ORIGINAL PAPER

Studies on light intensity distribution inside an open pondphoto-bioreactor

Ramakant Pandey1• Akhilesh Sahu1

• Vasumathi K. K1• Premalatha M1

Received: 23 March 2015 / Accepted: 29 March 2015

� Springer-Verlag Berlin Heidelberg 2015

Abstract Light intensity profiles inside an open tank

were studied using ANSYS Fluent. Experiments were

performed by taking Scenedesmus arcuatus, green mi-

croalgae at three different concentrations under actual

sunlight conditions. Absorption of light intensity at dif-

ferent depths was measured experimentally. The results

generated from CFD simulations were compared with the

experimental results and the cornet model. It has been

found that there is a good agreement between the light

intensity profile obtained from the CFD simulation and that

calculated using the Cornet’s model. Light intensity pro-

files at different depths were calculated using CFD

simulation by varying the dimensions of the tank. The ef-

fect of wall reflectivity, diffuse fraction and scattering

phase function on light profile in side open tank are also

studied using CFD simulation.

Keywords Microalgae � Open pond � Light intensity �CFD � Cornet’s model � Discrete ordinates model

List of symbols

PBR Photo-bioreactor

PAR Photo synthetically active radiation

(lmol m-2s-1 or photons)

RTE Radiative transport equation

DO Discrete ordinate Method

OD Optical density

A Absorbance

L Light path length (m)

n Refractive index of the medium

r Stefan–Boltzmann constant

T Local temperature (K)

A Phase function

X0 Solid angle (sr-1)

X Microalgae density (kg/m3)

Ea Mass absorption coefficient (m2/kg)

Es Mass scattering coefficient (m2/kg)

I0 Incident radiation (lmol m-2s-1)

I Local radiation intensity (lmol m-2s-1)

r! Position vector

s! Direction vector

s!0 Scattering direction vector

rs Scattering coefficient (m-1)

k Absorption coefficient (m-1)

b Extinction coefficient (m-1)

x Single scattering albedo

N Cell number density (cells/m3)

s Transmittivity

e Molar absorptivity

fd Diffuse fraction

q Radiative flux (W/m2)

Band-0 400–500 nm

Band-1 500–650 nm

Band-2 650–700 nm

Subscripts

k At particular wavelength

w Wall

In Incoming

Out Outgoing

a Absorption

s Scattering

d Diffuse

& Premalatha M

latha@nitt.edu

1 National Institute of Technology, CEESAT,

Tiruchirappalli, India

123

Bioprocess Biosyst Eng

DOI 10.1007/s00449-015-1398-3

Introduction

Microalgal bioreactors are often designed differently from

bioreactors which are used to grow other microorganisms.

This is because most microalgae are photo-autotrophs and

depend on light as energy source. Supply, distribution and

utilisation of light by microalgal cultures are therefore

central aspects, which receive particular attention in the

design of photo-bioreactors.

Basically, a photo-bioreactor (PBR) is a bioreactor that

incorporates some type of light source. Virtually any

translucent container could be called as a PBR; however,

the term is more commonly used to define a closed system,

as opposed to an open tank or pond. Growing algae in

PBRs reduces risk of contamination, improves the repro-

ducibility of cultivation conditions, provides control over

hydrodynamics and temperature, and allows appropriate

technical design [1].

Light is one of the important factors that affect com-

position of biomass and growth rate. Typical light intensity

requirements of microalgae are relatively low in compar-

ison to higher plants. For example, saturating light intensity

of Chlorella sp. and Scenedesmus sp. is around

200 lmol m-2 s-1 [2]. Density of algal culture affects

both the available light intensity as well as the light

penetration depth. It has been observed that optimal cell

density varies with the strain [3]. The wavelengths of light

used to cultivate the algae also affect the growth. The fact

is that more than 50 % of the incident solar radiation is not

useful for photosynthesis [1]. The quantity of light termed

as photons (lmol m-2 s-1) and available between wave-

lengths of 400–700 nm (visible spectrum) is only useful for

photosynthesis and this fraction of sunlight is called pho-

tosynthetically active radiation (PAR).

