t ube si de f l ow an al y si s f or t he sh e l l a nd t ub e … · 2018. 5. 6. · 3. e nerg y...

TUBE SIDE FLOW ANALYSIS FOR THE SHELL AND TUBE HEAT EXCHANGER

USING CFD

S.Anitha

1, R.Sathyapriya

2

Assistant Professor 1 2

Department of EEE, BIST, BIHER, Bharath University, Chennai.

[email protected]

Abstract—This paper deals about the investigation

on flow behavior in the tube side of typical shell and

tube heat exchanger. The flow behavior includes

Pressure Drop, Flow distribution (Velocity at

various section) etc. Which are the major factors to

be considered when evaluating the performance of

any heat exchanger. In this case, the above mention

parameter are predicted for the typical shell and

tube heat exchanger using on advanced tool namely

Computational Fluid Dynamic(CFD). The problem

consists of headers and branching lateral tubes

which is modeled and meshed using the commercial

advance CFD (STAR CCM+) tool. After modeling

to apply the boundary condition to solve the

described domain. The standard k-ξ turbulent model

is used for the analysis and the behavior if fluids

namely liquid sodium and their impact over the heat

exchanger performance are studied for different

flow rates. The pressure drop and velocities in

lateral tube side were simulated and compared with

numerical calculated values .Similar work did in

various mass and volume flow rate.

Key words: Tube side, k-ξ Turbulence modeling, velocities distribution, Pressure drop, CFD

STRA CCM+.

1. INTRODUCTION

1.1 Shell and tube Heat exchanger: The applications of shell-and-tube heat exchangers are quite large because these are widely used in

chemical, petroleum[1-5], power generation and

process industries. In these heat exchangers, one fluid flows through tubes while the other fluid flows in the

shell across the tube bundle.

The design of a heat exchanger requires a balanced

approach between the thermal design and pressure

drop. The pressure drop results in the increase of the

operating cost of fluid moving devices such as pumps and fans[6-9]. This show

that along with the design for the capacity for heat

transfer, the pressure drop determinations across the

heat exchanger are equally important. The

estimations for pressure loss for the fluids flowing inside the tubes are relatively simple[10-14], but

complex in the tube-side flow. To evaluate the

pressure drop in the shell, there is a need to know the

various internal flow paths and their individual

effects.

Due to the important role of shell-and-tube heat

exchangers, a considerable number of papers has

been devoted to the design optimization problem,

employing different techniques, such as, numerical

resolution of the stationary point equations of a

nonlinear objective function, graphical analysis of the

search space, simulated annealing[15-19],

genetic algorithms, Mixed integer nonlinear

programming, systematic screening of tube count

tables , among others.

These techniques were employed according to

distinct problem formulations in relation to: (i)

objective function: heat transfer area or total annualized costs (i.e. capital costs of the heat

exchanger and pumps/compressors associated to fluid

flow operating costs); (ii) constraints: heat transfer

and fluid flow equations[20-27], pressure drop and

velocity bounds, etc.; and (iii) decision variables:

selection of different search variables and its

characterization as integer or continuous (e.g., tube

diameter can be considered a fixed parameter, a

continuous variable or a discrete variable).

In spite of the algorithmic developments applied to

heat exchanger design, the complexity of the task allows some criticism of the effectiveness of

optimization procedures for real industrial problem

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 2077-2087ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

2077

1.2 An Overview Of The CFD Software:

Computational Fluid Dynamics (CFD) is a computer-based

tool for simulating the behavior of systems involving fluid

flow, heat transfer and other related physical processes. It

works by solving the equations of fluid flow over a region of

interest, with specified (known) conditions on the boundary of the region[28-33]. CFD has grown from a mathematical

curiosity to become an essential tool in almost every branch of

fluid dynamics, from aerospace propulsion to weather

prediction.

This CFD is commonly accepted as referring to the broad

topic encompassing the numerical solution, by computational methods, of the governing equations which describe the fluid

flow, the set of Navier-Strokes equations, continuity and any

additional conservation equations, for example energy (for

heat transfer). CFD plays an important role in design and

analysis of both external vehicle aerodynamics and sub-

component design[34-38]. The aim of this module is to

provide an introduction to the use and application of CFD. It

is now an established industrial design tool, helping to

reduce design time scales and improving processes

throughout the engineering world. CFD provide a cost-

effective and accurate alternative to scale model testing, with variation on the simulation being performed quickly,

offering obvious advantages.

