This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.
Many experimental and modeling attempts have been carried out to analyze the effects of fouling on heat exchanger efficiency. So far, the research has been focused on the deposition of fouling elements on the tube inner side and its corresponding thermal-hydraulic effects. This project aims at investigating these aspects inside the tube but also on the shell side of a shell and tube heat exchanger by CFD simulations.
The research project consists in: firstly, we examine whether the deposition models established for the tube side can be applied to the heat exchanger shell side too. Then we search in the literature for the existing shell side models. The next step starts with modeling of fouling in the inside and outside of a single tube, and then we refine and extend the model to more real cases by relaxing the limiting hypotheses. Finally, the numerical results for a shell and tube heat exchanger with a single tube will be compared with experimental data.
This literature review will summarize in the first part, the fundamentals of fouling phenomenon. The second part is related to heat exchanger description. Then a review of CFD modeling of fouling is given. The final part is dedicated to the project objectives and timeline.
The oil crisis of 1973 and 1979 pushed industries to rethink the management of their energy consumptions. In this context, heat exchangers have become a point of interest in the energy monitoring. They are used in all heat processes and power plants, they are present in most industrial sectors: chemical, petrochemical, materials processing, food and cosmetics, energy, etc.; transportation: automotive, aeronautics, but also in the residential and tertiary sectors: heating, air conditioning.
Therefore, it is essential to have exchangers that fullfil properly their function. However, heat exchangers are all subjected to fouling phenomena, and their design raises issues relating to the mechanical state (welding, manufacturing exchange surfaces of low thickness, resistance to high pressures and temperature ...). Fouling is the formation of unwanted deposits on heat exchange surfaces, causing a heat resistance which reduces exchanger performance. In order to overcome the presence of this thermal resistance, a fouling factor is often taken into account in the design, which leads to oversize equipment. However this design procedure is often criticized since it does not solve the fouling problem and leads to considerable energy losses and investment cost. Other solutions are suggested to counter the fouling like cleaning actions, the use of anti- fouling chemicals, etc. However, the best way, to counter fouling is to observe and understand the fouling phenomenon.
Introduction to fouling in heat exchangers
This chapter describes the basics and science of fouling process. Different types of fouling and mechanisms that generate fouling are explained in this part.
Different types of fouling
The fouling refers to the deposits that appear in the heat exchangers surfaces. It can be found in different shapes: crystallization, sediments, biological residues, chemical reaction products, etc. These deposits have a thermal conductivity between 0.2 and 1 W.m-1.K-1  that reduces the heat exchanger performance and lead to an early ageing of the facilities.
The fouling process occurs in five stages:
Initiation: the first stage is related to the time before the first appearance of deposits in the facilities
The deposits transport up to the wall
The deposit attachment: every particle does not necessarily settle on the wall
Particle removal: some particles can be detached from the deposit layer
Deposit ageing: the chemical layout or crystalline of deposit can change over time which reduces the particle bond and weaken the deposit.
Heat exchangers are in contact with fluid that may contain airborne particles. These particles can settle on the heat exchanger walls and accumulate particles creating a deposit.
Particle deposit mechanisms on the walls
Several processes are involved in the transfer of the particles to the wall.
Transfer due to Brownian diffusion: the airborne particles are subjected to random motions.
Transfer due to gravity: particles are subjected to the gravitation field (P=mparticle.g). The gravity effect is significant in horizontal installations; with a slow fluid flow and large particles size (particles with a size higher than 1Âµm).
Transfer due to centrifugal force: the bond attraction is high -under the centrifugal force- in areas where the fluid flow re-circulates as shown in Figure 1.
Figure 1: Flow profile in a right angle bend 
Transfer due to thermal precipitation
When the fluid is subjected to a temperature gradient, particles move to the areas where the fluid is the coldest. In a heat exchanger, particles move to the areas with hot/cold interface. Consequently, when there is a considerable temperature difference between the two streams of a heat exchanger, the bond to walls due to thermal precipitation is high.
Transfer due to electrical precipitation
For small particles (size under 1Âµm), the electrical interaction is stronger than the gravity force and so affects the particles motion.
Transfer due to turbulence
The flow turbulence projects particles against the wall creating deposits.
Figure 2 summarizes the mechanisms that generate the deposit:
Figure 2: Mechanisms creating deposit 
To conclude, the deposit is more likely to be generated from the gravitational and centrifugal forces in a horizontal heat exchanger and contains many bends. Besides, a high thermal gradient increases considerably the deposit. However, the deposit can be partly prevented by maintaining a high flow velocity in the heat exchanger.
