Numerical investigation of hydrodynamic and mixing conditions in a torus photobioreactor

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Abstract

It is well-known that the response of photosynthetic microorganisms in photobioreactor (PBR) is greatly influenced by the geometry of the process, and its cultivation parameters. The design of an adapted PBR requires understanding of the coupling between the biological response and the environmental conditions applied. Cells culture under well-defined conditions are thus of primary interest. A particular lab-scale PBR has been developed for this purpose. It is based on a torus shape, that enables light to be highly controlled while providing a very efficient mixing, especially along the light gradient in the culture, that it is known to be a key-parameter in PBR running. A complete characterization of hydrodynamic conditions is presented, using computational fluids dynamics (CFD). After validation by comparison with experimental measurements, a parametric study is conducted to characterize important hydrodynamics features with respect to PBR application (light access, circulation velocity, global shear-stress), and then to investigate a possible optimization of the process via modification of the impeller used for culture mixing. The final part of the study is devoted to a detailed investigation of mixing performance of the torus PBR, by numerically predicting dispersion of a passive tracer in various configurations. The high degree of mixing observed shows the great potential of such innovative geometry in the field of photosynthetic microorganisms cultivation, especially for the design of a lab-scale process to conduct experiments under well-controlled conditions (light and flow) for modeling purpose.

Introduction

Photosynthetic microorganisms like microalgae and cyanobacteria have a high potential in various areas, including food (as feed for larvae and juveniles of bivalve molluscs), pharmacology (bioactive molecules, toxins), cosmetics (pigments), environment (CO2 removal, wastewater treatment) and even energy production (H2). But, despite this well-known potential, examples of industrial valorizations remain scarce, and are mainly restricted to particular applications, like biomass or pigments production in mass culture (Lorenz and Cysewski, 2000, Olaizola, 2003). Difficulty of proposing adapted processes, called photobioreactors (PBR), that permits to reach sufficient productivity, is mainly explained by the complex interaction between the photosynthetic microorganisms growth and culture conditions. Preliminary investigations in a fully characterized process, where all pertinent parameters can be controlled with high accuracy, are thus of primary interest. By this way, culture parameters can be first optimized at the lab-scale, including a modeling approach, and an adapted industrial sized PBR with economic feasibility can next be proposed in a second time.

Many examples of PBRs are found in literature (Pulz, 2001; Tredici and Materassi, 1992) but generally developed for particular applications. There are only few examples of geometries for fundamentals studies under well-defined conditions (Cornet et al., 1994, Cornet et al., 1998; Csogör et al., 1999; Hoekema et al., 2002, Wu and Merchuk, 2001). Whatever is the application, light reveals to be the major factor controlling, and often limiting, the productivity of bioprocess involving photosynthetic microorganisms (Richmond, 2004). Because of the cell concentration, light is highly absorbed and diffused when crossing the culture (Cornet et al., 1998, Csogör et al., 2001). This leads to an heterogeneous radiation-field, that prevents light to be considered as a common substrate, like mineral nutrients for example, where a homogeneous concentration can often be supposed in a first assumption (well-mixed reactor). To relate the light supply to the culture growth, light attenuation in the biological turbid medium must be accurately described. This determination is not trivial, and is highly correlated to the PBR geometry (Cornet et al., 1998). Analytical and accurate solutions are facilitated if the one-dimensional hypothesis on the radiation-field can be done, i.e., light attenuation occurs in a unique main direction, perpendicular to the illuminated face of the PBR (Cornet et al., 1995, Cornet et al., 1998). For more complex geometries, numerical resolution of the radiative transfer equations has to be performed, but it is time-consuming, reducing interest in the field of a fully controlled process definition, where various parameters can be modified easily. This explains why most of PBRs, especially those involved in fundamental studies and modeling, are naturally designed under the one-dimensional hypothesis, like rectangular geometries with an incident perpendicular radiation-field (Chini Zitelli et al., 2000; Cornet and Albiol, 2000, Hoekema et al., 2002), cylindrical ones with external radial illumination (Cornet et al., 1998), or annular ones with internal radial illumination (Muller-Feuga et al., 2003a; Ogbonna et al., 1996).