1.3 Need for CFD:

Computational Fluid Dynamics is today an equal partner

with pure theory and pure experiment in the analysis and

solution of fluid dynamics problems. As a developing science,

Computational Fluid Dynamics has received extensive

attention throughout the international community, since the

advent of the digital and super computers. First, the desire to

be able to model physical fluid phenomena that cannot be easily simulated or measured with a physical experiment[39-

41], for example outlet temperature distribution in a heat

exchanger or flow distribution in hypersonic aerospace

vehicles. Secondly, the desire to be able to investigate physical

fluid system more cost effectively and more rapidly than with

experimental procedures.

In this project there is a need of systematic study on various

kinds of header and flow systems which necessitates a common platform usage, which can increase the data

availability for any type of geometric configuration of the total

flow system. With the availability of high-speed computers,

CFD analysis can be a better alternative to assess the performance of the flow system. The purpose of the study is to

get reliable results as that of the experimentation with a

relatively low cost and lesser time.

2. Fundamental elements in CFD:

The fundamental elements of any CFD simulation are:

• The fluid continuum is discretised; i.e. the field variables are approximated by their values at a finite

number of nodes.

• The equations of motion are discretised; i.e. approximated in term of values at the nodes.

• The system of algebraic equation is solved to find the values of all the variables at nodes.

2.1 Basic Governing Equations:

The governing flow equations are obtained by the

application of physical principle. The most important

equations are those governing the fluid dynamics namely:

1. Mass is Conserved (Continuity equation)

2. Newton’s second law, F=ma (Momentum

equation)

3. Energy is conserved (First law of thermodynamics

equation) The above governing equations are applicable over the

suitable model of flow 1. Finite control volume approach

I. Fixed in space

II.Moving with the fluid

2. Infinitesimal fluid element approach

I. Fixed in space

II.Moving with the fluid

A).Conservative form

The forms of the governing flow equation that are directly obtained from a flow model which is fixed in space

are, by definition called the conservative form.

B).Non-conservative form

The forms of the governing flow equation that are directly obtained from a flow model which is moving

with the fluid are, by definition called the Non- conservative form.

2.2 APPLICATIONS OF CFD:

Some of the areas in which computational fluid dynamics

(CFD) has been successfully applied are:

• Aerodynamics: Aircraft and automobiles

• Ship building: Hydrodynamics of ships

• Engine flows: IC engines and jet engines

• Turbo machinery: Pumps and turbines

• Heat transfer: Heating and cooling systems; furnaces, condensers

• Process engineering: Mixing and reacting chemicals

• Wind power: Forces and dynamic responses of structures

Pure Experimental

CFD

Pure theory

• Environmental engineering: Transport of pollutants

and effluent

• Hydraulics: Pipe networks, reservoirs, channels,

weirs, spillways

• Meteorology: Numerical weather forecasting

International Journal of Pure and Applied Mathematics Special Issue

2078

• Biomedical engineering: Blood flow in heart,

arteries, and veins

2.3 Finite volume discretisation in CFD:

In the finite volume formulation, computations are carried out in the physical flow domain. The computational

domain is divided into a network of finite volume/ cells. The

generation of the body fitted grid using curvilinear co-

ordinates and the solution process are decoupled since no global transformation is used. The required data concerning

the grid are only the Cartesian co-ordinates of the vertices of

every cell in the given mesh. Elementary volumes are formed

by joining the vertices by straight lines. The main advantage

of the finite volume method is its flexibility in treating

arbitrary geometries efficiently[42-45]. Nowadays, it has

become very popular for two and three dimensional flow

computation. In this approach the governing equations are considered in their integral form. The derivatives are not

approximated by the difference quotients as in the finite

difference method. Instead, the divergence theorem is used

over a control volume to get the divergence of the vector

field. If V is the volume bounded by a closed surface S and A

is a vector function of position with continuous derivatives,

then

r r v v v

• Selecting the physical models which are to be

included in the simulation.

• Specifying the properties of the fluid

• Specifying the boundary conditions

• Creating a mesh for control volume

2.4.2 The Solver:

The solver is a component, which solves CFD problem,

producing the desired results. It does this as follows

• The integral equations are converted to a system of algebraic equations by generating a set of

approximations for the terms in integral equations.

