<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0123-2126</journal-id>
<journal-title><![CDATA[Ingeniería y Universidad]]></journal-title>
<abbrev-journal-title><![CDATA[Ing. Univ.]]></abbrev-journal-title>
<issn>0123-2126</issn>
<publisher>
<publisher-name><![CDATA[Pontificia Universidad Javeriana]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0123-21262012000200002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Evaluation of Microalgal Mortality in a Centrifugal Pump of a Tubular Photobioreactor]]></article-title>
<article-title xml:lang="es"><![CDATA[Evaluación de la mortalidad microalgal en una bomba centrífuga de un fotobiorreactor tubular]]></article-title>
<article-title xml:lang="pt"><![CDATA[Avaliações de mortalidade de microalgas em uma bomba centrífuga de um fotobiorreator tubular]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ramírez-Duque]]></surname>
<given-names><![CDATA[José Luis]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Marín-Quintero]]></surname>
<given-names><![CDATA[David Alberto]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García-Pulido]]></surname>
<given-names><![CDATA[Cristian Hernán]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Autónoma de Occidente  ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Autónoma de Occidente  ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A03">
<institution><![CDATA[,Universidad Autónoma de Occidente  ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2012</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2012</year>
</pub-date>
<volume>16</volume>
<numero>2</numero>
<fpage>333</fpage>
<lpage>347</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0123-21262012000200002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0123-21262012000200002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0123-21262012000200002&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Las bombas centrífugas son de gran utilidad industrial y dentro de sus aplicaciones se puede encontrar el bombeo de fluidos que contienen microorganismos vivos en suspensión. Sin embargo, este tipo de bombeo puede afectar el desarrollo de los microorganismos, ya que genera altos esfuerzos cortantes, que no son soportables por sus paredes celulares, lo cual se traduce en una elevada mortalidad celular. En este artículo se analizó computacionalmente una bomba centrífuga utilizada para el bombeo de cultivos microalgales en fotobiorreactores tubulares. Para ello, se modeló la geometría tanto de la voluta como del impeler en CAD, para posteriormente efectuar una simulación en CFX según las condiciones de operación de un fotobiorreactor. La evaluación de la distribución de velocidad y de los esfuerzos cortantes dentro de la bomba llevó a concluir que es inviable la utilización de estos mecanismos de bombeo, dada la alta mortalidad que se puede presentar para ciertas especies microalgales, como es el caso de la Chaetoceros muel-leri, en la cual su viabilidad se puede reducir hasta niveles del 52%.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Industrially, the centrifugal pumps are very useful and within their applications, it can be found pumping fluids containing living microorganisms in suspension. However, this type of pumping can affect the growth of microorganisms because it generates high shear stresses, which are not supported by their cell walls, resulting in high cell mortality. In this article, we analyzed computationally a centrifugal pump used for pumping microalgal cultures in tubular photo-bioreactors. To do this, we modeled in CAD both the impeller and the volute; and then we conducted a simulation in CFX under the operation conditions of a photobioreactor. The evaluation of the velocity distribution and shear stresses inside the pump, led to conclude that it is impractical to use these pumping mechanisms, due to the high mortality rate that is expected for some microalgae species, such as the Chaetoceros muelleri; for which its viability can be reduced to levels of 52%".]