A second important parameter is the hydrodynamics applied in the geometry. The culture must be sufficiently mixed to prevent flowing cells from sedimentation and to homogenize nutrients concentration. But, it is indeed known from an experimental basis that hydrodynamics can have additional complex effects on photosynthetic microorganisms (Muller-Feuga et al., 2003a, Muller-Feuga et al., 2003b; Richmond, 2004, Wu and Merchuk, 2002). This influence can be related to two different reasons, that are the shear-stress effect on living cells, and the homogenization of the light received per cell. The first one is a common problem encountered in all cell-sensitive cultures, as with mammalian cells for example (Curran and Black, 2004; Elias et al., 1995), but despite its apparent simplicity, shear-stress effect on living medium is very difficult to fundamentally investigate (Ghadge et al., 2005; Pruvost et al., 2004b). It is indeed well-known that some species are especially sensitive to the mechanical shear that appears in a disturbed flow, and the mixing can then be in extreme cases the critical parameter of the application (Barbosa et al., 2004; Sanchez Miron et al., 2003; Wu and Merchuk, 2002). But how to characterize and formulate effects of shear-stress on a living cell is still a problem to solve. From a physical point of view, mechanical effects of a given hydrodynamics on a particle (a living cell in this case) can be of various forms (Ghadge et al., 2005), including the different components of the shear-stress tensor as well as pressure gradients, and their respective time variation if the flow is turbulent. From the biological point of view, cell response to shear-stress is highly related to the species considered, and can be of various natures, ranging from an alteration of the physiological behavior to the cell alteration and destruction (Jaouen et al., 1999). These responses are certainly a function of the shear-intensity, its nature and the time of exposition to a particular intensity. This complexity explains why effects of shear-stress on a living medium (and especially for photosynthetic microorganisms) remain rather unknown, and thus uncontrolled.

In contrary to the shear-stress, effects of mixing on the light received by each cell of the overall population is specific to the photosynthetic microorganisms (Wu and Merchuk, 2001, Wu and Merchuk, 2002). Indeed, because of the heterogeneous radiation-field in the photobiorector, each cell receives instantaneously a specific amount of light. It is thus important to generate hydrodynamic conditions that promote mixing along the light gradient so as to homogenize light received by each cell with respect to time. Each individual cell will have a behavior representative of the global culture, and the modeling of the biological response will then be performed more easily, using standard growth models applied on the overall biomass. Such approach is usually conducted in PBR modeling, but it must be noticed that it implies a well-mixed assumption of the culture with respect to the light gradient. If not the case, difference in residence time in different depths of culture will lead to a non-negligible influence of flow conditions (Cornet et al., 2003, Luo and Al-Dahhan, 2004, Pruvost et al., 2002). It must be added that, for certain species, a second possible effect can result from an intensive mixing along the light gradient, that makes photosynthetic microorganisms subjected to light intensity variations in PBR. This is especially the so-called light/dark cycles effects, as observed in many studies (Grobbelaar et al., 1996, Janssen et al., 1999, Lee and Lee, 2001, Merchuk et al., 1998). Influence of such a phenomenon on PBR performance remains, as for shear-stress, rather misunderstood. Light regime in PBR is indeed complex and can only be characterized if those light–dark cycles effects are known, that implies light attenuation and cells trajectory to be both determined, each being a physics complex problem (on its own). Assuming a radiative model is available, cells trajectory can be obtained by, for example, radioactive particle tracking (Luo et al., 2003), or with a Lagrangian approach (Muller-Feuga et al., 2003b; Pruvost et al., 2002). For the last one, the flow-field must be well-determined in the all geometry. The light regime finally obtained has then to be linked to the physiological response, that is another delicate problem considering its complexity (Cornet et al., 2003, Janssen et al., 1999, Luo and Al-Dahhan, 2004, Pruvost et al., 2002).

In this study, a laboratory-scale PBR designed to conduct cultures under well-defined and controlled conditions is presented and investigated. In addition to classical bioreactor controls like pH or temperature, the set-up allows a simple and accurate determination of the light received by the culture, while providing good mixing conditions. To satisfy both conditions, the PBR presents flat surface and an internal torus shape (Fig. 1(a)). Light transfer aspect in such geometry has been treated elsewhere (Pottier et al., 2005), and the assumption of the one-dimensional hypothesis for radiative transfer modeling was especially verified. This study is especially focused on hydrodynamic aspects. With regard to mixing, some studies have shown interest of loop configurations like torus shape reactors, but in the field of biochemical applications like enzymatic reactions (Legrand et al., 1997, Nouri et al., 1997), or heterogeneous liquid–liquid reaction (Tanaka and O’Shima, 1988). A high dispersion is attained, because of Dean vortices generated by the reactor bends, and of the rotation of the marine impeller that generates a three-dimensional swirling motion in the geometry (Pruvost et al., 2004c). The combination of these two effects leads to an absence of dead volumes in the reactor. Torus reactors appear thus as an interesting alternative to classical cylindrical stirred tanks usually employed in mixing applications. For microalgae culture, and especially if reactors of high efficiency are needed, tank geometries are not suitable because of a limited surface to volume ratio compared to flat geometries. By combination with good mixing conditions, the proposed torus PBR allows a large illumination front surface for a given culture volume, that makes it interesting for preliminary laboratory investigations. One possible drawback of such a geometry is the eventual shear-stress field that is not perfectly controlled (but it is also the case in stirred tanks), and remains heterogeneous, as in the impeller region, where relative high shear-stress can be achieved. But, the loop configuration of the torus geometry has theoretically two advantages. The first is that the recirculation in the loop implies the entire culture to cross the impeller region at each new revolution in the geometry, and thus all cells are subjected to undergo an almost identical history with respect to shear-stress. This will facilitate the understanding of the global response of the culture to shear-stress generated in the geometry. The second advantage of the loop configuration is that low impeller rotation speeds generally allow an efficient mixing. It is thus expected that in such geometries, shear-stress will be kept sufficiently low to prevent from adverse effects on the culture.

