Design of Vapour Condensers for Pans and Evaporators

Introduction

The function of the condenser is, self evidently, to condense the vapour being driven off the syrup or massecuite in an evaporator or vacuum pan. This is done in order to create a vacuum in the pan or final effect evaporator. The vacuum pump's function is to remove the incondesible gases that find their way into the vapour stream. The incondensible gases come from the following sources:

Direct Contact Condensers

In this kind of condenser the condensing medium (cold water) is in direct contact with the vapour. The amount of cold water required is calculated from an energy balance around the condenser

ΣHin = ΣHout
where
H
= enthapy [kJ]
or in more detail
mc· hc + mv· hv = mt· ht
also
mc + mv = mt
hence
mc = mv· (hv - ht) / (ht - hc)
and so
Qc = mc/ρ
where
m
represents mass flow [kg/s]
h
represents specific enthalpy [kJ/kg]
Q
represents volume flow [m3/s]
ρ
represents density [kg/m3]
subscripts
c
represents cooling water
v
represents vapour
t
represents tailpipe water

Condenser Designs

A number of different designs are discussed by Hugot (pg 798 3rd ed). Single perforated tray rain-type condensers are discussed in Moult JM and Smits JH, Single Tray Rain Type Condensers, Proc S Afr Sugar Technol Assoc 1979, pg 98.

condenser

This design consists of a single perforated plate tray, with a number of so-called chimneys to allow incondensible gases to pass from below the tray to above to be drawn off by the vacuum pump.

Tray Design

10% of the water flowing into the tray leaves the tray via the circumferential holes and 10% overflows the tray. This is to ensure the walls of the condensor are continually wetted. It is understood that most of the condensation happens on the walls. The remaining 80% of the inflowing water leaves via the perforated plate tray bottom. The cicumferential holes and the plate perforations are sharp edged orifices and the volume flow through a sharp edged orifice is

Qp=π/4·d2·CD√(2·g·h)
Now the number of perforations,
N
is given by
N = 0.80·Qc/Qp
Furthermore it can be shown that the per unit open area of a perforated plate is given by
puOA = π/(2· √3)· d2/p2
now
puOA · tray area = N · perforation orifice area
OR
π/(2· √3)· d2/p2· π/4· D2 = N· π/4· d2
which gives
D = (N·2·√3/π)0.5· p
This calculation does not take into account the area given up to the incondensible gas chimneys or the unperforated section directly below the water inlet. The actual tray diameter will have to be larger to account for these.
where
Qp
is volume flow through one perforation orifice [m3/s]
d
is orifice diameter [m]
CD
is co-efficient of discharge = 0.65
g
= 9.81 m/s2
h
is head of liquid above orifice centre line [m]
D
is tray diameter [m]
p
is perforated plate hole pitch [m]

The tray should be of the order of 1.8m to 2m above the vapour inlet pipe centre line. Usually there are four chimneys, their total cross sectional area is about twice the incondensible outlet cross sectional area. The incondesible gas outlet is sized so that the flow velocity is 15m/s. There are as many ideas on the amount of incondensibles as there are authors and designers; a consevative figure to use is about 0.7% by volume on vapour into the condenser. The vapour inlet nozzle is sized so that the flow velocity is less than 60m/s. The cooling water inlet nozzle is sized so that the flow velocity is less than 2m/s.

The tailpipe is sized to be self venting PD Hills 1983 in which

JL* < 0.3
and
JL*=4·Q/(π·d2· √(g·d))
Hills PD (1983) Designing Piping for Gravity Flow. Chem Eng 90, 9, 111-114