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[As bombas centrífugas são de grande utilidade industrial e nas suas aplicações pode se encontrar o bombeamento de fluidos que contem micro-organismos vivos em suspensão. Contudo, este tipo de bombeio pode afetar o desenvolvimento de microrganismos, pois gera fortes cisalhamentos, nem sempre suportados pelas paredes celulares, o que resulta em uma elevada mortalidade das células. Este artigo analisou computacionalmente uma bomba centrífuga usada para bombeamento de cultivos de microalgas em fotobiorreatores tubulares. Para isso, modelou a geometria tanto da voluta quanto do impulsor em CAD, para posteriormente proceder a uma simulação em CFX, em acordo com as condições de funcionamento de um foto-biorreator. A avaliação da distribuição da velocidade e dos cisalhamentos no interior da bomba levou a concluir que a utilização de tais mecanismos de bombeamento é inviável, dada a elevada taxa de mortalidade que pode estar ocorrendo a certas espécies de microalgas, como o caso da Chaetoceros muelleri, na que a viabilidade pode se reduzir até níveis de 52%.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Esfuerzo cortante]]></kwd>
<kwd lng="es"><![CDATA[fotobiorreactor]]></kwd>
<kwd lng="es"><![CDATA[bio-masa microalgal]]></kwd>
<kwd lng="es"><![CDATA[dinámica de fluidos computacional]]></kwd>
<kwd lng="en"><![CDATA[Shear stress]]></kwd>
<kwd lng="en"><![CDATA[Photobioreactor]]></kwd>
<kwd lng="en"><![CDATA[Microalgae biomass]]></kwd>
<kwd lng="en"><![CDATA[Computational fluid dynamics (CFD)]]></kwd>
<kwd lng="pt"><![CDATA[Cisalhamento]]></kwd>
<kwd lng="pt"><![CDATA[fotobiorreator]]></kwd>
<kwd lng="pt"><![CDATA[biomassa de microalgas]]></kwd>
<kwd lng="pt"><![CDATA[dinâmica de fluidos computacional]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font size="2" face="verdana">     <p align="center"><font size="4"><b>Evaluation of Microalgal Mortality in a Centrifugal Pump of a Tubular Photobioreactor<sup>1</sup></b></font></p>     <p align="center"><font size="3"><b>Evaluaci&oacute;n de la mortalidad microalgal en una bomba centr&iacute;fuga de un fotobiorreactor tubular<sup>2</sup></b></font></p>     <p align="center"><font size="3"><b>Avalia&ccedil;&otilde;es de mortalidade de microalgas em uma bomba centr&iacute;fuga de um fotobiorreator tubular<sup>3</sup></b></font></p>     <p align="center"><i>Jos&eacute; Luis Ram&iacute;rez-Duque<sup>4</sup>    <br> David Alberto Mar&iacute;n-Quintero<sup>5</sup>    <br> Cristian Hern&aacute;n Garc&iacute;a-Pulido<sup>6</sup></i></p>     <p><sup>1</sup>This article is derived from the research project Design of a Photobioreactor for Biomass Production from Algae as a Cleaner Energy Source in the Department of Valle del Cauca, developed by the research group GRUBIOC of Universidad Aut&oacute;noma de Occidente, Cali, Colombia.    <br> <sup>2</sup>Fecha de recepci&oacute;n: 27 de octubre de 2011. Fecha de aceptaci&oacute;n: 28 de abril de 2012. Este art&iacute;culo se deriva del proyecto de investigaci&oacute;n <i>Dise&ntilde;o de un prototipo de fotobiorreactor para la producci&oacute;n de biomasa a partir de algas como fuente de energ&iacute;a m&aacute;s limpia, en el departamento del Valle del Cauca, </i>desarrollado por el grupo de investigaci&oacute;n GRUBIOC, de la Universidad Aut&oacute;noma de Occidente. Cali, Colombia.    <br> <sup>3</sup>Data de recebimento: 27 de outubro de 2012. Data de aceite: 28 de abril de 2012. Este artigo derivou-se do projeto de pesquisa <i>Desenho de prototipo de fotobiorreator para a produ&iexcl;do de biomassa a partir de algas como fonte de energia mais limpa,no departamento do Valle del Cauca, </i>desenvolvido pelo grupo de pesquisa GRUBIOC, da Universidade Aut&oacute;noma de Ocidente. Cali, Colombia.    ]]></body>
