A mathematical model of microalgal growth in light-limited chemostat culture

A mathematical model for light-limited growth of a continuous microalgal culture is proposed. Average light intensity inside the photobioreactor was calculated, taking light attenuation by algae into account. The biomass absorption coefficient was determined by means of two new parameters, the pigment-free biomass, Y_B, and the total pigment absorption, Y_p (absorption coefficient normalized to total pigment content). The model reproduced the steady states reached and the dynamic behaviour of the system when the dilution rate was changed.     

Simulation of algae growth in a bench scale internal loop airlift reactor

The growth of red marine alga Porphyridium sp. cultivated in an internal loop airlift (ALR) photobioreactor was simulated. The model proposed integrates a dynamic formulation of the kinetics of photosynthesis, photoinhibition, and the fluid dynamics of the ALR, including shear stress effects on the kinetics of growth. The kinetic parameters obtained previously for a system under defined light/dark cycles were used, and satisfactory agreement was found. The maintenance term was modified to take into account the detrimental effects of shear stress in the bioreactor on the rate of growth. A hybrid method for approximate solution of the equations is proposed. The conditions of gas flow rate and illuminance required for positive growth were found. This is the first mathematical model that predicts the effect of gas flow rate, column height, column diameter, and cross-sectional areas on the productivity of a photosynthetic process in an airlift bioreactor. Extrapolations done using the model indicate the possibility of predicting the optimal diameter for an assembly of ALR photobioreactors.     

各向同性湍流中颗粒弥散的直接数值模拟

对三维气粒两相各向同性湍流进行了直接数值模拟以研究悬浮在其中的颗粒的运动.重点考察了颗粒惯性对颗粒和颗粒所见流体速度的自相关以及颗粒弥散特性等的影响.颗粒的Lagrangian积分时间尺度随颗粒惯性单调增加,颗粒所见流体速度的Lagrangian积分时间尺度保持相对稳定;当颗粒的弛豫时间尺度与流体的Kolmogorov时间尺度相当时,流体Lagrangian积分时间尺度有较大偏离.当颗粒的惯性很小时,颗粒扩散随惯性增大而增强,但当颗粒的惯性大于一定值时,颗粒的扩散性反而减弱,局部富集明显时颗粒扩散系数最大,此时颗粒的涡扩散系数可比流体的高约30%.τ_p/τ_k≈1.0的颗粒的浓度场显示,由于局部富集效应颗粒倾向于集中在低涡度高剪切的区域.     

Collision rate of small particles in a homogeneous and isotropic turbulence

A theoretical equation is derived for the collision rate of aerosol particles in a homogeneous and isotropic turbulent system. This equation takes into account the relative velocity between fluid and particles. The calculated results indicate that the relative velocity between fluid and particles is the main factor in the turbulent coagulation (agglomeration, coalescence) of unequally sized particles in an air flow. This hold true, even when the particle sizes are less than 1 micron. For particles of equal radii the coagulation coefficient reaches its minimum value, because the effect of motion relative to the fluid now becomes zero and only the spatial variation of turbulent motion remains to cause collisions between the particles. For particles following a fluid motion completely, as in a water stream, the equation for the collision rate reduces to the Saffman and Turner equation.     

Direct numerical simulations of aggregation of monosized spherical particles in homogeneous isotropic turbulence

Direct numerical simulations of turbulent solid–liquid suspensions have been performed. The liquid is Newtonian, and the particles are identical spheres. The spheres have a tendency to aggregate since they are attracted to one another as a result of a square‐well potential. The size of the particles is typically larger than the Kolmogorov scale, albeit of the same order of magnitude. In such situations, the particle dynamics (including the aggregation process), and turbulence strongly interact which explains the need for direct simulations. The lattice‐Boltzmann method combined with an immersed boundary method for representing the no‐slip conditions at the spherical solid–liquid interfaces was used. The results show that the aggregate size distributions depend on both the strength of particle–particle interactions and the intensity of the turbulence. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2589–2600, 2012     

Measurements of pollen grain dispersal in still air and stationary, near homogeneous, isotropic turbulence

The dispersal of ragweed, pine and corn pollen as well as polystyrene spheres in still air and stationary, near homogeneous, isotropic turbulence (HIT) was investigated using high-speed, digital inline holographic cinematography enabling Lagrangian tracking of the particles. Mean still air settling velocities were similar as reported literature values. Small discrepancies were most likely related to species/size differences and water content of the grains. Near-HIT was generated by loudspeakers mounted on the corners of a 40 cm³ chamber and the turbulent flow field at the center of the chamber was validated using stereoscopic Particle Image Velocimetry (PIV). Results showed near homogeneity and near isotropy with mean velocities 5–10 times smaller than the corresponding rms values of velocity fluctuations. The turbulent kinetic energy dissipation rate was determined from the PIV data sets and used to calculate the Kolmogorov scales and Taylor microscales. Experiments were carried out for two different loudspeaker amplifications corresponding to Taylor microscale Reynolds numbers, R_λ=144 and 162, respectively. The mean settling velocity in turbulent conditions was in all cases higher than the corresponding still air value, the difference becoming smaller as particle Stokes numbers increased. For the present conditions, the still air particle settling velocity was lower than the rms values of air fluctuating velocities. As a result, dispersion was dominated by inertia and for a given R_λ, particle fluctuating velocity autocorrelations fell more rapidly as the particle Stokes number decreased; corresponding particle diffusion coefficients also decreased. Transverse particle diffusion coefficients were lower than those in the direction of gravity in agreement with the continuity effect. Under the present range of experimental parameters, results showed that inertial particles (0.6<St<11) in highly turbulent conditions disperse more effectively than the air.     

