# Design Optimization of a Hybrid Steam-PCM Thermal Energy Storage for Industrial Applications

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## Abstract

**:**

## 1. Introduction

## 2. Optimization Model

#### 2.1. Storage Design Estimation Procedure

#### 2.2. Constraints

- At the initial state, the whole PCM is liquid and the temperature is equal to the phase-change temperature;
- The PCM properties are constant and equal for the solid and liquid phase;
- Inside the PCM, only heat conduction is taken into account;
- The sensible energy is neglected;
- The temperature of the heat source is constant.

#### 2.3. Cost Function

#### 2.4. Ruths Steam Storage Design

#### 2.5. Model Verification

## 3. Use Cases

#### 3.1. Initial Condition and Limits

#### 3.2. Results

## 4. Hybrid Storage Design

#### 4.1. Requirements

**Economic requirements:**(simple production, modular design, and easy ex-changeability of PCM). This takes into account the simplest possible production of the LHTES in order to reduce production costs. The modular design is necessary in the long term to manufacture the LHTES in large quantities. This requires a design that does not have to be completely specially adapted to every kind of storage geometry. In addition, the hybrid storage concept enables the use of different PCMs. This requirement can be easily met with a modular design. Also, simple exchangeability is required due to the degradation of the PCM and its maximum number of charging cycles—see also [41]. The subsequent removal of the PCM cells by simple replacement is therefore a necessary condition for keeping costs as low as possible.**Technical requirements:**(high elasticity of the PCM shell, resistance of the shell against corrosion by the PCM). The elasticity of the PCM casing is essential to withstand volume expansions during phase change. If this is not considered, the container cover will be subjected to strong cyclic loads, which can fatigue the material and lead to thermal stretching. In addition, the internal pressure changes the characteristics of the PCM, which can lead to a change in the phase change properties. To ensure a long latent-heat storage life, the PCM must be prevented from corroding its shell.**Physical requirements:**(good heat transfer between the container and PCM, high thermal conductivity of the PCM). The heat exchange between the water of the liquid/steam volume and the PCM of the LHTES tank should be as large as possible. For this purpose, good heat-conducting casing of the PCM must be used on the one hand, and contact resistance must be minimized on the other. In the present design principle, the use of heat conducting foils is necessary for this purpose. Another essential criterion is the high thermal performance of the PCM. If the thermal conductivity of the PCM is too low, the heat cannot be stored and released quickly enough. This requires the selection of a suitable system to increase thermal conductivity. In addition, the voltage series must be taken into account and prevented when selecting different materials that are in direct contact with each other.

#### 4.2. Consideration Concerning the Hybrid Storage Design

**Increase of overall heat transfer coefficient:**the overall heat transfer coefficient between the water in the RSS and the phase-interface in the LHTES is of great interest for the hybrid storage concept. In addition to the temperature difference, it determines the current heat flow between the two thermal storages. Between water and PCM, the vessel wall and the shell of the PCM is arranged. The container cover of the PCM must be corrosion-resistant and highly thermally conductive. Therefore, alumina is suggested for this purpose, and the resistance of the aluminum to the PCM must be checked. The thickness of the vessel wall of a steam storage depends itself on the diameter as well as the maximum permissible pressure, and is usually made of steel. In the case of thick-walled components, two-dimensional heat conduction phenomena that will influence the heat-affected zone must also be taken into account.**Increase the thermal conductivity of the PCM:**numerous methods have been investigated to try and improve the thermal conductivity of PCM. Of the many possibilities for improving heat transfer across the phase change zone that have a high potential for the hybrid storage concept, two are particularly promising in this context: (1) the sandwich concept presented by Steinmann and Tamme [27], and (2) a composite material. Bayon et al. [42], carried out experiments with the sandwich concept consisting of graphite foil (1 mm) and PCM (10 mm), whereby significant improvements in heat transport were observed. In the present concept, a combination of aluminum and PCM is preferred for cost reasons to keep the CAPEX as low as possible.**Enlargement of the heat transfer surfaces:**Approaches for increasing the heat transfer surface area also provides good results with regard to improving the heat transfer. One option is to increase the heat transfer surfaces by attaching fins. Since the steam storage tank is a pressure vessel which is operated at elevated temperatures, a precise strength analysis of the welded joints must be carried out and the fatigue strength ensured before fins are attached to the inside or outside of the pressure vessel. A strength analysis for welded joints of the external ribs has to be carried out to a different extent when using a sandwich concept, since with this LHTES type, a material connection with the pressure vessel is not absolutely necessary.

