Device and method for measuring thermal charging state in latent heat thermal energy storage systems
A device and a method for measuring a thermal charging state in a latent heat thermal energy storage (LHTES) system are provided. The device includes an energy storage unit with a phase change material (PCM) and one or more thermistor wires disposed along the length of the PCM. A control circuit is electrically connected to the thermistor wires. The control circuit passes an electric current through the one or more thermistor wires and measures the resulting resistance change. A processor, in communication with the control circuit, is configured to determine the thermal charging state of the PCM based on the measured resistance change. This configuration allows for an integrated thermal measurement along the entire length of the PCM to provide an accurate assessment of the stored energy.
1 . A device for measuring a thermal charging state in a latent heat thermal energy storage (LHTES) system comprising:
an energy storage unit comprising a phase change material (PCM);
one or more thermistor wires, each disposed along a length of the PCM;
a control circuit electrically connected to the one or more thermistor wires to pass an electric current to the one or more thermistor wires and measure a resistance change of the one or more thermistor wires during passage of the electric current; and
a processor in communication with the control circuit configured to determine a thermal charging state of the PCM based on at least the measured resistance change of the one or more thermistor wires.
2 . The device of claim 1 , wherein the resistance change is measured as a resistance-time series dataset, and the processor is further configured to determine the thermal charging state using the resistance-time series dataset.
3 . The device of claim 1 , wherein the processor is configured to compute the thermal charging state of the PCM by analyzing a relationship between the measured resistance change and a temperature of the one or more thermistor wires using a thermistor calibration equation.
4 . The device of claim 1 , wherein the processor is configured to compute the thermal charging state of the PCM using a Steinhart-Hart equation:
1
T
=
a
+
b
·
ln
(
R
)
+
c
·
ln
(
R
3
)
where T is a temperature determined from a resistance R of the one or more thermistor wires, and
a, b, and c are thermistor material-specific coefficients.
5 . The device of claim 1 , wherein the processor is configured to estimate a thermal conductivity of the PCM based on the measured resistance change of the one or more thermistor wires over a selected time and a corresponding temperature change.
6 . The device of claim 1 , wherein the processor is configured to compute a charging percentage of the energy storage unit by comparing the measured resistance change to a plurality of stored reference resistance change values for a solid and a liquid PCM state.
7 . The device of claim 1 , wherein the processor is configured to compute an overcharged or over-discharged state of the energy storage unit by computing an average PCM temperature based on a linear relationship between the measured resistance change and a temperature of the one or more thermistor wires.
8 . The device of claim 1 , wherein the processor is configured to estimate a stored sensible heat in the PCM based on a temperature of the one or more thermistor wires and one or more PCM properties.
9 . The device of claim 1 , further comprising a pair of conductive rings provided at opposite ends of the PCM,
wherein the one or more thermistor wires is linearly connected between the pair of conductive rings.
10 . The device of claim 1 , wherein the one or more thermistor wires has a diameter between 1 mm and 2 mm.
11 . The device of claim 1 , wherein the control circuit is configured to pass an electric current of less than 1A through the one or more thermistor wires to generate heat.
12 . The device of claim 1 , wherein the processor is configured to compute the thermal charging state of the PCM by analyzing a relationship between the measured resistance change and temperature of the one or more thermistor wires over a period of up to 120 seconds.
13 . A method of measuring a thermal charging state in a latent heat thermal energy storage (LHTES) system comprising:
providing an energy storage unit comprising a phase change material (PCM) and one or more thermistor wires, each disposed along a length of the PCM;
passing a controlled electric current to the one or more thermistor wires to generate heat along a length of the one or more thermistor wires;
measuring a resistance change of the one or more thermistor wires during the passing of the electric current; and
transmitting data including the measured resistance change to a processor to determine a thermal charging state of the PCM.
14 . The method of claim 13 , further comprising measuring the resistance change as a resistance-time series dataset and computing the thermal charging state using the resistance-time series dataset.
15 . The method of claim 13 , wherein computing the thermal charging state comprises calculating a temperature (T) of the one or more thermistors wires using a Steinhart-Hart equation based on the measured resistance (R) of the one or more thermistor wires, wherein
1
T
=
a
+
b
·
ln
(
R
)
+
c
·
ln
(
R
3
)
where a, b, and c are thermistor material-specific coefficients.
16 . The method of claim 13 , further comprising calculating a thermal conductivity (k) of the PCM using Fourier's Law of heat conduction, wherein a temperature change (ΔT) is modeled as being proportional to a natural logarithm of elapsed time (ln(t)), as determined from the measured resistance change of the one or more thermistor wires.
17 . The method of claim 13 , further comprising computing an overcharged or over-discharged state of the energy storage unit by computing an average PCM temperature (T) based on a linear relationship between the measured resistance change and temperature of the one or more thermistor wires, wherein:
T
=
T
1
+
(
R
-
R
1
R
2
-
R
1
)
×
(
T
2
-
T
1
)
where R 1 and R 2 are resistances at known temperatures T 1 and T 2 , respectively.
18 . The method of claim 13 , further comprising estimating a stored sensible heat in the PCM using a specific heat formula:
Q=m·C p ·( T−T m )
where Q is the heat added, m is a mass of the PCM, C p is a specific heat capacity of a liquid PCM, T is an average PCM temperature, and T m is a melting temperature of the PCM.
19 . The method of claim 13 , further comprising computing a charging percentage (P) of the energy storage unit using a comparison of the measured resistance change with a plurality of stored reference resistance change values for a solid and a liquid PCM states.
20 . The method of claim 13 , further computing the thermal charging state based on a stored dataset of experimental resistance-time values for calibration.