Journal of Applied Phycology

, Volume 24, Issue 3, pp 357–363 | Cite as

Simulated cell trajectories in a stratified gas–liquid flow tubular photobioreactor

  • Annelie K. Moberg
  • Gary K. Ellem
  • Graeme J. Jameson
  • Joseph G. Herbertson


The fluid dynamic environment within a photobioreactor is critical for performance as it controls mass transfer of photosynthetic gases (CO2 and O2) and the mixing environment of the algal culture. At a cellular level, light fluctuation will occur when cells move between the “light”, well-illuminated volume of the culture near the light source and the “dark”, self-shaded zone of the culture. Controlled light/dark frequency may increase the light to biomass yield and prevent photoinhibition. Knowledge of cell trajectories within the reactor is therefore important to optimize culture performance. This study examines the cell trajectories and light/dark frequencies in a stratified gas–liquid flow tubular photobioreactor. Commercially available computational fluid dynamics software, ANSYS Fluent, was used to investigate cell trajectories within the half-full solar receivers at different liquid velocities and reactor tube diameters. In the standard configuration 96-mm solar receiver tube, the light/dark cycle frequencies ranged from 0.104 to 0.612 Hz over the liquid velocity range of 0.1 to 1 m s−1. In comparison, the smaller diameter 48- and 24-mm tubes exhibit higher light/dark frequencies, 0.219 to 1.30 Hz and 0.486 to 2.67 Hz, respectively.


Computational fluid dynamics (CFD) Design Hydrodynamics Mixing Particle tracking 



Computational fluid dynamics




Microalgal biomass can be used for a wide range of products and have several advantages over more conventional crops. Production can take place in regions and climates not suitable for farmland and forests, with no requirement for freshwater (Borowitzka and Moheimani 2011). Compared to land grown plants, they also exhibit faster growth and shorter harvesting cycles. In addition, the production of algal biomass can be synergistic with environmental applications such as carbon dioxide sequestration and wastewater remediation (Schenk et al. 2008).

Due to the high cost of production, microalgae products are currently only used within high value sectors such as pharmaceuticals and health foods (Pulz and Gross 2004). However, should large-scale microalgal biomass production be made economically viable, it has the potential to be a part of future sustainable communities as a source of protein for food and feed, lipids for renewable fuel, and other energy or carbon sequestration products. For microalgal biomass to be economically competitive for such purposes, reliable, high-performance, large-scale production systems will be needed. Closed culturing systems (photobioreactors) provide intrinsic advantages over open systems such as raceway ponds in terms of process control and productivity, but the challenge is to realize these benefits at low capital costs (Pulz 2001; Carvalho et al. 2006).

It is also critical to have a comprehensive understanding of the variables involved in microalgae cultivation and their impact on biomass production and composition. One important criterion for optimized microalgal production is sufficient mass transfer of photosynthetic gases so that the culture growth is limited only by the light availability and a suitable light regime on a cellular level.

The project industry partner, The Crucible Group Pty Ltd (Newcastle, Australia), has developed a photobioreactor designed to incur low capital cost without losing the inherent advantages of closed reactor designs. It consists of a vertical section designed to induce liquid flow (e.g., an airlift pump) and a horizontal tubular section (solar receiver) in which the algae cells are exposed to light (Fig. 1). The solar receiver is operated partially full such that there is stratified gas–liquid flow within this section. The reactor floats on a body of water, which provides cooling and structural support.
Fig. 1

Schematic description of the photobioreactor under study. There are two main sections, the airlift section and the partially full solar receiver section

Mass transfer within the design takes place in both sections and has previously been investigated (Moberg et al. 2009; Moberg et al. 2010). These studies analyzed the relationships between productivity, liquid velocity, gas composition, and reactor length to support high productivity operations. The focus of the current study is radial mixing within the liquid phase, its effect on the light regime, and how that varies with liquid velocity and the diameter of the solar receivers.

