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Computational Fluid Dynamics for the Prediction of Temperature Profiles and Hygienic Design in the Food Industry
0960–3085/06/$30.00+0.00 # 2006 Institution of Chemical Engineers Trans IChemE, Part C, June 2006 Food and Bioproducts Processing, 84(C2): 157– 163
www.icheme.org/fbp doi: 10.1205/fbp.04261
COMPUTATIONAL FLUID DYNAMICS FOR THE PREDICTION OF TEMPERATURE PROFILES AND HYGIENIC DESIGN IN THE FOOD INDUSTRY K. ASTERIADOU1 , A. P. M. HASTING2, M. R. BIRD3 and J. MELROSE2 1
Unilever R&D, Vlaardingen, The Netherlands 2 Unilever R&D, Bedford, UK Department of Chemical Engineering, University of Bath, Bath, UK
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any factors need to be considered to ensure that food process lines consistently deliver microbiologically safe products. These factors include process and equipment design, and in particular the interaction between the product and the equipment geometry. Computational fluid dynamics (CFD) has recently been used within the food industry in a number of applications. In this work a commercial finite volume CFD code, FLUENT, has been used to predict those parameters critical to the prediction of velocity and temperature profiles for low viscosity fluids in typical, complex equipment geometries and compared these with experimental data. A comparison of the temperature distribution using predictive modelling and experiments is encouraging, and qualitatively satisfactory and reliable for laminar and turbulent flows. Application of this approach will enable the interaction between food products and equipment geometries to be predicted, and provide an improved method of assessing the implications for the microbiological safety of foods. Keywords: hygienic design; modelling; CFD; turbulence; food processing; food safety.
INTRODUCTION
certain period of running a food production line, cleaning will be necessary, during which production is interrupted. The duration of cleaning depends on the product processed, the residual soil on the equipment and the cleaning conditions selected. Cleaning of food process plant aims to remove all product residues from the product contact surfaces and leave the surfaces in an acceptable condition for subsequent production. This may require disinfection or sterilization of the surfaces as part of the cleaning process. However, even if the above can be carried out successfully, there are sometimes parameters that are difficult to account for. For example, unhygienic features in the pipe geometry, such as up-stands or junctions can lead to significant difficulties. Other examples can be valves, crevices and even surface roughness. These can favour product entrapment and create conditions for microbial growth leading to recontamination. Hence, it is important to have a clear understanding of what happens within such geometries and be able to predict the effect they are going to have in the whole process domain. In this work, a T-piece has been studied as a typical example of a stagnant region. Results from a computational fluid dynamics (CFD) code have been validated against experimental work performed at the University of Bath. Initially, CFD was applied in the aerospace and automotive industries to predict air flow, for instance around planes and cars. However, CFD has been successfully
The objective of the food industry is to deliver high quality, safe and stable products. Consumer demand is high for products with less preservatives, more natural tastes and textures. At the same time, longer shelf life is expected and costs must remain low enough for the products to be purchased. Another factor that puts pressure on the food industry are the regulatory checks on both products and lines. Industry increasingly needs to employ advanced manufacturing techniques, which allow greater process flexibility and reduced energy use and waste generation. Hence the pressure to improve hygiene standards from both consumers and legislation is continually increasing (Hasting, 1999). It is therefore of great importance to maintain microbial safety during the processing of foods, which is directly linked to the possibility of microbial survival and growth in the final product. This is avoided by treating the product at high temperatures for a defined period of time to inactivate the micro-organisms of concern and then ensure the conditions in the rest of the line do not result in unacceptable levels of recontamination. The most common heat treatment processes are sterilization and pasteurization. After a Correspondence to: Dr K. Asteriadou, Unilever R&D, Vlaardingen, The Netherlands. E-Mail: [email protected]
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applied in the food industry in recent years. Scott and Richardson (1997) describe several applications connected to the food industry, including (1) the prediction of air flows around buildings that showed that the method can be used to predict air flow movement inside items of food processing equipment, (2) baking oven performance simulation with CFD in order to quantify heat and mass transfer to and from the product surface, (3) the prediction of air and temperature distribution inside chillers and retail spray cabinets. Air was the first fluid that had its flow modelled for the food industry application improvements. Subsequently, models were developed for both Newtonian and non-Newtonian fluids. Phase change has also been monitored, for equipment such as driers. Mixers and pumps have also been included in CFD modelling. CFD has also been used by Friis and Jensen (2002) to model flows in upstands and valves during CIP flows. They used the finite volume method code STAR-CD. Validation was carried out using the standardized cleaning test proposed by the European Hygienic Engineering and Design Group (EHEDG). Other applications for CFD modelling include extrusion, mixing operations and food safety (Dhanasekharan et al., 2004). Thermal processes such as pasteurization and sterilization are commonly used in the food industry. These are well understood ways of reducing or eliminating microorganisms in food products. Pasteurization aims to kill pathogens that are of high risk for health, whereas sterilization involves higher temperatures in order to eliminate all vegetative spores and bacteria that might survive the pasteurization process. These heating processes may result in fouling of the product contact surfaces, which is the deposition or accumulation of product residues such as proteins, fats, minerals or micro-organisms upon various surfaces (Verran, 2002), causing contamination of the product afterwards. Also some stagnant areas, where the product has a prolonged residence time, may be sources of microbial growth and subsequent recontamination of the product. Cleaning in place (CIP) processes are widely used in the food industry in order to remove fouling deposits. CIP is a means of cleaning equipment without dismantling it by circulating detergent solutions through it. Flow velocities and shear stresses are critical for effective cleaning (Timperley, 1981). CIP cleans and where necessary disinfects or sterilizes the product contact surfaces. It reduces the cleaning shutdown periods of a plant, so it is a considerable way of cost saving. The efficiency of cleaning can be improved by the right combination of temperature, concentration of cleaning solution and flow (van Asselt et al., 2002). The science of CIP is based on applying the required amount of energy to the equipment to ensure that it is cleaned. The energy is provided by the temperature of the solution (thermal energy), the detergent or the solvent (chemical energy) and the application of suitable fluid velocities or pressure (kinetic energy). The fluid velocity has been shown to be a particularly important parameter (Timperley, 1981). The shear stress developed on the walls of the equipment can be critical for the rate of microbial fouling removal (Lelievre et al., 2002) as can the thickness of the boundary layer, both of which are affected by fluid velocity. For this reason, turbulent flows are essential since they have a strong interaction with boundary layers. Laminar flow is often found when processing viscous products
whereas CIP is generally carried out under highly turbulent conditions. In both CIP and process lines there are equipment geometries such as dead-ends, T-junctions, down-stands, up-stands and expansions (Friis and Jensen, 2002) and are not always convenient or practical to remove (e.g., instruments, valves). It was therefore considered important to model different flows in domains that comprise these kinds of geometries in order to see how useful the CFD modelling can be for predicting thermal and velocity variations. For CIP processes turbulent flows are of interest, whilst for thermal processes laminar flows are more often encountered. Cleaning is a very important step, since it follows production and guarantees safe changeovers. This part of the work brings together food processing conditions, CFD modelling tools and risky geometries where flow cannot be solved and predicted analytically. FLUENT was chosen because it applies the finite volume method and the creators consider that it can cope very well with 3D and turbulent flows (FLUENT, 2005). CFD solves the Navier –Stokes equations as well as the energy equation, when this is selected by the user. Growth or inactivation of micro-organisms is dependent on the temperature profile and the residence time of the product (Zwietering and Hasting, 1997) within the system. The temperature and residence time, in their turn, depend on the fluid velocity. For these reasons, it is important to have correct estimations of the velocity and temperature so that the microbial kinetics can be predicted as accurately as possible and hence the implications for food safety.
