Improving flushing processes through targeted control of the temperature boundary conditions

In this contribution the authors investigate how flushing of chocolate using a follow‐up chocolate in a straight horizontal pipe is affected by temperature. The authors investigate a non‐uniform distribution of temperature across the considered domain. This is done using two cases, where the first exhibits a wall temperature deviating from the normal process temperature and the second exhibits a differently tempered follow‐up chocolate. The investigations are performed using unsteady three‐dimensional numerical simulations with an OpenFOAM multiphase solver, which is extended to include an additional equation for energy conservation. The physical properties of the chocolate are analyzed with respect to their dependence on temperature and implemented in a new model in OpenFOAM. The results of both cases are assessed according to industrially relevant questions. Among others, they include the amount of follow‐up chocolate needed to achieve a set goal of cleanliness. The time needed to achieve this is also considered. A dimensionless time is used to compare the different cases. Recommendations are provided on how different temperature of pipe wall and follow‐up chocolate may lead to improved flushing processes and which savings may be achieved with this strategy.


INTRODUCTION
The international standard ISO 14159 [1] describes the hygiene requirements for the design of machinery in the food industry and defines cleaning as the removal of any unwanted matter.Cleaning is necessary to avoid the unwanted change of the product, which may be caused by biological, chemical or physical factors.An example for the latter is the contamination of a follow-up product by remains of previous product and will be the focus of this contribution.Different cleaning strategies may be followed.Easily accessible parts of a production plant may be dismantled and cleaned manually using scrapers or cloths.Large containers are either cleaned manually or by an impinging jet of cleaning fluid.Hard to reach internal areas, such as long pipes or heat exchangers, are typically cleaned by flushing the area with a cleaning fluid, such as water or detergents.For products with low water activity and high viscosity, such as chocolate, the use of water can deteriorate the quality of the final product significantly [2].The use of water may lead to an increased viscosity requiring more energy for pumps.It may also result in unwanted properties of the final product, such as a sandy taste [2].
The increased variety of produced chocolates often requires multiple different chocolates to be produced on the same line.After one batch of chocolate is finished and before the follow-up chocolate is produced, the unwanted previous chocolate has to be removed and the area has to be filled with the follow-up chocolate.Both of these steps can be combined using a flushing process, where the flushing fluid is the follow-up product.Benefits of this practice include the small change-over time between products, time savings from not requiring the disassembly and reassembly of the line and no contact of chocolate with water, that is, no decrease in final product quality.This paper investigates ways to influence flushing processes of chocolate in straight horizontal pipes with the aim of reducing either the required energy, the required flushing time or the required flushing product, to enable more sustainable processes in the future.
Flushing processes for pipes may be divided into two stages [3,4].The starting point is a situation where the system is filled entirely with previous product.During the first stage, the front of the follow-up fluid displaces the core of the pipe filled with previous fluid.The stage is therefore referred to as "core removal".
The first stage smoothly transitions into the second stage, during which the thin layer of remaining previous fluid on the wall is removed by the shear stress on the interface of both chocolates.This shear stress drives the mass flow in the thin layer of previous chocolate remaining near the wall.
In this process, the viscosity impacts two different effects.One results from the overall level of viscosity which reduces the shear stress at the wall and, hence, the required energy to drive the flow.The second effect results from different viscosities of the two fluids.Here, in particular, it is advantageous if the viscosity of the follow-up product is larger than that of the previous, so that the less viscous core region of previous fluid can be pushed out by a solid plug of follow-up fluid.This results in quick and efficient core removal, resulting in shorter flushing times.When the driving pressure difference is constant, a low viscosity of the previous fluid is beneficial, as it results in a higher bulk velocity and thus a higher velocity in the remaining layer, also leading to shorter flushing times.
From this reasoning an interesting approach for applications may be to control the viscosity of the previous and followup product.Viscosity modification may be achieved through targeted control of the temperature.The present study, therefore, is dedicated to investigating flushing processes where the previous and follow-up product have different temperatures, to study the effect of the changed relative viscosity on the overall process.Secondly, the influence of the pipe wall temperature is studied.For a heated wall, the layer removal phase is expected to exhibit higher mass flows due to the reduced viscosity.
To investigate the two cases, this paper is structured as follows.First, the material properties of two real chocolates are determined and modelled in Section 2. The simulation model is introduced in Section 3 and the results are discussed in Section 4.

