Heating coil

File: heater humidity.doc

Last edition: 2003-03-20/MK

Author: Lars Halling

History: 96-03-01/HN First released version

96-10-04/MK Updated to Menta 1.20

97-09-02/MK New FDB layout
Updated to Menta 3.0

98-12-16/MK New file namne.

2003-03-20/MK Updated to Menta 4.0

Description

This is a simple model of a heating coil controlled by a mixing valve. This heating coil model takes humidity relations into consideration. Therefore this model should be used when we have an application with humidity control.

We assume that the water flow and the air flow through the coil are constant. It can be shown that the temperature rise for the air in this kind of application is mainly determined by the coil efficiency, eps, defined as:

eps = (Twi-Two)/(Twi-Tai)

where

Twi = temperature of water entering the coil, °C.

Two = temperature of return water, °C.

Tai = temperature of air entering the coil, °C.

Note that eps is a constant property for a given heating coil if the water and air flows are kept constant. eps may in theory vary between 0 and 1. The actual value for a given coil can be determined from dimensioning data.

The temperature relation is assumed to be independent of the moisture content of the air. Once the temperature has been calculated we can easily obtain the relative humidity of the outgoing air since we know that the humidity ratio of the air does not change during the heating process.

Example

Assume that the return water temperature will be 42°C when the incoming water holds 60°C and the incoming air holds 0°C. In this example we have

eps = (60-42)/(60-0)= 0.3

The dynamics of the return water temperature and of the air leaving the coil is obtained simply by filtering in a first order filter with nominal time constant = 30 s.

REFERENCES

ASHRAE. (1992):"1992 ASHRAE HANDBOOK, HVAC Systems and Equipment," SI-edition. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc, Atlanta.

ASHRAE. (1993):"1993 ASHRAE HANDBOOK, FUNDAMENTALS," SI-edition. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc, Atlanta.

Grindal, A. (1988):"Reguleringsteknikk för ingeniören," Skarland Press A/S, ISBN 82-90033 117, första utgåvan.

Inputs

(Real) Air temperature before heater, °C. (Tai)

(Real) Relative humidity before heater, %. (FiA)

(Real) Boiler temperature, °C (Tb)

(Real) Control signal, % (Uc)

Outputs

(Real) Rel. Hum. after Heater, %. (FiB)

(Real) Temp. after Heater, °C. (Tao)

(Real) Return Water Temp., °C. (Two)

Constants

(Real) eps = coil efficiency. Nominal value = 0.3.

(Real) qa = air flow (m³/s). Nominal value = 5.0 m³/s.

(Real) qw = water mass flow (kg/s). Nominal value = 1.0 kg/s.

(Real) ca = air heat capacitivity ( kJ/(kg*K) ) = 1.02 kJ/(kg*K).

(Real) cw = water heat capacitivity ( kJ/(kg*K) ) = 4.18 kJ/(kg*K).

(Real) Tc = time constant (s). Nominal value = 20 s.

(Real) Patm = atmospheric pressure (Pa) = 101315 Pa.

(Real) rho = density of air (kg/m³) = 1.2 kg/m³, at P = 101315Pa and 20°C.
(1993 ASHRAE HANDBOOK, FUNDAMENTALS).

(Real) c8-c18 = constants in calculation of saturation pressure, see (1993 ASHRAE HANDBOOK, FUNDAMENTALS).

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