METHODS AND MATERIALS Experiments The study described in this paper is based on water flow past a T-junction in which the vertical arm is blocked (Figure 1), thus creating a potentially dead space where stagnant product may remain for extended periods of time. Both pipes have a diameter of 0.023 m. Before and after the junction there are horizontal sections of length 1.5 m and 0.5 m, respectively. The length of the dead-leg is 0.2325 m, measured from the centre of the horizontal tube. Such T-junctions are undesirable configurations in a process line but are frequently present and may be difficult to remove due to production pressures. Such a geometry is relatively simple and allows temperature measurements to be taken along its length during experiments. It is therefore
Figure 1. Schematic of the pipework geometry studied.
Trans IChemE, Part C, Food and Bioproducts Processing, 2006, 84(C2): 157– 163
CFD FOR PREDICTION OF TEMPERATURE PROFILES AND HYGIENIC DESIGN valuable to be able to predict the conditions in such an unhygienic piece of equipment and thus be able to make a judgement of the risk that such a particular geometry poses to the product. The horizontal pipe was insulated, so that constant temperatures can be maintained along the length, which is the desired condition in heating processes in order to achieve adequate amount of heat penetrating the product. However, the vertical pipe is not lagged so there are heat losses to the air via natural convection around the T-piece. Hence, the heating of the contents of the vertical pipe is observed at steady state conditions that can represent runs in a process plant, where dead ends might be encountered (such as drainage valves, sensor locations). In the experimental set-up, 6 k-type thermocouples, of diameter 0.5 mm are located along the centre line of the vertical pipe. The temperature profiles from the thermocouples, under steady state conditions, were compared with the predictions of the CFD simulation. The flows varied between 150 l h21 (0.084 m s21) and 1000 l h21 (0.56 m s21), corresponding to fully developed horizontal flow Reynolds numbers of between 1900 and 13 000 when using water. Hence both laminar/transitional and turbulent flow regimes were examined. The temperature at the inlet of the horizontal part of the pipework was maintained at ca 508C, to provide a significant temperature difference from ambient conditions and hence create a measurable temperature gradient down the unlagged pipe. The simulations were compared against experiments at steady state for the water flow rates mentioned above. CFD The aim of this work is the development of a modelling approach to predict the implications of processing on microbiological growth and hence the safety of food products. The tool selected for this purpose is FLUENT, a commercial CFD code. CFD is widely applied in the industry sector, although there has been very limited reporting of its use in combining engineering unit operations, such as fluid flow and heat transfer, with biological processes such as microbiological growth and inactivation. The design of the 3D mesh geometry was done in GAMBIT (Figure 2), which is an integrated processor for CFD analysis, and standard wall functions were chosen for solution very close to the wall, for the turbulent flows. Figure 2 depicts a vertical cut of the mesh applied in order to show a more detailed view. For the low flow of 150 l h21 (the pipe flow based on a Reynolds number of 1900) the laminar flow model was compared with less robust turbulence models such as SST k-v, with the transitional option activated and RNG k-1, with the differential viscosity option on. For the transitional flow of 300 l h21 (Re 3800) the standard (STD) k-1 was used. For higher flows, such as 1000 l h21 (Re 13 000), the renormalized (RNG) k-1 was used (FLUENT Inc., 2001), after comparing the various options of modelling turbulence in FLUENT. The models chosen for the above flows are summarized in Table 1. For the wall boundary condition of the dead-leg, an average natural convection heat transfer coefficient was used to calculate the heat flux between the wall and the
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Figure 2. Vertical cut surface showing meshed geometry of interval size 0.003 m.
Table 1. Models chosen for simulating the flows in FLUENT. Flow (l h 21) Model in CFD
150 (Re 1900)
300 (Re 3800)
1000 (Re 13 000)
Laminar
k-1 STD
k-1 RNG
environmental air. The above coefficient, h, was calculated using the following equation (Coulson and Richardson, 1996): n 3 2 hl 0 bgDTl r Cp m ¼C k m2 k
(1)
where C0 and n are constants determined for the specific geometry, g is the gravitational acceleration (ms22), Cp is the specific heat of atmospheric air (J kg21 K21), k is the atmospheric air thermal conductivity (W m21 K 21), T is the absolute temperature (K), DT is the temperature difference between wall and environmental air (K), l is the vertical pipe length (m), m is the atmospheric air viscosity (kg m21 s21), r is the atmospheric air density (kg m23) and b is the cubical expansion coefficient (K21) The physical properties of air were calculated at the average temperature of the wall surface and the environmental temperature. b is taken as 1/T, and DT ¼ Twall Tenv
(2)
where Twall is temperature of the wall and Tenv is the temperature of the surrounding air. RESULTS AND ANALYSES Steady state experiments were carried out for different flows varying from laminar, through transitional to turbulent. The models in FLUENT are three dimensional. The importance of the kind of flow lies in the fact that there
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Figure 3. Velocity vectors at the dead-leg area for flows of (a) 150 and (b) 1000 l h21.