Rheology
Liquid chocolate is a suspension of solid cocoa, milk and sugar particles embedded in a continuous phase of liquid cocoa butter.Low stresses  <  0 are unable to break up the particles at rest and the fluid behaves like a solid.This results in a yield stress  0 .For stresses  >  0 , a shear-induced loss of structure occurs which leads to a lower apparent viscosity.With increasing shear stress, the shear-induced loss of structure is more and more counterbalanced by a rebuilding of structure.This results in an equilibrium viscosity  ∞ being reached at high shear rates [5].Chocolate therefore exhibits non-Newtonian behavior with a non-linear relationship between shear rate and viscosity.An apparent viscosity can be described for any given shear rate.Several studies have shown that the viscosity of liquid chocolate strongly depends on the particle size distribution of the solid particles within the continuous phase [6], the manufacturing process [7], the ingredients, for example, milk powder type [8,9], the chocolate type [10] and the temperature [7,11].Other studies were conducted to determine a suitable model to describe the resulting shear stress as a function of the strain rate [10,12,13].They obtained good fits with established models, for example, Bingham and Herschel-Bulkley.Glicerina et al. [10] showed that the fit quality of the Casson, Power-Law and Windhab model to their experimental data was high, regardless of the chosen model.The Internation Confectionary Association (ICA) has introduced an analytical method [14], in which the is recommended to describe the flow behavior of chocolate, which was used in this work.Additional model parameters are the shear rate at which the maximum of shear induced loss of structure occurs γ * , the equilibrium viscosity reached at high shear rates  ∞ and  1 , which is an extrapolated value based on the asymptotic behavior of the model [5].
Following the analytical method, the Windhab model parameters were determined using regression for both a white and a dark chocolate at constant temperatures  = [28, 35, 40, 45, 52] • C. It is important to note, that the yield stress  0 is an extrapolated value that cannot be measured directly and only results from the regression of the measured data.With increasing temperature the viscosity decreases, which is manifested in decreasing values for  0 ,  1 , and  ∞ .
Often, the dependence of the dynamic viscosity of pure fluids on temperature is described using an Arrhenius equation.A similar approach is employed here, to model the kinematic viscosity  = ∕( γ).The temperature dependency of each parameter  in Equation ( 1) is modeled using where   ,   ,   are the modeling constants for the quantity .Since chocolate solidifies at room temperature,   was introduced, which enables the description of asymptotic behavior when this temperature is reached.For the scope of this work, the modeling constants for each parameter were determined as follows: First, the rheological measurements at isothermal conditions were evaluated and the Windhab model was fitted to the data, resulting in values for  0 ,  1 , γ * , and  ∞ at discrete temperatures.Second, the values of each parameter were fitted across the temperature range using Equation (2), which finally lead to twelve model parameters to describe the temperature dependent viscosity.It is important to note, that a limit was imposed for   to avoid asymptotic behavior in the range  = 40 … 52 • C where numerical calculations are carried out.The lower limit is derived from industrial practice, where flushing below  = 40 • C is not carried out because the chocolate is too thick and not flowable enough.The upper limit,  = 52 • C, was set because changes in chocolate quality are likely for temperatures higher than this value [16].For white chocolate, the resulting parameter values for  ∞ and γ * from the first step of the fitting procedure resulted in very low variations and were therefore assumed to be linear ( ∞ = −0.04Pa s∕ • C  + 2.87 Pa s) and constant respectively.The model equations were implemented in Open-FOAM as temperature and shear rate dependent viscosity.The final model parameters for both dark and white chocolate are listed in Table 1.

Thermal properties
Besides the rheological properties the thermal properties of both chocolates were modeled as well.For the thermal conductivity , values from literature were used [17], values for the density  were obtained from own measurements, and the heat capacity  was measured and shown to be linearly dependent on temperature, that is,  =  1 +  2 .An overview of all model constants employed is given in Table 2.

