École Nationale Supérieure du Génie des TechnologiesIndustrielles

Modelling of a co-axial heat exchangerComputational Fluids Dynamics project

Author:Younes Ajeddig

Teacher :Frédéric Marias

January 29, 2019

Abstract

The process and chemical engineer have many tools to anticipate the behavior of fluids in their processes.CFD (Computational Fluids Dynamics) is one of the most powerful tool he has to solve problems about fluidsmechanics and its various problem of heat exchange and reaction. The reasons why we assist ourselves withcomputer are that computer are a lot more faster in iterative calculation than human. The fact is that at thisday, there is no analytic solution to the equation of Navier Stokes and it is very difficult to solve the equationof the fluids mechanics coupled with energy equation or/and reaction.

The aim of this project is to learn the basics of CFD modelling with a commercial software well known asANSYS Fluent and his various software like DesignModeler and Meshing. CFD studies are used in manyindustries and it is a real advantage to be prepared to use a CFD software.

We will learn the basics by designing and modelling a co-axial heat exchanger in a commercial CFD software.We will study what make a CFD simulation relevant and compare this results with the prevision we can makewith the DTML method and with a simulation with a commercial process software like ProSIM R©.

Contents

1 Co-axial heat exchanger 11.1 Scheme of the heat exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Specification and hypothesis of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 ∆Tmln method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Meshing criticizing 52.1 Angle inclinaison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Dimensionless distance to the wall — Y + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Calculation and results of the simulation 93.1 Residu calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Heat exchanger performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2.1 Counter courant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.2 Co courant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.3 Analysis and criticizism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Modelling of the heat exchanger completed with partition or baffles . . . . . . . . . . . . . . . . . 113.4 Analysis and criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Conclusion 11

Chapter 1

Co-axial heat exchanger

This chapter will explain what exactly we are modelling and the results we have obtained with the ∆Tmlnmethod.

1.1 Scheme of the heat exchanger

Figure 1.1: Scheme of the heat exchanger

The aim of the co-axial heat exchanger is to heat the cold fluid which are flowing in the shell. The cold fluidis liquid acetone at 300K at the inlet. The hot fluid in the internal tube is liquid water at 363K at the inlet.The heat exchanger material is steel and he is surrounded by insulating material.

Here the rest of the size we need to design the object.

Description Size [mm]

Internal tube diameter 48,3

Internal tube thickness 3,25

Shell diameter 88,9

shell thickness 4,05

Internal diameter of the tubes for supply and outlet of the shell 48,3

Thickness of the tubes for supply and outlet of the shell 3,25

We are designing a realistic heat exchanger because of the thickness of the wall and the direction of the inletand outlet supply in the shell which are perpendicular to the flow inside.

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1.2 Specification and hypothesis of the problemAll the physical, thermic and thermodynamic data are provided by the project subject and the commercialsoftware. They are all considered constant and independent from the temperature.

Hot fluid

Liquid water

Cold Fluid

AcetoneSteel

Insulating

material

Mass flow inlet [kg/s] 1 0,05 — —

Density [kg/m3] 998,2 791 8030 40

Thermic conductivity [W/m/K] 0,6 0,18 16,27 0,04

Dynamic viscosity [kg/m/s] 1,00E-03 3,31E-04 — —

Heat capacity [J/kg/K] 4182 2160,846156 502,48 1000

The inlet flows have a turbulence intensity of 5% for a 0,02mm hydraulic diameter.The hypothesis that are admit here is that all the physical parameter are all considered constant and inde-

pendent from the temperature and the only phenomena linked to heat losses is convection with the surroundingair at 298K. The convection coefficient exchange is 15W/m2/K

1.3 ∆Tmln methodThe method stands on the multiple expression of the heat exchanged between the fluids :

Φ = ṁColdF luidCpColdF luid(TCold,out − TCold,in) (1.1)Φ = ṁHotF luidCpHotF luid(THot,in − THot,Out) (1.2)Φ = KS∆Tmln (1.3)

We are not going to develop the demonstration of the method, and we are admitting the following expression :

K =1

1

hcold+e

λ+

1

hhot

(1.4)

∆Tmln =∆T1 −∆T2

ln(∆T1∆T2

)(1.5)

