measurement of characteristics of a flow- through …
TRANSCRIPT
3. Measurement
MEASUREMENT OF CHARACTERISTICS OF A FLOW-
THROUGH TYPE WATER BOILER
1 Aim of the measurement
Given a flow-through type boiler, the aim of the measurement is
to measure the heat-up curve (temperature change as a function of time) and
to determine its temperature rise and efficiency as a function of the flow rate.
2 Measurement of temperature
Many methods have been developed for measuring temperature. Most of these rely on
measuring some physical property of a working material that varies with temperature, e.g.:
glass thermometer
thermocouples
thermistors
bimetallic temperature gauge
2.1 Glass thermometer
One of the most common devices for measuring
temperature is the glass thermometer. This consists of a glass
tube filled with mercury or some other liquid, which acts as the
working fluid. Temperature increases cause the fluid to expand,
so the temperature can be determined by measuring the volume
of the fluid. Such thermometers are usually calibrated so that
one can read the temperature simply by observing the level of the
fluid in the thermometer.
2.2 Thermocouples
A thermocouple is a junction between two different metals
that produces a voltage related to a temperature difference. Any
junction of dissimilar metals will produce an electric potential
related to temperature. Thermocouples for practical measurement of
temperature are junctions of specific alloys which have a predictable and repeatable
relationship between temperature and voltage. Thermocouples are a widely used type of
temperature sensor for measurement and control and can also be used to convert heat into
electric power. They are inexpensive and interchangeable, are supplied fitted with standard
connectors, and can measure a wide range of temperatures. The main limitation is
accuracy: system errors of less than one degree Celsius can be difficult to achieve.
2.3 Thermistors
A thermistor is a type of resistor whose resistance varies
significantly with temperature. Thermistors are widely used as inrush
current limiters, temperature sensors, self-resetting overcurrent
protectors, and self-regulating heating elements. Thermistors typically
achieve a high precision within a limited temperature range [usually
−90°C to 130°C].
2.4 Bimetallic temperature gauge
A bimetallic strip can be used to convert a temperature change into mechanical
displacement. The strip consists of two strips of different metals which expand at different
rates as they are heated, usually steel and copper, or in some cases brass instead of copper.
The different expansions force the flat strip to bend one way if heated, and in the opposite
direction if cooled below its initial temperature. The metal with the higher coefficient of
thermal expansion is on the outer side of the curve when the strip is heated and on the
inner side when cooled.
A direct indicating dial thermometer (such as a patio thermometer or a meat
thermometer) uses a bimetallic strip wrapped into a coil. One end of the coil is fixed to the
housing of the device and the other drives an indicating needle. A bimetallic strip is also
used in a recording thermometer.
3 Description of the measuring equipment
The measuring equipment is the model of an electrically heated through-flow-type
boiler. Its sketch is shown in the Figure below.
The mass rate of flow of water m flowing through the instrument can be changed by
valve V. The electric heater H - which can be switched in two different power stages - warms
continuously the cold water flown in. The mass rate of flow can be measured on the
principle of volume meter tank (V, tVMT).
3.1 Theory and equations
The specific overall enthalpy of the entering water is 1
2
1
1
1
12
uv
ghp
eO
The specific overall enthalpy of the water at exit is 2
2
2
2
2
22
uv
ghp
eO
The change of overall enthalpy due to warming is
2
2
1
2
2
1212
12vv
hhguupp
eO
The internal energy of the entering water: 11
ctu
The internal energy of water at exit: 22
ctu
The difference of the internal energies: tcttcctctuuu 121222
The specific heat capacity of the water is Ckg
Jc
4187
After substituting the change of overall enthalpy we obtain
2
4187
2
1
2
2
12
12vv
hhgtCkg
Jppe
O
The following assumptions can be made:
( )
1 2
v v
thus, we have
Oe c t
The power-balance of the boiler - in steady state - is as follows:
envOelOPemPem
21 ,
where
m is the mass rate of flow, through the device, (kg/s)
e01 is the specific overall enthalpy of water entering the device, (J/kg)
e02 is specific overall enthalpy of water at exit (J/kg)
Pel is the power of heater, (W)
Penv is the power given to the environment, power loss, (W)
Upon rearranging, we obtain
el O env useful lossP m e P P P
i.e. the power of heater increases the overall enthalpy of the flowing water (useful power, Pu)
and another part leaves the system towards the environment.
3.2 The characteristic curve
After switching the device on the heating temperature T of the water increases but
after a certain time it will not change; it reaches its constant value t2 = Tconst. (t1 = T1 is the
entering temperature of the water). The constant value of the temperature difference
between the inlet and outlet is
1TTT
constconst
If the loss towards the surroundings is neglected, we have
Thus, for a given input electric power, the temperature rise is inversely proportional to
the mass flow rate:
4 The measuring exercise
a) The steps of the measurement are as follows:
i) Set a flow rate and keep it constant for the following steps.
ii) Measure the flow rate with the metering glass tube and stopwatch.
iii) Set the first heating power and wait until the output temperature stabilizes. Read
the output temperature.
iv) Set the second heating power and wait until the output temperature stabilizes.
Read the output temperature.
v) Go back to step i), set the next flow rate and repeat the measurement.
Draw the diagrams of Pel parameters with the measured points (4 flow rates for each
curve). The scales can be chosen optionally but suitably.
Given quantities:
deg25.0
deg141871000
3
AVccc
Ckg
Jc
m
kgIUP
Equations:
1TTT
t
VmIUcP
constconst
VMT
Pel
The heading of the measurement table
Serial
number
V
[dm3]
tVMT
[s]
m
[kg/s]
Tconst
[°C]
T1
[°C]
ΔTconst
[°C]
U’
[deg]
I’
[deg]
Pel
[kW]
5 Preparation questions
1. Describe 3 ways of measuring temperature.
2. Give the equations of the total enthalpy of the fluid before and after the boiler.
3. Assuming constant input power, describe the temperature rise-mass flow rate
relationship qualitatively.
4. Draw a sketch of the test rig.