Integrating Two-Stage Phase Change Material Thermal Storage for Cascaded Waste Heat Recovery of Diesel-Engine-Powered Distributed Generation Systems: A Case Study

: Thermal energy storage using the latent heat of phase change materials (PCMs) is a promising technique to solve the time mismatch between the availability and usage of ﬂue gas heat in distributed generation systems (DGSs). A diesel-engine-powered DGS integrated with two-stage tube-type PCM modules for exhaust gas heat recovery was developed and studied. Energy and exergy analysis for the PCM storage unit was carried out to verify the e ﬀ ectiveness of the PCM modules for heat recovery and to highlight the merits of the cascaded conﬁguration through a practical engineering case. Furthermore, the performance of the DGS was evaluated to study the contribution of PCM storage to improving system e ﬃ ciency. The results showed that 56.4% energy and 48.3% exergy of the input ﬂue gas were stored by the two-stage storage unit. Additional integration of the low-temperature PCM module to the high-temperature module improved the average storage e ﬃ ciency from 33.6% to 62.3% for energy and 33.1% to 50.8% for exergy. By utilizing the stored energy for heating water, the thermal e ﬃ ciency of the diesel engine was increased from the original 35.8% to 41.9%, while the exergy e ﬃ ciency was improved from 29.5% to 29.7%. This paper presented a practical application case to demonstrate that cascaded PCM thermal storage could provide an e ﬀ ective solution against the time mismatch between thermal energy availability and demand as well as improve the working e ﬃ ciency of the DGS. The outcome of this investigation could provide theoretical support and guidance for the engineering application of cascaded PCM storage for DGSs.


Introduction
Distributed generation systems (DGSs) with an internal combustion engine as the prime mover are recognized as an effective way to utilize fuel energy and reduce greenhouse gas emissions [1,2]. In addition to electricity generation, the exhaust gas heat from the engine can be recovered by various techniques such as the Rankine cycle [3][4][5], heat exchangers [6][7][8], thermoelectric generators [9,10], and so forth. However, the availability and usage of waste heat are often unsynchronized in time, and such a mismatch will reduce the overall efficiency of heat recovery and fuel utilization. The key to solving the problem is to detach the time of heat generation and consumption by integrating an energy buffer between supply and demand, that is, introducing thermal storage to DGSs [11].
Using the latent heat of phase change materials (PCMs) is a proven efficient thermal energy storage method [12]. Compared with sensible energy storage, the latent scenario has high storage density with relatively stable energy storage/release temperatures. Hence, many studies have been conducted using

System Components
(1) Power generation unit: a diesel generator (maximum power output = 200 kW) consumed fuel to generate electrical power with stable voltage and frequency. Table 1 shows the temperature and flow rate of the discharged gas, as well as the fuel consumption of the diesel engine measured at steady state under various loads. About 12%-27% of the thermal energy from the fuel combustion was exhausted by the flue gas when the load changed from 16 to 192 kW. Recovering this part of abandoned energy is essential to improve the efficiency of the diesel engine. According to the calculation results using Equation (1) shown in Figure 3, the operation efficiency of the diesel engine improved as the load increased and could maintain a relatively high value when the load was close to the rated condition. In this case study, the power output of the engine was set as 176 kW for driving the production process composed of 11 loads, where each load was 16 kW.
where η ther diesel and η elec diesel denote the thermal and electric efficiency of the diesel engine, respectively; Pdiesel and Vfuel denote the power output and fuel flow consumption of the engine; ρfuel = 8.5 × 10 2 kg m -3 and LHV = 43.4 × 10 3 kJ kg -1 denote the density and lower heating value of fuel, respectively; and φ = 85% is the efficiency of the generator.

System Components
(1) Power generation unit: a diesel generator (maximum power output = 200 kW) consumed fuel to generate electrical power with stable voltage and frequency. Table 1 shows the temperature and flow rate of the discharged gas, as well as the fuel consumption of the diesel engine measured at steady state under various loads. About 12%-27% of the thermal energy from the fuel combustion was exhausted by the flue gas when the load changed from 16 to 192 kW. Recovering this part of abandoned energy is essential to improve the efficiency of the diesel engine. According to the calculation results using Equation (1) shown in Figure 3, the operation efficiency of the diesel engine improved as the load increased and could maintain a relatively high value when the load was close to the rated condition. In this case study, the power output of the engine was set as 176 kW for driving the production process composed of 11 loads, where each load was 16 kW.
where η ther diesel and η elec diesel denote the thermal and electric efficiency of the diesel engine, respectively; Pdiesel and Vfuel denote the power output and fuel flow consumption of the engine; ρfuel = 8.5 × 10 2 kg m -3 and LHV = 43.4 × 10 3 kJ kg -1 denote the density and lower heating value of fuel, respectively; and φ = 85% is the efficiency of the generator.