## 5. Retrofitting of Existing Ruths Steam Storages

#### 5.1. Method

#### 5.2. Results

## 6. Conclusions

## 7. Patents

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Variables and Parameters | |

C | total investment costs (€) |

${c}_{m}$ | specific highly thermally conductive material costs ($\u20ac{\mathrm{kg}}^{-1}$) |

${c}_{p}$ | specific heat capacity (Jkg${}^{-1}$K${}^{-1}$) |

${c}_{pcm}$ | specific PCM costs ($\u20ac{\mathrm{kg}}^{-1}$) |

${c}_{s}$ | specific other costs ($\u20ac{\mathrm{m}}^{-2}$) |

${C}_{s}$ | other costs (€) |

${c}_{v}$ | specific pressure vessel costs ($\u20ac{\mathrm{kg}}^{-1}$) |

${C}_{v}$ | pressure vessel costs (€) |

D | diameter (m) |

e | constant (-) |

${E}_{latent}$ | latent stored energy (J) |

${E}_{sensible}$ | sensible stored energy (J) |

${E}_{stored}$ | stored energy (J) |

f | liquid fill level (-) |

${f}_{m}$ | maximum highly thermally conductive material volume fraction (-) |

h | specific enthalpy (Jkg${}^{-1}$) |

${h}_{pcm}$ | latent heat (Jkg${}^{-1}$) |

i | index |

L | length (m) |

$L{D}_{min}$ | minimum ratio between pressure vessel length and diameter (-) |

m | mass (kg) |

${m}_{stored}$ | stored mass (kg) |

n | number of storage vessels (-) |

p | pressure (bar) |

${R}_{m}$ | mean tensile strength (Nmm${}^{-2}$) |

${R}_{p,20}$ | 20%-yield strength (Nmm${}^{-2}$) |

s | layer thickness (m) |

S | surface (${\mathrm{m}}^{2}$) |

t | time (s) |

T | temperature (K) |

${T}_{m}$ | node temperature (K) |

${T}_{pc}$ | phase change temperature (K) |

V | volume (m${}^{3}$) |

x | steam quality (-) |

z | weld seam factor (-) |

Greek Symbols | |

$\alpha $ | heat transfer coefficient (Wm${}^{-2}$K${}^{-1}$) |

$\Delta $ | difference (-) |

$\lambda $ | thermal conductivity (Wm${}^{-1}$K${}^{-1}$) |

$\rho $ | density ($\mathrm{kg}{\mathrm{m}}^{-3}$) |

${\sigma}_{max}$ | maximum allowable stress (Nmm${}^{-2}$) |

Subscipts and Superscripts | |

eff | effective |

m | highly thermally conductive material |

max | maximum |

min | minimum |

pcm | phase change material |

sl | steam/liquid |

w | wall |

’ | liquid water |

” | steam |

Abbreviations | |

CAPEX | capital expenditure |

HS | hybrid storage |

LHTES | latent heat thermal energy storage |

OPEX | operational expenditure |

PCM | phase change material |

RSS | Ruths steam storage |

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**Figure 4.**(

**a**) Difference between charging and discharging steam mass flow as function of time. (

**b**) Stored steam mass as function of time.

**Figure 6.**Schematic sketch of the hybrid storage design consisting of the RSS and the surrounding LHTES modules [43].

**Figure 7.**Schematic sketch of the PCM container mounting: (

**a**) front view. (

**b**) top view. (

**c**) sectional view A-A. According to [43].

**Figure 8.**Charge/discharge time vs costs for additional storage capacity with hybrid and Ruths variant. Al content in PCM is given in vol%.

**Figure 9.**Cost savings comparing hybrid with Ruths, i.e., savings are the ratio of Ruths steam storage costs to hybrid costs. Al content in PCM is given in vol%.

**Figure 10.**Calculated cost savings with additional capacities of 10%, 20%, 30%, and 40%, and resulting discharge times.