Scaling is a type of fouling that appears in the presence of calcium (Ca2+), magnesium (Mg2+) and bicarbonate (HCO3) ions in water. This is exemplified by a limestone deposit (calcium carbonate CaCO3) on the walls, according to the following reaction:
Ca2+ + CO32- â†” CaCO3 (1.1)
Water hardness, characterized by the presence of magnesium and calcium ions, is a significant scaling risk factor.
Another factor to bear in mind is the water temperature. Indeed, the increase in water temperature leads to the release of carbon dioxide which accelerates the previous reaction. That is why scaling is low on cold water pipes while it is common on hot water pipes such as water heaters.
A third risk factor is the presence of other ions in water such as iron Fe2+ ion that favors deposit. Conversely, when copper or zinc ions are present, the limestone does not attach the walls but stays airborne in water. The amount of these elements necessary to cause fouling is very low, around 10-5 g.L-1. Therefore, copper pipes must be favored.
Scaling is a type of fouling that is most commonly found within aqueous environment. It is often combined with other fouling mechanisms such as corrosion fouling.
Like scaling, corrosion fouling results from a chemical reaction. This reaction is an oxidation- reduction equation:
metal + n. H+ â†’ metal ions + n/2 (H2) (1.2)
Figure 3: Corrosion fouling mechanism 
Figure 3 shows the corrosion mechanism: it results from redox reactions that correspond to material migration and create cavities.
Biological fouling is the result of the growth of micro- organisms that attach heat exchanger surfaces. Three types of micro- organisms are involved in this phenomenon: bacteria, algae and fungi.
Bacteria: the bacteria growth is due to nutrient such as hydrocarbons, ammonia, etc. The bacterial cell is a living cell capable of feeding, growing and multiplying in the environment in which it operates.
Algae: they are living organisms that grow in the presence of solar energy with photosynthesis. Green and brown algae are those commonly found in cooling system. It is of high importance to identify the presence of algae because it causes silica deposit which can create blockages.
Fungi: these plants have neither root nor stem or leaf. They grow thanks to nutrients, but mainly thanks to changes in their physical conditions such as pH, humidity and ambient temperature.
Chemical reaction fouling
This type of fouling occurs when a chemical reaction takes place next to a heat exchange surface and the solid products of the reaction attach the surface. Often, it consists in a polymerization by auto- oxidation that spreads like a chain reaction with free radicals. Molecular oxygen plays a controlling role.
The reaction scheme is the following:
Initiation: RH + Z- â†’ R- + HZ (1.3)
Propagation: RÂ¨ + O2 â†’ ROOÂ¨ (1.4)
ROOÂ¨ + RH â†’ ROOH + RÂ¨ (1.5)
Stop: RÂ¨ + RÂ¨ â†’ RR (1.6)
ROOÂ¨ + RÂ¨ â†’ ROOR (1.7)
RH is a hydrocarbon molecule and ZÂ¨ is a free radical originates from metal ions and nitrogen or sulfur compounds.
Chemical reaction rates depend on temperature, pressure, concentration and the presence of catalysts.
This type of fouling is mainly found in petrochemical and food industries, and as well as heating circuits using an organic fluid.
This type of fouling results from a pure liquid solidification in contact with a sub- cooled exchange surface. It is an ice layer formatted inside the pipe. It can also refer to the deposit of an element in its high melting point within a liquid that is in contact with a cold surface exchange. Vapor may attach as well as a solid, without passing through the liquid state which corresponds to the frost formation.
Five major fouling categories are identified: particulate fouling, crystallization fouling, corrosion fouling, chemical reaction fouling and biological fouling. Installations can be subjected, at the same time, to several of these mechanisms that create a deposit.
The parameters that affect the fouling rate of exchange walls are various: temperature, pressure, the fluid nature and velocity, materials used in the exchanger construction, etc. Consequently, fouling does not affect all exchangers in the same way because their configurations are dissimilar.
Impact of fouling
Coletti  summarized main fouling problem in four categories:
Health and safety hazards while cleaning"
The fouling deposits have thermal conductivity that lead to the reduction of the heat transfer coefficient. Therefore, the energy efficiency is impacted as well and extra energy is required. Sikos and Klemes  have estimated that the energy consumed in crude distillations units because of fouling is between 10-20% higher than if it was cleaned.