System Components
(1) Power generation unit: a diesel generator (maximum power output = 200 kW) consumed fuel to generate electrical power with stable voltage and frequency. Table 1 shows the temperature and flow rate of the discharged gas, as well as the fuel consumption of the diesel engine measured at steady state under various loads. About 12-27% of the thermal energy from the fuel combustion was exhausted by the flue gas when the load changed from 16 to 192 kW. Recovering this part of abandoned energy is essential to improve the efficiency of the diesel engine. According to the calculation results using Equation (1) shown in Figure 3, the operation efficiency of the diesel engine improved as the load increased and could maintain a relatively high value when the load was close to the rated condition. In this case study, the power output of the engine was set as 176 kW for driving the production process composed of 11 loads, where each load was 16 kW.
where η ther diesel and η elec diesel denote the thermal and electric efficiency of the diesel engine, respectively; P diesel and V fuel denote the power output and fuel flow consumption of the engine; ρ fuel = 8.5 × 10 2 kg m −3 and LHV = 43.4 × 10 3 kJ kg −1 denote the density and lower heating value of fuel, respectively; and ϕ = 85% is the efficiency of the generator.   The exergy input of the fuel (diesel oil) to the DGS can be approximately obtained by [29,30] fuel fuel fuel and the exergy efficiency of the diesel engine can be calculated by (2) Cascaded PCM storage unit: transferring gas heat to a tube-type PCM exchanger via convection is an effective approach applied in latent storage systems [27,28,[31][32][33]. Good transfer performance can be achieved considering both the compactness factor and the thermal resistance in this configuration. Referring to Figure 4, a dual-channel module based on the structure of the double tube exchanger was designed to separate the channels of charging and discharging in order to obtain a clean HTF for residential usage. Composite PCMs were synthesized using carbonate and nitrate and equipped in the space between the inner and outer wall of the tubes to form HTM and LTM, respectively. The main physical properties of the PCMs are shown in Table 2. A swirl plate was installed at the waste gas inlet of the module to produce a uniform flow for heat transfer. When the flue gas entered the module, the convection heat transfer was dominant between the gas and outer wall of the steel tubes, which were arranged in a staggered manner. Then, the heat was transmitted to the PCMs by conduction. The release channel was located in the center of the tube and the stored thermal energy could be discharged by the heat transfer between the ambient air and the inner wall of the tubes. The released thermal energy was used to heat water to 315 K by the air- The exergy input of the fuel (diesel oil) to the DGS can be approximately obtained by [29,30] Ex fuel = 1.0338V fuel · ρ fuel · LHV (2) and the exergy efficiency of the diesel engine can be calculated by (2) Cascaded PCM storage unit: transferring gas heat to a tube-type PCM exchanger via convection is an effective approach applied in latent storage systems [27,28,[31][32][33]. Good transfer performance can be achieved considering both the compactness factor and the thermal resistance in this configuration. Referring to Figure 4, a dual-channel module based on the structure of the double tube exchanger was designed to separate the channels of charging and discharging in order to obtain a clean HTF for residential usage. Composite PCMs were synthesized using carbonate and nitrate and equipped in the space between the inner and outer wall of the tubes to form HTM and LTM, respectively. The main physical properties of the PCMs are shown in Table 2. A swirl plate was installed at the waste gas inlet of the module to produce a uniform flow for heat transfer. When the flue gas entered the module, the convection heat transfer was dominant between the gas and outer wall of the steel tubes, which were arranged in a staggered manner. Then, the heat was transmitted to the PCMs by conduction. The release channel was located in the center of the tube and the stored thermal energy could be discharged by the heat transfer between the ambient air and the inner wall of the tubes. The released thermal energy was used to heat water to 315 K by the air-water heat exchanger, the efficiency of which could reach 98.5%. The pipes for the HTF transmission and the outer casings of the modules were insulated to reduce heat loss to the surroundings. water heat exchanger, the efficiency of which could reach 98.5%. The pipes for the HTF transmission and the outer casings of the modules were insulated to reduce heat loss to the surroundings.  Based on the standard size of the seamless tube and the produced PCM shape, the PCM tube, the outer and inner diameters of which were Φ88 × 4 and Φ30 × 3, respectively, was manufactured to form the storage modules. The mass of PCMs and steel used in an individual tube was 7.46 and 12.34 kg for HTM and 10.37 and 15.43 kg for LTM. The heat stored in the steel cannot be ignored when evaluating the performance of the storage unit. Therefore, the PCMs and steel tubes were considered as the main storage component of the module in the current study. Referring to Table 1, the stable temperature of the exhaust flue gas at a load of 176 kW reached 883 K. Assuming that the average difference between the inlet and outlet gas temperatures of the module in the storage process was 250 K after the stabilization process (approx. 1 h), the number of tubes in the module could be estimated by the following equation when the heat transfer efficiency γ was set as 60%: where mgas and cgas denote the mass and specific heat capacity of the flue gas, respectively; T in gas and T out gas denote the inlet and outlet gas temperature of the module, respectively; ΔTgas denotes the temperature difference of the gas which was assumed as 250 K; mpcm and mtube denote the mass of the PCMs and steel tube, respectively; cpcm and ctube denote the specific heat capacity of the PCMs and steel tube, respectively; ΔTmod denotes the temperature increase of the module, which was set as 300 and 100 K for the HTM and LTM, respectively; ψ = 70% denotes the usage rate of the latent heat; and Nr = 1.1 denotes the redundant factor. Details of the storage modules are listed in Table 3.  Based on the standard size of the seamless tube and the produced PCM shape, the PCM tube, the outer and inner diameters of which were Φ88 × 4 and Φ30 × 3, respectively, was manufactured to form the storage modules. The mass of PCMs and steel used in an individual tube was 7.46 and 12.34 kg for HTM and 10.37 and 15.43 kg for LTM. The heat stored in the steel cannot be ignored when evaluating the performance of the storage unit. Therefore, the PCMs and steel tubes were considered as the main storage component of the module in the current study. Referring to Table 1, the stable temperature of the exhaust flue gas at a load of 176 kW reached 883 K. Assuming that the average difference between the inlet and outlet gas temperatures of the module in the storage process was 250 K after the stabilization process (approx. 1 h), the number of tubes in the module could be estimated by the following equation when the heat transfer efficiency γ was set as 60%: where m gas and c gas denote the mass and specific heat capacity of the flue gas, respectively; T in gas and T out gas denote the inlet and outlet gas temperature of the module, respectively; ∆T gas denotes the temperature difference of the gas which was assumed as 250 K; m pcm and m tube denote the mass of the PCMs and steel tube, respectively; c pcm and c tube denote the specific heat capacity of the PCMs and steel tube, respectively; ∆T mod denotes the temperature increase of the module, which was set as 300 and 100 K for the HTM and LTM, respectively; ψ = 70% denotes the usage rate of the latent heat; and N r = 1.1 denotes the redundant factor. Details of the storage modules are listed in Table 3.
A data acquisition platform based on the National Instrument (NI) hardware was designed for the storage modules and the arrangement of the measurement points are shown in Figure 5. For each module, nine K-type thermocouples, namely, Front (A-C), Middle (A-C), and Back (A-C) were placed in the axial geometric center of the tubes for monitoring the temperature variation of the PCMs. The additional three points, Passage (A-C), were placed in the vertical center plane of the module chamber to study the profile of the flue gas temperature.
A data acquisition platform based on the National Instrument (NI) hardware was designed for the storage modules and the arrangement of the measurement points are shown in Figure 5. For each module, nine K-type thermocouples, namely, Front (A-C), Middle (A-C), and Back (A-C) were placed in the axial geometric center of the tubes for monitoring the temperature variation of the PCMs. The additional three points, Passage (A-C), were placed in the vertical center plane of the module chamber to study the profile of the flue gas temperature.