<body><![CDATA[<br> <sup>4</sup>Ingeniero mec&aacute;nico, Universidad Tecnol&oacute;gica de Pereira, Pereira, Colombia. Mag&iacute;ster en Ingenier&iacute;a Mec&aacute;nica, Universidad del Valle, Cali, Colombia. Estudiante del Doctorado en Ingenier&iacute;a Mec&aacute;nica, Universidad de S&atilde;o Paulo, S&atilde;o Paulo, Brasil. Profesor de tiempo completo, Universidad Aut&oacute;noma de Occidente. Cali, Colombia. Correo electr&oacute;nico: <a href="mailto:ioslurad@hotmail.com">i</a><a target="_blank" href="mailto:%c2%a1oslurad@hotmail.com">oslurad@hotmail.com</a>.    <br> <sup>5</sup>Ingeniero mec&aacute;nico, Universidad Aut&oacute;noma de Occidente. Cali, Colombia. Independiente., Universidad Aut&oacute;noma de Occidente. Cali, Colombia. Correo electr&oacute;nico: <a target="_blank" href="mailto:david_alberto.marin@uao.edu.co">david_alberto.marin@uao.edu.co</a>.    <br> <sup>6</sup>Ingeniero mec&aacute;nico, Universidad Aut&oacute;noma de Occidente. Independiente. Universidad Aut&oacute;noma de Occidente. Cali, Colombia. Correo electr&oacute;nico: <a target="_blank" href="mailto:cristian_her.garcia@uao.edu.co">cristian_her.garcia@uao.edu.co</a>.</p>     <p>Submitted on: October 27,2011. Accepted on: April 28,2012.</p> <hr>     <p><font size="3"><b>Resumen</b></font></p>     <p>Las bombas centr&iacute;fugas son de gran utilidad industrial y dentro de sus aplicaciones se puede encontrar el bombeo de fluidos que contienen microorganismos vivos en suspensi&oacute;n. Sin embargo, este tipo de bombeo puede afectar el desarrollo de los microorganismos, ya que genera altos esfuerzos cortantes, que no son soportables por sus paredes celulares, lo cual se traduce en una elevada mortalidad celular. En este art&iacute;culo se analiz&oacute; computacionalmente una bomba centr&iacute;fuga utilizada para el bombeo de cultivos microalgales en fotobiorreactores tubulares. Para ello, se model&oacute; la geometr&iacute;a tanto de la voluta como del <i>impeler </i>en CAD, para posteriormente efectuar una simulaci&oacute;n en CFX seg&uacute;n las condiciones de operaci&oacute;n de un fotobiorreactor. La evaluaci&oacute;n de la distribuci&oacute;n de velocidad y de los esfuerzos cortantes dentro de la bomba llev&oacute; a concluir que es inviable la utilizaci&oacute;n de estos mecanismos de bombeo, dada la alta mortalidad que se puede presentar para ciertas especies microalgales, como es el caso de la <i>Chaetoceros muel-leri, </i>en la cual su viabilidad se puede reducir hasta niveles del 52%.</p>     <p><b>Palabras clave:</b> Esfuerzo cortante, fotobiorreactor, bio-masa microalgal, din&aacute;mica de fluidos computacional.</p> <hr>     <p><font size="3"><b>Abstract</b></font></p>     <p>Industrially, the centrifugal pumps are very useful and within their applications, it can be found pumping fluids containing living microorganisms in suspension. However, this type of pumping can affect the growth of microorganisms because it generates high shear stresses, which are not supported by their cell walls, resulting in high cell mortality. In this article, we analyzed computationally a centrifugal pump used for pumping microalgal cultures in tubular photo-bioreactors. To do this, we modeled in CAD both the impeller and the volute; and then we conducted a simulation in CFX under the operation conditions of a photobioreactor. The evaluation of the velocity distribution and shear stresses inside the pump, led to conclude that it is impractical to use these pumping mechanisms, due to the high mortality rate that is expected for some microalgae species, such as the Chaetoceros muelleri; for which its viability can be reduced to levels of 52%&quot;.</p>     <p><b>Key words: </b>Shear stress, Photobioreactor, Microalgae biomass, Computational fluid dynamics (CFD).</p> <hr>     ]]></body>
<body><![CDATA[<p><font size="3"><b>Resumo</b></font></p>     <p>As bombas centr&iacute;fugas s&atilde;o de grande utilidade industrial e nas suas aplica&ccedil;&otilde;es pode se encontrar o bombeamento de fluidos que contem micro-organismos vivos em suspens&atilde;o. Contudo, este tipo de bombeio pode afetar o desenvolvimento de microrganismos, pois gera fortes cisalhamentos, nem sempre suportados pelas paredes celulares, o que resulta em uma elevada mortalidade das c&eacute;lulas. Este artigo analisou computacionalmente uma bomba centr&iacute;fuga usada para bombeamento de cultivos de microalgas em fotobiorreatores tubulares. Para isso, modelou a geometria tanto da voluta quanto do impulsor em CAD, para posteriormente proceder a uma simula&ccedil;&atilde;o em CFX, em acordo com as condi&ccedil;&otilde;es de funcionamento de um foto-biorreator. A avalia&ccedil;&atilde;o da distribui&ccedil;&atilde;o da velocidade e dos cisalhamentos no interior da bomba levou a concluir que a utiliza&ccedil;&atilde;o de tais mecanismos de bombeamento &eacute; invi&aacute;vel, dada a elevada taxa de mortalidade que pode estar ocorrendo a certas esp&eacute;cies de microalgas, como o caso da <i>Chaetoceros muelleri, </i>na que a viabilidade pode se reduzir at&eacute; n&iacute;veis de 52%.