ME410 MECHANICAL ENGINEERING SYSTEMS LABORATORY

Experiment 3: Mass and Energy Balances in Psychrometric Processes

1. Objective

The objective of this experiment is to observe four basic psychrometric processes which are heating,

cooling, humidification and dehumidification in an air conditioning unit. The air velocity, dry bulb

temperature, relative humidity and the amount of water added/removed will be measured to check

the mass and energy balances of these processes.

2. Introduction

The function of an air conditioning equipment is to change the state of entering air to a desired state

by controlling temperature and humidity of the specified space.

Air conditioning applications are divided into two types according to their purpose:

a. Comfort air conditioning,

b. Industrial air conditioning.

The primary function of air conditioning is to modify the state of the air for human comfort. The

industrial air conditioning meets the temperature and humidity requirements of an industrial or

scientific process.

In comfort air conditioning, it is necessary to control simultaneously the temperature, relative

humidity, cleanliness and distribution of air to meet the comfort requirements of the occupants.

According to the comfort chart given by the American Society of Heating, Refrigeration and Air-

conditioning Engineers (ASHRAE), comfort conditions can be obtained at 20-23°C dry bulb temperature

with 50 ± 20% relative humidity in winter and 24-27°C dry bulb temperature with 50 ± 20% relative

humidity in summer. In order to maintain these requirements, the state of the air is modified in an air

conditioning apparatus such that the varying summer and winter loads are balanced.

3. Theory

In air conditioning, air is taken as a mixture of dry air and water vapor. The maximum amount of water

vapor that can be present in the air is limited by total air temperature and pressure. When the amount

of water vapor in the air is at this limit, the mixture is called saturated air. Any excess water vapor will

either condense or freeze, depending on the air temperature.

3.1. Basic Psychrometry Terminology

Humidity: One of the most fundamental terms of psychrometry, humidity refers to the water content

of air. Often, to find the humidity, specific and relative humidity are calculated.

Specific humidity (𝜔): The ratio of water vapor mass to the dry air mass;

𝜔 =𝑚𝑤

𝑚𝑎. (1)

Relative humidity (Φ): The ratio of partial pressure of water vapor in air to the saturation pressure of

water at the given temperature;

Φ =𝑃𝑤

𝑃𝑤_𝑠𝑎𝑡. (2)

Relative humidity is usually expressed as percentage. When the relative humidity of air is 100%, then

the air is saturated and cannot hold any more water vapor. If saturated air is further cooled (thus

lowering the saturation pressure of water vapor), then the water will start to condense or freeze,

depending on the temperature.

Using the ideal gas equation of state, specific and relative humidity can be related;

𝑃𝑤𝑉 = 𝑚𝑤𝑅𝑤𝑇 and 𝑃𝑎𝑉 = 𝑚𝑎𝑅𝑎𝑇 (3)

or,

𝑚𝑤 =𝑃𝑤𝑉

𝑅𝑤𝑇 and 𝑚𝑎 =

𝑃𝑎𝑉

𝑅𝑎𝑇 . (4)

With 𝑅𝑎 = 0.287 kJ/kg∙K and 𝑅𝑤 = 0.4615 kJ/kg∙K, and inserting (4) into (2), we obtain

𝜔 = 0.622

𝑃𝑤

𝑃𝑎= 0.622

𝑃𝑤

𝑃 − 𝑃𝑤 (5)

where 𝑃 is the total air pressure.

Dry Bulb temperature (𝑇𝑑𝑏): The temperature that can be measured by thermometer or a

thermocouple.

Wet Bulb Temperature (𝑇𝑤𝑏): Temperature measured when the tip of the thermometer (or any other

temperature measuring device) is wetted. For unsaturated moist air, the measured value is less than

dry bulb temperature, with the difference being proportional to the relative humidity. In practice, 𝑇𝑤𝑏

is a ssumed to be equal to adiabatic saturation temperature, 𝑇𝑠𝑎𝑡, which would be reached if moisture

is added in an adiabatic process until the air becomes saturated. Thus, 𝑇𝑤𝑏 ≅ 𝑇𝑠𝑎𝑡.