Methodology
Based on energy conservation, the following equation could be obtained for the assumed period of time during the heat charging and discharging processes: discharging : where Q in gas denotes the input gas heat to the module; Q out gas denotes the gas heat flowing out of the module; Q sto mod and Q sto gas denote the thermal energy stored by the PCM tubes and the gas inside the module, respectively; Q out air denotes the air heat flowing out of the module; Q in air denotes the input air heat to the module; Q rel mod and Q rel gas denote the thermal energy released by the PCM tubes and the gas inside the module, respectively; and Qloss denotes the heat dissipated into the surroundings.

Methodology
Based on energy conservation, the following equation could be obtained for the assumed period of time during the heat charging and discharging processes: where Q in gas denotes the input gas heat to the module; Q out gas denotes the gas heat flowing out of the module; Q sto mod and Q sto gas denote the thermal energy stored by the PCM tubes and the gas inside the module, respectively; Q out air denotes the air heat flowing out of the module; Q in air denotes the input air heat to the module; Q rel mod and Q rel gas denote the thermal energy released by the PCM tubes and the gas inside the module, respectively; and Q loss denotes the heat dissipated into the surroundings. Among these, the energy stored or released by the modules and HTF for a certain duration could be obtained simply according to their initial and end temperature data by avoiding the consideration of the complex heat transfer process and heat loss assessment in the system-level apparatus. Similarly, for the energy quality analysis, although there was exergy deterioration caused by the temperature difference, the evaluation of the total exergy possessed by the modules and the available exergy for the user could be carried out using the measured temperature status. The modeling approach has been recognized as an appropriate method to conduct total energy and exergy analysis for a latent storage system [34,35].

Charging Process
Referring to Figure 6, the following aspects should be considered for the initial stage of the charging process when the temperature of the module is close to the ambient temperature: Part of the input heat will be transferred to the internal gas in the module because of the relatively small thermal resistance compared with the convective resistance between the HTF and tubes.

2.
Due to the temperature gradient of the inlet gas in the axial direction, there are differences in the thermal energy flow passing through the radial planes (i.e., Planes A and B).