Fouling also causes a reduction in cross- sectional area which creates pressure drops and consequently affects the hydraulic performances of the heat exchanger. At that point, additional pumping is required which leads to additional energy (electricity) consumption.
Costs can increase for several reasons. As explained previously, the extra energy consumption (like fuel) to counter the drops due to fouling leads to higher costs.
To reduce the fouling effects, cleaning actions are conducted but it induces the line activity to stop (for instance in a refinery) and consequently economic losses. Besides, the cleaning actions are complex and time- consuming processes that require expenses. However, they represent limited costs compared to the losses in the throughput and energy expenses.
Finally, to prevent these losses in heat transfer efficiency, some companies asked for the design of larger heat transfer surfaces or the use of anti- fouling chemicals which increase the capital costs. Particularly, these chemicals reduce considerably the fouling (65% reduction ) and the occurrence of cleaning actions but their implementations are costly.
The extra energy consumption caused by fouling is also responsible of environmental effects as it conducts to higher carbon dioxide emissions, for instance when more fuel is burnt in refineries. The second impact is of ecological aspect due to the presence of "carbonaceous deposits"  that can be found in the exchangers surfaces affected by fouling.
Health and safety hazards
The cleaning actions require meticulous safety procedures and scheduling as many damages can occur during each process, especially while cleaning pressurized unit and in the oil industry.
For the reasons described above, the impact of fouling is considerable on the performance of heat exchangers and more broadly on the entire process of generating. The goal is to understand, predict and minimize fouling in heat exchangers.
Description, fouling and caution of shell and tube heat exchangers
A great number of heat exchangers exist to meet the needs of the different industrial sectors. The aim of this chapter is to present these different heat exchangers by specifying the fouling risks according to their design.
2.1 Shell and tube heat exchangers'
This is one of the most common heat exchangers used in the industry. It is composed of a bundle of tubes in a shell. One of the fluids circulates inside the tubes while the other circulates outside the tubes, through the shell side.
Baffles are often added inside the shell and guide the fluid flow in the shell. The baffles generate turbulence, possibly increase the fluid velocity and improve the heat transfer coefficient. However, they can create at the same time a resistance to the flow, therefore pressure drop, and damaging vibrations. There are also recirculating regions at the corners that favor fouling and limit the heat exchange area. Consequently many studies on baffle types have been carried out involving CFD modeling . For instance, we can find in the literature the following baffles that have been designed for shell and tube heat exchangers: rod [8- 9], orifice  and helical baffles [11- 12]. More recently, a numerical modeling of the shell side of a shell- and- tube heat exchanger with flower baffles  have been developed and validated by experimental data. The computation results with the flower baffles shows a better overall thermal hydraulic performance than the heat exchanger with the helical baffles. These latter were so far considered to have outstanding thermal hydraulic performance, low vibrations and less subjected to fouling.
FigureÂ 4: Shell and Tube heat exchanger 
The tubes are supported at their ends by tube sheets. These are the sensitive parts of the heat exchangers as they are easily subjected to corrosion fouling.
Two tube configurations can be found in the literature: in square and in triangular pitch. The square pitch gives access to all of the external part of the tubes while the triangular pitch is more compact as shown in Figure 5.
FigureÂ 5: Square pitch (on the left), triangular pitch (on the right) 
2.2 Fouling risks and caution
If a very fouling fluid is being used, U-type exchangers should be avoided because they do not allow mechanical cleaning of the tubes. Besides, it is essential to circulate the more fouling fluid inside the tubes since tube side is easier to clean than the shell side. As explained previously, the square pitch is a better configuration for cleaning matters.
The baffle's configuration should be considered regarding the flow in the shell. In order to have a uniform velocity and to avoid re-circulating flows that lead to deposit, it is essential to consider the following recommendations:
to define a limited clearance between the baffles and the shell
to set a distance between the baffles slightly smaller than the shell diameter
baffles should define an opening of approximately 20% of the shell diameter
Clearance between the baffles and the shell
Distance between baffles
Figure 6: Baffle's configurations 
By implementing vents in the installation, the corrosive vapors can be released out of the exchanger. To avoid further fouling, preexisting micro cracks in the material should be minimized.
To conclude, the equipment configuration has important effects on the way fouling occurs, especially in the shell side where baffles can take different shapes and arrangements. Indeed, this side is subjected to many phenomena that make the modeling difficult: turbulence, flow recirculation in the corner between baffles and the tube, fouling. Therefore, it is important to investigate in details temperature, velocity and pressure fields and especially capture the flow behavior in the shell side.
