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Energy, exergy, and economic (3E) analysis of air bubbles injection into plate heat exchangers

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Abstract

This study aims to experimentally investigate the impact of air bubbles injection on the combined energetic, exergetic, and economic performance characteristics of a plate heat exchanger (P-HEX) with a parallel fluid flow configuration. Cold water, with a fixed volume flow rate of 290 LPH, is mixed with air bubbles (flow rates ranging from 150 to 840 LPH) before entering the P-HEX. The hot water was studied in seven different volume flow rates (280 to 880 LPH) and kept at 50 °C. The results show remarkable increments in the enhancement factors of the number of transfer units and effectiveness, up to 33.17 and 5.5%, respectively, compared to single-phase flow. Furthermore, cold-water side injection boosts the maximum enhancement in the number of transfer units by 2.68 folds, compared to hot water side injection. The maximum entropy generation rate is dampened by 2.45 folds when injecting the cold-water stream instead of the hot one, and the maximum system efficiency is increased from 96.9 to 97.6%. The thermo-economic assessment further highlights the potential of air injection as one of the promising techniques for P-HEXs’ performance, where a maximum specific net profit of 0.45 USD kJ−1 is estimated.

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Data availability

All analyzed data in this study are described in the article itself or its electronic annex.

Abbreviations

ABI:

Air bubble injection

CWB:

Cold-water bench

CWS:

Cold-water side/stream

EGM:

Entropy generation minimization

HEX:

Heat exchanger

HTR:

Heat transfer rate

HWB:

Hot water bench

HWS:

Hot water side/stream

P-HEX:

Plate heat exchanger

TBL:

Thermal boundary layer

THP:

Thermo-hydraulic performance

\(A\) :

Heat transfer area (m2)

\({A}_{\mathrm{p}}\) :

Plate area (m2)

\(\mathrm{AOT}\) :

Annual operating time (s)

\(\mathrm{AEGN}\) :

Augmentation entropy generation number

\(C\) :

Heat capacity rate (J s−1 K−1)

\({C}_{\mathrm{p}}\) :

Specific heat capacity (J kg−1 K−1)

\(\mathrm{CF}\) :

Capital recovery factor (-)

\(\mathrm{EGN}\) :

Entropy generation number (-)

\(\mathrm{EGR}\) :

Entropy generation rate (W K−1)

ER:

Effectiveness enhancement ratio (-)

\(\mathrm{Ex}\) :

Exergy (J)

\({\mathrm{Ex}}_{\mathrm{des}}\) :

Exergy destruction rate (W)

\(f\) :

Friction factor (-)

\(h\) :

Heat transfer coefficient (W m−2 K−1)

\(i\) :

Interest rate (%)

\({I}_{\mathrm{i}}\) :

Initial cost of P-HEX (USD)

\(\mathrm{LMTD}\) :

Logarithmic mean temperature difference (°C)

\(\dot{m}\) :

Mass flow rate (kg s−1)

\(N\) :

Number of plates (-)

\(n\) :

Lifetime of P-HEX (years)

\(\mathrm{NP}\) :

Net profit value (USD)

\(\mathrm{Nu}\) :

Nusselt number (-)

\({N}_{\mathrm{t}}\) :

Number of P-HEX plates (-)

\(\mathrm{NTU}\) :

Number of heat transfer units (-)

NR:

NTU enhancement ratio (-)

\(P\) :

Pressure (Pa)

\(\dot{Q}\) :

Heat transfer rate (W)

\(\mathrm{Re}\) :

Reynolds number (-)

\(\mathrm{SV}\) :

P-HEX’s salvage value (USD)

\(T\) :

Temperature (°C)

\(U\) :

Overall heat transfer coefficient (W m−2 K−1)

\(u\) :

Uncertainty (-)

\(\dot{V}\) :

Flow rate (LPH)

\(\mathrm{WF}\) :

Worth capital factor (-)

\(\Delta P\) :

Pressure losses (Pa)

\(\Delta {E}_{\mathrm{p}}\) :

Gain of thermal exergy (J)

\(\Delta E_{{\text{q}}}\) :

Lost exergy due to friction (J)

\(\varepsilon\) :

Energy effectiveness (-)

\({\varepsilon }_{\mathrm{p}}\) :

Cost of each unit of friction exergy (USD J−1)

\({\varepsilon }_{\mathrm{q}}\) :

Cost of each unit of thermal exergy (USD J−1)

\({\varepsilon }_{\mathrm{Ex}}\) :

Exergy effectiveness (-)

\({\eta }_{\mathrm{P}}\) :

Net profit per unit transferred heat load (USD kJ−1)

\({\eta }_{W-S}\) :

Witte-Shamsundar efficiency (%)

\(\rho\) :

Density of water (kg m−3)

\(a\) :

Ambient

\(\mathrm{actual}\) :

Actual

\(\mathrm{air}\) :

Air

\(\mathrm{avg}\) :

Average

\(c\) :

Cold fluid

\(h\) :

Hot fluid

\(i\) :

Inlet or initial

\(\mathrm{max}\) :

Maximum

\(\mathrm{min}\) :

Minimum

\(o\) :

Outlet

\(p\) :

Plate

\(\mathrm{sp}\) :

Single-phase fluid flow

\(t\) :

Total

\(\mathrm{tp}\) :

Two phase fluid flow

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Funding

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Cairo Governorate, Egypt

    Zakaria M. Marouf

  2. Mechanical Power Engineering Department, Faculty of Engineering, Cairo University, 12613, Giza, Egypt

    Muhammed A. Hassan & Mahmoud A. Fouad

  3. Universite de Pau et des Pays de l’Adour, E2S UPPA, LaTEP, Pau, France

    Muhammed A. Hassan

Authors
  1. Zakaria M. Marouf
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  3. Mahmoud A. Fouad
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Contributions

ZMM helped in conceptualization, methodology, software, validation, formal analysis, investigation, data curation, visualization, writing—original draft, writing—review and editing, resources. MAH contributed to conceptualization, formal analysis, visualization, writing—original draft, writing—review & editing, supervision. MAF was involved in writing—review and editing, supervision.

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Correspondence to Zakaria M. Marouf.

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Marouf, Z.M., Hassan, M.A. & Fouad, M.A. Energy, exergy, and economic (3E) analysis of air bubbles injection into plate heat exchangers. J Therm Anal Calorim 148, 6311–6325 (2023). https://doi.org/10.1007/s10973-023-12143-y

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