3.
The resistance of heat conduction inside the tube exists and the temperature uniformity of the tube takes time to reach. Among these, the energy stored or released by the modules and HTF for a certain duration could be obtained simply according to their initial and end temperature data by avoiding the consideration of the complex heat transfer process and heat loss assessment in the system-level apparatus. Similarly, for the energy quality analysis, although there was exergy deterioration caused by the temperature difference, the evaluation of the total exergy possessed by the modules and the available exergy for the user could be carried out using the measured temperature status. The modeling approach has been recognized as an appropriate method to conduct total energy and exergy analysis for a latent storage system [34,35].

Charging Process
Referring to Figure 6, the following aspects should be considered for the initial stage of the charging process when the temperature of the module is close to the ambient temperature: 1. Part of the input heat will be transferred to the internal gas in the module because of the relatively small thermal resistance compared with the convective resistance between the HTF and tubes. 2. Due to the temperature gradient of the inlet gas in the axial direction, there are differences in the thermal energy flow passing through the radial planes (i.e., Planes A and B). 3. The resistance of heat conduction inside the tube exists and the temperature uniformity of the tube takes time to reach.
Therefore, it is not suitable to evaluate the overall heat storage state of the tubes by the PCM temperature at the axial center of the tube due to the uneven temperature distribution in this direction. Considering the relatively low temperature of the module in the initial storage process, the heat that dissipated into the surroundings from the module was assumed to be zero under the function of the outer casing insulation, and the following equation is given to characterize the thermal storage status: where X denotes the total number of measurement period j during charging, and Q sto gas can be evaluated using the HTF temperature at the measurement points (average temperature of Passages A-C).
When the temperature distribution in the tube reached a uniform state (the temperatures of the PCMs and steel were considered to be equal in each tube), the total energy and exergy stored in an individual tube could be calculated by Equations (7) and (8): Therefore, it is not suitable to evaluate the overall heat storage state of the tubes by the PCM temperature at the axial center of the tube due to the uneven temperature distribution in this direction.
Considering the relatively low temperature of the module in the initial storage process, the heat that dissipated into the surroundings from the module was assumed to be zero under the function of the outer casing insulation, and the following equation is given to characterize the thermal storage status: where X denotes the total number of measurement period j during charging, and Q sto gas can be evaluated using the HTF temperature at the measurement points (average temperature of Passages A-C). When the temperature distribution in the tube reached a uniform state (the temperatures of the PCMs and steel were considered to be equal in each tube), the total energy and exergy stored in an individual tube could be calculated by Equations (7) and (8): where T pcm and T 0 pcm denote the current and initial temperature of the PCM, respectively; T 0 denotes the ambient temperature taken as 293 K; T start spc and T end spc denote the start and end temperatures of the solid-liquid phase change, respectively; and H pcm and T pc denote the phase change enthalpy and phase change temperature of the PCM, respectively. The energy and exergy stored by the whole module can be represented by To simplify the evaluation of the quantity and quality of the thermal energy stored in the module, it was assumed that the uniform temperature inside the tube could be achieved when the Q sto mod calculated by Equations (6) and (9) were equal.
On the other hand, the input energy and exergy possessed by the HTF to the storage unit is given by Equation (10): where ρ gas denotes the density of the flue gas, and V gas and T in gas denote the flow rate and temperature of gas input to the module in the charging process, respectively. The energy and exergy efficiency of the storage process can be defined by where, for example, the energy storage efficiency η sto Q is the ratio between the total heat stored by the module and the input gas heat.

Discharging Process
Assuming that the heat release is carried out with a uniform temperature distribution in each tube (initial temperature of PCMs T 0 pcm > T start lpc ), the total energy and exergy discharged from an individual tube can be represented by the following Equations (12) and (13): where T start lpc and T end lpc denote the start and end temperature of liquid-solid phase change, respectively. The energy and exergy of the HTF absorbed from the module are given by Equation (14)  where Y denotes the total number of measurement period k during discharging; ρ air and c air denote the density and specific heat of the air; and V air and T in air denote the flow rate and temperature of air input to the LTM in the discharging process. Then, the energy and exergy efficiency of the release process is defined by the following equation: where, for example, the energy release efficiency η rel Q is the ratio between the total heat absorbed by the air from the module and the total heat stored in the module during the charging process.
It is worth noting that the transient model of the thermal storage system should be based on the energy conservation law, so that could refer to the relationship between heat rate, enthalpy rate of

Results and Discussion
Experimental investigations were performed according to the DGS operation scheme shown in Figure 2. The temperature profiles of the PCMs and HTF over time during the charging and discharging processes were mainly studied after calibrating. Then, the energy and exergy analysis for the cascaded storage unit was implemented and the efficiency evaluation of the DGS was carried out. The main factors that affected the experimental results were the possible errors in the measurement of PCM temperature (U 1 ), HTF temperature (U 2 ), flow rate (U 3 ), the mass of PCMs (U 4 ), and phase change enthalpy (U 5 ). As shown in Table 4, the standard uncertainties presented in the measurements were determined according to the verification report of the sensors and measuring devices.

