# Analysis Of A Shell And Tube Heat Exchanger Engineering Essay

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The analysis of flow maldistribution in a shell and tube heat exchanger is presented. The flow field in the inlet and headers was obtained through the numerical solution of the governing partial differential equations including the conservation equations of mass and momentum in addition to the equations of the turbulence model. The flow maldistribution inside the header was investigated using 3-D computational method. The 3-D numerical simulation was carried out by using commercial codes of GAMBIT and FLUENT. The uniformity of flow distribution was increased with increase in header length, where as it decreased with increase in flow rate. Maldistribution of flow in the header affects the heat transfer performance. So, the effects of the pressure drop, velocity distribution in the header part were analyzed. Flow distribution through the shell side tubes is analyzed.

Fig1 represents a Shell and tube Heat exchanger. These are the most versatile type of heat exchangers. They are used in the process industries, in conventional and nuclear power stations as condensers, steam generators in pressurized water reactor power plants, and feed water heaters and they are proposed for many alternative energy applications including ocean, thermal and geothermal. They are also used in some air conditioning and refrigeration systems [21].

Shell and tube Heat exchangers provide relatively large ratios of heat transfer area to volume and weight and they can be easily cleaned. They offer great flexibility to meet almost any service requirement. Reliable design methods and shop facilities are available for their successful design and construction. Shell and tube Heat exchangers can be designed for high pressure relative to the environment and high pressure difference between the fluid streams [1].

## Background:

Most of the heat exchangers which are used in industries are shell and tube heat exchangers. The important assumption in basic heat exchanger designing is the flow will be distributed uniformly at the inlet of the heat exchanger on each fluid side and throughout the core. But in general it is not uniform and maldistribution of flow leads to lower heat transfer performance [2]. For a tube side flow through a bundle of tubes, uniform distribution means equal amount of fluid in each tube or that each particle of fluid has an equal residence time in each tube. However, fluid can flow at same rate or at different rates [3].

Main causes of maldistribution:

Mechanical causes due to the design of headers and inlet ducts acting upon the flow distribution or Manufacturing tolerance effects in compact type exchangers.

Two phase flow distribution

Fouling/corrosion effects

Maldistribution caused by heat transfer process itself like viscous flow coolers or thermoacoustic oscillations [3,4].

Gotoda and Izumi[5] measured the velocity maldistribution at the tube sheet of the shell and tube heat exchangers for several header arrangements. Kutchey and Julien [6] presented data for a specific header design and demonstrated how the distribution can be improved with a revised design. Cichelli and Boucher [7] presented a design for the special case of a low-hold up and uniform distribution header for a shell and tube exchanger. Wilson[8] discusses the effect of regenerators and proposes a design procedure. Putnam and Rohsenow [9] calculated the pressure drop versus flow rate curves for cooling an oil in a five-tube exchanger. Muller [ 10] proposes a method for determining a point for a single point and any pressure drop which is greater than that point would avoid the maldistribution problem. Vist et.al [11] classified the parameters of fluidization distribution into operating parameters, such as heat quantity in each pipe, mass flux, geometric parameters etc. Fraas et al [12] described the extent of maldistribution using the velocity ratio between maximum and minimum values in tube. Lalot et al [13] did experimental and computational works for velocity distribution in an electric heater. They came to a conclusion that the computed velocity ratio (maximum velocity/minimum velocity) deviated from the experimental results. This paper will deal with steady type of maldistribution.

## Method of solution:

The header part was created with the given dimensions in GAMBIT and all the boundary conditions are applied. Then the meshing is done. The mesh which was created was a uniform staggered grid mesh. The meshed geometry is then exported to FLUENT. In fluent the problem is solved by using finite volume method. Finite Volume method discretizes the integral form of the conservation equations directly in the physical space. The computational domain is subdivided into finite number of contiguous control volumes, where the resulting statements express the exact conservation of relevant properties for each of the control volumes. At the centroid of each of the control volumes the variables are calculated. Interpolation is used to express variable values at the control volume surface in terms of center values and suitable quadrature formulae are applied to approximate the surface and volume integrals. An algebraic equation for each of the control volumes can be obtained in which a number of the neighboring nodal values appear[17].

Steady state flow modeling using FLUENT was performed. For the flow analysis, laminar model and standard k-epsilon turbulence model were approached. In FLUENT, the conservation equations of mass, momentum are solved using the finite volume method. The complete models of turbulence are two-equation models in which solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined. The standard k-epsilon turbulence model falls under this category and it is widely used for practical flow modeling calculations.

Transport Equations for the Standard - Model:

1

2

In the above equations

GK represents generation of turbulence kinetic energy due to the mean velocity gradients

Gb represents generation of turbulence kinetic energy due to buoyancy

Ym represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate.

C1E, C2E, C3E are constants.

ÏƒK, ÏƒE are the turbulent Prandtl numbers for and

SK , SE are user-defined source terms

The model constants are:

SIMPLE algorithm is used for pressure-velocity coupling and the solution is iterated until convergence was achieved so that the residual for each equation will fall below the value 10-3 [18]. In the present study, CFD (computational fluid dynamics) modeling for flow pattern in header part was used to investigate the characteristics of their velocity distribution and pressure distribution in a shell and tube heat exchanger was shown. The main objective of this project is to analyze the flow phenomena in the header part of the heat exchanger and to see whether is there any maldistribution takes place and also to analyze the pressure drop and velocity inside the header. Maldistribution was observed for both laminar and turbulent flow models and it was compared. With the change in header length how the maldistribution effects was analyzed.