• The algebraic equations are solved iteratively

• An iterative approach is required because of the nonlinear nature of the equations and the solution

approaches the exact solution it is said to be

converged. For each iteration, an error or residual is

reported as a measure of the overall conservation of

the flow properties.

• How close the final solution to the exact solution is depends on number of factors, including the size and

shape of the control volumes and the size of the final

residuals.

The solution process requires no user interaction and is

∫∫∫∇.AdV V

= ∫∫ A.ndS = ∫ A.dS S S

therefore carried out as a batch process.

2.4.2 The post-processor:

Discretizing the governing equation directly,

Net mass flow = (ρu)eAe - (ρu)wAw + (ρv)eAe - (ρv)wAw

The finite volume method is popular in fluid mechanics

because it:

• Rigorously enforces conservation

• It is flexible in terms of both geometry and physical phenomena

• It is directly related to physical quantities.

2.4 Various stages in CFD:

The main stages in CFD study are:

• The post-processor is a component used to

analyses and present the results. Post-processing

includes anything from obtaining point values to

complex animated sequences.

• Examples of some important features of post processor are

• Visualization of control volumes and geometry

• Vector plot showing the direction and magnitude of

flow

• Visualization of the Path Lines through the domain.

• Quantitative numerical calculations

• Chart showing graphical plots of variables.

• 2.5 Turbulence Modeling:

Pre-

processing

Solver Post-

processing

Turbulence is an irregular motion, which in general makes

its appearance in fluids, when they flow past solid surfaces or

even when neighboring streams of the same fluid flow past

1. Pre-processing: Formulate problem, Governing equations and boundary conditions; Construct mesh.

2. Solving: Numerical solution of the given equation. 3. Post- processing: Plot and analyses the results.

2.4.1 The Pre-Processor:

The pre-processor is a component used to create the input

for the solver. Pre-processing involves:

• Defining the geometry of region of interest.

one over another. The flow is characterized by the presence of

a large range of excited length and time scales. The irregular

nature of turbulence stands in contrast to laminar motion.

Virtually every engineering flow is turbulent.

This turbulence is modeled in the analysis using Standard k- ε model. It is basically a two-equation model based on

transport equations for the turbulence kinetic energy (k) and its

dissipation rate (ε). The segregated solver based on implicit approach was

chosen to solve the above equations. A first order upwind

differential scheme was initially applied for differencing of


2079

momentum, turbulence kinetic energy and turbulence

dissipation rate. Discretisation scheme for pressure is standard

and pressure velocity coupling is through SIMPLE algorithm. 2.7 The mathematic model:

START

Pre-processing

Other

START There are some assumptions in the CFD simulation: (1) the flow is stable in the test section; (2) the fluid flow meets the

Boussinesq assumption and (3) the fluid in the test section is

incompressible Newtonian fluid.

2D or3D

Mesh

-geometry set up

Geometry

CAD/CAE/pro-E

packages

In this work, CFD software STAR CCM+ was employed to

simulate the fluid flow distribution in the tube side of shell and

Post-processing -mesh import and adoption

-physical models

-boundary conditions

2.6 The physical model:

A schematic view of conventional tube side is shown in Fig.

1, which has the geometrical characteristics listed as follows.

The diameter of the inlet flow pipe is 920mm, the single tube

diameter is 156.69 mm and it is 1742.5 mm in length, which are all the same with actual dimensions.. Composite

constructive grids are used in the analog computation and the

finest implemented grid involved about 145,025 cells (Fig. 2). There are selective refined grids in some local place where

parametric variation is severe.

tube heat exchanger heat exchanger. STRA CCM+ is one of the most widely used commercial codes for simulating

engineering fluid flow due to its accuracy, robustness and

convenience. In STAR CCM+, the conservation equations of

mass, momentum are solved using the finite volume method.