The radiation properties of microalgae were ex-

perimentally determined in [4, 5]. They measured extinc-

tion coefficients of each species from normal–normal

transmittance measurements in the wavelength range of

400–800 nm using UV–Vis–NIR spectrophotometer. They

observed that absorption coefficient is strongly dependent

on the wavelength of the light used and scattering phase

function for Chlorella sp., B. braunii and C. littorale mi-

croalgae peaks in the forward direction which is almost

constant for the wavelength studied. Similar observations

were reported by [6]. Moreover, they found that the value

of scattering albedo was approximately 0.9.

Houf and Incropera [7] compared various methods of

determining radiation transfer through aqueous suspensions

to predict radiative flux and absorption profiles within the

suspension, as well as overall absorption and reflection by

the suspension. They calculated various radiation pa-

rameters such as scattering albedo, bottom reflectance,

overall optical depth, and directional distribution of the

incident radiation and found reasonable agreement among

three flux, six flux and discrete ordinate method for various

conditions. On the other hand, absorption effects were

consistently under predicted by forward scattering method

and over predicted by Delta-Eddington method.

Lambert–Beer’s law can give reasonable estimate of

light distribution within algae suspensions but it does not

consider differential wavelength absorption by algae and

scattering effect explicitly. Cornet et al. [8–10] proposed a

model which separately accounts for absorption and scat-

tering and is able to produce good results for mono-di-

mensional approximation. This approach is very useful to

analyse the effect of light intensity distribution on the

growth of microalgae.

Acien et al. [11] proposed an empirical model to de-

termine light attenuation which is hyperbolic in nature and

requires only geographic, geometric, and solar position

parameters.

The present state of art of CFD simulation for PBR was

reviewed by [12] and modelling of light intensity distri-

bution inside the PBR was identified as one of the major

factors for getting accurate results through simulation. In

order to model the light transfer in three dimensions, one

has to solve the radiation transport equation. The radiative

transport equation (RTE) is a semi-empirical integro-dif-

ferential equation and analytical solution is possible only

for very simple mono-dimensional cases.

Pareek et al. [13, 14] determined light intensity distri-

bution in photo-catalytic reactor by solving RTE nu-

merically. They used finite volume approach of discrete

ordinate (DO) method available with FLUENT to solve the

RTE. They evaluated the effects of wall reflectivity, cata-

lyst loading and phase function parameter on light intensity

distribution. They found that, for relatively low catalyst

loadings, the wall reflectivity strongly influenced the light

intensity distribution. However, for an optically thick

medium, the wall reflectivity had negligible effect. Pareek

[15] simulated light intensity distribution, in dual lamp

photo-reactor filled with titania-slurry, using conservative

variant of discrete ordinate method and performed CFD

simulation for both homogeneous as well as heterogeneous

reactors. The model predictions were used to evaluate the

effect of catalyst loading on light intensity distribution for

various reactor configurations.

Duran et al. [16] modelled irradiation in annular photo-

reactors using finite volume method and found that the

models with diffused radiation emission showed better

overall irradiance prediction capabilities. The available

literature indicates that there is a huge possibility of ap-

plying CFD simulations to analyse radiation characteristics

of solid in suspension, the effect of concentration on light

Bioprocess Biosyst Eng

123

profile and the effect of geometry on light distribution in-

side the reactor.

Hence in this work, radiation characteristics of Scene-

desmus arcuatus were determined experimentally and light

intensity profile inside an open tank under actual solar ra-

diation was measured using online PAR sensor. Ex-

perimentally measured radiation characteristics were used

for CFD simulation and then CFD simulations were

validated with the theoretical Cornet’s model.

Light intensity Profile

Experimental method

Green microalgae S. arcuatus available at bio-energy lab,

CEESAT, National institute of technology Trichy, Tamil

Nadu, India was used as living culture in aqueous medium.