are areas formed in the T-piece where the fluid is stagnant and stays at the bottom, or forms eddies that recirculate without interacting with the bulk flow, while some others do interact with it (Corcoran, 2003). This can be visualized by comparing the velocity vectors and magnitudes for different flows [Figure 3(a) and (b)]. For the lowest and highest flows, the circulating flow extends (a) 7.5 cm and (b) ca 13 cm down the dead leg, respectively. Further observation of the pathlines (obtained by following tracks of massless particles that follow the flow, released from selected areas in the domain) [Figure 4(a) and (b)] along the T-piece, for the lowest flow (150 l h21) reveals that there are vortices formed in the first 7 cm of T-piece depth that interact with the bulk flow [Figure 4(a)]. The effect is more pronounced at higher flows [1000 l h21, Figure 4(b)] where the interaction between the dead-leg and the bulk flow occurs in the space
starting from the top and going down to approximately 13 cm down the dead end. FLUENT recommends two models in order to solve flows that lie within the Reynolds number limits of 1500 and 2000. That kind of flow can be considered either laminar or transitional (an unstable, unsteady state flow regime which is difficult to predict) (Yakhot and Orszag, 1986). The transitional models were quite recently developed, therefore it was considered necessary to compare them with the laminar flow model. For 150 l h21, where the Reynolds number is around 1900, the solution was obtained with two transitional models: SST k-v, with transitional option activated and RNG k-1, with the differential viscosity option on. Although the standard k-1 model is strictly for high Reynolds number flows, the renormalized theory with the analytically-derived differential formula for effective viscosity accounts for low Reynolds number. The same
Figure 4. Pathlines of massless particles that follow the flow in the T-piece, coloured by residence time (in s) for (a) 150 l h21 and (b) 1000 l h21.
Trans IChemE, Part C, Food and Bioproducts Processing, 2006, 84(C2): 157– 163
CFD FOR PREDICTION OF TEMPERATURE PROFILES AND HYGIENIC DESIGN
Figure 5. Comparison of temperature profiles along the centre of the dead leg between simulations using different models and experimental results for transitional/laminar flow of 150 l h21 (Re ¼ 1900).
application has the shear-stress transport (SST) k-v model, with transitional option activated. The plot on Figure 5 shows the comparison between the measured temperatures for the 150 l h21 flow in the centre of the T-piece, compared to the two transitional modelling options and the laminar model. The k-1 model is evidently overestimating the heat transfer from the horizontal pipe to the vertical, especially at the point where it starts dropping. The k-v and laminar models give similar predictions and are reasonably close to the experimental values, both predict similar values towards the end of the pipe. The k-v model seems to cope better within the area in the first half of the tube. It gives good agreement for the point at which the temperature starts to drop. The SST k-v is therefore considered suitable for modelling flows in the transitional regime (Re 1500 – 2000). For all experiments it was noticed that the second thermocouple recorded lower values than the third, while the latter was deeper down the vertical pipe. This is not physically correct and is possibly an experimental artefact. After the run, the thermocouple was removed and a replacement inserted and several tests were carried out proving that the temperature measured at the second thermocouple was very sensitive to its location. Furthermore, the pressure build up at that location during the experiment could dislodge the sensor and push it closer to the wall, where the temperature was slightly lower. For 300 l h21, where Reynolds number is around 3800, the flow is considered transitional in engineering books,
Figure 6. Comparison of temperature along the centre of the dead leg between the simulations and experiment for transitional Reynolds turbulent flow of 300 l h21 (Re ¼ 3800).
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Figure 7. Comparison of temperature along the centre of the dead leg between the simulations and the experiment for high Reynolds turbulent flow of 1000 l h21 (Re ¼ 13 000).
but previous investigations in turbulence (Versteeg and Malalasekera, 1995) consider it turbulent and various models are applied in finite element and finite volume methods in order to handle it. So, comparison was obtained between SST k-v with transitional option activated, standard (STD) k-v, which incorporates modifications for low Reynolds effects and the k-1 STD and RNG models with the later being built for higher Reynolds number (Figure 6). Figure 6 shows that generally the differences between the predictions are not especially pronounced, although the k-v STD and SST (transition checked), slightly overestimate the point down the pipe where the temperature starts dropping. k-1 models (STD and RNG) behave according to the k-1 standard, which is not as demanding as RNG, giving a slightly better agreement with the overall distribution given by the measurements after the point where temperature drop is more evident. This model might not be as close as the one chosen for the 150 l h21, but compared to the rest, the shape of the inclination is similar to the temperature distribution given by the thermocouples. Finally, for the high turbulent flow of 1000 l h21 (Re 13 000) more rigorous models were used in order to cope more accurately with the highly swirled flux. In Figure 7 it can be seen that the k-1 models provide a better
Figure 8. Temperature contours along the dead leg for various flows.
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description of the threshold where temperature starts dropping and heat transfer by conduction becomes more significant than convection, since velocities start dropping by orders of magnitude. Towards the end of the tube the behaviour of the various models are similar, with an overestimation in calculating the temperature. The overall appearance of k-1 RNG shows that the model follows the temperature in the centre of the pipe better. By gradually increasing the flow we can see the influence on the temperature distribution down the geometry of interest. This can be visualized by comparing the contours of temperature on a surface cut along the centre of the vertical area (Figure 8). The temperature starts dropping at longer distances down the geometry as the flow becomes higher. So, for 150 l h21 this happens at around 7.5 cm, for 300 1 h21, this occurs at ca 8.5 cm and for 1000 l h21 this occurs at 13 cm. At the same locations eddies appear, and there is interaction with the bulk flow in the main horizontal pipe (Figure 4). An overall view of the velocity distribution down the vertical pipe at various flows is presented in Figure 9, where the x-axis refers only to the dead leg length and up to the point where values are significant. This means that it starts from the point where the horizontal and vertical tube merge and finishes at the bottom of the vertical one. There, it can be observed how the velocity drops further down along the centre of the tube as the flow increases. For the same flows, the results of the temperature distribution are on Figure 10, where the increasing active length can be seen and the x-axis starts from the mid point of the horizontal tube. This shows that as long as the velocity remains relatively high, convection is the driving force for the heat transfer down the T-piece. SST k-v, k-1 STD and k-1 RNG are the models chosen for the various flows as they increase. It can be noticed that when velocity is practically zero and stagnation takes place, the temperature goes down due to conduction in the fluid, which is a slower mechanism, and due to heat transfer from the walls. DISCUSSION The validation of the temperature distribution for the particular geometry shows that FLUENT is an appropriate method for the prediction of temperature and residence time profiles. The modelling solution overestimates the depth in the pipe where the centre line temperature starts to drop, especially for the turbulent flow cases. Overall, a
Figure 9. Velocity magnitude distribution along the centre of the T area for the different flows, where the x-axis refers only to the vertical length.
