introduction to condensation heat transfer over horizontal tubes and

INTRODUCTION TO CONDENSATION HEAT TRANSFER OVER HORIZONTAL TUBES AND ENHANCEMENT TECHNIQUES

Nishant Gupta IIT Delhi

TUTOR-Prof. Ravi Kumar IIT Roorkee

Indo-German Winter Academy-2009

Introduction to condensation heat transfer over horizontal tubes and enhancement techniques

Outline

What is Condensation Heat Transfer?Types of condensation Condensation over a

1.Vertical Plate2.Horizontal tube

Introduction of integral fin tubesEnhancement techniques for condensation outside the tube

1.Condensate Flooding2. Drainage Strips3.Vapor Velocity4.Condensate inundation


Introduction

What is condensation ?

Condensation is the heat transfer process by which a saturated vapor is converted into a liquid by means of removing the latent heat of condensation.

Condensation occurs when the enthalpy of the vapor is reduced to the state of saturated liquid.


Introduction

MECHANISM OF CONDENSATION

Drop-wise condensation

Film condensation

Direct Contact condensation

Homogenous condensation


Introduction

DROP-WISE CONDENSATIONDrops of liquid form from the vapor at particular nucleation sites on a solid surface and drops remain separate during growth until carried away by vapor shear or gravity

FILM-CONDENSATIONDrops formed quickly coalesce to produce a continuous film of liquid

DIRECT CONTACT CONDENSATIONThe vapor condenses directly on the (liquid) coolant surface which is sprayed in the vapor space

HOMOGENOUS CONDENSATIONLiquid forms directly from the supersaturated vapor-away from any macroscopic surface

Various Modes of Condensation

a)Film-wise Condensationb)Homogenous Condensationc)Film-wise Condensationd)Direct Contact Condensation(Ref1)


Condensation over a vertical plate

Film Condensation over a vertical plate(Ref1)



ASSUMPTIONS The flow is laminar Temperature profile is linear Heat transfer is by one-dimensional heat conduction across the film to the

wall. Vapor temperature is uniform and is at its saturation temperature Gravity is the only external force Adjoining vapor is stagnant and doesn’t exert drag force on the film Fluid properties are constant Sensible cooling is neglected with respect to the latent heat The curvature of the interface is negligible



Falling laminar film on a vertical plate(Ref1)


Condensation over a vertical plate ANALYSIS At a distance z from the top, the thickness of the film is δ. Ignoring inertia effects i.e. no acceleration of the flow, the force balance on

the liquid element gives

________(1)

gravity force-buoyancy force=shear force uy denotes that velocity is a function of y.

a unit width of the plate is assumed. This expression is also valid for an inclined plane as long as the angle of

inclination is sufficient for drainage of the condensate. Only g is replaced by g sinβ, where β is the angle of the plane relative to

the horizontal.



Now rearranging and integrating the above equation using the boundary conditions that uy = 0 at y=0(No slip), the velocity profile at any location y in the film is given by

______(2)

Integrating this velocity profile across the film, the mass flow rate per unit width of the plate Γ is

______(3)

Γ has dimensions kg/ms



Now differentiating it with respect to δ,the rate of increase of the film flow rate with film thickness is

______(4)

Taking the film temperature as Tsat and the wall temperature as Tw ,the heat conducted across the film element of length dz with a thermal conductivity of kL is

______(5)

Applying an energy balance this rate of heat transfer by conduction is equal to the rate of the latent heat removed from the vapor at the interface which means that dq=hFG dΓ

hFG is the latent heat of condensation per unit mass.



The rate of condensation on this element(dΓ) is

_______(6)

Substituting equation 6 in equation 4 and then integrating from δ=0 at z=0 gives

______(7)

Rearranging the expression for the local film thickness, we get

______(8)



As we see from the equation 7 the film thickness is proportional to ¼ thpower of the temperature difference

This means larger temperature difference( Tsat– Tw ) results in higher condensation rates

From the thermal conductive resistance across the film, the local condensation heat transfer coefficient αf (z) at any point z from the top of the plate is given by

______(9)

The local Nusselt number using z as the characteristic length______(10)



Integrating from z=0 to z, the mean heat transfer coefficient for the plate up to point z is

______(11)

Taking a closer look we find that mean heat transfer coefficient is 4/3 times the value of the local heat transfer coefficient at z.

The mean heat transfer coefficient can also be obtained from

______(12)



Combining equation 12 and 6 to eliminate Tsat - Tw ,we get the thickness as

______(13)

Eliminating δ by combining equation 13 and 3

______(14)

where λL=k = kL



Integrating the above equation we get the average heat transfer coefficient,

______(15)


Condensation over horizontal tube

For laminar film condensation on smooth horizontal tubes, Nusseltobtained the following relation-

here d is the diameter of the tube Chato obtained the expression for condensation of refrigerants at low vapor

velocities inside smooth horizontal tubes-


Condensation over a horizontal tube

Condensation over horizontal tube(axis is perpendicular to the plane)(Ref1)



Taking the same assumptions as we did on the vertical plate

Energy balance between one dimensional heat conduction across the liquid film of thickness δ and the latent heat absorbed by the liquid from the condensing vapors at the interface will give

______(16)



Gravitation gsinβ is applied along the circumference of the tube where β is the angle around the perimeter from the top