It was inoculated in a rectangular tank (0.56 9

0.36 9 0.36 m3) filled with pure water. The culture was

supplied with CO2 as a carbon source three times a day

which also maintained a PH, the original morphology of

Scenedesmus sp. was changed from colonies (a group

generally found as 8 or 4) to single cells upon supply of

100 % pure CO2 [17]. In order to avoid absorption and

scattering effects due to nutrient particles, no nutrients

were supplied and culture was allowed to grow in diffuse

sun light with the average PAR value varying between of

200 and 250 lmol m-2 s-1.

The optical density was measured using Vis spec-

trophotometer (HACH, DR2800). The calibration curves

were drawn by measuring the dry cell weight and the

number of cells per unit volume of suspension at different

optical densities (OD). The absorbance of the microalgae

was measured at 440 nm in cuvette with the path length of

1 inch using a UV–Vis spectrophotometer. Then, the cell

number (N) was determined using the haemocytometer and

Image J software.

Finally, to find the dry weight, a known volume of mi-

croalgae suspension was filtered through mixed cellulose

filter membranes with 0.45 lm pore size and dried at 85 �C

for 15 h. The dried filters were weighed immediately after

being taken out of the oven on a precision balance with a

least count of 1 mg. Calibration curves for cell number

(N) and dry mass density per unit volume (X) versus OD at

440 nm are shown in Fig. 1a, b, respectively. The cell

number, density combined with microalgae shape, size

distribution, and chlorophyll content are important for

theoretically predicting radiation characteristics of algal

suspensions. In measuring the radiation characteristics it is

assumed that the microalgae were well mixed and ran-

domly oriented. Single scattering albedo for a particular

species does not vary significantly with concentration

although it changes slightly with wavelength [4]. It can be

observed from this literature, that single scattering albedo

is not varying much for Chlorella sp, B. braunii and C.

littorale. Hence, in this work, single scattering albedo of S.

arcuatus is considered equal to that of single scattering

albedo of C. littorale. The average radiation characteristics

calculated corresponding to the wavelength range are

shown in Table 1 as derived from [4].

Beer lamberts law relates Extinction coefficient with

absorbance and is given below

A ¼ � log10

I

Io

� �¼ eLC ¼ bL ð1Þ

Absorbance of Scenedesmus sp. at concentrations men-

tioned in Table 2 was measured and extinction coefficient

was calculated using Eq. 1, now Eq. 2 relates extinction

coefficient with scattering albedo and scattering coefficient,

Fig. 1 a, b Calibration curve showing cell density concentration and dry weight concentration as a function of optical density at 440 nm and for

1 inch path length

Bioprocess Biosyst Eng

123

hence scattering coefficient was calculated using Eq. 2 and

absorption coefficient was calculated by putting the values

of extinction coefficient and scattering coefficient in Eq. 3.

Table 2 shows the radiation characteristics of Scenedesmus

sp. Thus obtained,

xk ¼rk

bkð2Þ

bk ¼ kk þ rk ð3Þ

Light intensity at different depths along the centre line of

the tank was measured using online PAR sensor (HYDRO-

LAB, Spherical, L1-COR, USA). The instrument was set to

register reading for every minute and the average radiation

measured over 15 min is indicated in Table 3. The readings

correspond to 28th April 2014 between 11:15 a.m. and 11:45

a.m., for Tiruchirappalli (Tamil Nadu, India) location (lati-

tude = 10.81�N, longitude = 78.69�E). The radiation mea-

surements were carried out at different depths corresponding

to a cell concentration of 3.82 9 1011 cells/m3.

Experiments were also performed to find the absorbance

of the species between 400 nm to 700 nm at 3.82 9 1011,

5.01 9 1011 and 6.91 9 1011 cells/m3 (Fig. 3).