Figure 10. Temperature distribution along the centre of the T area for different flows applying SST k-v, k-1 STD and k-1 RNG as flow increases, where the x-axis refers to the length starting form the centre of the horizontal tube.
qualitative comparison shows an encouraging degree of agreement. Microbial kinetics, being strongly dependent on temperature (McMeekin et al., 1993), cannot be predicted with any confidence without realistic assessment of temperature and residence time distribution. The post processing of the above models includes plots of the contours, vectors and pathlines and shows that there is interaction between the bulk flow and the dead-leg at various lengths that increases when the flow increases. This means that when the right range of conditions is applied the risk can be controlled more efficiently, although existing geometries might be objectively considered unhygienic. However, for the specific geometry considered here, which is quite long for a dead end, the flows applied were not high enough, since there is always stagnant material at the bottom of the T-piece. So, with the existing conditions, the T-junction modelled would undoubtedly provide an unacceptable risk to the product. However, the application of computational methods, such as CFD, for predicting process conditions, illustrate the likelihood that different shapes or dimensions can be cleaned, when the correct cleaning regime is implemented. Another issue that arises is the use of the code, which demands a good knowledge of the engineering aspects. Application of more accurate models for turbulence and sufficient understanding of wall boundary conditions has a significant impact on the results and makes the code an even safer tool to use, since there is reasonable agreement with the experimental measurements. Turbulence has always been difficult to predict from an engineering perspective, and previous modifications to the equations describing turbulence have helped researchers to integrate it within their models. (Wilcox, 1975, 1994). Most of these options are included in finite volume codes and the appropriate one can be chosen for modelling turbulence more accurately. Laminar flow modelling or even low turbulence can be predicted more confidently with finite volume analysis compared to fully developed turbulence for higher flows. The above results showed that the validation of turbulent flows can be predicted qualitatively but is difficult to apply quantitatively. This is due to the fact that in the same domain various flow regimes coexist: turbulent flow can be present in the horizontal pipe whilst in the vertical pipe the velocity gradually decreases, bringing the flow into the laminar regime.
Trans IChemE, Part C, Food and Bioproducts Processing, 2006, 84(C2): 157– 163
CFD FOR PREDICTION OF TEMPERATURE PROFILES AND HYGIENIC DESIGN Moreover, knowing that the temperature is closely coupled with the velocity profile, FLUENT can be used to visualise the recirculation areas and the parts of the dead-leg that are going to interact with the bulk flow. It is therefore possible to predict whether product will accumulate, and when cleaning may be ineffective, and whether temperatures and residence times will allow the growth of bacteria and create potential product contamination. CONCLUSIONS In this study, engineering principles, hygienic design issues and process conditions that can affect microbial survival and growth in the planktonic phase have been combined. Based on these principles, the integration of kinetic models for bacterial growth and inactivation into the solution of the code for the flow and temperature conditions will be possible. Temperature and time are the critical parameters that determine the growth and survival of micro-organisms, although other factors such as pH, water activity and dissolved oxygen are also critical. Depending on the time-temperature profile within the equipment, the CFD code will be able to predict whether particular species of bacteria in will be inactivated, survive or grow in the planktonic phase. This information is a necessary prerequisite in developing any model that predicts biofilm development by cell transfer from planktonic to biofilm phases. NOMENCLATURE 0
C Cp g h k l n Re T
constant determined for various geometries specific heat of atmospheric air, J kg21 K21 gravitational acceleration, m s22 natural convection heat transfer coefficient, W m22 K21 thermal conductivity of atmospheric air, W m21 K21 length of the vertical pipe, m constant determined for various geometries Reynolds number absolute temperature, K
Greek symbols m viscosity of atmospheric air, kg m21 s21 r density of atmospheric air, specific heat, kg m23 b coefficient of cubical expansion, K21 DT temperature difference between wall and environmental air Subscripts env ambient air property in inlet condition wall property on equipment wall
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Coulson, J.M. and Richardson, J.F., 1996, Chemical engineering, Volume 1, Fluid Flow, Heat Transfer and Mass Transfer, (eds). 5th edition, 385–386 (Butterworth-Heinemann, Oxford, UK). Dhanasekharan, K.M., Grald, E.W. and Mathur, R., 2004, How flow modelling benefits the food industry, Food Technology, 58(3): 32– 35. FLUENT, 2005, electronic citation, http://www.fluent.com/solutions/aerospace/index.htm. FLUENT Inc., 2001, FLUENT 6 User’s Guide, Volume 2, 10-8/10-43. Friis, A. and Jensen, B.B.B., 2002, Prediction of hygiene in food processing equipment using flow modelling, Food and Bioproducts Processing, 80(C4): 281–285. Hasting, A.P.M., 1999, Fouling and cleaning in the food industry: introduction and overview, Trans IChemE, Part C, 77: pp. 73–74. Lelievre, C., Antonini, G., Faille, C. and Benezech, T., 2002, Cleaning-inplace—Modelling of cleaning kinetics of pipes soiled by Bacillus spores assuming a process combining removal and deposition, Food and Bioproducts Processing, 80(C4): 305 –311. McMeekin, T.A., Olley, J., Ross, T. and Ratkowsky, D., 1993, Predictive Microbiology: Theory and Application, 1st edition, (Research Studies Press Ltd., Taunton, Somerset, UK). Scott, G., and Richardson, P., 1997, The application of computational fluid dynamics in the food industry, Trends in Food Science & Technology, 8: 119–124. Timperley, D.A., 1981, The effect of Reynolds number and mean velocity of flow on the cleaning in place of pipelines, in Fundamentals and Applications of Surface Phenomena Associated with Fouling and Cleaning in Food Processing, Hallstrom, B., Lund, D.B. and Tragardh, Ch. (eds). (Tylosand, Sweden), 402– 412. van Asselt, A.J., van Houwelingen, G. and Giffel, M.C.T., 2002, Monitoring system for improving cleaning efficiency of cleaning-in-place processes in dairy environments, Food and Bioproducts Processing, 80(C4): 276 –280. Versteeg, H.K. and Malalasekera W., 1995, An Introduction to Computational Fluid Dynamics: The Finite Volume Method (Addison-Wesley Longman Higher Education, UK). Verran, J., 2002, When a biofilm not a biofilm—and does it really matter? Proceedings Fouling, Cleaning and Disinfection in Food Processing, Wilson, D.I., Fryer, P.J. and Hasting, A.P.M., (eds). 49–54, Department of Chemical Engineering, University of Cambridge, UK. Wilcox, D.C., 1975, Turbulence model transition predictions, AIAA Journal, 13: 241–243. Wilcox, D.C., 1994, Simulation of transition with a 2-equation turbulence model, AIAA Journal 32: 247–255. Yakhot, V. and Orszag, S.A., 1986, Renormalisation group analysis of turbulence: I. Basic theory, Journal of Scientific Computing, 1(1): 1–51. Zwietering, M.H. and Hasting, A.P.M., 1997, Modelling the hygienic processing of foods— influence of individual process stages, Food and Bioproducts Processing, 75(C3): 168–173.
ACKNOWLEDGEMENTS
REFERENCES
Konstantia Asteriadou would like to thank the technicians at the Chemical Engineering Department in the University of Bath (Fernando Acosta, Robert Brain and John Bishop) for their help in setting up the experimental rig. Konstantia Asteriadou appreciates the financial support provided by a Marie Curie fellowship.