Figure 1.2: Meaning of the ∆T1 and ∆T2 in a co-axial heat exchanger

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Here the data and calculation that we did in a Excel R© sheet :

ESTIMATION OF THE

CONVECTION COEFFICIENT FOR

THE HOT AND COLD FLUID

HOT FLUID

Liquid water

COLD FLUID

Acetone

Mass flow [kg/s] 1 0,05

Hydraulic diameter [m] 0,0483 0,0341

Density[kg/m3] 998,2 791

Thermal conductivity [W/m/K] 0,6 0,18

Dynamic viscosity [kg/m/s] 0,001003 0,000331

Heat capacity [J/kg/K] 4182 2160,846156

section [m2] 0,001832248 0,003848585

Reynolds 26282,22 1338,43

Prandtl 6,99091 3,973555988

Nusselt.

Colburn correlation

with a correction (x/D

Residu squared residu

-2,36355E-10 5,58637E-20

-1,60867E-10 2,58782E-20

7,54881E-11 5,69845E-21

Sum of residu 8,74403E-20

Residu squared residu

-4,81805E-10 2,32136E-19

-5,20458E-10 2,70877E-19

-3,86535E-11 1,49409E-21

Sum of residu 5,04507E-19

We have a basic expectation of how our heat exchanger should work. The method used is really approximativebecause of the Colburn correlation. This kind of correlation is really good to show how the phenomena evolvebut it is really not accurate.

We tried to make an other estimation of the exchanger’s performance by using a process simulation software.We have used ProSim Plus R©.

STREAM ACETONE INLET ACETONE OUTLET WATER INLET WATER OUTLET

ALIMENTATION

ACETONEEXCHANGER

ALIMENTATION

WATEREXCHANGER

PARTIAL FLOW kg/s kg/s kg/s kg/s

WATER 0 0 1 1

ACETONE 0,05 0,05 0 0

TOTAL FLOW kg/s 0,05 0,05 1 1

TEMPERATURE K 300 308,5049864 363 362,7929437

This results are close to what we have found with the DTLM method. We are not expecting an importantvariation of the temperature either for the cold or the hot fluid.

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Chapter 2

Meshing criticizing

It is not relevant to show how to draw the pieces of our model. But it is to criticize the meshing of our model.This can be done by reaching two informations within the commercial software ANSYS Fluent. We will atfirst talk about the inclinaison angle to avoid weirdly shaped element, and the importance of the dimensionlessdistance to the wall when we are simulating a k-� turbulent model.

2.1 Angle inclinaisonThe angle inclinaison consist to count the element that have any of their angle too low. That make the elementweirdly shaped and flat. The presence of this kind of element make the meshing low in quality and the calculationcan go wrong. The ultimate condition to have a good meshing is to avoid the existence of an element with a

Figure 2.1: Element repartition by the angle inclinaison criteria - no element is above 0.98

angle inclinaison criteria above 0.98 . Here in the figure 2.1, the maximum reached is 0.94 . So our meshing isfine.

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2.2 Dimensionless distance to the wall — Y +

The dimensionless distance to the wall, usually called Y + is an dimensionless value. It is representing the sizeof the first element at the wall between a fluid and a solid.

Y + =u∗y

ν(2.1)

Where u∗ is the frictional velocity, y is the real size of the first element from the wall and µ is the kinematicviscosity. The value of u∗ is often 5% of the average velocity of the fluid.

This came from the theory of the boundary layer.When Y + ∈ [0, 1] the mechanical behavior in the boundary layer is linear. In the other hand, if Y + ∈

[30,+∞] the mechanical behavior in the boundary layer is logarithmic. We stay in the dark concerning what ishappening when Y + ∈ [1, 30] and the usual thing to do is to go beyond 30. This habit has many advantage :

• To go beyond 30, we need to increase the size of the elements near the wall so the software will usethe predictive function in the boundary layer. This results to less elements in the meshing and an lesscalculation

• We obtain something more accurate with less calculation cost

There is some cases where it is less difficult to have our Y + ∈ [0, 1].We can see how much is the Y + only after the calculation were we can print the contour on a surface just

between the fluid and the wall.