Cornet’s model

Generally cornet’s model is used to validate the simulation

results. This is the only model which considers both

absorption and scattering effects separately and is ex-

pressed as

I

I0

¼ 4a1

1þ a1ð Þ2ea2 � 1� a1ð Þ2e�a2

ð4Þ

Where Ek and Es are mass absorption and mass scattering

coefficients, respectively, which provides relation between

a1 and a2. X is the cell concentration and L is the path

length.

a1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Ek

ðEk þ EsÞ

sð5Þ

and

a2 ¼ Ek þ Esð Þ � a1 � X � L ð6Þ

Ek ¼k

Xand Es ¼

rX

Radiation characteristics of Scenedesmus sp. reported in

Table 2 are substituted in Eq. 4 to predict the light inten-

sity at different depths corresponding to three different

concentrations as mentioned in Table 4.

CFD simulation

Geometrical details

In pre-processing, geometry design and meshing is done in

ANSYS Workbench 14.5 and FLUENT is used as a solver.

There are four face zones and one cell zone. Face zones are

divided into top, bottom, side and interior. Top, bottom and

side faces have been considered as walls, while cell zone as

liquid volume. The working volume is having following

dimensions: length (y) = 0.56 m; width (x) = 0.36 m and

depth (z) = 0.36 m. Grid independency check is done to

avoid the effect of grid size on the final results.

Table 1 Radiation

characteristics for cell density

N = 3.02 x 1011 cell/m3

Wavelength band (nm) Average absorbance Scattering albedo Extinction coefficient

400–500 0.191 0.785 7.514

500–650 0.161 0.94 6.354

650–700 0.1607 0.9066 6.329

Table 2 Absorption and

scattering coefficient of

Scenedesmus arcuatus

Wavelength band (nm) 3.82 9 1011 cells/m3 5.01 9 1011 cells/m3 6.91 9 1011 cells/m3

kk rk kk rk kk rk

400–500 2.09 7.63 2.90 10.60 3.64 13.29

500–650 0.58 9.14 0.81 12.69 1.02 15.91

650–700 0.91 8.82 1.21 12.24 1.58 15.35

Table 3 Experimental results (lmol m-2 s-1) on 28-04-14 for

N = 3.82 9 1011 cells/m3

Depth (m) 11:15 a.m. 11:30 a.m. 11:45 a.m.

0 1144 2040 2578

0.11 550 985 1256

0.20 356 630 802

0.28 264 468 597

0.33 230 451 521

Bioprocess Biosyst Eng

123

Governing equations

Radiative transport equation is the basic governing equa-

tion to describe the radiation transfer. It comprises of solar

radiation transfer within absorbing, scattering, and non-

emitting media such as micro-organism suspensions. The

basic RTE at position r!, in the direction s!, can be written

as’

dI r!; s!� �

dsþ k þ rsð ÞI r!; s!

� �

¼ kn2 rT4

pþ rs

4p

Z 4p

0

I r!; s!0� �

U s!: s!0� �

dX0 ð7Þ

The phase function U( s!. s!0) accounts for scattering

from the direction s!0, to the direction s!, and determines

the fraction of in-scattering radiation. This equation indi-

cates that intensity depends on spatial position and angular

direction. The sum of the absorption coefficient and the

scattering coefficient is often called the extinction coeffi-

cient (b = k ? rs).

Radiation model

Conservative variant of discrete ordinate method has

been used to solve the RTE since DO models account

for exchange of radiation between gas and particulates.

It also allows modelling semi-transparent walls of var-

ious types, specular reflection and computing non-grey

radiation.

Non-grey radiation model is used to account for the non-

grey nature of solar radiation. Following inputs were given

to solar calculator for Tiruchirappalli location. Solar cal-

culator available with ANSYS FLUENT was used to de-

termine the direction of beam radiation for the day and

time under consideration. Solar radiation in PAR region

(400–700 nm) (Fig. 2) was divided into three bands: Band

0 (400–500 nm); Band 1 (500–650 nm) and Band 2

(650–700 nm). Green microalgae S. arcuatus having re-

fractive index of the culture as 1.339 were used as a

medium for absorption of light inside the tank. Radiation

characteristics such as absorption coefficient and scattering

coefficient for three different wavelength bands obtained

from experimental results were used for simulation

(Table 2).