Corcoran, B., 2003, CFD analysis of pharmaceutical pipe dead-legs, Fluent user’s meeting September 2003, Sheffield, proceedings of the conference.
The manuscript was received 14 September 2004 and accepted for publication after revision 15 February 2006.
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www.icheme.org/fbp doi: 10.1205/fbp.04261
COMPUTATIONAL FLUID DYNAMICS FOR THE PREDICTION OF TEMPERATURE PROFILES AND HYGIENIC DESIGN IN THE FOOD INDUSTRY K. ASTERIADOU1 , A. P. M. HASTING2, M. R. BIRD3 and J. MELROSE2 1
Unilever R&D, Vlaardingen, The Netherlands 2 Unilever R&D, Bedford, UK Department of Chemical Engineering, University of Bath, Bath, UK
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any factors need to be considered to ensure that food process lines consistently deliver microbiologically safe products. These factors include process and equipment design, and in particular the interaction between the product and the equipment geometry. Computational fluid dynamics (CFD) has recently been used within the food industry in a number of applications. In this work a commercial finite volume CFD code, FLUENT, has been used to predict those parameters critical to the prediction of velocity and temperature profiles for low viscosity fluids in typical, complex equipment geometries and compared these with experimental data. A comparison of the temperature distribution using predictive modelling and experiments is encouraging, and qualitatively satisfactory and reliable for laminar and turbulent flows. Application of this approach will enable the interaction between food products and equipment geometries to be predicted, and provide an improved method of assessing the implications for the microbiological safety of foods. Keywords: hygienic design; modelling; CFD; turbulence; food processing; food safety.
INTRODUCTION
certain period of running a food production line, cleaning will be necessary, during which production is interrupted. The duration of cleaning depends on the product processed, the residual soil on the equipment and the cleaning conditions selected. Cleaning of food process plant aims to remove all product residues from the product contact surfaces and leave the surfaces in an acceptable condition for subsequent production. This may require disinfection or sterilization of the surfaces as part of the cleaning process. However, even if the above can be carried out successfully, there are sometimes parameters that are difficult to account for. For example, unhygienic features in the pipe geometry, such as up-stands or junctions can lead to significant difficulties. Other examples can be valves, crevices and even surface roughness. These can favour product entrapment and create conditions for microbial growth leading to recontamination. Hence, it is important to have a clear understanding of what happens within such geometries and be able to predict the effect they are going to have in the whole process domain. In this work, a T-piece has been studied as a typical example of a stagnant region. Results from a computational fluid dynamics (CFD) code have been validated against experimental work performed at the University of Bath. Initially, CFD was applied in the aerospace and automotive industries to predict air flow, for instance around planes and cars. However, CFD has been successfully
The objective of the food industry is to deliver high quality, safe and stable products. Consumer demand is high for products with less preservatives, more natural tastes and textures. At the same time, longer shelf life is expected and costs must remain low enough for the products to be purchased. Another factor that puts pressure on the food industry are the regulatory checks on both products and lines. Industry increasingly needs to employ advanced manufacturing techniques, which allow greater process flexibility and reduced energy use and waste generation. Hence the pressure to improve hygiene standards from both consumers and legislation is continually increasing (Hasting, 1999). It is therefore of great importance to maintain microbial safety during the processing of foods, which is directly linked to the possibility of microbial survival and growth in the final product. This is avoided by treating the product at high temperatures for a defined period of time to inactivate the micro-organisms of concern and then ensure the conditions in the rest of the line do not result in unacceptable levels of recontamination. The most common heat treatment processes are sterilization and pasteurization. After a Correspondence to: Dr K. Asteriadou, Unilever R&D, Vlaardingen, The Netherlands. E-Mail: [email protected]
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applied in the food industry in recent years. Scott and Richardson (1997) describe several applications connected to the food industry, including (1) the prediction of air flows around buildings that showed that the method can be used to predict air flow movement inside items of food processing equipment, (2) baking oven performance simulation with CFD in order to quantify heat and mass transfer to and from the product surface, (3) the prediction of air and temperature distribution inside chillers and retail spray cabinets. Air was the first fluid that had its flow modelled for the food industry application improvements. Subsequently, models were developed for both Newtonian and non-Newtonian fluids. Phase change has also been monitored, for equipment such as driers. Mixers and pumps have also been included in CFD modelling. CFD has also been used by Friis and Jensen (2002) to model flows in upstands and valves during CIP flows. They used the finite volume method code STAR-CD. Validation was carried out using the standardized cleaning test proposed by the European Hygienic Engineering and Design Group (EHEDG). Other applications for CFD modelling include extrusion, mixing operations and food safety (Dhanasekharan et al., 2004). Thermal processes such as pasteurization and sterilization are commonly used in the food industry. These are well understood ways of reducing or eliminating microorganisms in food products. Pasteurization aims to kill pathogens that are of high risk for health, whereas sterilization involves higher temperatures in order to eliminate all vegetative spores and bacteria that might survive the pasteurization process. These heating processes may result in fouling of the product contact surfaces, which is the deposition or accumulation of product residues such as proteins, fats, minerals or micro-organisms upon various surfaces (Verran, 2002), causing contamination of the product afterwards. Also some stagnant areas, where the product has a prolonged residence time, may be sources of microbial growth and subsequent recontamination of the product. Cleaning in place (CIP) processes are widely used in the food industry in order to remove fouling deposits. CIP is a means of cleaning equipment without dismantling it by circulating detergent solutions through it. Flow velocities and shear stresses are critical for effective cleaning (Timperley, 1981). CIP cleans and where necessary disinfects or sterilizes the product contact surfaces. It reduces the cleaning shutdown periods of a plant, so it is a considerable way of cost saving. The efficiency of cleaning can be improved by the right combination of temperature, concentration of cleaning solution and flow (van Asselt et al., 2002). The science of CIP is based on applying the required amount of energy to the equipment to ensure that it is cleaned. The energy is provided by the temperature of the solution (thermal energy), the detergent or the solvent (chemical energy) and the application of suitable fluid velocities or pressure (kinetic energy). The fluid velocity has been shown to be a particularly important parameter (Timperley, 1981). The shear stress developed on the walls of the equipment can be critical for the rate of microbial fouling removal (Lelievre et al., 2002) as can the thickness of the boundary layer, both of which are affected by fluid velocity. For this reason, turbulent flows are essential since they have a strong interaction with boundary layers. Laminar flow is often found when processing viscous products
whereas CIP is generally carried out under highly turbulent conditions. In both CIP and process lines there are equipment geometries such as dead-ends, T-junctions, down-stands, up-stands and expansions (Friis and Jensen, 2002) and are not always convenient or practical to remove (e.g., instruments, valves). It was therefore considered important to model different flows in domains that comprise these kinds of geometries in order to see how useful the CFD modelling can be for predicting thermal and velocity variations. For CIP processes turbulent flows are of interest, whilst for thermal processes laminar flows are more often encountered. Cleaning is a very important step, since it follows production and guarantees safe changeovers. This part of the work brings together food processing conditions, CFD modelling tools and risky geometries where flow cannot be solved and predicted analytically. FLUENT was chosen because it applies the finite volume method and the creators consider that it can cope very well with 3D and turbulent flows (FLUENT, 2005). CFD solves the Navier –Stokes equations as well as the energy equation, when this is selected by the user. Growth or inactivation of micro-organisms is dependent on the temperature profile and the residence time of the product (Zwietering and Hasting, 1997) within the system. The temperature and residence time, in their turn, depend on the fluid velocity. For these reasons, it is important to have correct estimations of the velocity and temperature so that the microbial kinetics can be predicted as accurately as possible and hence the implications for food safety.