Now using the same force balance as we did in the case of vertical plate-

here g is gsinβ

____(17)

(Ref1)



This equation when integrated with boundary conditions that u=0 at y=0 gives

_______(18)

Integrating this velocity profile from the wall to the film interface gives the total mass flow rate per unit length of the tube Γ at any angle β ,

________(19)



Now length from the top of the tube i.e. z is related to β as β=z/r where r is the radius of the tube

Now taking its derivative with respect to z and introducing it in the equation of heat balance, we get

_____(20)

Now integrating from the top of the tube when at β=0 ,Γ=0 and at β=π,Γ=Γ, we get the condensate flow rate on one side of the tube per unit axial length of the tube

_____(21)



Now an energy balance on the circumference of the tube gives the mean heat transfer coefficient for the perimeter of the tube as

______(22)

Substituting the value of Γ in equation 6 in the above equation we get

______(23)

As we have seen earlier that the numerical solution gives a value of 0.725 while the actual analytical value comes out to be 0.728.


Condensation on the horizontal integral fin tubes

Integral fin tubes have higher heat transfer coefficient than the smooth tubes They have been used in surface condensers in the refrigeration and process

industries Primary concern increase the surface area Lead to compact heat exchanger devices.

Common integral fin tubes in use today(Ref2)



Integral finned tube(Ref1)



No generalized theory to predict accurately the thermal performance of surface condensers

Basic questions to be answered are-1.What is the fin shape?2.What is the fin size?3.What is the fin spacing?for the maximum heat transfer coefficient

And there are other considerations that need to be discussed before the decision is taken about the tube

1.Condensate Flooding 2.Condensate Inundation3.Vapour velocity4.Drainage Strips


Condensate Flooding

Horizontal finned tubes when come in contact with a highly wetting liquid, to be retained between fins on the bottom part of tube

This is known as liquid “hold up”, “retention” or “flooding”

First measured by Katz et al.(over static liquids) Different amount of flooding observed with different fluids Flooding under dynamic and static conditions was same

Masuda and Rose found out that liquid also retained on the upper part of the tube in the form of wedges between the flanks and the tube surface in the inter-fin space.

A critical value of inter-fin spacing bc is there when the tube is fully flooded


Drainage Strips Amount of flooding decreased significantly by using longitudinal

condensate drainage strips

They are placed at the very bottom of the tube

It creates a low pressure region at the bottom of the tube, pulling the condensate into its pores

However a liquid wedge persists at the base of the fin to the top

Using of drainage strips has drastically increased the heat transfer coefficient

Largest increase occurs for the tube with the smallest fin spacing


Other Effects

Honda et al. arrived at following relation for h(height) >b(inter-fin spacing)/2

Φf = cos-1 ((2σcosθ/ρgbR0) -1) ______(24)Φf is the flooding angle.R0 is the integral fin tube outer radius.

More flooding should occur as the fin density is increased and/or surface tension/density ratio is increased

Design trade off- Fin density increasing-more total surface area Fin density increasing-more flooding Optimum fin spacing must exist.


Effect of Condensate Inundation

Mechanisms of condensate inundation(Ref1)


Effect of Condensate Inundation

Shell side condensation in an actual condenser is widely different from a single tube

One of the reasons for this difference is condensate inundation Nusselt considered the case with smooth tubes and assumed condensate

drains by gravity as a continuous laminar sheet He arrived at the following result-

αN / α1 = N-s

where αN is the average heat transfer coefficient for a vertical column of N tubes,

α1 is the heat transfer coefficient at the tops =1/4

Kern assumed condensate drains as discrete droplets or columns, which causes disturbances in the film and hence s=1/6


Effect of Vapor Velocity

Large vapor velocity

Large interfacial shear force

Different condensate flow around the tube

Appreciable change in the heat transfer


Effect of Vapor Velocity

The data of effect of vapor velocity on integral fin model is almost non-existent

Gogonin and Dorokhov found out that the effect of vapor velocity on the finned tube is very small in comparison to the effect for smooth tubes.

Ref3


Summary

Condensation over vertical plates Condensation over horizontal tubes For the condensation outside tubes condensate flooding

significantly affects finned tube performance Drainage strips can be used for better enhancements Effects of Vapor Velocity on integral finned tubes Decrease in the total heat transfer coefficients in bundle

of tubes


Acknowledgement

Thanks to Prof Ravi Kumar, IIT Roorkee for hisinvaluable support by the way of providing mestudy material and motivation


References

Condensation inside and outside smooth and enhanced tubes — a review of recent researchby A. Cavallinia,*, G. Censia, D. Del Cola, L. Dorettia, G.A. Longob,L. Rossettoa, C. Zilioa,2003

An evaluation of Film Condensation on Horizontal Integral-Fin tubes by P.J.Marto,1988

Heat Transfer by J.P.Holman Engineering data handbook (Wolverine Tube

inc.)

Image References

Ref1-Wolwerine tube inc Engineering data book

Ref2-http://www.tradekorea.com/products/integral_fin_tube.html

Ref3-An evaluation of Film Condensation on Horizontal Integral-Fin tubes by P.J.Marto,1988

Thank You!!!

introduction to condensation heat transfer over horizontal tubes and

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