Modeling of heat exchangers undergoing chemical reaction fouling
Numerical modeling methods are sought increasingly to study the performance of heat exchangers. One of the main advantages of this method compared to the experimental method is economical. In addition, it allows visibility of some phenomena inaccessible to experimentation and often saves time compared to experimental approach. However, the modeling of loaded configurations is complex and often requires a simplification of the studied element and validation of computation results by comparison with experimental data.
3.1 Mathematical modeling
This research project focuses on the chemical reaction type of fouling. As explained previously, the tubes located in each pass can be represented by one single tube model, assuming that they are subjected to similar thermal influences. The common method to assess the fouling dynamics is to calculate the fouling resistance that would be added to the heat transfer equations.
3.1.1 Governing heat transfer equations
The calculation of the fouling resistance is commonly used in modeling. We can find in the literature two main methodologies for heat exchanger design that take into account fouling: the LMTD (log mean temperature difference) method  and the Îµ- NTU approach  .
The following figure shows the fouling phenomenon for a single tube heat exchanger and describes the nomenclature used in the mass transfer equations detailed below. This model is distributed axially (one dimension).
Figure 7: Fouling layer within the tube and the shell side 
First, the heat duty Q (W) is calculated for both (shell and tube) sides of the tube wall:
Where and (kg.s-1) are the mass flow rate of the hot and cold fluids, and (J.kg-1.K-1) the specific heat capacity,, and, (K) the inlet and outlet temperature of the two fluids.
The total heat transfer Q (W) in the exchanger can also been expressed by the Hausbrand formula:
where U (W. m-2. K-1) is the overall heat transfer coefficient; S (mÂ²) is the heat transfer surface area of the exchanger, Î”Tlm is the appropriate mean temperature difference between the hot and cold fluids. According to the heat exchanger configuration, the mean temperature is adjusted with a dimensionless coefficient Îµ departing from the counter- current flow so that:
Î”Tlm = Îµ Î”TÂ°lm (3.3)
where Î”TÂ°lm is the mean temperature for a counter- current flow configuration. 
The logarithmic mean temperature is defined by:
The overall heat transfer coefficient U (W.m-2.K-1) is equal to the sum of the resistances including the tube- side and shell- side fouling resistances, Rf,t and Rf,s:
where So (mÂ²) and Si (mÂ²) are the outer and inner heat transfer areas, , ht and hs are the tube- side and shell- side convective heat transfer coefficients, Î´w is the wall thickness, Î»w is the thermal conductivity Â (WÂ·m-1Â·K-1), Sm is the logarithmic mean area :
Fouling resistance values to design heat exchangers can be found in the Tubular Heat Exchangers Manufacturers Association tables (TEMA) . However, these tables are increasingly challenged [19- 22] as they do not take into account some important parameters such as the dynamic nature of fouling and its dependence on process variables (fluid velocity, temperature and composition). Indeed, the calculation of the fouling resistance implied assumptions and rise up uncertainties as constant density and specific heat capacity. Other tables can be found in the literature and sometimes companies set up their tables based on their own calculations and experiments  .
3.1.2 Fouling model
Many correlations have been developed over the years for fouling model trying to take into account the variables which affect fouling (composition, temperature, pressure, velocity, shear stress and surface conditions) . Epstein  has carried out a review of different existing fouling models. Many of them lead to a considerable difference between the simulation results and the experimental data. Indeed, these models can present limitations. The fouling threshold concept  has been evocated according to experiments, at some velocities, the fouling deposition does not occur. However this type of models like all lumped models, does not take into account the local variations such as the variation in the heat transfer coefficient. 
Through these models, Schreier (1194)  established three criteria the model should take into account:
- "the rates of the processes lead to deposition
- the temperature distribution and deposit thickness profile
- the effect of flow on deposition and re-entrainment." 
Efforts should be put in establishing dynamic model of heat exchangers that takes into account the fouling properly. Roetze and Xuan  developed an extensive distributed model where the fouling is represented following a simple asymptotic model.
Aging process of the fouling must be considered as well. Indeed, over the time, the fouling deposit is subjected to chemical changes that alter its physical composition as mentioned by Coletti et al. : "a soft, gel- like material to a harder, coke- like". The physical properties such as the viscosity, thermal conductivity, etc. can also be altered. Ishiyama et al.  and later Coletti et al. , have developed respectively aging lumped and distributed model to represent this process.