METHODS AND MATERIALS Experiments The study described in this paper is based on water flow past a T-junction in which the vertical arm is blocked (Figure 1), thus creating a potentially dead space where stagnant product may remain for extended periods of time. Both pipes have a diameter of 0.023 m. Before and after the junction there are horizontal sections of length 1.5 m and 0.5 m, respectively. The length of the dead-leg is 0.2325 m, measured from the centre of the horizontal tube. Such T-junctions are undesirable configurations in a process line but are frequently present and may be difficult to remove due to production pressures. Such a geometry is relatively simple and allows temperature measurements to be taken along its length during experiments. It is therefore
Figure 1. Schematic of the pipework geometry studied.
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CFD FOR PREDICTION OF TEMPERATURE PROFILES AND HYGIENIC DESIGN valuable to be able to predict the conditions in such an unhygienic piece of equipment and thus be able to make a judgement of the risk that such a particular geometry poses to the product. The horizontal pipe was insulated, so that constant temperatures can be maintained along the length, which is the desired condition in heating processes in order to achieve adequate amount of heat penetrating the product. However, the vertical pipe is not lagged so there are heat losses to the air via natural convection around the T-piece. Hence, the heating of the contents of the vertical pipe is observed at steady state conditions that can represent runs in a process plant, where dead ends might be encountered (such as drainage valves, sensor locations). In the experimental set-up, 6 k-type thermocouples, of diameter 0.5 mm are located along the centre line of the vertical pipe. The temperature profiles from the thermocouples, under steady state conditions, were compared with the predictions of the CFD simulation. The flows varied between 150 l h21 (0.084 m s21) and 1000 l h21 (0.56 m s21), corresponding to fully developed horizontal flow Reynolds numbers of between 1900 and 13 000 when using water. Hence both laminar/transitional and turbulent flow regimes were examined. The temperature at the inlet of the horizontal part of the pipework was maintained at ca 508C, to provide a significant temperature difference from ambient conditions and hence create a measurable temperature gradient down the unlagged pipe. The simulations were compared against experiments at steady state for the water flow rates mentioned above. CFD The aim of this work is the development of a modelling approach to predict the implications of processing on microbiological growth and hence the safety of food products. The tool selected for this purpose is FLUENT, a commercial CFD code. CFD is widely applied in the industry sector, although there has been very limited reporting of its use in combining engineering unit operations, such as fluid flow and heat transfer, with biological processes such as microbiological growth and inactivation. The design of the 3D mesh geometry was done in GAMBIT (Figure 2), which is an integrated processor for CFD analysis, and standard wall functions were chosen for solution very close to the wall, for the turbulent flows. Figure 2 depicts a vertical cut of the mesh applied in order to show a more detailed view. For the low flow of 150 l h21 (the pipe flow based on a Reynolds number of 1900) the laminar flow model was compared with less robust turbulence models such as SST k-v, with the transitional option activated and RNG k-1, with the differential viscosity option on. For the transitional flow of 300 l h21 (Re 3800) the standard (STD) k-1 was used. For higher flows, such as 1000 l h21 (Re 13 000), the renormalized (RNG) k-1 was used (FLUENT Inc., 2001), after comparing the various options of modelling turbulence in FLUENT. The models chosen for the above flows are summarized in Table 1. For the wall boundary condition of the dead-leg, an average natural convection heat transfer coefficient was used to calculate the heat flux between the wall and the
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Figure 2. Vertical cut surface showing meshed geometry of interval size 0.003 m.
Table 1. Models chosen for simulating the flows in FLUENT. Flow (l h 21) Model in CFD
150 (Re 1900)
300 (Re 3800)
1000 (Re 13 000)
Laminar
k-1 STD
k-1 RNG
environmental air. The above coefficient, h, was calculated using the following equation (Coulson and Richardson, 1996): n 3 2 hl 0 bgDTl r Cp m ¼C k m2 k
(1)
where C0 and n are constants determined for the specific geometry, g is the gravitational acceleration (ms22), Cp is the specific heat of atmospheric air (J kg21 K21), k is the atmospheric air thermal conductivity (W m21 K 21), T is the absolute temperature (K), DT is the temperature difference between wall and environmental air (K), l is the vertical pipe length (m), m is the atmospheric air viscosity (kg m21 s21), r is the atmospheric air density (kg m23) and b is the cubical expansion coefficient (K21) The physical properties of air were calculated at the average temperature of the wall surface and the environmental temperature. b is taken as 1/T, and DT ¼ Twall Tenv
(2)
where Twall is temperature of the wall and Tenv is the temperature of the surrounding air. RESULTS AND ANALYSES Steady state experiments were carried out for different flows varying from laminar, through transitional to turbulent. The models in FLUENT are three dimensional. The importance of the kind of flow lies in the fact that there
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Figure 3. Velocity vectors at the dead-leg area for flows of (a) 150 and (b) 1000 l h21.
are areas formed in the T-piece where the fluid is stagnant and stays at the bottom, or forms eddies that recirculate without interacting with the bulk flow, while some others do interact with it (Corcoran, 2003). This can be visualized by comparing the velocity vectors and magnitudes for different flows [Figure 3(a) and (b)]. For the lowest and highest flows, the circulating flow extends (a) 7.5 cm and (b) ca 13 cm down the dead leg, respectively. Further observation of the pathlines (obtained by following tracks of massless particles that follow the flow, released from selected areas in the domain) [Figure 4(a) and (b)] along the T-piece, for the lowest flow (150 l h21) reveals that there are vortices formed in the first 7 cm of T-piece depth that interact with the bulk flow [Figure 4(a)]. The effect is more pronounced at higher flows [1000 l h21, Figure 4(b)] where the interaction between the dead-leg and the bulk flow occurs in the space
starting from the top and going down to approximately 13 cm down the dead end. FLUENT recommends two models in order to solve flows that lie within the Reynolds number limits of 1500 and 2000. That kind of flow can be considered either laminar or transitional (an unstable, unsteady state flow regime which is difficult to predict) (Yakhot and Orszag, 1986). The transitional models were quite recently developed, therefore it was considered necessary to compare them with the laminar flow model. For 150 l h21, where the Reynolds number is around 1900, the solution was obtained with two transitional models: SST k-v, with transitional option activated and RNG k-1, with the differential viscosity option on. Although the standard k-1 model is strictly for high Reynolds number flows, the renormalized theory with the analytically-derived differential formula for effective viscosity accounts for low Reynolds number. The same
Figure 4. Pathlines of massless particles that follow the flow in the T-piece, coloured by residence time (in s) for (a) 150 l h21 and (b) 1000 l h21.