Charging Process
As shown in Figure 7, compared with the instantaneous change of power output to the steady state, the temperature of the flue gas at the engine outlet experienced a stabilization process (0-5000 s). After that, the gas temperature difference between the engine outlet and HTM inlet remained at approximately 30 K due to the heat loss during the gas transmission. On the other hand, the outlet gas temperature of HTM and LTM increased gradually with the charging procedure.  (15) where, for example, the energy release efficiency η rel Q is the ratio between the total heat absorbed by the air from the module and the total heat stored in the module during the charging process.
It is worth noting that the transient model of the thermal storage system should be based on the energy conservation law, so that could refer to the relationship between heat rate, enthalpy rate of flue gas, and rate of the enthalpy change of the module material and PCM material. The proposed approach may be treated as a kind simplification of this transient model.

Results and Discussion
Experimental investigations were performed according to the DGS operation scheme shown in Figure 2. The temperature profiles of the PCMs and HTF over time during the charging and discharging processes were mainly studied after calibrating. Then, the energy and exergy analysis for the cascaded storage unit was implemented and the efficiency evaluation of the DGS was carried out. The main factors that affected the experimental results were the possible errors in the measurement of PCM temperature (U1), HTF temperature (U2), flow rate (U3), the mass of PCMs (U4), and phase change enthalpy (U5). As shown in Table 4, the standard uncertainties presented in the measurements were determined according to the verification report of the sensors and measuring devices.