While there are a considerable number of numerical modeling studies to improve the performance of the tube side [30-34], there is little knowledge on the shell side in the literature and even fewer studies considering fouling. This is due to the complexity of the velocity and temperature fields increased by the complicated geometry (baffles) of this side. Indeed, the pressure drop calculations usually used to calculate the flow patterns and the wall shear stress cannot be calculated on the shell side. Fryer and Slater  explored the shell side by developing a distributed model that integrates milk fouling on the shell side. However, this model does not take into account the heat transfer through the tube wall. Besides, it cannot be extended to multipass heat exchangers .
Computational Fluid Dynamics (CFD) appears to be an appropriate approach to overcome these limitations. One of the few CFD researches that can be found in the literature and investigates the shell side has been led by Clarke and Nicolas . To simplify the configuration as a matter of computation load, they considered the shell side as a porous medium modeling the baffles influence. However the tube side model is limited to a linear temperature variation and with a constant heat transfer coefficient. Therefore, the interaction between the shell side and tube side is not taken into account in this simulation: this is one of the challenges of my research project.
In summary, we mostly find in the literature lumped models that do not take into account properly the dynamic, or we find distributed models that describe the dynamic but do not consider or otherwise simplify fouling.
3.1.3 Studied approaches: A dynamic and distributed model of shell- and- tube heat exchangers undergoing fouling 
According to Figure 7 the physical system that is composed of five distinct to be modeled: the shell side, the shell- side fouling layer, the tube wall, the tube- side fouling layer and the tube side.
Coletti and Macchietto (2010)  have developed a distributed modeling that explore the tube- side fouling in shell- and tube exchangers and so the fouling effects over the exchanger hydraulic and thermal performances. The model is based on estimates of plant measurements such as temperature or flow rates rather than the calculation of derived fouling resistance. For each domain, the heat balance equation is defined neglecting the heat losses as shown below. As mentioned previously, this model does not explore the shell side fouling, so the scheme is composed of only four domains.
220.127.116.11 Thermal governing equations
For this domain, the heat balance equation is expressed in only one dimension that is to say in the axial coordinate (z axis):
where ÏS(z) is the shell side fluid density, cp,s(z) is its heat capacity, Ts(z) is the shell fluid temperature, Î»S is the thermal conductivity, As is the shell cross- section area, Np is the number of tube passes, Ps,n is the wetted perimeter, Tw,n is the wall temperature of the tube n. The second term of the equation (3.7) is negative if we are modeling a first tube pass in a counter- current arrangement. The shell- side heat transfer coefficient hs is defined by the Bell- Delaware method :
where hid is the heat transfer coefficient for an ideal cross- flow that depends on the space position regarding the z axis. are the simplified correction factors that include "the segmental baffle window, the baffle leakage, the bypass tube bundle to shell, the laminar heat transfer and the no equal inlet/ outlet baffle spacing" . However, for some cases, these simplified factors do not meet all requirements if the fluid is different or if there is fouling on the shell side or if the geometry is modified or for a different heat transfer surface, etc. Consequently, this model is limited, especially for the shell- side fouling in which is interested. One solution would be to add a "shell- side fouling correction factor" but no table or empirical relations have been provided, and besides, the other limitations expressed previously would still remain. Thus shell- side modeling requires a more sophisticated approach.
The tube wall satisfies the standard conduction equation that is expressed in polar coordinate in both axial and radial directions:
where Ïw is the density, cp,w is the heat capacity of the metal wall and Tw,n(z,r) is the temperature.
Tube side fouling
This domain is defined for z comprised between 0 and L, the tube length and between the tube inner radius Ri and the deposit interface of the fouling layer Rflow expressed as:
where Î´n is the deposit thickness with respect to the z axis. To determine Î´n, the fouling resistance Rf,n(z) needs to be calculated. The most common method to find the fouling resistance is given by the Ebert- Panchal  modeling. Coletti et al  have adjusted this model here to distributed model and according to local conditions. Hence, the thickness is calculated by:
The heat balance equation is expressed as a conduction phenomenon like for the tube wall:
where ÏL is the constant density of the deposit layer, cp,L is its constant heat capacity. Î»L,n is the thermal conductivity of the layer and TL,n the temperature. These latter depend on the spatial position (with respect to the axis z and the radial position r).
To solve this partial differential equation, they introduced a dimensionless number defined by:
Consequently the equation (3.11) becomes for the domain defined by r* comprised between 0 (in case r is equal to Ri) and 1 (in cas r is equal to Rflow):
Fouling aging distributed model has been considered by Coletti  here as well; details of the mathematical model can be found in Coletti et al.  and their previous publications.