Mixing and fast chemical reaction-VIII: Initial deformation of material elements in isotropic,homogeneous turbulence

The kinematics of the deformation of fluid elements, having a size on the order of the Kolmogoroff velocity microscale, are needed when describing fast reactions in turbulent fluids as competition between molecular diffusion and chemical reaction in shrinking laminae. Starting from the statistical theory of turbulent diffusion, a new kinematic relationship has been derived, which applies to short diffusion times. Comparisons with two previously used equations, valid for simple shear and a certain elongational flow, confirm the useful properties of the new equation. Its application to fast reac requires knowledge of the kinematic viscosity of the fluid, the rate of energy dissipation (e.g. by stirring) and the initial thickness of the laminae. parametric sensitivity of the predicted product distribution from fast, competitive, consecutive reactions with respect to the initial thickness, which on the order of the Kolmorgoroff scale, is relatively low.     

Simulation of reversible nylon-66 polymerization in homogeneous continuous-flow stirred tank reactors

Experimental data of Ogata¹ has been curve-fitted to obtain the forward and reverse rate constants for nylon-66 polymerization. Its molecular weight distribution (MWD) has been simulated in homogeneous continuous-flow stirred tank reactors (HCSTR) for 11 h of residence time when the reaction mass is very close to equilibrium. The set of algebraic equations have been solved using Brown's algorithm,² which was found to be more efficient compared to the Gauss-Jordon techniques of solution. The MWD thus obtained is compared with our earlier simulation of the molecular weight distribution from batch reactors³ and was found to differ significantly. In HCSTR, the weight fraction distribution does not undergo a maximum and the polydispersity index ρ of the polymer formed is much higher than that obtained from batch reactors. The number and weight average of the polymer formed in HCSTR is found to be significantly lower.     

Euler–euler anisotropic gaussian mesoscale simulation of homogeneous cluster‐induced gas–particle turbulence

An Euler–Euler anisotropic Gaussian approach (EE‐AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster‐induced turbulence (CIT). A three‐dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite‐volume framework. The particle‐phase volume‐fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open‐source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. The results demonstrate that the proposed EE‐AG methodology is able to produce comparable results to EL simulations, and this moment‐based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2630–2643, 2017     

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.     

不同氮磷比对藻类生长及水环境因子的影响

试验研究了不同氮磷比对水体藻类生长以及对水环境因子的影响。通过设置水样的氮磷质量比(m(N)/m(P))分别为3、5、10、20、30、50,并对其进行长期连续观测,结果表明,当m(N)/m(P)为3.0～10.0时,有利于藻类的生长;m(N)/m(P)大于10.0时,将抑制藻类生长。在适合藻类生长的培养水体中,磷是限制藻类生长的主要因素。不同m(N)/m(P)对于藻类生长周期各个阶段出现的时间和持续时间影响效果不显著;藻类暴发前pH值与DO浓度都会出现峰值,据此可以建立藻类暴发预警系统。     

Predictive capability of Large Eddy Simulation for point-wise and spatial turbulence statistics in a confined rectangular jet

Large Eddy Simulations (LESs) were performed for a confined rectangular liquid jet with a co-flow and compared in detail with particle image velocimetry (PIV) measurements. A finite-volume CFD library, OpenFOAM, was used to discretize and solve the filtered Navier–Stokes equation. The effects of grid resolution, numerical schemes and subgrid models on the LES results were investigated. The second and fourth order schemes gave similar performance, while the fourth order scheme costs much more computationally. Subgrid model comparison showed that the locally dynamic procedure is necessary for complex flow simulation. Model validation was performed by comparing LES data for the point-wise velocity statistics such as the mean and the root-mean-square velocity, shear stress, correlation coefficient, velocity skewness and flatness with the PIV data. In addition, LES data for the two-point spatial correlations of velocity fluctuations that provide structural information were computed and compared with PIV data. Good agreement was observed leading to the conclusion that the LES velocity field accurately captures the important characteristics of all the turbulent length scales present in the flow, from the fully resolved energy-containing eddies to the subgrid-scale dissipative eddies.     