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Figure 5. Comparison of temperature profiles along the centre of the dead leg between simulations using different models and experimental results for transitional/laminar flow of 150 l h21 (Re ¼ 1900).
application has the shear-stress transport (SST) k-v model, with transitional option activated. The plot on Figure 5 shows the comparison between the measured temperatures for the 150 l h21 flow in the centre of the T-piece, compared to the two transitional modelling options and the laminar model. The k-1 model is evidently overestimating the heat transfer from the horizontal pipe to the vertical, especially at the point where it starts dropping. The k-v and laminar models give similar predictions and are reasonably close to the experimental values, both predict similar values towards the end of the pipe. The k-v model seems to cope better within the area in the first half of the tube. It gives good agreement for the point at which the temperature starts to drop. The SST k-v is therefore considered suitable for modelling flows in the transitional regime (Re 1500 – 2000). For all experiments it was noticed that the second thermocouple recorded lower values than the third, while the latter was deeper down the vertical pipe. This is not physically correct and is possibly an experimental artefact. After the run, the thermocouple was removed and a replacement inserted and several tests were carried out proving that the temperature measured at the second thermocouple was very sensitive to its location. Furthermore, the pressure build up at that location during the experiment could dislodge the sensor and push it closer to the wall, where the temperature was slightly lower. For 300 l h21, where Reynolds number is around 3800, the flow is considered transitional in engineering books,
Figure 6. Comparison of temperature along the centre of the dead leg between the simulations and experiment for transitional Reynolds turbulent flow of 300 l h21 (Re ¼ 3800).
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Figure 7. Comparison of temperature along the centre of the dead leg between the simulations and the experiment for high Reynolds turbulent flow of 1000 l h21 (Re ¼ 13 000).
but previous investigations in turbulence (Versteeg and Malalasekera, 1995) consider it turbulent and various models are applied in finite element and finite volume methods in order to handle it. So, comparison was obtained between SST k-v with transitional option activated, standard (STD) k-v, which incorporates modifications for low Reynolds effects and the k-1 STD and RNG models with the later being built for higher Reynolds number (Figure 6). Figure 6 shows that generally the differences between the predictions are not especially pronounced, although the k-v STD and SST (transition checked), slightly overestimate the point down the pipe where the temperature starts dropping. k-1 models (STD and RNG) behave according to the k-1 standard, which is not as demanding as RNG, giving a slightly better agreement with the overall distribution given by the measurements after the point where temperature drop is more evident. This model might not be as close as the one chosen for the 150 l h21, but compared to the rest, the shape of the inclination is similar to the temperature distribution given by the thermocouples. Finally, for the high turbulent flow of 1000 l h21 (Re 13 000) more rigorous models were used in order to cope more accurately with the highly swirled flux. In Figure 7 it can be seen that the k-1 models provide a better
Figure 8. Temperature contours along the dead leg for various flows.
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description of the threshold where temperature starts dropping and heat transfer by conduction becomes more significant than convection, since velocities start dropping by orders of magnitude. Towards the end of the tube the behaviour of the various models are similar, with an overestimation in calculating the temperature. The overall appearance of k-1 RNG shows that the model follows the temperature in the centre of the pipe better. By gradually increasing the flow we can see the influence on the temperature distribution down the geometry of interest. This can be visualized by comparing the contours of temperature on a surface cut along the centre of the vertical area (Figure 8). The temperature starts dropping at longer distances down the geometry as the flow becomes higher. So, for 150 l h21 this happens at around 7.5 cm, for 300 1 h21, this occurs at ca 8.5 cm and for 1000 l h21 this occurs at 13 cm. At the same locations eddies appear, and there is interaction with the bulk flow in the main horizontal pipe (Figure 4). An overall view of the velocity distribution down the vertical pipe at various flows is presented in Figure 9, where the x-axis refers only to the dead leg length and up to the point where values are significant. This means that it starts from the point where the horizontal and vertical tube merge and finishes at the bottom of the vertical one. There, it can be observed how the velocity drops further down along the centre of the tube as the flow increases. For the same flows, the results of the temperature distribution are on Figure 10, where the increasing active length can be seen and the x-axis starts from the mid point of the horizontal tube. This shows that as long as the velocity remains relatively high, convection is the driving force for the heat transfer down the T-piece. SST k-v, k-1 STD and k-1 RNG are the models chosen for the various flows as they increase. It can be noticed that when velocity is practically zero and stagnation takes place, the temperature goes down due to conduction in the fluid, which is a slower mechanism, and due to heat transfer from the walls. DISCUSSION The validation of the temperature distribution for the particular geometry shows that FLUENT is an appropriate method for the prediction of temperature and residence time profiles. The modelling solution overestimates the depth in the pipe where the centre line temperature starts to drop, especially for the turbulent flow cases. Overall, a
Figure 9. Velocity magnitude distribution along the centre of the T area for the different flows, where the x-axis refers only to the vertical length.