Boundary conditions

Bottom and side walls were considered opaque, while top

wall which is a phase boundary was considered as semi-

transparent wall. The top wall was exposed to solar ra-

diation. The PAR was divided in three wavelength bands and

used as radiation source for top wall. Radiation energy as-

sociated with each wavelength band was referred from [18].

Results and discussion

Validation of CFD simulation results

Table 5 shows the light intensity profile obtained from

CFD simulation. CFD results was compared with Cornet’s

model and Experimental method to check the validity of

CFD results.

It has been found that there is a good agreement be-

tween light intensity profile obtained from CFD and that

of calculated by Cornet’s model with maximum error of

14.2 % and average deviation of 5 %. Whereas max-

imum deviation of 15.3 % with an average deviation of

4 % between CFD and experimentally measured PAR

was observed. From Fig. 3 the results obtained from

CFD are lying in between the experimental results and

the results obtained from cornet model, hence it indi-

cates that the deviation between the CFD results and

experimental results is less as compared to that of results

obtained from CFD and cornet model. The result pre-

dicted by CFD is much closer then results predicted by

cornet model.

Radiation characteristics of Scenedesmus arcuatus

Figure 4 shows the absorption spectra of S. arcuatus

measured at three different concentrations. It is clear from

the absorption spectra that absorbance peaks at 440 and

680 nm. It can also be observed that the absorbance is

Table 4 PAR (lmol m-2 s-1) calculation using cornet’s model

Depth (m) 3.82 9 1011 cells/m3 5.01 9 1011 cells/m3 6.91 9 1011 cells/m3

11:15 a.m. 11:30 a.m. 11:45 a.m. 11:15 a.m. 11:30 a.m. 11:45 a.m. 11:15 a.m. 11:30 a.m. 11:45 a.m.

0 1145 2040 2578 1145 2040 2578 1145 2040 2578

0.11 681 1213 1532 573 1021 1291 492 877 1109

0.2 477 850 1074 362 645 815 283 505 638

0.28 357 637 805 249 444 561 180 321 406

0.33 301 536 678 200 356 449 138 246 310

Bioprocess Biosyst Eng

123

minimum and almost constant in the wavelength range

from 540 to 640 nm. Similar observations were reported by

[19].

They found that green algae had tendency to absorb

mainly blue and red colour light, whereas the absorption of

green colour (around 550 nm) was minimum. In this range

extinction of light is primarily due to scattering by algal

cells.

In the absorbance measurements of S. arcuatus, the ra-

diation properties of C. littorale [4] were used and shown

in Table 2, the absorption coefficients and scattering co-

efficients of Scenedesmus arcuatus were found between

400 and 700 nm at an interval of 50 nm and these coeffi-

cients were averaged between 400 and 500 nm, 500 and

650 nm and 650 and 700 nm. Table 2 shows the average

value of species over a specified wavelength range. It can

be observed that, for wavelength range of 500–650 nm,

absorption coefficient is the minimum and scattering co-

efficient is the maximum irrespective of concentrations.

Table 3 shows the light intensity measured at different

depths corresponding to a cell density of 3.82 9 1011 cells/

m3 and these experimental values were used for validation

of CFD model and Cornet model. It can be observed from

the Figure that, there is a rapid drop in intensity within the

first few centimetres of depth, indicating the light

attenuation is exponential. CFD simulations were also

performed corresponding to concentration of 5.01 9 1011

and 6.91 9 1011 cells/m3 and CFD results were also

validated with cornet model (Fig. 3b, c). It can be observed

from figures that CFD results were much closer to ex-

perimental results than the results obtained from cornets

model.

It can be observed from Fig. 3a, for 3.82 9 1011 cells/

m3 concentration, sufficient light intensity is available up to

a depth of 30 cm (200–250 lmol m-2 s-1).

From Fig. 3b, c, when cell concentration was increased

to 5.01 9 1011 cells/m3, the required PAR is available up

to 33 cm depth for first solar radiation condition (11:15

a.m.) and on further increasing the concentration to

6.91 9 1011 cells/m3, the required PAR is available up to a

depth of 26–28 cm for first solar radiation condition (11:15

a.m.) therefore further increase of concentration will de-

crease the depth of light intensity distribution inside the

tank [19].