Simulation of growth of methane-utilising bacteria in batch culture

A kinetic model for batch growth of a methane-utilising bacterium is presented, using data from previous experimental work on the specific rates of growth, respiration and methane consumption of the bacterium. A two-substrate model with respect to methane and oxygen was employed to represent the specific rate of methane consumption. Employing the various coefficients assessed previously, the bacterial growth was simulated in relation to changing partial pressures and mass-transfer coefficients for both gases. The simulated results are discussed in light of the experimental data published by other workers on both pure and mixed populations of methane-utilising bacteria. The optimal partial pressures of oxygen and methane derived from the model were found to play a decisive role in connection with inflammability.     

The nucleation and growth of a lead phosphate film on homogeneous lead amalgam

The electrochemical oxidation of Pb(Hg) in acidic phosphate medium results in formation of a monomolecular PbHPO₄ passivating film. Analysis of potentiostatic current-time transients demonstrated that the crystallization occurred through a 2-dimensional progressive nucleation and growth mechanism. The potential dependence of the combined nucleation and crystallization rate constants was [7.8 ± 0.7 mV/decade]^?1. The formation of a soluble lead phosphate species prior to film growth was observed under certain conditions. Examination of it curves in this region by the low overpotential form of the Cottrell equation indicated that the soluble species was PbHPO₄.     

A method for electrochemical growth of homogeneous nanocrystalline ZnO thin films at room temperature

We report the electrodeposition at room temperature (25 °C), in a potentiostatic mode, of cohesive nanocrystalline ZnO thin films from an oxygenated zinc chloride bath. It is shown that the bath saturation by molecular oxygen precursor is a key parameter to grow the oxide at low temperature. After low O₂ bubbling the solution is not saturated and the surface is more or less passivated by an amorphous Zn(OH)₂ veil-like thin layer. After intense and long molecular oxygen bubbling, the current density rapidly increases after an induction period of about 800 s. At the foot of the current onset, crystallized ZnO seeds appear entrapped in the initial amorphous layer. The film nucleation is a delayed process. The electrode is subsequently covered by a homogeneous ZnO film with structures of several hundreds of nanometers in length composed of nanocrystals with size of about 17 nm. The room-temperature photoluminescence spectrum of the film is dominated by a strong UV emission at 3.25 eV due to the recombination of excitons. The visible emission centered at 2.36 eV, due to deep defects, is less intense than the UV one showing the good structural quality of the ZnO nanocrystallized film. The films have interesting properties to be used as a seed layer for instance.     

The distribution of sterols in algae

Available analytical techniques are now sufficient for the separation and identification of sterols from complex mixtures in plants. Gas and thin layer chromatography and mass spectroscopy in particular, have been used to resolve some of the confusion concerning the sterol composition of algae. Red algae (Rhodophyta) contain primarily cholesterol, although several species contain large amounts of desmosterol, and one species contains primarily 22-dehydrocholesterol. Only a few Rhodophyta contain traces of C-28 and C-29 sterols. Fucosterol is the dominant sterol of brown algae (Phaeophyta), apparently the major sterol of every species examined. Most Phaeophyta also contain traces of cholesterol and biosynthetic precursors of fucosterol. The sterols of green algae (Chlorophyta) are much more varied and complex than those of other groups of algae. Whereas the Phaeophyta and Rhodophyta contain one primary sterol, many of the Chlorophyta contain a complex mixture of sterols such as occurs in higher plants. The Chlorophyta contain such sterols as chondrillasterol, poriferasterol, 28-isofucosterol, ergosterol, cholesterol and others. Sterol composition may be of value in the systematics of plants such as the Chlorophyta. Recently (for the first time) complex mixtures of sterols have been isolated in very small amounts in the blue-green algae (Cyanophyta). Available data on the sterols of other groups of algae are insufficient for making useful comparisons. One of 12 papers to be published from the “Sterol Symposium” presented at the AOCS Meeting, New Orleans, April 1970. Scientific Article No. A2606, Contribution No. 4331 of the Maryland Agricultural Experiment Station.     

A stochastic Lagrangian approach for simulating the effect of turbulent mixing on algae growth rate in a photobioreactor

It is well known that mixing caused by fluid turbulence can cause significantly increased growth rate of algae in photobioreactor flows under certain conditions. In general, flows in which the light penetrates into only a small fraction of the reactor flow field have the largest growth rate enhancement in the presence of fluid mixing. The current paper seeks to develop a computationally efficient prediction method for algae growth rate in practical photobioreactors using a combination of commercially available RANS turbulence models and a stochastic Lagrangian model for the turbulence fluctuations. The stochastic Lagrangian algae growth rate model is first validated by comparison with simulations of algae growth rate obtained by direct numerical simulation of homogeneous turbulence. We then demonstrate the stochastic Lagrangian model approach for prediction of algae growth rate in turbulent pipe flow, which is representative of the primary photoreaction component in many tubular algae production facilities. The results illustrate how algae growth rate increases as the pipe flow Reynolds number is increased.