Enthalpy (ℎ): The enthalpy of moist air at any state can be read from psychrometric charts or can be

calculated as:

ℎ = (𝑐𝑝𝑎 + 𝑐𝑝𝑤𝜔) × 𝑇 + ℎ𝑔@0℃𝜔

(6)

where

𝑐𝑝𝑎 = 1.0035 kJ/kg.K,

𝑐𝑝𝑤 = 1.8723 kJ/kg.K,

ℎ𝑔@0℃ = 2501.4 kJ/kg

and 𝑇 is in ℃.

Psychrometric Chart: A chart to determine all properties of moist air when two of these properties are

known. A psychrometric chart is drawn for a given elevation (or in other terms, pressure). A

psychrometric chart for 750m of elevation is given in the appendix.

3.2. Psychrometric Processes

The four basic psychrometric processes are sensible heating, sensible cooling, humidification and

dehumidification. These four processes are drawn on the psychrometric chart as seen in Figures 1 and

2.

Figures 1 and 2. Basic psychrometric processes.

Figure 1 shows the sensible heating and sensible cooling processes. During sensible heating and

sensible cooling, there is no change in the amount of water vapor; therefore specific humidity remains

constant. However, dry and wet bulb temperatures and therefore, enthalpy change, since there is

Tdb

ω

Sensible Heating

Sensible Cooling

Tdb

ω

Humidification

Dehumidification

energy transfer. Relative humidity also changes since the saturation pressure of water will change due

to temperature change.

Figure 2 shows the humidification and dehumidification processes. Humidification is the process of

adding water vapor to the air. It increases the specific and relative humidities, wet bulb temperature

and enthalpy. Dry bulb temperature may or may not change, depending on whether there is a

temperature difference between the air and vapor. Dehumidification, as the name suggests, is the

reverse process of humidification; removal of water from air. Usually, dehumidification is achieved by

cooling the air below its dew point temperature but absorbing of moisture by using a desiccant (a

drying agent), such as silica gel is also possible.

These four basic processes can be combined when needed. Figure 3 shows these combined processes.

Figure 3. Combined psychrometric processes.

Process 1-6 is heating with humidification. This is achieved by spraying water at a higher dry bulb

temperature than the air. Process 1-7 is heating with dehumidification. This could be achieved by

heating the flowing air over a desiccant. Process 1-8 is cooling with humidification. This is similar to

heating with humidification, with the only difference being the temperature of sprayed water. This

process is used in air washers, the water sprays used in outdoor cafés to achieve human comfort during

summer. Finally, process 1-9 is cooling with dehumidification. As mentioned before in the

dehumidification process, air is cooled below its dew point temperature to dehumidify the air. This is

the most common method for removing water from air. Theoretically, cooling with dehumidification

process is drawn on psychrometric chart as 1-9. However in practice, process 1-9’ occurs.

3.3. Mass and Energy Balances in Psychrometry

At steady state, the following relations can be obtained from the mass and energy balances for a

general process as shown in Figure 4.

Tdb

ω 1

6

7

8

9’ 9

Figure 4. Control volume for a simple psychrometric process.

The continuity equation for dry air is given by

�̇�𝑎1 = �̇�𝑎2 = �̇�𝑎 (7)

and for the water vapor,

�̇�𝑎1𝜔1 + �̇�𝑤 = �̇�𝑎2𝜔2 (8)

and the energy balance for the control volume,

�̇�𝑎1ℎ1 + �̇�𝑤ℎ𝑤 + �̇� = �̇�𝑎2ℎ2. (9)

Note that, during sensible heating and cooling, �̇�𝑤 = 0. Similarly for simple humidification and

dehumidification processes, �̇� = 0.

3.4. Refrigeration Cycle

Cooling the moist air with or without dehumidification is usually achieved by using a mechanical

refrigeration cycle which includes a compressor, a condenser, an expansion valve (or capillary tube for

small systems) and an evaporator.