Figure 10. Temperature distribution along the centre of the T area for different flows applying SST k-v, k-1 STD and k-1 RNG as flow increases, where the x-axis refers to the length starting form the centre of the horizontal tube.
qualitative comparison shows an encouraging degree of agreement. Microbial kinetics, being strongly dependent on temperature (McMeekin et al., 1993), cannot be predicted with any confidence without realistic assessment of temperature and residence time distribution. The post processing of the above models includes plots of the contours, vectors and pathlines and shows that there is interaction between the bulk flow and the dead-leg at various lengths that increases when the flow increases. This means that when the right range of conditions is applied the risk can be controlled more efficiently, although existing geometries might be objectively considered unhygienic. However, for the specific geometry considered here, which is quite long for a dead end, the flows applied were not high enough, since there is always stagnant material at the bottom of the T-piece. So, with the existing conditions, the T-junction modelled would undoubtedly provide an unacceptable risk to the product. However, the application of computational methods, such as CFD, for predicting process conditions, illustrate the likelihood that different shapes or dimensions can be cleaned, when the correct cleaning regime is implemented. Another issue that arises is the use of the code, which demands a good knowledge of the engineering aspects. Application of more accurate models for turbulence and sufficient understanding of wall boundary conditions has a significant impact on the results and makes the code an even safer tool to use, since there is reasonable agreement with the experimental measurements. Turbulence has always been difficult to predict from an engineering perspective, and previous modifications to the equations describing turbulence have helped researchers to integrate it within their models. (Wilcox, 1975, 1994). Most of these options are included in finite volume codes and the appropriate one can be chosen for modelling turbulence more accurately. Laminar flow modelling or even low turbulence can be predicted more confidently with finite volume analysis compared to fully developed turbulence for higher flows. The above results showed that the validation of turbulent flows can be predicted qualitatively but is difficult to apply quantitatively. This is due to the fact that in the same domain various flow regimes coexist: turbulent flow can be present in the horizontal pipe whilst in the vertical pipe the velocity gradually decreases, bringing the flow into the laminar regime.
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CFD FOR PREDICTION OF TEMPERATURE PROFILES AND HYGIENIC DESIGN Moreover, knowing that the temperature is closely coupled with the velocity profile, FLUENT can be used to visualise the recirculation areas and the parts of the dead-leg that are going to interact with the bulk flow. It is therefore possible to predict whether product will accumulate, and when cleaning may be ineffective, and whether temperatures and residence times will allow the growth of bacteria and create potential product contamination. CONCLUSIONS In this study, engineering principles, hygienic design issues and process conditions that can affect microbial survival and growth in the planktonic phase have been combined. Based on these principles, the integration of kinetic models for bacterial growth and inactivation into the solution of the code for the flow and temperature conditions will be possible. Temperature and time are the critical parameters that determine the growth and survival of micro-organisms, although other factors such as pH, water activity and dissolved oxygen are also critical. Depending on the time-temperature profile within the equipment, the CFD code will be able to predict whether particular species of bacteria in will be inactivated, survive or grow in the planktonic phase. This information is a necessary prerequisite in developing any model that predicts biofilm development by cell transfer from planktonic to biofilm phases. NOMENCLATURE 0
C Cp g h k l n Re T
constant determined for various geometries specific heat of atmospheric air, J kg21 K21 gravitational acceleration, m s22 natural convection heat transfer coefficient, W m22 K21 thermal conductivity of atmospheric air, W m21 K21 length of the vertical pipe, m constant determined for various geometries Reynolds number absolute temperature, K
Greek symbols m viscosity of atmospheric air, kg m21 s21 r density of atmospheric air, specific heat, kg m23 b coefficient of cubical expansion, K21 DT temperature difference between wall and environmental air Subscripts env ambient air property in inlet condition wall property on equipment wall
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Coulson, J.M. and Richardson, J.F., 1996, Chemical engineering, Volume 1, Fluid Flow, Heat Transfer and Mass Transfer, (eds). 5th edition, 385–386 (Butterworth-Heinemann, Oxford, UK). Dhanasekharan, K.M., Grald, E.W. and Mathur, R., 2004, How flow modelling benefits the food industry, Food Technology, 58(3): 32– 35. FLUENT, 2005, electronic citation, http://www.fluent.com/solutions/aerospace/index.htm. FLUENT Inc., 2001, FLUENT 6 User’s Guide, Volume 2, 10-8/10-43. Friis, A. and Jensen, B.B.B., 2002, Prediction of hygiene in food processing equipment using flow modelling, Food and Bioproducts Processing, 80(C4): 281–285. Hasting, A.P.M., 1999, Fouling and cleaning in the food industry: introduction and overview, Trans IChemE, Part C, 77: pp. 73–74. Lelievre, C., Antonini, G., Faille, C. and Benezech, T., 2002, Cleaning-inplace—Modelling of cleaning kinetics of pipes soiled by Bacillus spores assuming a process combining removal and deposition, Food and Bioproducts Processing, 80(C4): 305 –311. McMeekin, T.A., Olley, J., Ross, T. and Ratkowsky, D., 1993, Predictive Microbiology: Theory and Application, 1st edition, (Research Studies Press Ltd., Taunton, Somerset, UK). Scott, G., and Richardson, P., 1997, The application of computational fluid dynamics in the food industry, Trends in Food Science & Technology, 8: 119–124. Timperley, D.A., 1981, The effect of Reynolds number and mean velocity of flow on the cleaning in place of pipelines, in Fundamentals and Applications of Surface Phenomena Associated with Fouling and Cleaning in Food Processing, Hallstrom, B., Lund, D.B. and Tragardh, Ch. (eds). (Tylosand, Sweden), 402– 412. van Asselt, A.J., van Houwelingen, G. and Giffel, M.C.T., 2002, Monitoring system for improving cleaning efficiency of cleaning-in-place processes in dairy environments, Food and Bioproducts Processing, 80(C4): 276 –280. Versteeg, H.K. and Malalasekera W., 1995, An Introduction to Computational Fluid Dynamics: The Finite Volume Method (Addison-Wesley Longman Higher Education, UK). Verran, J., 2002, When a biofilm not a biofilm—and does it really matter? Proceedings Fouling, Cleaning and Disinfection in Food Processing, Wilson, D.I., Fryer, P.J. and Hasting, A.P.M., (eds). 49–54, Department of Chemical Engineering, University of Cambridge, UK. Wilcox, D.C., 1975, Turbulence model transition predictions, AIAA Journal, 13: 241–243. Wilcox, D.C., 1994, Simulation of transition with a 2-equation turbulence model, AIAA Journal 32: 247–255. Yakhot, V. and Orszag, S.A., 1986, Renormalisation group analysis of turbulence: I. Basic theory, Journal of Scientific Computing, 1(1): 1–51. Zwietering, M.H. and Hasting, A.P.M., 1997, Modelling the hygienic processing of foods— influence of individual process stages, Food and Bioproducts Processing, 75(C3): 168–173.
ACKNOWLEDGEMENTS
REFERENCES
Konstantia Asteriadou would like to thank the technicians at the Chemical Engineering Department in the University of Bath (Fernando Acosta, Robert Brain and John Bishop) for their help in setting up the experimental rig. Konstantia Asteriadou appreciates the financial support provided by a Marie Curie fellowship.
Corcoran, B., 2003, CFD analysis of pharmaceutical pipe dead-legs, Fluent user’s meeting September 2003, Sheffield, proceedings of the conference.
The manuscript was received 14 September 2004 and accepted for publication after revision 15 February 2006.
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