Figure 5 shows the light intensity profile inside the tank

generated from CFD simulation, it is clear from the figure

that up to 30 cm of depth 200 lmol m-2 s-1 intensity of

light is available, which is sufficient for micro algae cul-

tivation corresponding to the concentration of 3.82 9

1011 cells/m3.

Fig. 2 Visible light spectrum

Table 5 PAR (lmol m-2 s-1) Calculation using CFD

Depth (m) 3.82 9 1011 cells/m3 5.01 9 1011 cells/m3 6.91 9 1011 cells/m3

11:15 a.m. 11:30 a.m. 11:45 a.m. 11:15 a.m. 11:30 a.m. 11:45 a.m. 11:15 a.m. 11:30 a.m. 11:45 a.m.

0 1145 2040 2578 1145 2040 2578 1145 2040 2578

0.11 615 1099 1394 560 980 1208 522 945 1018

0.2 417 740 938 347 680 886 298 634 743

0.28 311 552 701 280 502 610 222 438 492

0.33 266 494 599 223 395 483 170 326 384

Bioprocess Biosyst Eng

123

Band wise light profile

Figure 6a, b represents the band wise light intensity

available at different depths of tank corresponding to the

concentration of 5.01 9 1011 and 6.91 9 1011 cells/m3,

respectively. In each figure radiation intensities of 1145,

2040, and 2578 lmol m-2s-1 are considered as solar light

source. It can be observed from the figures that irrespective

of the intensity of light source and the concentration of

micro algae the Band-0 (400–500 nm) is at minimum level

or is at the lowest level compared to the Band-1 and Band-

2, indicating that the light absorption of this species is

maximum in the wavelength band of 400–500 nm. The

position of Band-2 is above the Band-0 and below Band-1

for all the cases indicating that the light absorption of this

species is more in Band-2 compared to Band-1, the same

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

400

800

1200

1600

2000

2400

2800In

cide

nt ra

diat

ion

(pho

tons

)

Depth (m)

a b

c

3.82×1011 cells/m3 Experiment Cornet's model CFD simulation

11:15 am 11:15 am 11:15 am 11:30 am 11:30 am 11:30 am 11:45 am 11:45 am 11:45 am

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

400

800

1200

1600

2000

2400

Inci

dent

radi

atio

n (p

hoto

n)

Position (m)

5.01×1011 cells/m3 Cornet model CFD

11:15 am 11:15 am 11:30 am 11:30 am 11:45 am 11:45 am

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

400

800

1200

1600

2000

2400

Inci

dent

radi

atio

n (m

)

Position (m)

6.91×1011 cells/m3 Cornet model CFD

11:15 am 11:15 am 11:30 am 11:30 am 11:45 am 11:45 am

Fig. 3 a–c Comparison of Exp., cornet model and CFD results (3.82 9 1011 cells/m3)

400 450 500 550 600 650 7000.15

0.20

0.25

0.30

0.35

0.40

0.45

Abs

orba

nce

wavelength

N=3.82×10^11 cells/m^3 N=5.01×10^11 cells/m^3 N=6.91×10^11 cells/m^3

Fig. 4 Absorption spectra for three concentrations

Bioprocess Biosyst Eng

123

results have been obtained as a second peek in experiment

as shown in Fig. 4. Hence, the CFD results are validated

through experimental data. All the simulation results

indicate that the maximum light attenuation happens in

within 10 cm of the depth of the reactor irrespective of the

intensity of available light source, and concentration of the

species.

Light profile for different dimensions of tank

To analyse the effect of large volumes on light profile, the

following dimensions of tank were considered

(length 9 breadth 9 depth) m3

Geom 1 Geom 2 Geom 3

L 9 B 9 D 1 9 1 9 0.5 2 9 2 9 0.5 1 9 1 9 1

It could be referred from the profile that irrespective of

the depth or the other dimensions the light intensity profiles

remain the same, hence intensity profile is the function of

concentration of the species, source intensity and the

wavelength band (Figs. 6a, b, 7).

