Compact Model of Latent Heat Thermal Storage for Its Integration in Multi-Energy Systems

Round 1

Reviewer 1 Report

This work presents a 0D model of a Latent heat thermal storage system consistent on a heat and shell heat exchanger with finned tubes where the phase change material is stored in the shell. This 0D is obtained by correlating the results provided by a 2D numerical model for the charging and discharging processes. Based on the Rayleigh number the study neglects natural convection for the 2D model. 

 

The idea of the study expressed in the abstract section is interesting, but the paper lacks the required scientific rigor for a publication. 

 

The major comments detailed next justify the former statement (sorted in decreasing order of importance):

 

1 - The authors present a numerical model which has never been validated. Validation of the 0D model by using a self made not validated 2D model is not a validation. It just proves that the correlations are useful to fit the simulations which have been carried out. Validation is a key and unavoidable step when using numerical models. 

 

2 - Moreover, some considerations of the 2D model may result in an inaccurate representation of reality. The following must be taken into account: 

    2a -  According to the authors, based in [18], the flow is dominated by natural convection for Ra/A>500. In this case,  Ra= 374, then convection is neglected. This deduction is not straightforward, because a flow which is not dominated by natural convection may still have a significant natural convection effect. This point shall be clarified further and quantified. 

    2b - Equation (4) used to estimate the inner tube convection coefficient “h” is the one proposed by Dittus-Boelter (as expressed by the authors). However, this expression is valid for inner fluid cooling (LHTS charge). For heating (LHTS discharge), a different exponent for the Prandtl number shall be used. 

2c - Equation (4) lacks precision for a significant temperature difference between the wall and the fluid. The reason being the viscosity variation due to temperature differences. This means that it should be valid for the charging process, when temperatures are similar, but may result inaccurate for the discharge one. Sieder and Tate equation shall perform better in this case. 

 

3 - No consideration for heat losses is made in the studied cases, where charging and discharging processes are carried out with a time difference between them of more than 5 hours (Section 4.2).

Author Response

Dear Reviewer,

We are grateful for your precious comments. Please see the attachment for a point-by-point response.

Author Response File: Author Response.pdf

Reviewer 2 Report

This is a complete work including continuum modeling, reduced-order modeling, and optimization. The author uses two equations (eqs 8 and 9) to fit the 2D simulation of a given LHTS system, and study the effectiveness of LHTS in reducing peak heat demand. There are three questions I hope the author can provide further explanations.

1. How do you select the functionals of Eqs. 8 and 9? Is there any physical interpretation?

2. The depenence of thermal power on initial SOC implies a strong hysteresis in the phase changing process. What is the characterstic time of that hysteresis? How long does it take for a partially charged PCM to relax to equilibrium?

3. There would be a typo in the middle figure of Figure 4: '...in a the building...'

Author Response

Dear Reviewer,

We are grateful for your precious comments. Please see the attachment for a point-by-point response.

Author Response File: Author Response.docx

Reviewer 3 Report

Fig.10 is not clear. For example, in Fig.10 (c) and (D) I only can see one color data，however, the labels of (c) and (D) have five colors and two colors. Can the authors replot the Figure.10?  

The authors present a simple 0D model for a modular shell-and-tube LHTS. The model was obtained considering the main quantities affecting the charging/discharging evolution and through a fitting of the LHTS thermal power achieved with a more detailed CFD model. The compact model is achieved by parametrizing the 2D model results as a function of the LHTS initial states of charge in order to account for partial charge and discharge. Results show that the 0D model is extremely accurate.

They studied presents a new modeling approach to quickly characterize the dynamic behavior of an LHTS unit. The proposed model allows simulating even partial charge and discharge processes. This study is beneficial for thermal energy storage technology.

Author Response

Dear Reviewer,

We are grateful for your precious comments. Please see the attachment for a point-by-point response.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

This work presents a 0D model of a Latent heat thermal storage system consistent on a heat and shell heat exchanger with finned tubes where the phase change material is stored in the shell. This 0D is obtained by correlating the results provided by a 2D numerical model for the charging and discharging processes. Based on the Rayleigh number the study neglects natural convection for the 2D model. 

This model sacrifices precision for simplicity and calculation speed. Thus, it can be valid for long term simulations where the required precision is not high. 

 

The authors have answered the main reviewer concerns, but there are still some major points to be addressed. 

The authors have defended the validity of the 2D numerical model in the comments to the reviewer. According to the authors’ response, the validity of the model was tested by Sciacovelli, A.; Gagliardi, F. and Verda, V., but this is never mentioned in the paper (although the work is cited).  The validity of the model must be addressed in detail within the document (characteristics of the numerical and experimental models under comparison and their relation to the current 2D model).

One drawback of this work is that it does not provide information about its expected accuracy for a real case application (accuracy of the 2D model, the 0D model). Such information would be of high interest for a potential reader of the work. But no real experiment has been carried out and no comparison with a real facility is undertaken.

Other minor comments: 

• The non-dimensional numbers definition is not given (Rayleigh, Reynolds, Nusselt, …).
• R^2 is not a very appropriate error measurement. Please provide a more representative one, like the standard deviation.

Author Response

Dear reviewer,

Thank you for your useful comments. Please see the attachment for a point-by-point response.

Author Response File: Author Response.docx