Reactor mixing determines the light exposure pattern of individual cells in the culture. Microalgal cultures are self-shading, i.e., mutual shading occurs among cells. The available light decreases exponentially from the surface of the reactor that is closest to the irradiation source. The difference between light and dark parts of the culture increases with increased culture density or longer light paths (Merchuk et al. 1998; Molina Grima et al. 1999). Due to this mutual shading cells are not experiencing continuous illumination, but a pattern of light and darkness as they move through the light and dark volumes of the reactor. These illumination cycles are called light/dark (L/D) cycles. The frequency of these cycles and the ratio of L/D periods are important, as these parameters can be optimized to use high irradiances more effectively. Increased productivity is a result of the culture capturing more photons while avoiding light inhibition, which occurs when a cell is exposed to too much light (Richmond 1986). Light/dark cycling is effectively a way of diluting light by giving each cell a smaller dose of light during a given time span. In cultures of high cell density, a higher degree of mixing, and hence, L/D cycles of higher frequency, are needed to effectively utilize light. Ideally, the L/D cycle should be equal or close to the photosynthesis reaction time which is approximately 1–15 ms (Richmond et al. 2003; Carvalho et al. 2011). Such conditions are however difficult to achieve in practical fluid dynamic conditions, and would require short light paths and extremely good mixing conditions. Even if the maximum effect of L/D cycles cannot be reached, reactor design should aim for conditions with L/D frequencies within an order of magnitude of 1 Hz, where increases in culture efficiency have been shown to occur (Grobbelaar et al. 1996; Eriksen 2008; Posten 2009), and a photic volume of ca. 10% to yield 1:10 light to dark ratio L/D cycles (Richmond 1996; Degen et al. 2001).

Light/dark cycle frequencies within photobioreactors are seldom known, as they depend both on the cell trajectories and the radiative field within the reactor, both of which can be difficult to determine. A few studies on the characterization of the light regimes within photobioreactors have however been published, where the main approach used is to first determine cell trajectories and then combine the results with a light distribution profile (Eriksen 2008; Pruvost et al. 2008). Cell trajectories in photobioreactors have previously been determined by either schematic representation of the flow (bubble column, internal loop airlift, and thin layer cascade) (Wu and Merchuk 2002; Wu and Merchuk 2004; Masojídek et al. 2011), experimental measurement (bubble column, draft tube, and split airlift columns) (Luo et al. 2003; Luo and Al-Dahhan 2004; Merchuk et al. 2007) or simulations (annular cell, tubular with static mixers, spiral tubular, and draft tube airlift) (Pruvost et al. 2002; Perner-Nochta and Posten 2007; Wu et al. 2010; Luo and Al-Dahhan 2011).

This study examines cell trajectories within half-full solar receivers as a first step to characterize the light regime within the studied photobioreactor. Commercially available computational fluid dynamics (CFD) software, ANSYS Fluent, is used to investigate three half-full tubes of different diameters over a liquid velocity range. A simplified light distribution profile is then used to compare light regimes at different liquid velocities in the standard case 96-mm solar receiver tube. The results are then compared to two tubes of smaller diameter. The aim of the study is to investigate if any conclusions for reactor design and operating purposes may be drawn from the results, and to develop a light regime model that later can be used to calculate optimal combinations of culture density, solar receiver tube diameter, and liquid velocity to achieve suitable L/D cycle frequency and light to dark interval ratios for a chosen species and location.


Geometry and mesh generation

The examined photobioreactor consist of two sections, one airlift section and one tubular (solar receiver) section (Fig. 1). The airlift section is mainly dark and cells will experience negligible light exposure within this section. It was therefore not included in the following simulations. The solar receiver section consists of partially filled tubes with an inner diameter of 96 mm in the standard configuration. In this study, three different tube diameters were investigated: 96, 48, and 24 mm. The half-full tube (half-cylinders) geometries were created by extruding half-circles by 10,000 mm in the z-direction in ANSYS DesignModeler 12.1. Geometries were thereafter imported into ANSYS Meshing 12.1 where they were meshed by the sweep method. Face sizing and edge inflation were used to control the mesh size. The resulting 96-, 48-, and 24-mm diameter meshes consisted of approximately 990,000, 520,000, and 410,000 cells for the half-cylinder geometries.