Figure 2.2: Bad Y + on the surface between the cold fluid and the internal tube wall

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Figure 2.3: Bad Y + on the surface between the cold fluid and the shell wall

To fix this problem, we had to return to the Meshing software. The idea is to manage an inflation and tofix the size of the first layer. After many tries, we have obtained Y + ∈ [0, 1] .

Figure 2.4: Low and good Y + on the surface between the cold fluid and the internal tube wall

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Figure 2.5: Low and good Y + on the surface between the cold fluid and the shell wall

The angle inclinaison criteria has been checked out after the meshing manipulation and it is good. We canstudy the results of the simulation.

We can notice that in the industry, we prefer to have a high Y + when using the k − � model for turbulentflow, and a low Y + when using a k − ω model.

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Chapter 3

Calculation and results of the simulation

We will show in this chapter the residue of the calculation and the many results we have obtained from thismodelling.

3.1 Residu calculation

Figure 3.1: Plot of the residues of Fluent calculation

We can observe that the energy’s residual is anormaly increasing. Still, it is very low so we can accept theresults of the simulation.

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3.2 Heat exchanger performanceWe can evaluate the heat fluxes by the report tool of the Fluent calculation.

3.2.1 Counter courant

UtilityInlet temperature

[K]

Outlet temperature

[K]

Heat exchange

[W]

Cold fluid 300 326,65 -2882,4

Hot fluid 363 362,29 2902,3

Heat losses 8,9 W

3.2.2 Co courant

UtilityInlet temperature

[K]

Outlet temperature

[K]

Heat exchange

[W]

Cold fluid 300 326,78 -2893,373

Hot fluid 363 362,299 2973,402

Heat losses 80,03 W

3.2.3 Analysis and criticizismThe heat exchanger do not change much in a co courant or counter courant flow. We can easily understandthat the heat exchange performance depends a lot to the hydrodynamic condition. Here the velocity of the coldfluid may have been low to have a good exchange.

Some heat losses are here but the insulating material is protecting the most of it.We have to be really careful with these results. We do not know if the difference of heat losses is physically

correct.

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3.3 Modelling of the heat exchanger completed with partition or baf-fles

We have improved our co-axial heat exchanger to check the influence of partition in the way of the cold fluid.We added 24 baffles in the calander to increase the path the cold fluid has to do.

Figure 3.2: Velocity streamline view on top of the exchanger after the design of baffles

We can see the existence of swirl behind baffles, due to the turbulent flow. Here the results of a simulationin a counter current configuration.

UtilityInlet temperature

[K]

Outlet temperature

[K]

Heat exchange

[W]

Cold fluid 300 326,93 -2908,4

Hot fluid 363 362,93 2925,8

Heat losses 17,43 W

The presences of 24 baffles do not have an impact of the heat exchange. Regarding to the work of mycamarade, one of them succeed to increase the heat exchange by adding almost 50 baffles very thick.

3.4 Analysis and criticismThe low performance of the heat exchanger was expected after the DTLM estimation and the ProSIM R© simu-lation. We still have a difference of 15 to 20K between the estimation and the CFD simulation.

The DTLM method and the ProSIM R© simulation are based on correlation. The most of them are veryapproximative and their accuracy depends on the original experience they are based on. The only way we canknow if one of the three estimation or simulation is accurate is to do the study on a real exchanger.

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Conclusion

CFD simulation is a very common tool in the industry. This project is only a scratch of what we can do witha commercial software like ANSYS Fluent. We learned the very basics of CFD modelling and simulation.

At first it will be very interesting to experiment the heat exchanger to know how accurate CFD simulationare. This is important to know how our tool are relevant enough.

Then, we did not have enough time to explore the many possibilities that the software has to offer : Thesimulation of a complex flow with some chemical reaction could have been really pertinent for the student ofthe Computer Aided Process Design.

Finally, we did not have enough time to really criticize our meshing. Indeed this is the most important anddifficult aspect of CFD simulation, and before even thinking about running some calculation, we have to checkcorrectly our mesh.

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Co-axial heat exchangerScheme of the heat exchangerSpecification and hypothesis of the problemTmln method

Meshing criticizingAngle inclinaisonDimensionless distance to the wall — Y+

Calculation and results of the simulationResidu calculationHeat exchanger performanceCounter courantCo courantAnalysis and criticizism

Modelling of the heat exchanger completed with partition or bafflesAnalysis and criticism

Conclusion