Charging Process
As shown in Figure 7, compared with the instantaneous change of power output to the steady state, the temperature of the flue gas at the engine outlet experienced a stabilization process (0-5000 s). After that, the gas temperature difference between the engine outlet and HTM inlet remained at approximately 30 K due to the heat loss during the gas transmission. On the other hand, the outlet gas temperature of HTM and LTM increased gradually with the charging procedure. The temperature curves of the PCMs with respect to time at the measurement points are shown in Figures 8 and 9. Referring to Parts I and II, a decrease in the curve slope existed in the latent process because a large portion of heat was absorbed by the solid-liquid phase change. After The temperature curves of the PCMs with respect to time at the measurement points are shown in Figures 8 and 9. Referring to Parts I and II, a decrease in the curve slope existed in the latent process because a large portion of heat was absorbed by the solid-liquid phase change. After a fluctuation within a range in the melting process, the curve slope rapidly rose due to the absence of the phase change enthalpy in the liquid state. The slope value at the end point of fluctuation was used to represent the start and end slope of melting to approximately define the time length of the latent process for each tube: where ∆t denotes the time length of the latent process, and slp end spc and slp start spc denote the end and start slope of the PCM temperature curve in the melting process, respectively. The value of the slope at time t was defined using the following equation: where θ denotes the calculation period, which was set as 50 s in this study.
a fluctuation within a range in the melting process, the curve slope rapidly rose due to the absence of the phase change enthalpy in the liquid state. The slope value at the end point of fluctuation was used to represent the start and end slope of melting to approximately define the time length of the latent process for each tube: where Δt denotes the time length of the latent process, and slp end spc and slp start spc denote the end and start slope of the PCM temperature curve in the melting process, respectively. The value of the slope at time t was defined using the following equation: where θ denotes the calculation period, which was set as 50 s in this study.
(a) (b) For the HTM, after 7740 s of the heat storage process, the PCMs in the Front tubes (A-C) started to melt in succession. Taking the case of Front tube A as an example, the slope of the temperature curve dropped from the initial value of 4 × 10 -3 K s -1 to the minimum value of 0 K s -1 in the latent process. The melting processes of the tubes happened in different temperature ranges and their durations were also distinguished. The causes of the situation could be explained as follows: The uneven manufacturing level of the PCMs in engineering amplification led to the differences in density and uniformity of the materials. On the other hand, various arrangements of the tubes a fluctuation within a range in the melting process, the curve slope rapidly rose due to the absence of the phase change enthalpy in the liquid state. The slope value at the end point of fluctuation was used to represent the start and end slope of melting to approximately define the time length of the latent process for each tube: where Δt denotes the time length of the latent process, and slp end spc and slp start spc denote the end and start slope of the PCM temperature curve in the melting process, respectively. The value of the slope at time t was defined using the following equation: where θ denotes the calculation period, which was set as 50 s in this study.
(a) (b) For the HTM, after 7740 s of the heat storage process, the PCMs in the Front tubes (A-C) started to melt in succession. Taking the case of Front tube A as an example, the slope of the temperature curve dropped from the initial value of 4 × 10 -3 K s -1 to the minimum value of 0 K s -1 in the latent process. The melting processes of the tubes happened in different temperature ranges and their durations were also distinguished. The causes of the situation could be explained as follows: The uneven manufacturing level of the PCMs in engineering amplification led to the differences in density and uniformity of the materials. On the other hand, various arrangements of the tubes For the HTM, after 7740 s of the heat storage process, the PCMs in the Front tubes (A-C) started to melt in succession. Taking the case of Front tube A as an example, the slope of the temperature curve dropped from the initial value of 4 × 10 −3 K s −1 to the minimum value of 0 K s −1 in the latent process. The melting processes of the tubes happened in different temperature ranges and their durations were also distinguished. The causes of the situation could be explained as follows: The uneven manufacturing level of the PCMs in engineering amplification led to the differences in density and uniformity of the materials. On the other hand, various arrangements of the tubes induced differences in the thermal energy flow passing through the tubes. For the case of LTM, the Front tubes (A-C) were processing material fusion in the period from 11,000 to 16,095 s. Similar to the HTM scenario, various temperatures and durations of the latent process were exhibited among the tubes. However, due to the relatively low phase change enthalpy, the ratio of the slope reduction in the latent curve was not as obvious as that in HTM case. For example, the slope of the Front A curve at the start point of the latent process reached 1.0 × 10 −2 K s −1 and decreased to the minimum of 7.5 × 10 −3 K s −1 during the melting process. The ratio of the slope reduction was 25% compared with 100% of that in the case of HTM. Apart from the six tubes mentioned above, the other measured tubes were processing the sensible storage stage.