Fluid flow solution

Computational fluid dynamics calculates numerical solutions using the equations governing fluid flow. In this work, the flow solution was obtained using commercially available CFD software, ANSYS Fluent 12.1.4, processing in parallel (two processes), using the 3D double-precision solver. All calculations were performed with the steady-state pressure-based solver and the realizable kε-model with gravity enabled. The upper boundary in the half-cylinder geometries were set to be friction-free to emulate the situation in a half-filled tube (Fig. 2a). The culture medium was modeled based on the physical properties of water, with a density of 998.2 kg m−3 and a viscosity of 0.001003 kg m−1 s−1. Solutions for four average liquid velocities were determined for each tube diameter, 0.1, 0.3, 0.5, and 1 m s−1. In order to achieve a developed flow profile throughout the length of the geometry, the flow was calculated twice for each scenario with the outlet profile of the first solution serving as the inlet profile for the second calculation.
Fig. 2

a Schematic description (cross-section) of the geometry used for CFD simulations. The half-full reactor tube geometry was modeled as a half-cylinder with a half-circular cross-section and friction-free top boundary to imitate a free surface. b Schematic description of the light and dark zones which occur in the reactor tube due to self-shading of the cells. In this work, a simplified light–dark environment was modeled where the top fraction of the culture volume was assumed to be “light” whereas the bottom fraction volume was assumed “dark”

Determination of cell trajectories

Cell (particle) trajectories were calculated within ANSYS Fluent 12.1.4 using the stochastic Discrete Random Walk model. To emulate the properties of microalgae cells, particle reflection was included in the wall boundary conditions while “interaction with liquid phase” (used when particles exchange mass, momentum, and/or energy with the continuous phase) and “Saffman Liftforce” (used to model lift due to shear for sub-micron particles) options were neglected. Particles were defined as spherical particles with the diameter of 0.01 mm and a density of 1,000 kg m−3. Surface injection was chosen, meaning one particle per inlet face was released (983, 407, and 171 particles respectively for the 96-, 48-, and 24-mm geometries). Five surface injections were performed for each scenario. Recorded variables were the particle ID and the spatial (x, y, z) position of each particle over time.

Post processing and light regime calculations

For the purpose of this study, a simplified light/dark environment was modeled where the light source was assumed to be positioned vertically above the solar receiver. Refraction effects and diffuse light were neglected. The result is an upper volume of the culture assumed to be “light” and a bottom volume assumed “dark” (Fig. 2b). The volume fraction in each zone is determined by the light/dark cut-off level or light penetration depth. The light penetration depth is dependent on reactor geometry, light intensity, cell density, and the properties of individual algal species. In this study, the light penetration depth in each geometry was chosen so that the illuminated volume constituted 10%, a light to dark culture volume ratio of 1:9. The resulting cut-off levels were located 3.8, 1.9, and 0.94 mm below the surface of the 96-, 48-, and 24-mm half-cylinder geometries, respectively.

To calculate the light regimes of each particle the particle tracking variables recorded in ANSYS Fluent were imported and processed in MATLAB 7.7.0 (Mathworks). The particle tracks were separated by their particle ID and L/D cycles were calculated from the yz (distance from surface and distance from inlet) position at each time point. The mean light and dark intervals in each scenario were calculated from two vectors containing all light and dark intervals recorded (based on the L/D cut-off value) for all particles, and the mean L/D cycle as a sum of these two means. The frequency was calculated as the reciprocal of the length of a L/D cycle. The vectors containing light and dark intervals were also used for the calculation of interval residence time distributions. The light and dark intervals of individual particle tracks were visualized by calculating the binary light/dark pattern. When the position of a particle was above the light/dark cut-off level the particle was in the light zone and given the binary value of 1. When the particle was in the dark zone it was given a value of 0.


Cell trajectories and binary pattern

Using the example case of the 96-mm half-full solar receiver, a simulated liquid flow of 0.5 m s−1, a velocity contour plot of the developed flow solution can be seen in Fig. 3 The maximum velocity was found at the center of the tube, while the velocities near the tube wall are lower. Figure 4 illustrates the vertical mixing of particles as they move throughout the tube. The tracks exhibit a random pattern where small amplitude vertical movement occurs more often than larger amplitude cycles where particles move from top to bottom in the simulated geometry. Figure 5 shows example binary L/D patterns of tracked particles in the same scenario with a 3.8-mm L/D cut-off. The length of individual light and dark intervals varies from less than 1 ms to more than 25 s long. The longest L/D intervals belong to particles that flow through the whole simulated tube length of 10 m without crossing the light/dark cut-off. In a 96-mm tube with a simulated liquid velocity of 0.5 m s−1 and a 3.8-mm L/D cut-off, this is the case for an average of 38 out of 983 particles (3.9%) in each injection. To calculate the true longest light and dark intervals the simulated tube length needs to be extended, which would mean added complexity and calculation time and has therefore not been included in the current study.
Fig. 3