</p>     <p><b>Palavras-chave: </b>Cisalhamento, fotobiorreator, biomassa de microalgas, din&acirc;mica de fluidos computacional.</p> <hr>     <p><font size="3"><b>Introduction</b></font></p>     <p>Because of the high cost of the fossil fuels and the increasing concerns about their negative environmental impact, especially due to their influence on the climatic change; there is an increased interest in the use of designated biofuels, such as biodiesel and bioethanol (Rosello <i>et al., </i>2007). The biodiesel is a fuel that can be obtained from organic, vegetable or animal oils through a process designated transesterfication (Demirbas, 2007). To obtain vegetable oils we can find the green plants and the seaweeds cultivated in open or closed systems (pho-tobioreactors). To develop of sustainable way the crop and massive production of microalgae, it is essential to know and define some appearances such as the type of microorganisms that are going to be used, their conditions and requirements for an optimum growth, and the resistance to different environmental variables. The closed reactors or photobioreactors are the systems that provide the highest guarantees for the process because of the ease of control of these variables, which help achieving the best conditions for the correct growth and reproduction of microalgae.</p>     <p>The development of the technology to produce biofuel by microalgae cultures is important in Colombia because it can lead to the substitution of petroleum fuels and their derivatives, which are becoming scarcer. In addition, the process to obtain biodiesel through seaweed cultivation favores the decrease of global warming; through the sequestration of carbon dioxide (CO<sub>2</sub>) and release of oxygen (O<sub>2</sub>).</p>     <p>The first signs of algal cultures dates back to the time of the Second World War. Germans grew algae in open ponds mainly as food supplements. From the decade of the fifties, scientific studies were conducted with the purpose of obtaining, from microalgae, a new source of energy capable of replacing the use of oil and fossil hydrocarbons, which in turn could protect the environment (Ramirez and Ramos, 2011). In the late 1970's, the production of algae began in Eastern Europe, Israel and Japan; algae were grown in open tanks as healthy food. It is a fact that the purpose of algal growth depends on the specific needs of a population. U.S. microalgae pond systems were developed for the treatment of water; the biomass collected was used as an energy source (Burlew, JS, 1953). Over time, biomass, besides being used for bioenergetic purposes, has been used in pharmaceuticals, nutraceuticals, agrochemicals, food, etc. (Camacho <i>et al., </i>1999).</p>     <p>Due to the fact that the closed systems surpass the open systems, the design of the photobioreactors is the point of focus as it is the main point of control of the culture conditions in closed systems. The most effective systems use solar energy for photosynthesis necessary for mass production of microalgae. Among the most used photobioreactors are the tubular, columns of bubbles, and the signpost or plate.</p>     <p>The tubular photobioreactors are closed systems developed for the production of microalgae that prevent external contaminants from accessing the culture, since it remains isolated and prevents their contact with the outside air. There are several methods used to achieve the movement and circulation of the culture through it, including mechanical agitator and air injectors. (Camacho <i>et al., </i>1999). Commonly, these photobioreactors have a unit called airlift that, by air injection, generates the movement while performing the degasification in the collector, removing dissolved oxygen that results from the photosynthesis of the algae (Pruvost, Cornet, and Legrand, 2008). The airlift control also determines the magnitude of shear stress, which is one of the most important parameters in microalgae biomass production. With the airlift system, high magnitudes of shear stress can be prevented, which allows the protection of the cells of the algae. (Michels <i>et al., </i>2010).</p>     <p>In this study a centrifugal pump was designed and simulated through CAD and CAE packages. The clime conditions of Valle del Cauca (Colombia) were considered in the definition of initial parameters in the design of a pumping systems for a photobioreactor with a capacity of 250L.</p>     ]]></body>