Based on Equations (6) and (9), the uniform temperature distribution in each tube could be achieved when t = 965 s for HTM and t = 9700 s for LTM, respectively. The energy and exergy stored in the nine tubes of each module could be calculated by Equations (7) and (8), and the results are shown in Figures 10 and 11. During the melting processes shown in Parts I and II, the storage capacity of the tube improved significantly. For the Front tube A in the HTM, 17% and 22.6% of the total stored energy and exergy, respectively, in the charging process were achieved during the latent process, which only occupied 8.2% of the charging time.
Energies 2019, 12, x FOR PEER REVIEW 12 of 20 induced differences in the thermal energy flow passing through the tubes. For the case of LTM, the Front tubes (A-C) were processing material fusion in the period from 11,000 to 16,095 s. Similar to the HTM scenario, various temperatures and durations of the latent process were exhibited among the tubes. However, due to the relatively low phase change enthalpy, the ratio of the slope reduction in the latent curve was not as obvious as that in HTM case. For example, the slope of the Front A curve at the start point of the latent process reached 1.0 × 10 -2 K s -1 and decreased to the minimum of 7.5 × 10 -3 K s -1 during the melting process. The ratio of the slope reduction was 25% compared with 100% of that in the case of HTM. Apart from the six tubes mentioned above, the other measured tubes were processing the sensible storage stage. Based on Equations (6) and (9), the uniform temperature distribution in each tube could be achieved when t = 965 s for HTM and t = 9700 s for LTM, respectively. The energy and exergy stored in the nine tubes of each module could be calculated by Equations (7) and (8), and the results are shown in Figures 10 and 11. During the melting processes shown in Parts I and II, the storage capacity of the tube improved significantly. For the Front tube A in the HTM, 17% and 22.6% of the total stored energy and exergy, respectively, in the charging process were achieved during the latent process, which only occupied 8.2% of the charging time.  To simplify the evaluation of the storage status of the modules, referring to Figure 5, the HTM and LTM were divided into six and nine parts, respectively. The overall condition of the modules was described using the energy and exergy stored in the measured tubes, which were induced differences in the thermal energy flow passing through the tubes. For the case of LTM, the Front tubes (A-C) were processing material fusion in the period from 11,000 to 16,095 s. Similar to the HTM scenario, various temperatures and durations of the latent process were exhibited among the tubes. However, due to the relatively low phase change enthalpy, the ratio of the slope reduction in the latent curve was not as obvious as that in HTM case. For example, the slope of the Front A curve at the start point of the latent process reached 1.0 × 10 -2 K s -1 and decreased to the minimum of 7.5 × 10 -3 K s -1 during the melting process. The ratio of the slope reduction was 25% compared with 100% of that in the case of HTM. Apart from the six tubes mentioned above, the other measured tubes were processing the sensible storage stage. Based on Equations (6) and (9), the uniform temperature distribution in each tube could be achieved when t = 965 s for HTM and t = 9700 s for LTM, respectively. The energy and exergy stored in the nine tubes of each module could be calculated by Equations (7) and (8), and the results are shown in Figures 10 and 11. During the melting processes shown in Parts I and II, the storage capacity of the tube improved significantly. For the Front tube A in the HTM, 17% and 22.6% of the total stored energy and exergy, respectively, in the charging process were achieved during the latent process, which only occupied 8.2% of the charging time.  To simplify the evaluation of the storage status of the modules, referring to Figure 5, the HTM and LTM were divided into six and nine parts, respectively. The overall condition of the modules was described using the energy and exergy stored in the measured tubes, which were To simplify the evaluation of the storage status of the modules, referring to Figure 5, the HTM and LTM were divided into six and nine parts, respectively. The overall condition of the modules was described using the energy and exergy stored in the measured tubes, which were After 19,800 s (5.5 h), the energy stored in the HTM and LTM was 802.5 and 840.5 MJ and the exergy was 325.9 and 233.6 MJ, respectively. About 56.4% energy and 48.4% exergy of the input flue gas could be stored. It is worth noting that more energy but less exergy was stored in the LTM than in the HTM due to the quality difference of thermal energy. The storage efficiency calculated by Equation (11) is shown in Figure 12. The results indicated that, compared with the single HTM scenario, two-stage cascade thermal storage could effectively increase the storage efficiency. During the time period from 11,000 to 19,800 s when the melting process occurred in both modules, the average energy storage efficiency increased from 33.6% to 62.3%, and the average exergy efficiency also rose from 33.1% to 50.8%. After 19,800 s (5.5 h), the energy stored in the HTM and LTM was 802.5 and 840.5 MJ and the exergy was 325.9 and 233.6 MJ, respectively. About 56.4% energy and 48.4% exergy of the input flue gas could be stored. It is worth noting that more energy but less exergy was stored in the LTM than in the HTM due to the quality difference of thermal energy. The storage efficiency calculated by Equation (11) is shown in Figure 12. The results indicated that, compared with the single HTM scenario, two-stage cascade thermal storage could effectively increase the storage efficiency. During the time period from 11,000 to 19,800 s when the melting process occurred in both modules, the average energy storage efficiency increased from 33.6% to 62.3%, and the average exergy efficiency also rose from 33.1% to 50.8%.

