to that of McCabe and Thiele used in distillation column design. Such a graphical procedure provides a quick means to determine the adsorbate profiles along the adsorber for a given time and also the breakthrough curve, which reflects the performance of the adsorber.

Discrete cell model of pore‐mouth poisoning of fixed‐bed reactors

AbstractCatalyst deactivation in an isothermal fixed‐bed reactor under pore‐mouth poisoning conditions is investigated theoretically using a discrete mixing cell model. Two fundamental relationships which characterize the poisoning process in the reactor are identified and incorporated into the model to develop a simple graphical procedure for a quick, general insight into the problem. This graphical method is extended to design pellet impregnation profiles along the reactor which would give nondeteriorating reactor performance up to a given time. The effects of various system parameters on the lifetime and conversion performance of the reactor are also examined analytically, graphically and numerically.

Probability Density Functions of Speckle Intensity Produced by Weak Diffusers

By using the discrete cell model for the rough surface of objects, a general expression is derived which gives the probability density function of speckle intensity produced by weak diffusers having an arbitrary phase distribution and an arbitrary cell number, N, of contributions for the formation of speckles. In some special cases, it gives the probability density functions which have been previously derived and are well known in the statistics of speckles. In the case of the small number N = 2, an analytical solution of the probability density function is obtained from that general expression. Some features on the probability density functions of speckles are discussed for the case of small roughness and small number N.