<body><![CDATA[<p><font size="3"><b>1. Circulation of the culture medium and shear stress</b></font></p>     <p>The method for circulating the liquid through the photobioreactor is an important consideration in the design of these systems (Ramirez and Ramos, 2011), the rotary pallets in the open reactors, the positive displacement pumps, rotary or of screw and in general any method has a big disadvantage and that is the one to produce large shear stresses to cells, damaging them.</p>     <p>The hydrodynamic forces generated by these systems could cause shear stresses affecting algae (Mazzuca <i>et al., </i>2006; S&aacute;nchez <i>et al., </i>2000), reducing its rate of growth or causing cell death. This shear stress is directly related to the viscosity of the culture medium and the rate of deformation (Mott, 2005).</p>     <p>The tolerance of these microorganisms to shear stresses depends specifically on the microalgae-like species. In particular, the species Chaetoceros muelleri can tolerate stresses of 1.8Pa with no modification in their growth process (Michels <i>et al., </i>2010). The growth of the microalgae Spirulina platensis is affected when the microalgae is subjected to shear stresses over 0.3Pa (Mitsuhashi <i>et al., </i>1995) although there is no significant cell damage. While for the highly sensitive microalgae-like species Protoceratium reticulatum, there was a threshold of damage to an average shear stress of about 0.16 MPa (Garcia <i>et al., </i>2007); for the species Phaedactylum tricornutum, a value of shear stresses of 7Pa led it to the highest growth rate caused by a balance between the mass transfer limitations and shear damage (Contreras <i>et al., </i>1998).</p>     <p>In horizontally arranged tubular photobioreactors is common to use the hydro-pneumatic method based on the airlift principle (Richmond <i>et al., </i>1993; S&aacute;nchez <i>et al., </i>2000). The speed of culture medium in the tubes must be sufficient to ensure a turbulent flow that prevents growth in the tube wall or sedimentation of the cells; and to allow a favorable lighting regime system to establish an intense photosynthesis (Gudin and Chaumont, 1991; Camacho <i>et al., </i>1999; Molina <i>et al., </i>1999). A low flow of fluid (&lt; 15cm/s) almost always produces growth in the wall and a possible growth inhibition by high concentrations of dissolved O<sub>2</sub>. A liquid velocity in pipes of 30-50 cm/s is appropriate in most cases.</p>     <p><font size="3"><b>2. Methodology</b></font></p>     <p><b><i>2.1 Modeling of Parts</i></b></p>     <p>In order to explore the operation of the centrifugal pump it was necessary to model it using a CAD system; for this project it was used Solid Edge V20 where 3 basic parts were made: the volute, the impeller and a cylindrical region corresponding to the input of the working fluid (water) (<a href="#f1">Figure 1</a>).</p>     <center><a name="f1"><img src="img/revistas/inun/v16n2/v16n2a02f1.jpg"></a></center>     <p>For the modeling of parts, the size and actual operating conditions of the centrifugal pump were taken into account to be tested.</p>     ]]></body>
