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Heat transfer in filmwise steam condensation

In the process of filmwise condensation all the heat evolved on the film external bound is transferred to cooling surface. With laminar pattern of film flow heat is passed only by conduction (figure 5.1).

If we consider that temperature of condensate particles contacting the steam is equal to saturation temperature then heat flux passed through the unit surface can be determined like

,

where l – condensate heat conductivity coefficient, W/(m∙K);

d – film thickness, m;

t _w –surface temperature, °С.

On the other hand quantity of transferred heat can be established using Newton law

,

where from a= l/d.

So finding heat transfer coefficient is associated with determining film thickness d:

where l_s –condensate heat conductivity coefficient, ,

t _s – saturation temperature, °С;

v_s–coefficient of condensate cinematic viscosity, m²/s;

r –vaporization heat, J/kg;

g –acceleraation due to gravity, m/s²;

r’ – fluid density, kg/m³;

r’’ –steam density, kg/m³.

Average value of heat transfer coefficient for a vertical wall or tube with height h is determined by formula

, (а)

where Dt=t _s– t _w; .

If wall is inclined to horizon by angle y then following formula is used

.

Nusselt obtained dependence for determining average value of heat transfer coefficient for a horizontal tube

, (b)

where D – tube diameter.

It is reasonable to calculate characteristics of heat transfer process on condensation using Nusselt formula (b) with correction accounting for dependence of thermo-physical properties on temperature

, (*)

, (c)

where m -dynamic viscosity, Pa×s

According to experimental data heat transfer process goes more intensive on vertical planes or wall surfaces than it can be obtained from formula (*). It can be explained by wave character of condensate film flow

,

where Re –Reynolds number for condensate film.

,

where G – fluid mass flow rate per unit surface length, kg/(m∙s).

With Re≤4, e_v=1, because wave-flow is not set;

with Re=100, e _v=1.14;

with Re=400, e _v=1.2;

with Re=1600, e _v=1.27.

Using correction e _v accountingfor wave type of flow calcuation expression for heat transfer in steam condensation on vertical planes and walls surfaces can be written down as follows

, (d)

where – heat transfer coefficient determined by formula (а) when all the physical properties are taken at saturation temperature t _s.

With significant height of the vertical surface and temperature head condensate flow rate can be increased so much that film flow becomes turbulent.

It was discovered experimentally that turbulent flow of free moving condensate films usually starts with values of Reynolds number Re exceeding some critical value: Re_cr≈1600.

On figure 5.2.a scheme of condensate film flow along a vertical wall of big height is shown. With a certain value h _cr Reynolds number reaches its critical value Re_cr. After it condensate flow pattern becomes turbulent. With turbulent flow local intensity of heat transfer increases with rise of flow rate G and value of Re according to dependence

,

which can be explained by increase of fluid turbulent mixing intensity. Character of heat transfer change along vertical surface of significant length is given on figure 5.2b.

Values , at which turbulent flow in the film starts are determined from following expression

, (*)

that shows dependence of

on condensate physical properties and acceleration due to gravity.

Using this equation value can be calculated for any fluid.

When section with turbulent pattern of condensate flow is present on vertical surface calculation of heat transfer cannot be carried out using formula (d).

For these conditions value of average heat transfer coefficient is determined using following expression.

where ; – average tube surface temperature along perimeter.

With filmwise condensation of dry saturated steam on horizontal tubes perimeter average value of heat transfer coefficient is found using formula:

Re=3,25Z^0,75,

where ;

– reduced tube length;

– temperature head;

R – tube radius;

l, n and r – coefficients of heat conductivity, cinematic viscosity, and condensate density taken at temperature t _s;

r – vaporization heat.

Formula holds true with and laminar pattern of flow which is determined by condition Z<3900

,

where ; .

In filmwise condensation of dry saturated steam and laminar pattern of condensate film flow along vertical surfaces and tubes length average value of heat transfer coefficient is determined using following expression.

Re=3,8 Z ^0,78; ; .

This formula holds true with Re<1600 and therefore Z <2300

;

.

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