There are several turbulence models available in the code. The

turbulence flow was calculated by the Semi-implicit

SIMPLER Algorithm method in the velocity and pressure

conjugated problem, and a second order upwind differential scheme was applied for the approximation of the convective

terms. A standard k–e model was used to predict turbulent

flow in the header. The Reynolds transport equations in all the

three directions and the ‘k’ and ‘e’ equations can be written in

a generalized form as

Γ

Γ

Γ

..1

Figure 1: Full Set of Tube with Header

where stands for a generalized transport variable, which

is used for all conserved variables in a fluid flow problem,

including mass, momentum, and the turbulence variables k

and ξ. represents the effective diffusivity (sum of the eddy

diffusivity and the molecular diffusivity). S is the source

term for the respective dependent variable. The value of

source term S depends on the respective type of . The

solution of the above set of equations was applied to the

prediction of velocity and turbulence levels throughout the

tube side.

For both shell-side and tube-side, steady incompressible

flow of Newtonian fluid with constant thermo-physical

properties (density, viscosity, thermal conductivity and heat

capacity) is taken into account for the simulation. The flow of cold water over the studied heat exchanger is very similar to

the flow through tandem cylinders especially for over the

straight tubes. Therefore, for the shell-side, the conservation

equations of mass, momentum and energy equation can be

used in Cartesian three-dimensional domain as follows.

Continuity equation

…..2

Figure 2: After Mesh Non-conservation form

X-component


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Element Parameter value Tube diameter 156.69mm Tube length 1714.5mm Tube head 1984.8mm No of tube 21 No of header 2 Single tube diameter 38.1mm

5

= - -

!

!

"

"

# $ % % &

Y-component

'

!

!!

"!

2.8 Geometrical configurations

= - -- !

! " #! $ $ (

Z-component

)

= --

"

"

!"

!

""

"

#" $ % *

Table 1: Geometrical Configuration

Conservation form

X-component

%

+

!

!

"

"

3. Results and discussion:

3.1 Effect of Pressure drop distribution:

Y-component

# $ % ,

'

%

+ !

!

!!

!

"!

"

Figure 3: Pressure Distribution in tube/Header

Z-component )

#! $ $ % -

Here fig shows the pressure variation from bottom to top.

Maximum pressure obtained is about 0.55749 bars. The inlet

pressure is comparatively higher than others. Finally the outlet pressure is observed to be very closer to atm pressure.

% )

+ "

"

!"

!

""

"

#" $ % % .

Pressure in tube side: #12 34 8

/0 25 6

$ $ : 9

Here,

9

7

; <

….10

;)

The pressure drop owing to the return loss ∆Pr is given by,

2

/0= (4 >2

? $ $ 8

Total tube-side pressure drop:

@0A /0 /0= $ % % 88


2081

Figure 4: Pressure variation in inlet

The fig 4 shows the pressure variation in each point of

the inlet.


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The fig 7 shows the velocity variation in each point of the

inlet header.

Figure 5: Pressure variation in outlet

The fig 5 shows the pressure variation in each point of

the outlet.

3.2 Effect of velocities in tube side:

When 10m/s velocity is been given at inlet there will be

corresponding changes at input, output and tubes. Inlet

velocity is obtained as 10 m/s and outlet velocity obtained as

9.9 m/s, and in each tube the velocity is in the range of 1.78

m/s.

Figure 8: Velocity in outlet header

The fig 7 shows the velocity variation in each point of the

outlet header.

Here the below plot shows the velocity variation tube inlet and

outlet. The velocity at inlet is about 10 m/s and the velocity at outlet is about 9.9 m/s. Here its observed that the tube

velocity is comparatively lower to inlet and outlet velocities.

Finally its observed that velocity at the inlet header is 10 m/s

but when this flows into 21 tubes the velocities gets reduces in

each tube and variation is found to be in the range of 1.7 to

1.84 m/s.

Velocity chart 15

v

e 10

l

Figure 6: Velocity Distribution in the tube/header

o 5

c 0 i

t -5 y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

No of Tubes

velocities inlet outlet

Conclusion

.

Figure 7: Velocity in inlet header

In this research work, a Tube side flow Analysis for the Shell and Tube Heat Exchanger is investigated with CFD method

using STAR CCM+. The conclusions are summarized as

follows.

• In normal analysis, pressure and velocity variation in each point (inlet header, outlet header and in series of

tube) can’t be analyzed. But here in this work all the

profile is best observed.

• From the observation made the design can be further

modified so that time and cost can be reduced.

• In future, by using this observation various analysis like Heat Transfer, fouling, geometrical change etc

can be made.


2083

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t ube si de f l ow an al y si s f or t he sh e l l a nd t ub e … · 2018. 5. 6. · 3. e nerg y...

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