**Table 1.**Optimization variables with upper and lower bounds; ${h}_{min}^{\prime}$ ... specific enthalpy of the liquid phase at min. pressure, ${h}_{min}^{\u2033}$ ... specific enthalpy of the steam phase at min. pressure, ${\rho}_{min}^{\prime}$ ... density of the liquid phase at min. pressure, ${\rho}_{min}^{\u2033}$ ... density of the steam phase at min. pressure, ${L}_{max}$ ... defined max. length, ${V}_{sl,max}$ ... defined max. liquid/steam volume, ${n}_{max}$ ... defined max. number of storage vessels, ${h}_{pcm}$ ... latent heat, ${\lambda}_{pcm}$ ... PCM thermal conductivity.

Designation | Symbol | Lower Bounds | Upper Bounds |
---|---|---|---|

specific enthalpy at min. pressure | ${h}_{min}$ | ${h}_{min}^{\prime}$ | ${h}_{min}^{\u2033}$ |

density at min. pressure | ${\rho}_{min}$ | ${\rho}_{min}^{\u2033}$ | ${\rho}_{min}^{\prime}$ |

steam quality at min. pressure | ${x}_{min}$ | 0 | ∞ |

inner diameter | D | 0 | ∞ |

length | L | 0 | ${L}_{max}$ |

steam/liquid volume | ${V}_{sl}$ | 0 | ${V}_{sl,max}$ |

steel wall thickness | ${s}_{w}$ | 0 | ∞ |

number of storage vessels | n | 1 | ${n}_{max}$ |

PCM volume | ${V}_{pcm}$ | 0 | ∞ |

PCM layer thickness | ${s}_{pcm}$ | 0 | ∞ |

highly thermally conductive material volume | ${V}_{m}$ | 0 | ∞ |

effective latent heat capacity | ${h}_{pcm,eff}$ | 0 | ${h}_{pcm}$ |

effective PCM thermal conductivity | ${\lambda}_{eff}$ | ${\lambda}_{pcm}$ | ∞ |

Shell Diameter | Cylindrical Length | Mass | Vessel Costs | Other Costs |
---|---|---|---|---|

m | m | t | k€ | k€ |

2.8 | 6 | 11 | 95 | 53.5 |

3.6 | 10 | 32 | 180 | 124 |

2.5 | 9.5 | 46 | 250 | 85.5 |

4.2 | 13.7 | 73 | 310 | 164 |

4.0 | 20 | 100 | 400 | 235 |

4.2 | 22.5 | 120 | 470 | 358 |

Cost Coefficient | Value |
---|---|

${c}_{v1}$ €${\mathrm{kg}}^{-1}$ | 3.32 |

${c}_{v2}$ € | 72,784.91 |

${c}_{s1}$ €${\mathrm{m}}^{-6}$ | 0.04 |

${c}_{s2}$ €${\mathrm{m}}^{-4}$ | −20.44 |

${c}_{s3}$ €${\mathrm{m}}^{-2}$ | 3874.97 |

${c}_{s4}$ € | −122,323.04 |

${c}_{pcm}$ €${\mathrm{kg}}^{-1}$ | 0.50 |

${c}_{m}$ €${\mathrm{kg}}^{-1}$ | 2.15 |

Parameter | Case 1/2 |
---|---|

max. stored mass, t | 23/80 |

max. time, h | 2.7/10 |

charging steam pressure, bar | 30 |

max. pressure, bar | 29.5 |

min. pressure, bar | 18 |

max. liquid fill level, % | 85 |

Heat Transfer Coefficient ${\mathbf{Wm}}^{-2}{\mathbf{K}}^{-1}$ [36] | |
---|---|

steam (discharging) | 10 |

condensing steam (charging) | 5000 |

liquid water (charging) | 700 |

evaporating liquid water (discharging) | 1000 |

Wall [37] | |

density, ${\mathrm{kgm}}^{-3}$ | 7820 |

thermal conductivity, ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ | 48 |

specific heat capacity, ${\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$ | 461 |

20% Yield strength, ${\mathrm{Nmm}}^{-2}$ | 216 |

tensile strength, ${\mathrm{Nmm}}^{-2}$ | 470 |

yield strength, ${\mathrm{Nmm}}^{-2}$ | 315 |

Insulation [38] | |

density, ${\mathrm{kgm}}^{-3}$ | 80 |

heat conductivity, ${\mathrm{Wm}}^{-1}\mathrm{K}-1$ | 0.062 |

specific heat capacity, ${\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$ | 840 |