As for the tube side, like for the shell side, the heat balance equation is expressed in one dimension:
where Ïn(z) is the tube side fluid density, cp,n(z) is its heat capacity, Tn(z) is the shell fluid temperature, Î»n is the thermal conductivity that depends on the local conditions. Unlike the shell side, the cross sectional area here varies as a function of the flow radius Rflow,n as expressed in the equation:
18.104.22.168 Hydraulic aspects
Hydraulic performances are expressed by the velocities, pressure drop and the heat transfer coefficient that include the fouling impact inside the tube.
The velocity variation is expressed by:
where is the mass flowrate, Aflow,n is the flow area that depends on the flow radius Rflow,n varying according the fouling layer thickness.
The pressure drop is expressed by:
where Cf is the Fanning friction factor for rough tubes depending on the Reynolds number and defined by Yeap et al. (2004) .
Heat transfer coefficient
The heat transfer coefficient is expressed by:
where the pipe length is at least ten times greater than its pipe diameter and the Nusselt number is defined by the Dittus- Boelter relationship:
With Re > 104 and 0.7 < Pr < 160.
To summarize, this model gives assess to the thermo- hydraulic performances and takes into account the fouling only inside the tube. What we are trying to achieve then is the modeling of the inside tube fouling and in the shell side as well.
3.2 Computational Fluid Dynamic (CFD)
The CFD technique is found to be an appropriate approach to overcome the experimental limitations and to predict fouling behavior in heat exchangers. The success of this technique relies on both the model as discussed above, and a good mastery of the CFD code settings.
3.2.1 General descriptions of the CFD technique
This practice is based on five steps:
The commercial CFD codes (FLUENT, StarCCM+, etc.) usually allow solving the equations of fluid mechanics (Navier-Stokes, and continuity equation) by the finite volume method. The equations solved in the 2D or 3D model are:
Conservation equation of momentum (Navier-Stokes)
Conservation equation of mass
The mesh must be sufficiently thin in the areas where the gradients of pressure, velocity, turbulence, temperature are high. The boundary layers near the walls should be systematically checked because they often represent locations with mesh errors. Several types of mesh are available: trimmer, hexahedral, tetrahedral.
For each model, it is necessary to perform a mesh independence test by varying different parameters of the mesh properties to determine mesh density beyond which a solution value (velocity, temperature) do not vary any more.
mesh analysis 2.png
Figure 8: Mesh independence test 
The asymptotic character marks the stability and proper mesh density. The red cross corresponds to the minimum and appropriate number of cells that the mesh must contain.
The last step consists in fixing the solver parameter (two or tri dimension, segregated or coupled method, flow regime, laminar/ turbulent model, steady or unsteady state, etc.), physics and boundary conditions of the model: the materials (aluminum, copper,etc) in case of a solid, the fluid properties, type of scheme (convective, conductive, etc.), velocity profile (uniform or not), the outlet pressure difference, etc.
The iterative solver seeks to balance conservation equations of mass, momentum and energy. The solver defines residuals (difference between the calculated and the ideal solution). Residuals are calculated from the velocity, pressure and temperature corrections at each iteration. During the calculations, the residual values of continuity and momentum equations are followed. If the physics and mesh have been completed properly, â€‹â€‹then the residuals will converge rapidly towards the asymptotes.
3.2.2 CFD Modeling of the shell side of heat exchangers without fouling
As mentioned previously, You et al  have used a numerical modeling of heat transfer and flow resistance on the shell side of a shell- and- tube heat exchanger. The objective is to explore the effect of flower baffles configuration on the exchanger's performances. This is a distinctive investigation because due to computation load, most studies on the shell side are experimental.
The model is based on volumetric porosity and surface permeability as it reduces the computation load. Indeed, the fluid flow and heat transfer on the shell side take into account the influence of the tubes by a distributed flow resistance and heat source. Experimental data enabled to find correlations used to assign values for the distributed flow resistance and heat source. Then the tube- side and shell- side fluids were meshed in the same grid.