Velocity contour plot of the developed flow solution for a 96-mm half-full tube operating at an average velocity of 0.5 m s−1

Fig. 4

Cell trajectories 96-mm tube running at 0.5 m s−1. Five example particle tracks are shown

Fig. 5

Binary light and dark interval patterns of ten particle tracks in a half-full 96-mm tube running at 0.5 m s−1 with a light penetration depth of 3.8 mm (1:9 volume ratio). White areas represent light intervals and black areas dark intervals

Light regimes in the 96-mm tube

For each tested liquid velocity in the three geometries, the mean light and dark intervals of all particle tracks in all injections were calculated. The mean L/D cycle length and frequency was derived from this data. The results show an overall trend where a higher liquid velocity increases the rate of L/D cycling, as does smaller tube diameters.

In the standard case, 96-mm diameter half-full tube, the mean light intervals at a 1:9 volume ratio decreased from 1.80 to 0.292 s when the liquid velocity was increased from 0.1 to 1 m s−1. The corresponding dark intervals decreased from 7.79 to 1.34 s and the resulting mean L/D cycle length from 9.58 to 1.63 s (Fig. 6). The L/D cycle frequency increased from 0.104 Hz at 0.1 m s−1 to 0.612 Hz at 1 m s−1 (Fig. 8).
Fig. 6

Light and dark intervals in a half-full 96-mm tube running at liquid velocities of 0.1, 0.3 0.5, and 1 m s−1. The light to dark volume ratio is 1:9. The black portions of the bars represent the mean dark intervals whereas the white portions represent the mean light intervals. The total heights of the bars represent the mean light–dark cycle length at each velocity

Analysis of the light interval distribution showed that 19.9% of the intervals were equal to or shorter than 0.1 s, 86.4% of the light intervals were equal to or shorter than 1 s, and 99.6% were equal to or shorter than 3 s at a liquid velocity of 0.5 m s−1 (Fig. 7). The corresponding fraction of dark intervals shorter or equal to 1 s was 60.0%, 94.3% of intervals were shorter or equal to 10 s. The fraction of light intervals shorter than or equal to 1 s at 0.1 m s−1, 0.3 m s−1, and 1 m s−1 were 49.7%, 75.6%, and 96.05%, respectively. The fraction of corresponding dark intervals shorter than or equal to 10 s were 78.4%, 89.5%, and 99.0%, respectively.
Fig. 7

Light interval distributions in a half-full 96-mm tube with a light to dark volume ratio of 1:9 running at a liquid velocity of 0.1 m s−1 (a), 0.3 m s−1 (b), 0.5 m s−1 (c), and 1 m s−1 (d). The histogram bin size is 0.1 s and intervals up to 2 s are included. The dashed lines represent the mean light intervals

Light regimes in the 48- and 24-mm tubes

In addition to the standard configuration 96-mm solar receiver tube, two other diameters were investigated at a 1:9 volume ratio, 48 and 24 mm. In the half-full 48-mm case, the mean L/D cycle decreased from 4.56 s at 0.1 m s−1 to 0.769 s at 1 m s−1 (Fig. 8) and the corresponding L/D frequency increased from 0.219 to 1.3 Hz (Fig. 9). In the half-full 24-mm tube the mean L/D cycles decreased from 2.06 to 0.374 s (Fig. 8) and the L/D frequency increased from 0.486 to 2.67 Hz (Fig. 9) over the liquid velocity range.
Fig. 8

Mean light/dark cycle length in the three tested half-full tubes (96, 48, and 24 mm in diameter) at a liquid velocity of 0.1 to 1 m s−1. The light to dark volume ratio is 1:9

Fig. 9

Mean light/dark cycle frequency in the three tested half-full tubes (96, 48, and 24 mm in diameter) at a liquid velocity of 0.1 to 1 m s−1. The light to dark volume ratio is 1:9


This study has been based on particle trajectories calculated by the commercially available CFD code ANSYS Fluent 12.1.4. The particle tracking model is relying on the fluid flow simulation and it should be noted that the calculated solution is only an approximation of real flow. As the investigated solar receivers consist of basic geometries and fluid flows that are straightforward to model with CFD this approach was deemed sufficient for comparing different tube diameters and operating velocities for design purposes.

