CFD Final Report

CCB 3033

Advanced Transport Process

January 2015 Semester

CFD SIMULATION OF HEAT EXCHANGE EQUIPMENT

GROUP 4

MEMBERS:

Name ID

KANAPATHY A/L MOHANAN 18672

CHEN SWEE KEAT 18604

AZLAN BIN RAMALI 18645

Due Date : 17 April 2015

1

Table of contents

No Title Page

1. Introduction about heat exchanger 3-5

2. Governing Equations and Simulation Method 6-8

3. Flow Regime in Heat exchanger 9

4. Heat Transfer Coefficient 10-13

5. Result & Discussion

1. Geometry2. Velocity and temperature contours3. Profile and others

14-23

6. Conclusions 24

7. References 25

Introduction about Heat Exchanger

2

The technology of heating and cooling systems is one of the common areas in engineering. Whenever fluids are required to be heated up or cooled down, heat exchanger will be the desired equipment to achieve the objective. In general, they are used to heat and cool buildings, vehicles, food process industry and chemical plants. In a heat exchanger, heat energy is transferred from one fluid stream to another stream. In designing heat exchanger, heat transfer equations are applied to calculate the amount of energy transfer.

There are 3 different primary categories of heat exchangers in accordance to their flow arrangement namely parallel-flow, countercurrent-flow and cross-flow. In parallel-flow heat exchangers, two fluids will enter the exchanger at the same end and travel in parallel way until another end (exit). However, for countercurrent heat exchanger, the fluids will enter the exchanger from opposite ends. The directions of both fluids will be opposing each other in this case. This type of heat exchanger has the highest efficiency in terms of heat transfer. And for cross-flow heat exchanger, the fluids basically travel perpendicular to each other through the exchanger.

Heat exchangers are designed in such a way that it maximizes the wall surface area while minimising resistance to fluid flow through the heat exchanger. The performance of an exchanger also can be affected by the addition of fins or corrugations, thereby increasing the surface area and may channel fluid flow or induce turbulence.

The driving temperature across the heat transfer surface area varies with positions, however a mean temperature called Log Mean Temperature Difference (LMTD) can be defined. Other than finding the heat transfer through LMTD, NTU method can also be used.

Fig 1: Temperature differences between hot and cold process streams

3

Fig 2: Types of heat exchangers – (a) concentric-tube parallel-flow; (b) concentrictube counter-flow; (c) shell-and-tube; and (d) cross flow.

Types of Heat Exchangers

Double-pipe exchanger: One of the simplest and cheapest types of heat exchanger. It has simple concentric pipe arrangement, made up from standard fittings and useful where only a small heat-transfer surface area is needed.

Shell and tube exchanger: It is one of the most common equipment found in all plants especially chemical plants. The configuration gives a large surface area in a small volume. It can be constructed from a wide range of materials. In addition, cleaning of this type of exchanger is easy. It has well established design procedures. It contains on One Shell Pass and One Tube Pass.

Plate-fin exchanger: Consists of plates separated by corrugated sheets, which form the fins. It has a large surface area, compact and is low weight.

Plate heat exchanger

Advantages Disadvantages

4

Easier to maintain More flexible Low approach temperature Attractive when material costs are high

The selection of a suitable gasket is critical

Maximum operating temperature is limited up to about 250°C (gasket materials limitation)

Not suitable for pressures greater than about 30 bar

Air cooled heat exchanger: Air cooling heat exchanger usually becomes the best choice for minimum process temperature above 65°C. It consists of banks of finned tubes over which air is blown or drawn.

Direct contact heat exchanger: Hot and cold streams are brought into contact without any separating wall. Example of this type of heat exchanger is water-cooling towers. It can achieve high rates of heat transfer and suitable for use with heavily fouling fluids and liquids containing solids.

Fired heater: It is used when high flow rates and high temperatures are needed. The hired heater is directly heated by the products of combustion of a fuel.

Governing Equations

5

The governing equations for fluid flow and heat transfer are the Navier-Stokes or momentum equations and the First Law of Thermodynamics or energy equation. The governing pdes can be written as :

Continuity equation:

The two source terms in the momentum equations, Sω and SDR, are for distributed resistances and rotating coordinates, respectively. The distributed resistance term can be written in general as:

SDR=−(K i+ fd ) ρV 2

i

2−CnV i

where i refer to the global coordinate direction (u, v, w momentum equation), f- friction factor, d- hydraulic diameter, C – permeability and the other factors are descripted in table 1. Note that the K-factor term can operate on a single momentum equation at a time because each direction has its own unique K-factor.

The other two resistance types operate equally on each momentum equation. The other source term is for rotating flow. This term can be written in general as:

Sω=−2ρωi×V i−ρωi×ωi×ri

6

where i refer to the global coordinate direction, ω is the rotational speed and r is the distance from the axis of rotation. For incompressible and subsonic compressible flow, the energy equation is written in terms of static temperature:

The variables from these equations are defined in Table 1.