The governing equations for the shell side are based on few assumptions:
Reynolds's number is between 6Â 813 and 22Â 326
The shell side fluid is continuous, incompressible and Newtonian
The volumetric porosity and surface permeability are uniform contrary to the distributed heat source and flow resistance mentioned previously
Then, the conservation equations are expressed in Cartesian coordinate with the following shell- side fluid parameters:
Where Ï is the density, u is the velocity, p is the static pressure, T is the static temperature, Âµ is the dynamic viscosity (sum of the laminar and turbulent dynamic viscosities), cp is the specific heat capacity and Î» is the thermal conductivity of the shell side fluid. Fv is the volumetric porosity, fs is the surface permeability, f is the friction factor and Î© is the specific surface area of the tube wall. Tt is the fluid temperature on the tube side.
The distributed flow resistance is taking into account by the term in the (3.22) equation which is calculated thanks to empirical correlations. It represents the impact of the tubes on the shell- side fluid flow.
The distributed heat source is represented by the term K(Tt - T) in the equation (3.23). The parameter K is the overall heat transfer coefficient expressed by the following equation:
Where di is the inner diameter of tubes, do is the outer diameter of tubes, Î»w is the heat conductivity of tube walls. The heat transfer coefficient of the tube side ht is given by the Dittus- Boetler relation based on a turbulent flow (Reynolds's number comprised between 10Â 000 and 250Â 000; Prandtl's number comprised between 0.7 and 120):
The heat transfer coefficient hs on the shell side is calculated according to the Zukauskas empirical correlations . This coefficient depends on tubes configuration and the Reynolds's number:
- for staggered tube bundles:
- for in-line tube bundles:
Where St and Sl are respectively the transverse and longitudinal tube distances.
The governing equation (energy conservation) is expressed in one dimension since the flow follows the axial direction:
Where Ït is the density, ut is the velocity, cp,t is the specific heat capacity, fs,t is the surface permeability of tube- side fluid. The heat conduction is neglected.
The domain is defined as shown in Figure 9 where the shell is represented with baffles (flower type) inside and the inlet and outlet tubes. However, the thickness of baffles is ignored.
Figure 9: Computation domain 
The model and meshing are generated by Gambit which is a CFD preprocessor. The energy equation of the tube side is not considered in the model since the temperature variation is not significant. The commercial CFD code that has been used here is FLUENT. The method applied for the discretization of the conservation equations is the finite volume method, and the second- order upwind scheme is employed for the momentum and energy terms.
This CFD study enabled to get the temperature and velocity profiles as well as the convective heat transfer coefficient on the shell side. This simulation has been carried out for two cases: shell side with and without flower baffles. Therefore, the comparisons between thermal and hydraulic profiles enable to observe the impact of those baffles. The same approach can be conducted for our project with one simulation including the shell- side fouling and one without, so we can assess the impact of fouling by comparing the thermal and velocity profiles. The limitation of this model is again the fact that it does not take into account fouling inside and outside the tube in the conservation equations but it remains a good example of how to couple the tube and shell parts of a shell- and- tube heat exchanger.
3.2.3 CFD modeling of fouling
Few investigations of fouling with a CFD approach have been reported. In terms of the fouling structure, a CFD simulation of the crystallization of calcium sulfate on a flat plate has been conducted by Brahim et al. . Walker and Sheikholeslami  have explored the calcium sulfate as well regarding the velocity effects on the isothermal and non isothermal flow.
Zhang et al  have investigated the different influences such as the air speed, the flow turbulence, the particle size and surface orientations on the fouling deposit. The results of these simulations show that fouling is more likely to occur in a developing turbulent flow than in a fully settled turbulent flow. Furthermore, in case of ventilated flow, the air velocity and particle size represent the major impacts in the fouling deposition process.
Bayat et al  have developed an innovative CFD modeling of fouling in shell- and - tube heat exchangers that predict the probability of the fluid to deposit on the tube wall and the thickness of the fouling layer. The fouling rate is modeled in a turbulent flow (k-Ï‰ model) and this model takes into account the chemical components impacts and the shell- side heat transfer coefficient. The fluid considered here, is composed of the three following components: petroleum, asphaltene and salt. Their adhesion to the tube wall is predicted according to their viscosity and the shear stress on the wall. The molecular diffusion coefficients were considered in the model as well.
These authors have developed a 2D computational domain for the computational loaded concern. For the same reason and like in our project, they have focused their work on the modeling of one single tube (Figure 10). The model is considered in an unsteady state, the Reynolds averaged Navier- Stokes (RANS) equations are solved and the flow is assumed incompressible. The very objective of this study is to observe the behavior of the fouling and in particular each component for their prediction.