The unstructured cell trajectories (Fig. 4) and varying length of light and dark intervals (Fig. 5) show that the vertical/radial mixing of particles within the examined photobioreactor is not of a regular, but of a random nature. Particles will be subjected to L/D cycles of different length as they move through the solar receiver. Individual algae cells may therefore at times experience photoinhibition caused by too much light exposure, others may not be productive because of long dark periods. However, light and dark interval distribution analysis of the example case of a half-full 96-mm solar receiver operating at 0.5 m s−1 showed that a large fraction of light intervals, 19.9%, were shorter than or equal to 100 ms, 86.4% equal to or shorter than 1 s. Sixty percent of dark intervals were shorter than or equal to 1 s, and 94.3% were shorter than or equal to 10 s.

The 1:9 volume fraction light regime results show that there is a reasonably good mixing rate within the solar receiver, with L/D cycles in the range of seconds. For comparison, the L/D cycles in raceway ponds that have a similar light path length are in the order of seconds to minutes (Grobbelaar et al. 1996). In the standard case 96-mm half-full tube, L/D frequencies over the liquid velocity range of 0.1 to 1 m s−1 are 0.104 and 0.612 Hz (Fig. 9), within an order of magnitude of 1 Hz. Previous studies have reported conflicting results within this medium frequency range of 0.1–1 Hz (Grobbelaar et al. 1996; Janssen et al. 2000), but it is plausible that some productivity increase could be seen in this range compared to cultures experiencing lower L/D frequencies.

The 48- and 24-mm cases showed that an increased L/D frequency can be expected in smaller diameter tubes. Frequencies above 1 Hz were seen at the tested liquid velocity of 1 m s−1 in the 48-mm tube and at 0.3 m s−1 and above in the 24-mm tube (Fig. 9). In this range the vertical mixing is very likely to contribute to increased productivity through L/D cycling (Grobbelaar et al. 1996; Eriksen 2008; Posten 2009). This indicates that smaller diameter tubes could be advantageous in terms of light regimes, but other design considerations also need to be considered. This includes the impact on mass transfer within the solar receiver and the increased cell density necessary in a smaller diameter tube to create a suitable light regime within a shorter light path culture environment.

In conclusion, this study has shown that the fluid flow-induced radial mixing within the investigated photobioreactor design can support favorable light regimes. Light/dark frequencies of the order of 1 Hz were seen in all the tested scenarios, indicating that the reactor can be operated in a range where productivity increases are plausible compared to cultures experiencing lower frequency L/D cycles. The CFD-based cell trajectory model used in this study will be an important tool for further optimization of light exposure within the investigated photobioreactor design, and will form the basis of future work looking at the operational management and performance optimization of the reactor in realistic light and cell density environments. In conjunction with the previously developed mass transfer models (Moberg et al. 2010), these models form the basic tools for overall system optimization of the photobioreactor process parameters and design.

Future work will investigate how optimal combinations of culture density, solar receiver tube diameter, and liquid velocity can be calculated to achieve suitable L/D cycle frequency and light to dark interval ratios for a chosen species and location. Other implementations will include using a light gradient instead of a L/D cut-off level that will allow for more detailed calculation of average cell illumination history, from which conclusions can be drawn on a culture level. In an outdoor environment the irradiance levels are highly variable throughout the day, and the light regime may also change due to changing cell density in the culture. By using a developed light regime model, operational parameters, such as liquid velocity, may be adjusted to prevent photoinhibition and minimize energy use, thereby maximizing culture performance in a varying light environment.



This work is part of a PhD project investigating the process engineering fundamentals of microalgae production. The project is supported by the industry partner, The Crucible Group Pty Ltd, The Tom Farrell Institute for the Environment, and The University of Newcastle, Australia.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Annelie K. Moberg
    • 1
    • 2
  • Gary K. Ellem
    • 1
  • Graeme J. Jameson
    • 1
  • Joseph G. Herbertson
    • 2
  1. 1.The University of NewcastleCallaghanAustralia
  2. 2.The Crucible Group Pty LtdMayfield WestAustralia

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