Wall effects

Wall reflection is stated as one of the major factors to

enhance uniform light intensity profile inside tank. CFD

simulations were performed to find out the effect of walls

Fig. 5 Light intensity for 3.82 9 1011 cells/m3 at 1144 lE m-2 s-1

0 m 0.11 m 0.20 m 0.28 m 0.33 m0

400

800

1200

1600

2000

2400

2800

Rad

iatio

n (p

hoto

ns)

Depth (m)

a b5.01×1011 cells/m3

band-0 at 11:15 am band-1 at 11:15 am band-2 at 11:15 am band-0 at 11:30 am band-1 at 11:30 am band-2 at 11:30 am band-0 at 11:45 am band-1 at 11:45 am band-2 at 11:45 am

0 m 0.11 m 0.20 m 0.28 m 0.33 m

0

400

800

1200

1600

2000

2400

2800

Rad

iatio

n (p

hoto

ns)

Depth (m)

6.91×1011 cells/m3 band-0 at 11:15 am band-1 at 11:15 am band-2 at 11:15 am band-0 at 11:30 am band-1 at 11:30 am band-2 at 11:30 am band-0 at 11:45 am band-1 at 11:45 am band-2 at 11:45 am

Fig. 6 a, b Band wise profile at different solar Intensities and different algal concentration

0.0 0.1 0.2 0.3 0.4 0.5

200

400

600

800

1000

1200

1400

Inci

dent

radi

atio

n (p

hoto

n)

Position

Geometry 1 Geometry 2 Geometry 3

Fig. 7 Light profile corresponding for three different dimensions of

the tank

Bioprocess Biosyst Eng

123

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

200

a b

c d

e f

400

600

800

1000

1200

1400

1600

inci

dent

radi

atio

n (p

hoto

ns)

position (m)

maximum extinction coefficient 10.62-1

ref=0.1 ref=0.7 ref=0.3 ref=0.9 ref=0.5 ref=1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0

200

400

600

800

1000

inci

dent

radi

atio

n (p

hoto

ns)

position (m)

maximum extinction coefficient 44.86-1

ref=0.1 ref=0.5 ref=0.9 ref=1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

200

400

600

800

1000

1200

1400

1600

inci

dent

radi

atio

n (p

hoto

ns)

position (m)

maximum extinctioncoefficient 10.62-1

Fd=0 Fd=0.7 Fd=0.3 Fd=0.9 Fd=0.5 Fd=1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

200

400

600

800

1000

inci

dent

radi

atio

n (p

hoto

ns)

position (m)

maximum extinction coefficient 44.86-1

Fd=0.1 Fd=0.5 Fd=0.9 Fd=1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

400

800

1200

1600

2000

2400

inci

dent

radi

atio

n (p

hoto

ns)

Position (m)

maximum extinction coefficient 10.62-1

top Fd=0 top Fd=0.1 top Fd=0.3 top Fd=0.5 top Fd=0.7 top Fd=0.9 top Fd=1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

inci

dent

radi

atio

n (p

hoto

ns)

position (m)

maximum Extinction coefficient 44.86-1

top Fd=0 top Fd=0.1 top Fd=0.5 top Fd=0.9 top Fd=1

Fig. 8 a, b Effect of wall reflectivity. c, d Effect of diffuse fraction of side and bottom walls on light distribution. e, f Effect of diffuse fraction of

top wall on light distribution. g, h Effect of scattering phase function on light intensity profile

Bioprocess Biosyst Eng

123

on the light intensity profile inside the tank. Input pa-

rameters such as reflectivity, diffuse fraction and scattering

phase function were considered, and for the simulation, the

values are varied from zero to one.