Figure 10: Single tube model with boundary conditions 
The dynamic equations of the distributed model discussed previously and developed by Coletti et al. were implemented in the gPROMS modeling system  and used for the CFD. The scheme chose in the model is a second order centered finite difference. The following information required are according to the type of heat exchanger: number of passes, number of shells, number of tubes, diameters, fluid physical properties, fouling aging structure, etc.; and the following inputs: "inlet flow rates, temperatures, and pressure of the hot and cold steams". And finally, the boundary and initial conditions need to be set. Hence, this model can provide the outlet temperatures, the hydraulic variations (velocities, pressure drop) and information concerning the fouling structure, thickness and influence. These same information and outputs should be followed for the shell- side fouling. This CFD modeling enables to observe several aspects of the fouling such as the fouling process with respect to the local conditions, aging mechanism, the appropriate environments and the difference according to the heat exchanger geometry. The results presented and compared with some case data, they are in good agreement and validate this remarkable model. Therefore further studies such as extending the fouling model in the shell- side can be based on this work.
Fouling phenomenon is often encountered in the food process industry and few CFD approach can be found  on this subject. Grijspeerdt et al  observed the fouling process within a heat exchanger containing milk. The simulation enables to spot the most frequent locations of fouling which appeared to depend on the wall temperature. Bonis et al  studied the effect of fouling on the hydraulic performance of the same type of heat exchanger by observing the flow velocity profile. The results showed that the fouling rate increases as the Reynolds number increases. This result is counter intuitive.
To conclude, as the shell- side fouling modeling has not been studied satisfactorily so far, the problem is open to any approach. This problem requires a much complicated approach compared to the tube side fouling and the heat exchanger modeling without fouling.
To conduct this investigation, firstly, we consider an innovative approach that consists in coupling the tube side fouling model developed by Coletti in gPROMS and the CFD modeling of the shell- side with fouling. These two models are coupled via an interface that links the tube wall to the shell side fouling. To reach this goal, several stages have to be achieved as explained in the next chapter (4.2).
Research project objectives and planning
4.1 Problem definition and objectives
The objective of this ressearch project is to study the influence of fouling in the shell side on the heat exchanger's performances using CFD modeling. So far, most of the previous work considered that the fouling in the tube side is often the dominant resistance to heat transfer . Therefore and also because it presents more challenges, little research has focused on the shell side. However, considerable differences can sometimes be observed while comparing the numerical and experimental data which may raise questions on the credibility of neglecting shell- side fouling. This work will present a rare and interesting area of investigation. Besides, by considering the shell- side fouling, this project will enable to develop a more general model with a systematic strategy.
The idea is based on trying to apply to the shell side the numerical modelings developed for the tube side in the literature. For the sake of simplicity of the CFD simulation, the modeling of a shell-and-tube heat exchanger is firstly reduced to a single tube model.
The influence in the overall heat transfer of the shell side fouling will be evaluated by simulating the dynamic behavior and calculating thermo-hydraulic performances.
4.2 Project stages
Most of the models presented in the review did not take into account the shell-side fouling. This project represents a new venture. The idea is to use an existing model to study the shell-side fouling.
Firstly, the model presented by Coletti and Macchietto  will be tested. Since the models already exist in gPROMS for the tube side fouling, the work is to perform a CFD study for a single tube including fouling in the shell side. The commercial CFD code used will be FLUENT which requires a learning and familiarization period. An existing interface provides the connection between FLUENT and gPROMS. Three steps of simulation need to be achieved to reach this aim:
Task 1: first, we need to work on the coupling method between gPROMS and the CFD.
Task 2: then we will achieve the coupling between the tube side fouling model on gPROMS and the CFD modeling of the shell side without fouling. This step does not consider the fouling in the shell side and consequently represents a simpler problem. However, this is essential to verify the accuracy of the coupling system by observing a satisfactory flow dynamic prediction.
Task 3: finally this step brings us closer to the ultimate goal of coupling between the tube side fouling model in gPROMS and the CFD modeling of the shell side with fouling for a single tube in a shell.
Then, to validate the CFD study, the numerical results will be compared with experimental data. If successful, we will be able to extend the model to a second tube, and so on.
Throughout the project, new publications can appear and it is important to stay up-to-date.
Finally, in case of failure of the models proposed by Coletti et al , or in order to go further, other models found in the literature can be tested with a CFD approach.
These steps describe an ambitious project, and from experience, it is possible that constraints appear in the CFD simulation and delay the project.
Familiarization with FLUENT and tutorials
Extension to two tubes (possibly)
Simulation using other models and CFD approach (possibly)
Figure 11: Project timeline