# PHE (Plate Heat Exchanger) for Condensing Duties: Recent Advances and Future Prospects

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}and other harmful substances. The increase in energy usage efficiency can contribute to mitigating these effects. One option to achieve this is via enhanced heat energy recuperation between process streams in the industry and civic sector, with the utilization of heat wasted from the process technologies [1].

^{TM}, originally developed by Vicarb and now produced by Alfa Laval. It is capable of operating at a pressure of up to 42 bar and temperatures from −45 °C to 371 °C. The geometry of channels is the same as shown in Figure 2, but the entrance and exit of flow are at the full channel width, which makes the share of pressure losses at these zones much smaller than in GPHE. However, the cross flow at the channels give a considerable difference in thermal design (for more details, see e.g., [2]) Another type of WPHE is a plate-and-shell heat exchanger. It consists of a pack of round plates encapsulated in a cylindrical shell, and can provide a counter-current flow of streams in a one-pass or multi-pass mixed channels arrangement. In some modifications, it can operate at a pressure of up to about 150 bar and a temperature of up to 750 °C. The main difference from other PHE types is the feature of flow distribution from ports at opposite sides of the round plates on full plates width.

## 2. Heat Transfer in Two-Phase Condensing Flows Inside PHE Channels

#### 2.1. Overall Analysis of Published Studies

^{2}, which is questionable to obtain from such small plates. The comparison of correlation accuracy was performed on 237 data close to ORC cycle application conditions. It gave a somewhat better accuracy with the mean absolute percentage deviation of 15.8%, while some data deviations acceded 30%. One of the considered correlations was that presented in the paper by Zhang et al. [8], as having much better accuracy than others, but on the data set of the paper [7] it showed lower accuracy. Another review of different correlations was proposed in papers for heat transfer during condensation of refrigerants for ORC systems and heat pumps was presented by Zhang et al. [9]. A new correlation for these conditions was proposed that the error was within ±30% for 98% of data. It was observed that the development of correlations for heat transfer in PHEs applicable for a range of geometrical parameters still requires further study. Eleven different correlations presented in publications were analysed by Shah [10], based on comparison with data from 25 sources in the range of the plate corrugation angles from 30° to 75°, 17 different refrigerants and data from one paper on steam condensation. The best-examined correlations have accuracy ±50% for 93% of the data. The modified correlation is proposed that predicts 83% of data with accuracy ±30%. The author’s conclusion is that there is a need for improvement in heat transfer correlation accuracy. The comprehensive review of heat transfer intensification in PHE by Kumar et al. [11] contains one chapter on heat transfer in two-phase flows, with just a few papers mentioning condensation in PHE channels.

#### 2.2. Recent Developments in PHE Condensers for Waste Heat Recovery, Heat Pumps and ORC Cycle

#### 2.3. Studies of Refrigerants with Low Global Warming Potential

_{3}) in gasketed PHE was studied by Tao et al. [24]. The channels of GPHE had a small hydraulic diameter of 2.99 mm corrugations on plates inclined at 63°. The plate length between ports was 666 mm, which is much bigger than in small BPHEs. The data on heat transfer were compared with correlations previously published in the literature. The best predictions were achieved with deviations of ±30% for 98.1% of the data. The transparent model of the plate was made to analyse the flow structure in the PHE channel during the condensation of NH

_{3}, as described by Tao et al. [25]. Based on the experimental results, the map of flow patterns was built, indicating the structure of two-phase flow at the main corrugated field and at the channel entrance and exit. The flow patterns were predominantly film flow and partial film flow. The difference with other refrigerants condensation is discussed, and were mostly influenced by the bigger density’s ratio of phases. No correlations for heat transfer were proposed, formulating it as the task for the future.

#### 2.4. Local Process Parameters

^{2}s). It is an interesting result, even when the local heat transfer coefficients were determined by an equation for averaged values. At higher flow rates up to 30 kg/(m

^{2}s), the agreement with Nusselt theory still remains for vapour quality below 0.5. At a higher vapour quality, the heat transfer coefficients are increased due to vapour action on the condensate film. Other correlations obtained on the process averaged parameters give a better agreement at high vapour qualities and flow rates, but overall cannot adequately describe the local heat transfer coefficients distribution. With such a mechanism of process development, the approach proposed by Thonon and Bontemps [29] of modelling with small channel zones by averaging the heat transfer coefficients obtained by the Nusselt correlation, and by an equation for high-velocity vapour, could be promising.

#### 2.5. Condensation of Steam and Other Process Vapours

#### 2.6. The Accuracy of Heat Transfer Correlations for PHE

_{gc}is film heat transfer coefficient, W/(m

^{2}·°C) g is the acceleration of gravity, m/s

^{2}; ρ

_{L}and ρ

_{G}are densities of liquid and vapour, kg/m

^{3}; λ

_{L}is the thermal conductivity of liquid, W/(m °C; r is the latent heat of condensation, J/kg; μ

_{L}is the dynamic viscosity of the liquid, Pa·s; L

_{p}is plate length; ΔT is the difference of vapour saturation temperature and wall temperature, °C.

