scholarly journals The light/dark cycle of microalgae in a thin-layer photobioreactor

2020 ◽  
Author(s):  
Alessandro Chiarini ◽  
Maurizio Quadrio
Keyword(s):  
Thin Layer ◽  
Time Scale ◽  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Dark Cycle ◽  
Navier Stokes Equations ◽  
Time Resolved ◽  
Typical Time

AbstractA numerical study of the motion of algal cells in a representative thin-layer-cascade (TLC) photobioreactor is presented. The goal is to determine the time scale associated with the light/dark (L/D) cycle seen by the cells during their turbulent motion in the liquid culture. Owing to the limited reliability of the available numerical results which deal with time-averaged quantities and thus lack time-resolved information, the present study is based upon the Direct Numerical Simulation of the Navier-Stokes equations, a reliable but consequently expensive numerical approach which does not incur in turbulence modelling errors. Indeed, the simulation is successfully validated in terms of averaged velocity with experimental data. The availability of full temporal information allows algae cells to be followed in time along their trajectories. A large number (up to a million) of tracers is placed in the flow to mimic the algae cell. Their trajectories are statistically studied and linked to the turbulent mixing. Results indicate that, in a typical TLC reactor designed to mimic an experimental setup, cells undergo an L/D cycle with a time scale in the range 0.1–2 s. Such time scale, albeit much longer than the typical time scale of the photosynthesis, significantly benefits the productivity of the algae compared to a steady illumination.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

Experimental and Numerical Study of Vortex Induced Vibrations on a Spool Model

2018 ◽  
Author(s):  
David Gross ◽  
Yann Roux ◽  
Benjamin Rousse ◽  
François Pétrié ◽  
Ludovic Assier ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Perturbation ◽  
Industry Standards ◽  
Vortex Induced Vibrations ◽  
Recommended Practices ◽  
Decay Tests

The problem of Vortex-Induced Vibrations (VIV) on spool and jumper geometries is known to present several drawbacks when approached with conventional engineering tools used in the study of VIV on risers. Current recommended practices can lead to over-conservatism that the industry needs to quantify and minimize within notably cost reduction objectives. Within this purpose, the paper will present a brief critical review of the Industry standards and more particularly focus on both experimental and Computational Fluid Dynamic (CFD) approaches. Both qualitative and quantitative comparisons between basin tests and CFD results for a 2D ‘M-shape’ spool model will be detailed. The results presented here are part of a larger experimental and numerical campaign which considered a number of current velocities, heading and geometry configurations. The vibratory response of the model will be investigated for one of the current velocities and compared with the results obtained through recommended practices (e.g. Shear7 and DNV guidelines). The strategy used by the software K-FSI to solve the fluid-structure interaction (FSI) problem is a partitioned coupling solver between fluid solver (FINE™/Marine) and structural solvers (ARA). FINE™/Marine solves the Reynolds-Averaged Navier-Stokes Equations in a conservative way via the finite volume method and can work on structured or unstructured meshes with arbitrary polyhedrons, while ARA is a nonlinear finite element solver with a large displacement formulation. The experiments were conducted in the BGO FIRST facility located in La Seyne sur Mer, France. Particular attention was paid towards the model design, fabrication, instrumentation and characterization, to ensure an excellent agreement between the structural numerical model and the actual physical model. This included the use of a material with low structural damping, the performance of stiffness and decay tests in air and in still water, plus the rationalization of the instrumentation to be able to capture the response with the minimum flow perturbation or interaction due to instrumentation.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

A Conceptual Model of Flapping-Wing Mechanism Inspired from the Results of Numerical Study

2013 ◽  
Vol 397-400 ◽  
pp. 783-788
Author(s):  
Xing Wei Zhang ◽  
Chao Wang ◽  
Hang Liu
Keyword(s):  
Conceptual Model ◽  
Power Efficiency ◽  
Stokes Equations ◽  
Numerical Study ◽  
Flapping Wing ◽  
Numerical Results ◽  
Navier Stokes ◽  
Active Deformation ◽  
Navier Stokes Equations ◽  
Wing Model

This paper investigates the aerodynamic forces of several plunging wing models by means of computational fluid dynamics. A finite volume method was used to solve the two-dimensional unsteady incompressible Navier-Stokes equations. The forces and power efficiency have been calculated and compared between sets of different models. Current work found that the nonsymmetrical moving can enhance the lift and thrust forces. The numerical results also prove that the flexible wing model can be use to improve the efficiency and reduce the input. Additionally, a new conceptual model for flapping wing mechanism with active deformation and adaptive nonsymmetrical driving motion is proposed base on the numerical results.

scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

scholarly journals Numerical Study on the Solid Fuel Rocket Scramjet Combustor with Cavity

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1235 ◽  
Author(s):  
Chaolong Li ◽  
Zhixun Xia ◽  
Likun Ma ◽  
Xiang Zhao ◽  
Binbin Chen
Keyword(s):  
Solid Fuel ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Combustion Efficiency ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Particle Combustion ◽  
Scramjet Combustor ◽  
Cavity Configuration

Scramjet based on solid propellant is a good supplement for the power device of future hypersonic vehicles. A new scramjet combustor configuration using solid fuel, namely, the solid fuel rocket scramjet (SFRSCRJ) combustor is proposed. The numerical study was conducted to simulate a flight environment of Mach 6 at a 25 km altitude. Three-dimensional Reynolds-averaged Navier–Stokes equations coupled with shear stress transport (SST) k − ω turbulence model are used to analyze the effects of the cavity and its position on the combustor. The feasibility of the SFRSCRJ combustor with cavity is demonstrated based on the validation of the numerical method. Results show that the scramjet combustor configuration with a backward-facing step can resist high pressure generated by the combustion in the supersonic combustor. The total combustion efficiency of the SFRSCRJ combustor mainly depends on the combustion of particles in the fuel-rich gas. A proper combustion organization can promote particle combustion and improve the total combustion efficiency. Among the four configurations considered, the combustion efficiency of the mid-cavity configuration is the highest, up to about 70%. Therefore, the cavity can effectively increase the combustion efficiency of the SFRSCRJ combustor.

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