SIMULATION MODEL
The calculation of the flow field , pressure field  and temperature field  were conducted with the open source framework OpenFOAM using the finite volume method.The Navier-Stokes Equations ( 3)-( 4) and an energy equation were solved.Employing the relation dℎ =   d between enthalphy and temperature, the latter can be rewritten as Equation ( 5) for temperature when no phase change The resulting system of equations reads To distinguish between dark and white chocolate the volume of fluid method is used, where a scalar  is used to describe the volume fraction of one fluid inside a cell.For  = 1 a cell is filled completely with dark chocolate, for  = 0 it is completely filled with white chocolate.The volume fraction  throughout the computational domain is governed by the equation The computational domain consists of a horizontal straight pipe with length  = 1 m and radius  = 13 mm.The axis of the pipe is in positive -direction, as is the direction of the flow, whereas, the gravity vector  is directed in negative -direction.To save computational time, a symmetry plane in the - plane was used.Since the particles contained in chocolate suspensions can be up to  p = 100 μm in diameter, and are most commonly around  p = 30 μm in diameter [18], cells on the wall with Δ = 130 μm were created.This was done to ensure that the assumption of a continuous Windhab fluid was still valid in cells near the wall while simultaneously obtaining a fine resolution of the flow.The cells were coarsened towards the center of the pipe and linearly extruded along the -axis, resulting in a total of 840k cells.At the inlet (index in), a developed velocity profile based on the analytical solution of single phase pipe flow of a Windhab fluid [19] was imposed, with an average velocity of  b = 0.1 m∕s.Since dark chocolate is considered as follow-up product, the volume fraction at the inlet is  in = 1.At the outlet, a Neumann boundary condition was used for all variables.At the wall (index W), a no-slip boundary condition was set for the velocity,  W = 0, and a Neumann condition for the volume fraction.Initially, (index 0), the pipe was filled entirely with previous product at rest, that is, white chocolate  0 = 0 at  0 = 0.
Three groups of simulations with two simulations per group were conducted.The respective boundary conditions for temperature were varied by case and are listed in Table 3.The first group consists of isothermal simulations (I52 and I40) F I G U R E 1 Cleaned radius over dimensionless time for isothermal case: (A) for case I40 at different cross-sections; (B) for cases I40 and I52 using a logarithmic scale.
used as reference cases.The second group investigates the effect of heated product.In case P52 the follow-up product, that is, dark chocolate was given a higher temperature, making it less viscous, while the previous product, that is, white chocolate was kept at a lower temperature.In case P40 the previous product was heated, while the follow-up product was kept at a lower temperature.Finally, the last group investigates the influence of heated walls.In case W52 the wall was kept at a constant temperature, higher than that of the previous and the follow-up product and in case W40 the opposite was imposed.