Variable Description Variable Descriptioncp specific heat at constant pressure cp specific heat at constant pressurek thermal conductivity k thermal conductivityp pressure p pressureqV volumetric heat source qV volumetric heat sourceT temperature T temperaturet time t timeu velocity component in x-direction u velocity component in x-directionv velocity component in y-direction v velocity component in y-directionw velocity component in z-direction w velocity component in z-directionρ density ρ densityη dynamic viscosity η dynamic viscosity

The equations describe the fluid flow and heat transfer under steady-state conditions for Cartesian geometries. For the turbulent flow, the solution of these equations would require a great deal of finite elements (on the order of 106 – 108) even for a simple geometry as well as near infinitesimal time steps. COSMOS/Flow solves the time-averaged governing equations. The time-averaged equations are obtained by assuming that the dependent variables can be represented as a superposition of a mean value and a fluctuating value, where the fluctuation is about the mean[2]. For example, the velocity component in y-direction can be written:

V=V +v ’ ,[m /s ]

where V [m/s] – the mean velicity, v’ [m/s] – the fluctuation about the mean. This representation is introduced into the governing equations and the equations themselves are averaged over time.

Simulation Method

7

In COSMOS/Flow, the finite element method is used to reduce the governing partial differential equations (pdes) to a set of algebraic equations.The role of finite element method in numerical simulation is shown in figure 3. The dependent variables are represented by polynomial shape functions over a small area or volume (element). These representations are substituted into the governing pdes and then the weighted integral of these equations over the element is taken where the weight function is chosen to be the same as the shape function. The result is a set of algebraic equations for the dependent variable at discrete points or nodes on every element.

FLOW REGIME IN HEAT EXCHANGER

8

Flow regime can be determined from the Reynolds number.

Reynolds number = Inertia force/ Viscous force

(ρvL)/μ

Where ρ = density of the fluid

v = velocity of the fluid

L = Length of the fluid inlet

μ = dynamic Viscosity of the fluid

[999.9(kg/m3)*2.22*105(m/s)*0.05(m)] / [0.896*103]pa.s

1.23, which is in the limit of Laminar flow.

Hence, the flow regime can be considered as Laminar Flow.

9

18672

18604

18645

Heat Transfer Coefficient

Heat transfer coefficient,h (W/m2K)

Temperature at point 8 (K)


Average temperature,Tavg

(K)

Ideal Temperature, T2 (K)

Temperature Difference (K)

1 302.6944 317.5145 310.10445 331 20.895552 307.7513 331.2459 319.4986 331 11.50143 312.6847 342.4121 327.5484 331 3.4516

3.5 315.0586 347.3362 331.1974 331 0.19744 317.3965 352.013 334.70475 331 3.704755 321.9145 360.6896 341.30205 331 10.30205A. For student ID 18672

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5290

300

310

320

330

340

350

f(x) = 7.78812204081633 x + 303.379232040816R² = 0.994456468765064

Graph of Average Temperature against Heat Transfer Coefficient

Series2Linear (Series2)

Heat Transfer Coefficient (W/m²K)

Aver

age

Tem

pera

ture

(K)

Fig 3: Graph of Tavg against h for student (ID: 18672)

10

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

5

10

15

20

25

Graph of Temperature Difference against Heat Transfer Coefficient


Tem

pera

ture

Diff

eren

ce (K

)

Optimum point

Fig 4: Graph of Temperature difference against h for student (ID: 18672)

Note: at ideal temperature, T = 58°C = 331K ; h = 3.5 W/m2K

B. For student ID 18604




Average temperature,T (K)

Ideal Temperature, T2

(K)

Temperature Difference

(K)1 300.5271 318.2091 309.3681 331.15 21.78192 302.8229 331.9321 317.3775 331.15 13.77254 308.9857 352.0383 330.512 331.15 0.6385 312.1671 360.2818 336.22445 331.15 5.074456 315.2617 367.6061 341.4339 331.15 10.2839

11


0 1 2 3 4 5 6 70

5

10

15

20

25



Tem

pera

ture

Diff

eren

ce (K

)

Optimum point


Note: at ideal temperature, T = 58°C = 331K ; h = 4.1 W/m2K

12




Average temperature,T (K)

Ideal Temperature

(K)

Temperature Difference (K)

1 302.6366 316.6454 309.641 331 21.3592 307.2754 329.0949 318.18515 331 12.814853 311.5715 338.8142 325.19285 331 5.807154 315.5709 346.7758 331.17335 331 0.17335

4.5 317.4275 350.2717 333.8496 331 2.8496C. For student ID 18645


0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

20

25



Tem

pera

ture

Diff

eren

ce (K

)