In any case, to relate with accuracy process parameters to the biological response, conditions in the PBR need to be well-defined. To characterize hydrodynamics as a function of operating parameters in the torus shape PBR, computational fluids dynamics (CFD) will be employed. Such a tool has been successfully applied and validated on a reactor of almost similar geometry, but not devoted to photosynthetic microorganisms culture (Pruvost et al., 2004c). Major characteristics of flow in torus geometries were emphasized, especially the competition of Dean vortices that appear when an axial flow occurs in bends, with the solid-body rotation involved by the swirl flow generated by the impeller rotation. Because of the decay of the swirl intensity with the distance from the impeller, competition between both phenomena evolves in the geometry, resulting in non-established flow conditions with respect to the axial direction. It was especially shown that highest swirl motion was not achieved at higher impeller rotation speed. Under low rotation speeds of the impeller, due to the reduction of the axial pumping effect of the impeller and its influence on Dean vortices appearance, the swirl flow maintains further away in the reactor.

In this study, mixing conditions are especially investigated with respect to photosynthetic microorganisms application. After validating the numerical modeling of the PBR with experimental measurements obtained using particle image velocimetry (PIV), a complete numerical study is conducted and results for two types of impeller at various rotation speeds are presented. Some global values are defined to focus on the PBR application, by linking flow conditions to cells sedimentation, light access, shear-stress, etc. Next, by solving numerical dispersion of a passive tracer in unsteady state, performance of the reactor is investigated in term of mixing time. Finally, lateral dispersion in the reactor was characterized using a steady-state resolution of tracer dispersion. Combined with flow structure visualization, it allows a detailed study of the movement generated along the light attenuation, emphasizing interest of the torus PBR to generate effective light access conditions.

Section snippets

Photobioreactor description

The PBR is presented in Fig. 1(a). Illuminated surface of 0.0325m2 is of torus shape with an external radius Rc=0.13m, the length Lz of the loop being 0.82 m (Fig. 1(b)). The reactor is managed in PMMA (polymethyl methacrylate) and is thus fully transparent. To prevent from optical distortion and to avoid curved surface perpendicular to the emitting direction of the light source, the front surface is plane, and the torus channel is square-sectioned with a gap width Lx=Ly=0.040m, leading to a

Mesh consideration

A similar approach is conducted as already described in details in Pruvost et al. (2004c) for the simulation of another torus geometry using FLUENT software (Fluent Inc). Only main characteristics are presented in this study. The torus shape is three-dimensionally meshed using the GAMBIT software (Fluent Inc). The resulting grid is shown in Fig. 2. Because of the complex geometry of both impellers, hybrid meshes are retained, with an irregular zone composed of tetrahedral volumes and prisms in

Global characterization of hydrodynamics characteristics of the torus PBR

The first part of the numerical investigation is devoted to a global characterization of hydrodynamic conditions in the torus PBR as a function of the impeller speed and shape, in the scope of microorganisms cultivation. Hydrodynamic values linked to cells suspension, light access and shear-stress were thus especially considered. In the torus geometry, cells suspension is achieved if a minimum mean bulk velocity U0 is applied. Light access given by cells trajectories along the radiation-field

Conclusion

The flow-field generated in a PBR of torus geometry has been investigated. A commercial code was used for this purpose, and predictions were validated with PIV measurements. In the field of photosynthetic microorganisms application, various relevant values were calculated, like mean bulk velocity U0 related to cells sedimentation, averaged velocity component Vy reflecting light access conditions or averaged shear-stress ε, a criteria that should be adapted to cell fragility. Such

Notation

Cjpassive tracer concentration (Eq. (3)), molm-3
Djlaminar mass diffusivity of the passive tracer, m2s-1
Djtturbulent mass diffusivity of the passive tracer, m2s-1
kturbulent kinetic energy, m2s-2
Lxgap width of the torus photobioreactor, m
Lyphotobioreactor depth (Lx=Ly), m
Lzlength of the torus photobioreactor, m
Nrotation velocity of the impeller, rpm
Rcexternal torus photobioreactor radius, m
Re=ρU0Ly/μReynolds number
Rem=ρND2/μReynolds number (definition used for mixing tank, with Ly=D)
S

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