Isothermal cases
First, the group of isothermal simulations is evaluated, where the temperature throughout the computational domain does not change.Case I52, as in Table 3, has a uniform temperature of  = 52 • C whereas, case I40 has a uniform temperature of  = 40 • C. The cleaning process is evaluated using the cleaned radius  c .It is calculated by extracting a cross section of the pipe at a defined location   and determining the area filled with follow-up chocolate by integrating the volume fraction .From the circle of equivalent area the cleaned radius is then determined as In Figure 1A, the cleaned radius is non-dimensionalized using the pipe radius  and plotted across the non-dimensional time t as proposed by the present authors in [4] t =  max    (8) using the location of the cross section   , the physical time  and the maximum velocity  max .The latter was determined using the analytical solution for single phase flow [19].
Figure 1A shows the resulting temporal evolution of the cleaned radius for various positions along the -axis of the pipe.The respective stages of the flushing process can be distinguished very well.For t < 1 no cleaning occurs, as follow-up fluid has not reached the cross section.Afterwards the first stage begins, during which the core of the pipe is cleaned.This can be seen by the rapid increase of  c .It is important to note, that at t = 1 a jump from  c = 0 to a much higher value occurs which is about  0 = 2 0 ∕Δ.This is the plugflow radius arising from the yield stress  0 of the flushing fluid and the driving pressure difference across the pipe length Δ∕.Due to the different material properties of previous and follow-up chocolate a deformation of the velocity profile occurs, so that the single-phase relation for  0 is an approximation only.
The first stage smoothly transitions into the second phase, during which the removal of the remaining layer occurs.It is characterized by the slow increase in  c .It is further noteworthy, that the dimensionless representation of the process leads to a nearly common graph for all cross sections, resulting in an easier representation of the process which will F I G U R E 2 Cleaned radius over dimensionless time for different simulation groups: (A) for heated follow-up product P52 and heated previous product P40; (B) for a pipe wall at higher temperature than the contained products W52 and for a pipe wall at lower temperature than the contained products W40.be used throughout the paper.Figure 1B shows the results for both isothermal cases in comparison.A single graph was created from the data of the different cross sections and a logarithmic scale was employed.As can be seen, the cleaned radius for case I52 is slightly higher, but the difference between both cases is small.It is supposed that the influencing factor for the flushing process is the ratio of the follow-up fluid viscosity to that of the previous fluid.In heating both products to a higher temperature, both viscosities change by a nearly identical percentage, thus leading to a negligible difference in the viscosity ratio at the increased temperature.The required energy to heat both products by Δ = 12 K can be approximated from  = mcΔ, with  depending on  1 and  2 (see Table 2).In contrast, the energy required to power the pumps can be calculated from  = ΔΔ2 ∫  0 ()d.While the energy required for the pumps in case I40 is higher than that in case I52 by a factor of  I40 ∕ I52 = 1.4, the amount of energy required to heat the product for case I52 is higher by a factor of  I52 ∕ I52 = 1900.The energy required to heat both products to a higher temperature therefore exceeds the energy required to pump the fluid at a lower temperature by more than three orders of magnitude.

Heated product
The second investigated case considers different temperatures of previous and follow-up fluid.Heating one product to  = 52 • C while keeping the other at  = 40 • C influences the viscosity ratio of the two chocolates.In case P52 the followup product is heated, which results in a reduced viscosity and thus smaller viscosity ratio.In case P40, the previous product is heated, which leads to an increased viscosity ratio.The results of the cleaned radius over dimensionless time are shown in Figure 2A.Initially, the cleaned radius is larger for case P52.This can be attributed to a slightly larger plug flow radius  0 .During the core removal stage, the cleaned radius for case P40 is larger, due to the large viscosity ratio arising from the low and high temperature of the flushing and previous product respectively.A maximum difference of up to 10 % can be detected between both cases.This difference decays over time once core removal blends into layer removal.This is attributed to the decreasing temperature difference between follow-up and previous chocolate.In case P40, the layer of chocolate on the wall cools down to  = 40 • C, thus increasing the viscosity and decreasing the flow velocity in that layer.In case P52, it is heated by the passing flushing chocolate to  = 52 • C which leads to a decreased viscosity and therefore higher flow velocity in the layer.While a high viscosity ratio benefits the cleaning process during core removal, the influencing factor during layer removal is the viscosity of the layer itself which may be influenced using heated flushing product.For large dimensionless times no difference between the two cases can be distinguished.Furthermore, the cleaned radius, towards which both cases tend over time, is in very good agreement with the one obtained in the isothermal cases.The required energy for pumping remains the same as in the isothermal case  I40 ∕ I52 =  P40 ∕ P52 = 1.4 as the inlet temperatures  in are identical (see Table 3).The factor between the required energy for heating is slightly lower than in case I52 as only the follow-up fluid is heated in case P52  P52 ∕ I52 = 1600 and only the previous fluid is heated in case P40  P40 ∕ I52 = 200.In both cases, the energy saved by pumping the fluid at a higher temperature is exceeded by the energy required for heating, while the cleaned radius does not change significantly compared to the isothermal cases I40 and I52.