_{L}. This is shown in a series of Equation (2), illustrating the link between the average heat transfer coefficient h

_{gc}, averaged specific heat flux q [W/m

^{2}], liquid mass flowrate through the unit of the cross-section area G

_{L}[kg/(m

^{2}s)] and Re

_{L}. It accounts for the hydraulic diameter d

_{h}which is determined as the ratio of four cross-section areas f [m

^{2}] to the wetted perimeter Π [m].

_{eq}determined by Equation (4):

_{h}is the hydraulic diameter of the channel.

_{eq}at about 1600. At higher values of Re

_{eq}the heat transfer coefficients are calculated by correlations developed at conditions of shear-controlled condensation. In some studies, the bigger the values for heat transfer coefficients calculated by equations for gravity-controlled and shear-controlled condensation are taken. The analysis of the different correlation’s accuracy in predicting experimental data, based on big data banks (about 2000 data points), was presented in papers [6,10]. In both papers, the best accuracy results were obtained for the shear-controlled area correlation proposed by Longo et al. [35] with Equation (5).

_{L}is the liquid Prandtl number; ϕ is the plate’s surface area enlargement factor because of corrugations.

_{L}− ρ

_{G})d

_{h}/σ is Bond number; σ is surface tension, N/m.

#### 2.7. The Thermal Modelling and Design of PHE Condensers

## 3. Pressure Drop in Two-Phase Condensing Flows Inside PHE Channels

_{mx}is the pressure of condensing flow, Pa; dP

_{TP}/dx is pressure loss due to friction (including form drug) in two-phase flow, Pa/m; ρ

_{mx}is the density of two-phase mixture, kg/m

^{3}; W

_{mx}is the velocity of the two-phase mixture, m/s; x is coordinated along thechannel, m.

_{TP}/dx, which is complicated by the complex flow structure in the PHE channels of complicated geometry. In the majority of heat transfer studies on vapour condensation in PHE channels, considered here in Section 2, the pressure drop is also investigated.

#### 3.1. Correlations with Averaged Process Parameters

#### 3.2. Pressure Drop Prediction with Local Process Parameters

## 4. The Structure of Two-Phase Condensing Flows Inside PHE Channels

## 5. The Conclusions and Future Prospects

- Further development of theoretical analysis and fundamental knowledge on heat transfer and hydrodynamics in condensing two-phase flows inside criss-cross flow channels, formed by plates with inclined corrugations of different geometries.
- The experimental studies of heat transfer and pressure losses during different vapour condensation in PHE channels, with an emphasis on local process parameters at small zones of channels and their distribution on channels field accounting for plates corrugation geometry.
- Experimental and theoretical studies of two-phase flow maldistribution inside PHE channels and between different channels in a system of channels at PHE with different numbers of plates.
- A deeper understanding of condensing two-phase flow structures, the change between different flow regimes and their effect on heat transfer intensity and pressure losses based on the methods of flow visualisation and CFD modelling.
- Reliable methods of PHE modelling and design for condensing duties, based on one-dimensional mathematical models accounting for the distribution of local process parameters along the channel length and the effects of flow distribution zones and port areas at commercially produced plates.
- Developing the methods for optimisation of PHE and their plate constructions for specified conditions of the vapour condensation process.
- Further development of methods and software for PHE condensers design and selection as part of heat exchanger networks in complex heat recuperation systems.
- Improving constructions of PHE for condensation of different vapours, based on newly acquired knowledge of process phenomena with the increased potential of energy saving and a reduced footprint on the environment.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**A typical corrugated plate of commercially produced GPHE: 1—ports for streams entrances and exits; 2, 5—zones for flow distribution; 3—gasket; 4—the major heat transfer field.

**Figure 2.**The main field of a channel between two corrugated PHE plates (schematically): (

**a**) corrugations crossing; (

**b**,

**d**) sine-shaped corrugations; (

**c**,

**e**) triangle-shaped corrugations.

**Figure 3.**The number of experimental points data received in studies of PHEs with different angle of plates corrugation.

**Figure 4.**The number of experimental points data received in studies of PHEs with different condensing vapours.

Predicting Equations | Number of Data Points | MAE, % | % of Points with Error < 50% |
---|---|---|---|

Equations (1) and (5) | 2376 | 25.5 | 93 |

Equations (3) and (5) | 984 | 22.9 | 93 |

Equations (1) and (6) | 237 | 6.4 | 100− |

Equations (1) and (7) | 283 | 8.9 | 100− |

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**MDPI and ACS Style**

Kapustenko, P.; Klemeš, J.J.; Arsenyeva, O.; Tovazhnyanskyy, L.
PHE (Plate Heat Exchanger) for Condensing Duties: Recent Advances and Future Prospects. *Energies* **2023**, *16*, 524.
https://doi.org/10.3390/en16010524

**AMA Style**

Kapustenko P, Klemeš JJ, Arsenyeva O, Tovazhnyanskyy L.
PHE (Plate Heat Exchanger) for Condensing Duties: Recent Advances and Future Prospects. *Energies*. 2023; 16(1):524.
https://doi.org/10.3390/en16010524

**Chicago/Turabian Style**

Kapustenko, Petro, Jiří Jaromír Klemeš, Olga Arsenyeva, and Leonid Tovazhnyanskyy.
2023. "PHE (Plate Heat Exchanger) for Condensing Duties: Recent Advances and Future Prospects" *Energies* 16, no. 1: 524.
https://doi.org/10.3390/en16010524