�̇�𝑎1

𝜔1, ℎ1

�̇�𝑎2

𝜔2, ℎ2

�̇�𝑤

ℎ𝑤

�̇�

Figure 5. Refrigeration cycle

Figure 5 shows the component diagrams of a refrigeration cycle as well as 𝑃-ℎ and 𝑇-𝑠 diagrams of a

typical cycle. In practice, the compression process will be irreversible and there will be pressure losses

through the evaporator, the condenser and the connecting pipes. The isentropic efficiency of the

compressor is defined as

𝜂𝑠 =

�̇�𝑖𝑑𝑒𝑎𝑙

�̇�𝑎𝑐𝑡𝑢𝑎𝑙

=ℎ2𝑠 − ℎ1

ℎ2 − ℎ1 (10)

The parameters that are important to include are the compressor discharge temperature, cooling

capacity, power input and coefficient of performance of the cycle which may be defined as

𝐶𝑂𝑃 =

�̇�𝑒𝑣𝑎𝑝

�̇�𝑐𝑜𝑚𝑝

=ℎ1 − ℎ4

ℎ2 − ℎ1 (11)

Because of the irreversibility of the expansion valve and other parts, the 𝐶𝑂𝑃 becomes less than the

ideal value of a reversible (Carnot) cycle,

Condenser

Evaporator

P

h

1

Comp

.

Exp. valve

2 3

4

1

2s 3

4

T

1

2s

3

4

s

2

2

𝐶𝑂𝑃𝑐 =

𝑇𝑙𝑜𝑤

𝑇ℎ𝑖𝑔ℎ − 𝑇𝑙𝑜𝑤 (12)

4. Experimental Setup

The experimental setup can be seen in figure 6.

Figure 6. Experimental Setup

HVAC components of the system were donated by ISISO and the control system of the setup was

donated by Honeywell Turkey.

The system consists of an inlet duct, a fan to control the air flow, 4 preheaters, a humidifier, an

evaporator (and the corresponding refrigeration cycle components), 4 reheaters, outlet duct and a

return duct. A schematic representation of the setup can be seen in Figure 8, which shows a screenshot

from the controller software of the system.

Figure 7. Components of the setup. From left to right: Fan, preheaters, humidifier and evaporator

Reheaters and preheaters are simple electric heaters. Each heater dissipates 700W of power.

Refrigeration cycle is a simple vapor-compression cycle with R-407C as the refrigerant.

The return duct is used for adiabatic mixing. The mixing ratio can be controlled by adjusting

damper positions.

4.1. Measurements

There are a number of different types of sensors in the setup. First is the anemometers; anemometers

are used to measure the air velocity. In the setup, anemometers are placed at inlet, outlet and return

ducts.

Figure 8. Screenshot from the controller software.

Temperature and humidity of air are measured with thermometers and hygrometers, respectively.

There is a pair of thermometer and hygrometer at each section (see figure 8).

There are two flowmeters for water; one to measure the steam flow rate at the humidifier and one to

measure the condensed water rate at the condenser. There is also another flowmeter to measure the

flow rate of the refrigerant in the refrigeration cycle.

5. Procedure

5.1. During the Experiment

Make sure that the setup has reached the steady state. Then record the following;

Air velocities at inlet, outlet and return duct,

Temperature and relative humidity values in each section

Temperature and pressure readings at evaporator inlet and outlet (FOR LONG REPORT

ONLY)

Mass flow rate through the humidifier

Mass flow rate of the condensed water

Energy consumption readings of the heaters

Energy consumption of the compressor and refrigerant flow rate (FOR LONG REPORT

ONLY)

5.2. Writing the Report

Draw the process on the psychrometric chart according to your readings.

Find ℎ and 𝜔 for every state, using the Equations (1)-(6).

Write and solve the mass and energy balances at every section. Start by finding the mass

flow rate of dry air, 𝑚𝑎.

Draw the refrigeration cycle on the P-h diagram provided and find the power consumption

of the compressor (𝑊𝑐̇ ), refrigerant flow rate (𝑚𝑟̇ ), isentropic efficiency (𝜂𝑠) and the COP

(FOR LONG REPORT ONLY).

Comment on the possible reasons of deviations of measured values from theoretical

values. What kind of errors can be causing these deviations and how does it affect the

overall deviation? Also explain on how these deviations can be minimized.