Heated walls
Now the influence of a heated wall is evaluated and in comparison to that a case, where the wall is cooler than the products inside the pipe.In case W52, the previous and follow-up product have a low temperature of  = 40 • C compared to the wall heated to  W = 52 • C. In case W40, the temperatures of the fluids and wall are switched.
Figure 2B shows the cleaned radius over time for both cases.During core removal, the initial trend is similar to that of cases I40 and I52.The temperatures of previous and follow-up chocolate are identical, resulting in a nearly identical viscosity ratio for both cases which leads to the same cleaned radius.Once core removal transitions into layer removal, the difference between both cases increases to up to 3%.For case W52, where the wall is heated, the wall-adjacent layer of previous fluid obtains a higher temperature, resulting in a decreased viscosity which aids in removing the remaining layer.This can be seen by the increasingly higher cleaned radius in Figure 2B.In comparison, case W40 shows a much lower cleaned radius (note the logarithmic axis), due to the low temperature and thus high viscosity of the remaining layer.Case W52 tends to a cleaned radius about 1% higher than that of case W40.The latter exhibits the same value as cases I40, I52, P40, and P52.It is therefore the only case which results in a significantly higher cleaned radius than all other investigated cases.The energy required can be determined from the Nusselt number for developed, laminar pipe flow with walls at constant temperature Nu = 3.66 [20].
For case W52 the energy required to keep the wall at its constant temperature of  W = 52 • C differs by a factor of  W52 ∕ I52 = 50.Since both previous and follow-up fluid are kept at  in =  0 = 40 • C, no additional energy is needed for heating the product in case W52.This means, however, that the follow-up product is pumped at a lower temperature compared to case I52, and therefore the energy required for pumping is increased by a factor of  W52 ∕ I52 = 1.4.In case W40 previous and follow-up product are heated resulting in more energy needed for heating  W40 ∕ I52 = 1900.Overall, case W52 requires less energy than case W40, but yields the highest cleaned radius out of all simulations.

CONCLUSIONS
All simulations exhibit the same qualitative trend and show the two stages typical for flushing processes.Influencing the temperature of both previous and follow-up chocolate barely has an effect on the flushing process.This is due to the viscosity ratio of both chocolates, which does not change, when the temperature of both changes accordingly.The energy required to heat both products to the process temperature of  = 52 • C is much higher than the energy saved by pumping a less viscous fluid at higher temperature.Heating only the follow-up product requires around eight times more energy than heating the previous product.Therefore the investigated cases may be ranked by the required energy from least to most as I40, W52, P40, P52, W40, and I52.With the exception of case W52, which shows a larger cleaned radius, all other cases result in nearly the same cleaned radius.For isothermal conditions, the flushing time and required amount of product for the flushing process does not decrease significantly with increasing temperature, while the energy requirement increases by multiple orders of magnitude, making isothermal processes at higher temperatures less energy efficient.Instead of heating both previous and follow-up product, just one of the products may be heated.In these cases, the amount of energy required for heating still exceeds the energy savings of the pump by a large factor.Moreover, neither the cleaned radius nor the required amount of follow-up product is significantly decreased compared to the isothermal case at  = 40 • C. It should be noted, however, that in the case of heated previous product the cleaned radius  c is higher during the core removal phase.The difference to the case of heated follow-up fluid reduces during the layer removal phase.
The most promising approach to save both energy, time and follow-up product is heating the walls to a higher temperature than the contained products.This combines the benefit of a high viscosity ratio during core removal phase and a low viscosity of the remaining fluid on the wall during the layer removal phase.Out of the investigated cases, case W52 has the second lowest energy requirement.Compared to an isothermal case more energy is required to heat the walls, however, this also results in a higher cleaned radius.For industrial applications, the goals of the flushing process, that is, low energy consumption and large cleaned radius, need to be weighed to decide which strategy to follow for a given flushing process.
For chocolates with different properties the results are expected to vary, especially when the viscosity ratio between both chocolates differs significantly from the one used in this work.

A C K N O W L E D G M E N T S
Open access funding enabled and organized by Projekt DEAL.

TA B L E 1
Modeling constants for the rheology of dark and white chocolate.
Thermal properties ,  and modeling constants  1 ,  2 for dark and white chocolate.Temperature boundary conditions for the different investigated cases.
TA B L E 2