Effect of reflectivity of side and bottom walls on light

profile

In order to determine the effect of reflectivity of side and

bottom walls (opaque) on light distribution, CFD simula-

tions were carried out for range of wall reflectivity ranging

from zero to one. S. arcuatus suspensions having extinction

coefficient 10.62 m-1 (optically thin medium) and

44.86 m-1 (optically thick medium) are considered. The

extinction coefficients are calculated using Eq. 3 and ex-

trapolating the data given in Table 2. The cell concentra-

tions corresponding to optically thin and optically thick

medium are 4.2 9 1011 and 18.75 9 1011 cells/m3 re-

spectively. It could be inferred from Fig. 8a, b that the

bottom and side wall reflectivity has an impact on light for

optically thin medium and for optically thick medium the

effect of reflectivity is much less.

Effect of diffuse fraction of side and bottom walls on light

profile

Figure 8c, d shows the XY plots of light intensity profile

from top to bottom along centre line for various diffuse

fractions of side and bottom walls for S. arcuatus suspen-

sions using optically thin and optically thick media, re-

spectively. It means that diffuse fraction equal to zero

represents opaque walls and diffuse fraction 1 represents

transparent walls. From the figure, it could be inferred that

the diffuse fraction has no impact on light profile for

optically thick medium, which indicates that light is com-

pletely absorbed by the cells and is not available at the

walls for the diffusion, it could also be seen from the graph

at a depth corresponding to 0.15 m the light availability is

450 and 180 lmol m-2s-1 (fd = 1).

Thus, for optically thin medium, specularly reflecting

opaque walls should be used in order to have better light

intensity distribution.

Effect of diffuse fraction of top wall on light profile

For optically thin medium a material having diffuse frac-

tion 0.7 is acceptable and for optically thick medium ma-

terial having 0.5 is acceptable and material with lower fd

helps to control the high light intensities available and

admitting only the required light into the tank, which will

be helpful to reduce the photo inhibition effect.

Effect of scattering phase function on light distribution

To investigate the effect of scattering phase function on

light intensity distribution, CFD simulations were per-

formed for Delta-Eddington phase functions with various

forward scattering factors and with zero scattering coeffi-

cient. These simulations are performed for S. arcuatus

suspensions in open tank. XY plot of these simulations is

shown in Fig. 8g, h.

It can be observed that, for Delta-Eddington phase

function, with the increase in the value of forward scat-

tering factor, radiation inside the tank tends to be more

homogeneous and for a forward scattering factor of 1, in-

tensity is equal to the light intensity with zero scattering,

i.e. intensity behaves as if there is no scattering at all.

g h

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

200

400

600

800

1000

1200

inci

dent

radi

atio

n (p

hoto

ns)

position (m)

scattering f=0 f=0.7 f=0.8 f=0.9 f=1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

200

400

600

800

1000

inci

dent

radi

atio

n (p

hoto

ns)

position (m)

forward scattering factor=1 scattering=0

Fig. 8 continued

Bioprocess Biosyst Eng

123

Conclusion

Light profile inside the tank is effected by the type of

species, its concentration and source light intensity. CFD is

a powerful tool to investigate the effect of such parameters

on light profile inside the tank and it is found that the

required amount of light for photosynthesis is available up

to a depth of 30–35 cm inside the tank corresponding to the

conditions studied. The absorbance of Scenedesmus sp. is

maximum in the wavelength range of 400–500 nm. For

optically less dense medium, reflectivity and diffusivity of

opaque wall, greatly affect the light intensity distribution

and for such cases specularly reflecting wall should be

used. And for optically thick media, effect of wall reflec-

tivity and wall diffusivity is negligible. Diffusivity of semi-

transparent walls should be selected based on the local

available light intensities to allow only required light in-

tensity inside i.e. higher the available light intensity, lower

should be the transmissivity of the transparent wall to avoid

photo-inhibition effect. Otherwise, use of innovative mix-

ing mechanism could also be helpful to avoid such effects.

Acknowledgments We greatly acknowledge Department of Sci-

ence and Technology (DST), Government of India, New Delhi for

funding this project (DST/IS-STAC/CO2-SR-12/07).

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