Highly Thermally Conductive Material (Aluminum) [39] | |

density, ${\mathrm{kgm}}^{-3}$ | 2800 |

specific heat capacity, ${\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$ | 869 |

thermal conductivity, ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ | 205 |

PCM [40] | |

phase change temperature, ${}^{\circ}\mathrm{C}$ | 220 |

specific latent heat capacity, ${\mathrm{kJkg}}^{-1}$ | 100 |

density, ${\mathrm{kgm}}^{-3}$ | 2000 |

specific heat capacity, ${\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$ | 1515 |

thermal conductivity, ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ | 0.515 |

Parameter | Case 1/2 |
---|---|

max. storage length, m | 30 |

max. liquid/steam volume, ${\mathrm{m}}^{3}$ | 300 |

max. number of storage vessels, 1 | 5/8 |

min. liquid fill level, % | 50 |

min. length diameter ratio, 1 | 2 |

max. aluminum fraction, 1 | 0.2 |

**Table 7.**Results of the storage design optimization (The results written in bold indicate the best results for integer values of the number of storage vessels).

Case 1 (23 t) | Case 2 (80 t) | |||||||
---|---|---|---|---|---|---|---|---|

Storage Type | RSS | HS | RSS | HS | ||||

Temperature Difference Fraction | - | 0.4 | 0.3 | 0.2 | - | 0.4 | 0.3 | 0.2 |

First Optimization Run: | ||||||||

number of storage vessels | 1.79 | 1.70 | 1.72 | 1.75 | 6.30 | 5.30 | 5.45 | 5.67 |

inner diameter, m | 5.39 | 4.54 | 4.70 | 4.88 | 5.39 | 3.20 | 3.58 | 3.98 |

length, m | 12.94 | 15.63 | 15.06 | 14.45 | 12.94 | 22.84 | 20.29 | 18.06 |

liquid/steam volume, ${\mathrm{m}}^{3}$ | 295 | 253 | 261 | 270 | 295 | 184 | 204 | 225 |

steel wall thickness, mm | 58 | 43 | 50 | 52 | 58 | 34 | 38 | 43 |

PCM layer thickness, mm | - | 85 | 68 | 48 | - | 231 | 194 | 150 |

PCM volume, ${\mathrm{m}}^{3}$ | - | 17 | 13 | 9 | - | 48 | 39 | 29 |

aluminum volume, ${\mathrm{m}}^{3}$ | - | 3 | 2 | 2 | - | 10 | 9 | 6 |

effective thermal conductivity, ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ | - | 34 | 33 | 31 | - | 37 | 37 | 37 |

total volume per vessel, ${\mathrm{m}}^{3}$ | 310 | 286 | 290 | 295 | 310 | 250 | 261 | 272 |

minimal liquid fill level, % | 77 | 76 | 76 | 76 | 77 | 72 | 73 | 74 |

total costs, k€ | 1260 | 1104 | 1133 | 1166 | 4426 | 3192 | 3 353 | 3 560 |

Second Optimization Run: | ||||||||

number of storage vessels | 1 | 1 | 1 | 1 | 6 | 5 | 5 | 5 |

inner diameter, m | - | - | - | - | - | 3.44 | 3.91 | 4.45 |

length, m | - | - | - | - | - | 21.68 | 19.11 | 16.90 |

liquid/steam volume, ${\mathrm{m}}^{3}$ | - | - | - | - | - | 201 | 230 | 263 |

steel wall thickness, mm | - | - | - | - | - | 37 | 42 | 48 |

PCM layer thickness, mm | - | - | - | - | - | 234 | 198 | 153 |

PCM volume, ${\mathrm{m}}^{3}$ | - | - | - | - | - | 49 | 40 | 31 |

aluminum volume, ${\mathrm{m}}^{3}$ | - | - | - | - | - | 11 | 9 | 7 |

effective thermal conductivity, ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ | - | - | - | - | - | 38 | 39 | 40 |

total volume per vessel, ${\mathrm{m}}^{3}$ | - | - | - | - | - | 270 | 290 | 314 |