Discharging Process
After 0.5 h of self-heat preservation and blower flow adjustment, ambient-temperature air entered the LTM and HTM in sequence to absorb the stored heat at a flow rate of 480 Nm 3 h -1 . Similar to the charging process, the value of the curve slope at the start of the rapid increase after solidification was adopted to define the time length of the liquid-solid phase change process: where slp end lpc and slp start lpc denote the end and start slope of liquid-solid phase change, respectively. Referring to Part I in Figure 13 and Part II in Figure 14, the Front tubes in LTM and HTM started to experience solidification at 3495 and 350 s, respectively. Similar to the storage scenario, differences in the temperature range and duration of the latent process were observed. Additionally, the average temperature of the solidification was mostly noticed to be lower than that in the melting process. The main reason for this phenomenon can be concluded to be the supercooling of the PCMs, which is consistent with the results discussed in the literature [36][37][38].

Discharging Process
After 0.5 h of self-heat preservation and blower flow adjustment, ambient-temperature air entered the LTM and HTM in sequence to absorb the stored heat at a flow rate of 480 Nm 3 h −1 . Similar to the charging process, the value of the curve slope at the start of the rapid increase after solidification was adopted to define the time length of the liquid-solid phase change process: where slp end lpc and slp start lpc denote the end and start slope of liquid-solid phase change, respectively. Referring to Part I in Figure 13 and Part II in Figure 14, the Front tubes in LTM and HTM started to experience solidification at 3495 and 350 s, respectively. Similar to the storage scenario, differences in the temperature range and duration of the latent process were observed. Additionally, the average temperature of the solidification was mostly noticed to be lower than that in the melting process. The main reason for this phenomenon can be concluded to be the supercooling of the PCMs, which is consistent with the results discussed in the literature [36][37][38]. The energy and exergy released by the tubes were calculated according to Equations (12) and (13). Referring to Figures 15 and 16, the release capacity of the tubes was enhanced during the solidification process. Still considering the case of Front tube A in HTM, in 11.2% of the discharging time, about 46.3% of the energy and 47.4% of the exergy stored in the tube were discharged.  The energy and exergy released by the tubes were calculated according to Equations (12) and (13). Referring to Figures 15 and 16, the release capacity of the tubes was enhanced during the solidification process. Still considering the case of Front tube A in HTM, in 11.2% of the discharging time, about 46.3% of the energy and 47.4% of the exergy stored in the tube were discharged.  The energy and exergy released by the tubes were calculated according to Equations (12) and (13). Referring to Figures 15 and 16, the release capacity of the tubes was enhanced during the solidification process. Still considering the case of Front tube A in HTM, in 11.2% of the discharging time, about 46.3% of the energy and 47.4% of the exergy stored in the tube were discharged. The energy and exergy released by the tubes were calculated according to Equations (12) and (13). Referring to Figures 15 and 16, the release capacity of the tubes was enhanced during the solidification process. Still considering the case of Front tube A in HTM, in 11.2% of the discharging time, about 46.3% of the energy and 47.4% of the exergy stored in the tube were discharged.  As shown in Figure 17, the ambient air was heated up to an average temperature of 500 and 640 K in sequence after absorbing the heat in the LTM and HTM. The energy and exergy absorbed by the air determined by Equation (14) are shown in Figure 18. After a 3 h release process, 413.6 and 295.4 MJ of energy and 97.5 and 128.4 MJ of exergy were released from LTM and HTM, respectively. Although LTM output more energy, the HTM could supply more exergy to the user because of the higher-temperature-level heat it had stored. The release efficiency of the storage unit defined by Equation (15) was calculated and is shown in Table 5.    As shown in Figure 17, the ambient air was heated up to an average temperature of 500 and 640 K in sequence after absorbing the heat in the LTM and HTM. The energy and exergy absorbed by the air determined by Equation (14) are shown in Figure 18. After a 3 h release process, 413.6 and 295.4 MJ of energy and 97.5 and 128.4 MJ of exergy were released from LTM and HTM, respectively. Although LTM output more energy, the HTM could supply more exergy to the user because of the higher-temperature-level heat it had stored. The release efficiency of the storage unit defined by Equation (15) was calculated and is shown in Table 5. As shown in Figure 17, the ambient air was heated up to an average temperature of 500 and 640 K in sequence after absorbing the heat in the LTM and HTM. The energy and exergy absorbed by the air determined by Equation (14) are shown in Figure 18. After a 3 h release process, 413.6 and 295.4 MJ of energy and 97.5 and 128.4 MJ of exergy were released from LTM and HTM, respectively. Although LTM output more energy, the HTM could supply more exergy to the user because of the higher-temperature-level heat it had stored. The release efficiency of the storage unit defined by Equation (15) was calculated and is shown in Table 5.     As shown in Figure 17, the ambient air was heated up to an average temperature of 500 and 640 K in sequence after absorbing the heat in the LTM and HTM. The energy and exergy absorbed by the air determined by Equation (14) are shown in Figure 18. After a 3 h release process, 413.6 and 295.4 MJ of energy and 97.5 and 128.4 MJ of exergy were released from LTM and HTM, respectively. Although LTM output more energy, the HTM could supply more exergy to the user because of the higher-temperature-level heat it had stored. The release efficiency of the storage unit defined by Equation (15) was calculated and is shown in Table 5.     The thermal energy absorbed by the water can be calculated by the following equation: Q water = Q rel air η user = m water c water (T water − T 0 ) where η user = 98.5% denotes the efficiency of the air-water heat exchanger, and m water and c water = 4.2 kJ kg −1 K −1 denote the mass and specific heat capacity of the water, respectively. About 7.6 tons of ambient water can be heated up to T water = 315 K to meet the cleaning and washing demand. In this case, the exergy increment of the water is Ex water = m water c water [(T water − T 0 ) − T 0 ln(T water /T 0 )] = 25 MJ.
Based on Equations (1) and (3), the thermal and exergy efficiency of the diesel engine in a daily working period can be determined as follows: η ther diesel = P diesel /ϕ×t diesel +Q water V fuel ·ρ fuel ·LHV·t diesel = 41.9% η exergy diesel = P diesel ×t diesel +Ex water 1.0338×V fuel ·ρ fuel ·LHV·t diesel = 29.7%

Conclusions
A demonstration DGS integrated with two-stage tube-type PCM modules for diesel engine flue gas heat recovery was developed and investigated in the current study. According to the daily production scheme of the DGS, 5.5 h of heat charging and 3 h of heat discharging were conducted. The temperature profiles of the PCMs and HTF over time were studied in detail to evaluate the energy and exergy performance of the cascaded storage unit. Furthermore, the efficiency improvement of the DGS through the recovery and management of the flue gas heat using cascaded PCM storage was investigated.
The following conclusions can be drawn based on the demonstration results: (1) In 5.5 h of the heat charging process, about 56.4% of the energy and 48.4% of the exergy of the input flue gas can be stored by the two-stage modules. Compared with the single HTM unit, additional integration of the LTM can increase the average storage efficiency from 33.6% to 62.3% for energy and 33.1% to 50.8% for exergy.
(2) In 3 h of the heat discharging process, about 49.2% of the energy and 41.8% of the exergy stored in LTM and 36.8% of the energy and 39.4% of the exergy stored in HTM were released from the storage unit. The ambient air can be heated up to the average temperature of 500 and 640 K in sequence by absorbing the heat in the LTM and HTM.
(3) By storing and shifting the flue gas heat using cascaded PCM storage, about 7.6 tons of ambient water can be heated up to 315 K to meet the cleaning and washing load of the workers. In this case, 25 MJ of additional exergy can be obtained from the DGS daily operation. The thermal efficiency of the diesel engine can be increased from the original 35.8% to 41.9%, and the exergy efficiency can also be improved from 29.5% to 29.7%. It should be noted that, in the current application study, the high-quality heat released from the storage unit was used to provide civil-use hot water, which led to the low degree of exergy improvement for the DGS. High exergy efficiency of the diesel engine could be achieved when the stored energy was used to generate power using techniques such as the steam turbine, air expander, and so forth. This paper presented a practical application case to demonstrate that cascaded PCM thermal storage could provide an effective solution against the time mismatch between thermal energy availability and demand as well as improve the working efficiency of the DGS. The outcome of this investigation could provide theoretical support and guidance for the engineering application of cascaded PCM storage for DGSs.