Optimum point


Note: at T = 58°C = 331K , h = 4.0 W/m2K

13

RESULTS AND DISCUSSION

ID: 18672; X = 0.14, Y = 0.1

14

Figure 1. Geometry Figure 2. Mesh

Figure 3. Temperature profile (thermal view)

Figure 4. Temperature profile (rainbow view)

Figure 5. Velocity profile (z component)

Figure 6. Outlet temperature surface

15

Figure 7. Temperature plot isosurface

Figure 8. Line graphFigure 8. Temperature distribution at different z position

Figure 9. Relationship between heat transfer coefficient and T2

Figure 10. Trial and error process to determine heat transfer coefficient

16

ID: 18604; X = 0.22, Y = 0.1

17






18


Figure 8. Line graphFigure 8. Temperature distribution at different z position



19

ID: 18645; X = 0.06, Y = 0.12

20






21


Figure 8. Temperature distribution at different z position



22

Discussion

From the model which is considered for the present heat exchange in mixing system simulation in COMSOL Multiphysics, we can observe the inlet and outlet from which the flow enters and exits the domain. Considered model is a 2-Dimensional axis symmetric geometry heat exchanger.

From the figure that represents the mesh generation for the considered geometry, we can say that the free triangular mesh has been generated. For getting a better accuracy in the results, finer mesh has been generated. We can also observe that the mesh is very fine near the area where the heat flux generation occurs. As it is a 2-Dimensional geometry, efforts were made to perform a simple discretization throughout the domain. From this is mesh, It is hoped that the considered momentum and energy governing Navier-Stokes can be easily solved. The quality for the generated mesh for the considered geometry is around 92%. . From the figure, we can say that the free triangular mesh created has obtained a good efficient mesh quality, from the range, maximum domain covers the mesh quality with around 0.96. The minimum quality of the domain is obtained as 0.82. This means, mesh quality is above 82%. For achieving this quality, finer mesh has been generated. We can also observe that very less regions stay in the quality of 0.82 and most of the domain stays in above 0.9 quality. As it is a 2-Dimensional geometry, obtaining a mesh quality with above 85% is may not be challenging, still near the area of curvature, this geometry has achieved a better mesh quality.

From the figure that represents the temperature profile for the considered geometry, we can say that the free triangular mesh created has obtained a good efficient result, from the temperature range displayed; maximum temperature is obtained near the heat flux generation region. With respect to the flow, the temperature has a fluctuating profile and reaches the outlet with 331K. As no inlet temperature is specified, simulation is performed with the initial and operating conditions. Therefore, we can observe a temperature of 300K near the inlet. Then, gradually, heat flux is released which makes the temperature profile to rise till 454K and gradually decrease till the outlet. The accuracy of the temperature profile plot is because of the good mesh quality. We can see the heat flux generated near the circular domains. As a much finer mesh is generated in that region, temperature profile is accurately predicted.

From the figure that represents the Velocity profile for the considered geometry, we can say that the free triangular mesh created has obtained a good efficient result, from the velocity range displayed; maximum Velocity is obtained near the inlet and it gradually decreased due to the fluctuations in the geometry. After achieving a uniform flow, the velocity raised and headed to a high velocity near the outlet.

From the calculations performed, the flow regime is said to be laminar flow. Hence, the velocity throughout the domain is between 0 to 1 m/s. With respect to the flow, the velocity is zero near the walls which follows the no slip condition. As at inlet, velocity is specified as 0.07[m/min], i.e. 0.0012 m/s, it represents the same near inlet and then, due to the flow fluctuations, it decreased and then increased accordingly.

23

Conclusion

In this study, three basic questions regarding conduction, convection, and radiation are solved successfully. As a foundation, the part of theoretical methods benefit on analyzing and solving. The project offers solutions of the three questions. By this means, it can understand how to analyze and to solve the problems on heat transfer. Furthermore, we can apply Comsol Multiphysics software to solve three questions. Comparing the results from the theoretical method with Comsol Multiphysics software, it has been proved that Comsol Multiphgysics software can offer accurate analysis. Meanwhile, it is a very efficient tool for solving heat transfer problem, especially for those completed problems.

When we compare the three different types of x (in meter) which is 0.14,0.12 and 0.06 given to us to build the heat exchanger, we found that increase in the length of x (in meter) results in decrease of overall temperature of the heat exchanger. This can be seen on the surface temperature profile in results part. Moreover, decrease in x value, makes the velocity streamline flows easily, shown on the Streamline Velocity field. In addition, the outlet temperature surface shows higher temperature when x value (in meter) is greater.

Besides, when we look at the temperature distribution curve for all the three x values, we can see that x = 0.06 gives a more consistent curve with less oscillations compare to the other two values. This shows that the heat exchanger with x = 0.06 has a stable temperature distribution. Therefore, it is the best heat exchanger design among the three.

24

References

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