minimal liquid fill level, % | - | - | - | - | - | 72 | 74 | 75 |

total costs, k€ | - | - | - | - | - | 3196 | 3363 | 3583 |

Third Optimization Run: | ||||||||

number of storage vessels | 2 | 2 | 2 | 2 | 7 | 6 | 6 | 6 |

inner diameter, m | 5.03 | 3.98 | 4.19 | 4.42 | 5.04 | 2.69 | 3.21 | 3.77 |

length, m | 13.30 | 16.83 | 16.01 | 15.18 | 13.29 | 26.18 | 21.90 | 18.70 |

liquid/steam volume, ${\mathrm{m}}^{3}$ | 264 | 210 | 221 | 233 | 265 | 149 | 177 | 209 |

steel wall thickness, mm | 54 | 43 | 45 | 47 | 54 | 29 | 34 | 40 |

PCM layer thickness, mm | - | 85 | 67 | 48 | - | 226 | 191 | 149 |

PCM volume, ${\mathrm{m}}^{3}$ | - | 16 | 13 | 9 | - | 46 | 38 | 29 |

aluminum volume, ${\mathrm{m}}^{3}$ | - | 3 | 2 | 1 | - | 9 | 8 | 6 |

effective thermal conductivity, ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ | - | 32 | 31 | 29 | - | 34 | 35 | 36 |

total volume per vessel, ${\mathrm{m}}^{3}$ | 278 | 239 | 247 | 256 | 279 | 211 | 231 | 254 |

minimal liquid fill level, % | 85 | 85 | 85 | 85 | 77 | 71 | 73 | 74 |

total costs, k€ | 1266 | 1115 | 1142 | 1174 | 4445 | 3209 | 3364 | 3565 |

**Table 8.**Results of the storage design optimization and results of the verification with a dynamic simulation model.

Case 1 (23 t) | Case 2 (80 t) | |||||||
---|---|---|---|---|---|---|---|---|

Storage Type | RSS | HS | RSS | HS | ||||

Temperature Difference Fraction | - | 0.4 | 0.3 | 0.2 | - | 0.4 | 0.3 | 0.2 |

total costs, k€ | 1266 | 1115 | 1142 | 1174 | 4445 | 3196 | 3363 | 3565 |

cost reduction, % | - | 12 | 10 | 7 | - | 28 | 24 | 20 |

number of storage vessels | 2 | 2 | 2 | 2 | 7 | 5 | 5 | 6 |

storage system total volume | 556 | 477 | 493 | 511 | 1953 | 1350 | 1452 | 1522 |

(without insulation), ${\mathrm{m}}^{3}$ | ||||||||

max. pressure exceeding, % | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 1 |

min. pressure lower deviation, % | 0 | 5 | 3 | 1 | 0 | 2 | 1 | 0 |

**Table 9.**Cost comparison of Ruths and PCM retrofit of seven 265 m${}^{3}$ storage devices with 10 h charge/discharge time.

Additional Storage Capacity | Ruths Retrofit Costs | Hybrid Retrofit Costs | Savings |
---|---|---|---|

10% | 476.9 k€ | 341.3 k€ | 28.4% |

20% | 953.9 k€ | 752.2 k€ | 21.1% |

30% | 1329.6 k€ | 1477.3 k€ | −11.1% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hofmann, R.; Dusek, S.; Gruber, S.; Drexler-Schmid, G. Design Optimization of a Hybrid Steam-PCM Thermal Energy Storage for Industrial Applications. *Energies* **2019**, *12*, 898.
https://doi.org/10.3390/en12050898

**AMA Style**

Hofmann R, Dusek S, Gruber S, Drexler-Schmid G. Design Optimization of a Hybrid Steam-PCM Thermal Energy Storage for Industrial Applications. *Energies*. 2019; 12(5):898.
https://doi.org/10.3390/en12050898

**Chicago/Turabian Style**

Hofmann, René, Sabrina Dusek, Stephan Gruber, and Gerwin Drexler-Schmid. 2019. "Design Optimization of a Hybrid Steam-PCM Thermal Energy Storage for Industrial Applications" *Energies* 12, no. 5: 898.
https://doi.org/10.3390/en12050898