<body><![CDATA[<p>It was important to take into account dimensions like the entrance and exit diametersof the impeller, the impeller thickness and the thickness of the blade, the form of the volute and the outlet diameter of it. Likewise some characteristics were retained like the number of blades and their measures.  <a href="#t1">Table 1</a> indicates the operating characteristics of the pump.</p>     <center><a name="t1"><img src="img/revistas/inun/v16n2/v16n2a02t1.jpg"></a></center>     <p>Where:</p> <ul>     <li>&beta;<sub>1</sub> </b>and &alpha;<sub>1</sub>correspond to angles of the triangle of input speeds and provide information on the tilt angle of the blade (Mataix, 1986).</li>     <li>U<sub>2</sub> speed corresponds to the absolute velocity of the vane at the inlet and the angle &beta;<sub>2</sub> is the output blade angle (Mataix, 1986).</li>     </ul>     <p><b><i>2.2 Meshed and Boundary Conditions</i></b></p>     <p>In order to simulate and analyze this pump, it was applied a meshing to the final assembly of the pump; for this, the Mesh application of CFD in Ansys was used. The mesh type selected for this application was an independent tetrahedral due to the snail shape and the impeller blades. The mesh was made with a size of element of 1E<sup>-3</sup> m. The result of the meshing can be seen in  <a href="#f2">Figure 2</a>.</p>     <center><a name="f2"><img src="img/revistas/inun/v16n2/v16n2a02f2.jpg"></a></center>     <p>To apply the boundary conditions in the simulation program, three fluid domains were created.</p>     ]]></body>
<body><![CDATA[<p>The impeller which formed the rotary fluid domain with an angular speed of 1750 RPM, had the wall boundary conditions for the blades and the upper and lower sides of it.</p>     <p>The snail or volute that formed the static fluid domain; in this domain was the wall condition to the outer edges of the snail, and the outlet exit condition with a normal speed of 0.48 ms/1.</p>     <p>The inlet region which conformed a fluid domain; in this domain was the wall condition at the bottom of this region and the inlet condition that is responsible of recognizing a mass flow of 1.1 kg/s<sup>-1</sup>.</p>     <p>Apart from the process described previously, some conditions of interface were applied in areas with which fluids interact. These interfaces were applied where the domains of the impeller and the inlet region are connected, as well as where the volute and the impeller are connected.</p>     <p><a href="#f3">Figure 3</a> shows the pump with the boundary conditions of inlet and outlet in the inlet and outlet regions of the volute respectively.</p>     <center><a name="f3"><img src="img/revistas/inun/v16n2/v16n2a02f3.jpg"></a></center>     <p><font size="3"><b>3. Results and computational analysis</b></font></p>     <p>Once the boundary conditions were implemente, we proceeded to perform the simulation using the SST model (shear stress transport). Subsequently, the analysis of the simulation results were conducted.</p>     <p>In <a href="#f4">Figure 4</a> we can see the results of the speed values in the volute wall. It can be concluded that it achieves a maximum value of 12 m/s<sup>-1</sup> through the entire path except in the exit where the magnitude decreases due to border conditions where the speed value was 0.48 m/s<sup>-1</sup>. The tool used to determine the value of the velocity within the volute is Streamlines, which give us an idea of the water path into the shell.</p>     <center><a name="f4"><img src="img/revistas/inun/v16n2/v16n2a02f4.jpg"></a></center>     ]]></body>
<body><![CDATA[<p><a href="#f5">Figure 5</a> shows the velocity of the fluid within the impeller; this domain corresponds to the rotary fluid. This figure was obtained using velocity values corresponding to a plane passing through the middle of the impeller; one can see the maximum speed value of 8 m/s-1, that are located in bordering areas with the interface. Between the blades one can see speeds of order 3.4 m/s<sup>-1</sup>; it is also noticeable how the fluid that is close to the front face of the blades has minimum speeds, while the fluid in the rear face reaches higher speeds. In this figure it is possible to determine why in this type of pump are such high shear stresses, as there are high variations in the fluid velocity, which is directly related to the velocity gradients occurring in the pump.</p>     <center><a name="f5"><img src="img/revistas/inun/v16n2/v16n2a02f5.jpg"></a></center>     <p>The Streamlines tool was used to determine the velocity in the static fluid domain immersed in the shell. Starting at the interface with the impeller, we observed a variation of speed of 13 m/s<sup>-1</sup> to 2 m/s<sup>-1</sup> (<a href="#f6">Figure 6</a>). In the final section of the volute there were very few Streamlines due to the outlet condition of flow in the volute.