## Model Generated in Gambit:

(a) (b)

Fig2: Model of Shell and tube Heat exchanger header part

Fig2 shows a schematic representation of header part of a shell and tube heat exchanger with the main geometrical characteristics listed.

Three dimensional model geometry was generated. The header is of 1.2 m-ID

It has one inlet nozzle with (0.25m-ID)

Two header lengths were considered (700mm and 900mm).

80 tube side outlets represented in Fig3

Fig3: Schematic representation of number of tubes

## Boundary conditions:

No-slip wall boundary condition with wall motion as stationary is applied on all wall surfaces with in the computational domain. The velocity-inlet and outflow boundary conditions are applied on the inlet and outlet sections respectively. The inlet and outlet conditions are corresponding to the average velocity distribution at the inlet and fully developed flow at the outlet [14]. The value of velocity at the inlet is obtained from Reynolds number. Two different values are considered (1000 and 2300). Working fluid is considered as water with density as 998.2kg/m3 and viscosity as 0.001003.

## Model after meshing:

The 3D grid system is generated using the commercial software GAMBIT based on the 3D geometry created in CATIA. Firstly, face mesh is generated with element type Tri and type Pave and finally volume mesh is created with element type Tet/Hybrid. Fig4 represents the model with mesh that is generated in GAMBIT. The mesh which is obtained here is very denser which leads to accurate results. The computational time required for iterations to get converged is high because the mesh is denser. To reduce the computational time and cost we can decrease the mesh density and simulate the results. Grid independence is also achieved for this model by trying different mesh densities. The finest implemented mesh involved about 141773 cells for 700mm header length and 1368440 cells for 900mm header length. The commercial code FLUENT is adopted to simulate the flow in the computational model. The governing equations are discretized by the finite volume method [14,15]. The convergence criteria is that, the residuals should be 10-3 for the flow field. Computation is performed on Core 2 Duo cpu with 2GB memory by using FLUENT and each simulation took 48h to get converged results[16].

## (c ) (d)

Fig 5: Contours of Pressure distribution inside the header

(a) 700mm header length with flow rate of Re=2300, (b) 900mm header length with flow rate of Re=2300, (c) 700mm header length with flow rate of Re=1000, (d) 900mm header length with flow rate of Re=1000

Fig 6: Flow Rate Vs Pressure

Fig 5 shows that flow maldistribution is present inside the header. The highest pressure occurs in the central zone of the header. In the remaining parts of the tubes as there is non - uniformity in the distribution of flow the pressure drop is less. Fig 6 illustrates the effect of Reynolds number or flow rate on flow maldistribution is obvious and more flow maldistribution occurs with increase in Reynolds number. It is also evident that with the increase in the flow rate the pressure drop is increasing. With the increase in the header length the pressure drop increased and the pressure is high at higher Reynolds numbers. It is found that the pressure drop in the high flow rate passages would be higher than those in the low flow rate passages due to the flow maldistribution in the header part of shell and tube heat exchanger. It is found that CFD results are in good agreement with experimental data, so CFD technology is capable to closely predict the flow distribution in a shell and tube heat exchanger [20].

## (c) (d)

Fig 7: Velocity distribution inside the header

(a) 700mm header length with flow rate of Re=2300, (b) 900mm header length with flow rate of Re=2300, (c) 700mm header length with flow rate of Re=1000, (d) 900mm header length with flow rate of Re=1000

Fig 8: Flow Rate Vs Velocity

Fig 7 shows the velocity distribution inside the header part of heat exchanger. Velocity vector collided against the exit side to pass predominantly through holes leaving several holes through which the flow rate did not flow. So, uniform stream is not present in this type of header. The velocity is very high at some tubes than in other tubes, this is because of the flow maldistribution. From this Fig7 we can clearly see that the flow is not uniformly distributed throughout the header. It shows a streamline of flow that is passing through the header. From this we can clearly see that the flow it is not uniform and maldistribution of flow is taking place. Maldistribution of flow will leads to lower heat transfer performance. Fig 8 illustrates the effect of Reynolds number or flow rate on flow maldistribution is obvious and more flow maldistribution occurs with increase in Reynolds number. It is also evident that with the increase in the flow rate the velocity is increasing. With the increase in the header length the velocity is decreasing which is obvious and the velocity is high at higher Reynolds numbers. It is found that the velocity in the high flow rate passages would be higher than those in the low flow rate passages due to the flow maldistribution in the header part of shell and tube heat exchanger.

## Conclusions:

The analysis of flow maldistribution in a shell and tube heat exchanger is presented. The uniformity of flow distribution was increased with increase in header length, where as it decreased with increase in flow rate. Maldistribution of flow in the header affects the heat transfer performance. So, the effects of the pressure drop, velocity distribution in the header part were analyzed. The highest pressure occurs in the central zone of the header. In the remaining parts of the tubes as there is non - uniformity in the distribution of flow the pressure drop is less. It is also evident that with the increase in the flow rate the pressure drop is increasing. With the increase in the header length the pressure drop increased and the pressure is high at higher Reynolds numbers. It is found that the pressure drop in the high flow rate passages would be higher than those in the low flow rate passages due to the flow maldistribution in the header part of shell and tube heat exchanger. With the increase in the flow rate the velocity is increasing. With the increase in the header length the velocity is decreasing which is obvious and the velocity is high at higher Reynolds numbers. To increase the performance of the heat exchanger maldistribution of flow among the tubes should not be present. So by changing the geometry of the header part according to that will leads to better results.