</p>     <center><a name="f6"><img src="img/revistas/inun/v16n2/v16n2a02f6.jpg"></a></center>     <p><a href="#f6">Figure 7</a> shows the behavior of the velocity at the outlet of the volute with a view of the YZ plane, which shows how the fluid velocity on the walls takes a value of 0 m/s<sup>-1</sup> while in the middle of the duct, it takes the value assigned to the outlet condition.</p>     <p>In order to find the shear stress between the fluids it was applied the Eq. 1 for Newtonian fluids. According to this equation knowing the kinematic viscosity of water and the velocity gradient in the Y axis (Z was the coordinates axis of our design) it is possible to find the shear stress presented. To find it, a line was inserted in a section of the volute in order to determine the value of the velocity gradient in this specific line (<a href="#f8">Figure 8</a>). It can be seen that this line is located to the sides of the volute walls in order to analyze a point where the shear stress is high.</p>     <center><a name="f8"><img src="img/revistas/inun/v16n2/v16n2a02f8.jpg"></a></center>     <p><img src="img/revistas/inun/v16n2/v16n2a02e1.jpg"></p>     <p>Where:</p>     <p>&tau;, shear stress.    ]]></body>
<body><![CDATA[<br> &mu;, dynamic viscosity of water.    <br> <i>&delta;u/&delta;y, </i>velocity gradient in Y direction.</p>     <p>Data values of the velocity gradient were exported and once this step was done they were tabulated for the shear stress graph, which is presented in  <a href="#f9">Figure 9</a>. The greater observed stress was 0.4 Pa.</p>     <center><a name="f9"><img src="img/revistas/inun/v16n2/v16n2a02f9.jpg"></a></center>     <p>This chart was made taking into account the values of the volute. In  <a href="#f10">Figure 10</a> one can see this line but in the rotary fluid domain (i.e., the impeller), which in this case reached values of 1200 s<sup>-1</sup>. These values are greater than the values found in the volute as this domain is exposed to the blades movement.</p>     <center><a name="f10"><img src="img/revistas/inun/v16n2/v16n2a02f10.jpg"></a></center>     <p>In <a href="#f11">Figure 11</a> it is shown the graph of shear stress vs. shear rate in the rotating fluid domain, which gives a value of maximum stress of 1.2 Pa.</p>     <center><a name="f11"><img src="img/revistas/inun/v16n2/v16n2a02f11.jpg"></a></center>     <p>This value of shear stress supposes a potential risk for the microalgae culture, because as mentioned before, diverse microalgal species, such as the Spirulina platensis, reduce their growth rate at magnitudes above 0.3 Pa. This is concerning if it is considered that there are many other species of greatest sensitivity.</p>     <p>In the study developed by Michels <i>et al., </i>(2010), the answer of the species Chaetoceros muelleri is analyzed as the shear stress is increased. The authors found that values of the shear stress up to 1 Pa, had no effect on the feasibility of the culture. But shear stress levels above 1.3 - 1.8 Pa produce a strong fall of the culture feasibility, which can reach feasibility values between 52 and 66% (<a href="#f12">Figure 12</a>).</p>     ]]></body>
<body><![CDATA[<center><a name="f12"><img src="img/revistas/inun/v16n2/v16n2a02f12.jpg"></a></center>     <p>It is evident, therefore, that these values of shear stress to which microalgae are subjected in a pumping system as the analyzed in this paper, are in the stress limits at which microalgae life begins to be negatively affected.</p>     <p><font size="3"><b>4. Conclusions</b></font></p>     <p>Using pumping mechanisms for microalgal culture such as those described in this article are not recommended due to the high cell mortality that is produced. The computational analysis indicate that the shear stresses that are formed inside the centrifugal pump reach values ranging from 0.4 Pa in the volute of the pump to 1.2 Pa in the impeller. This large shear stress in the last section of the pump are due to the movement of the blades. According to previous studies, at the this values, the feasibility of algae cultures could be reduced to 52% (Michels et al., 2010). 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