# Analysis of the Working Characteristics of the Ejector in the Water Heating System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{3}/f

_{r}

_{1}.

## 1. Introduction

_{2}O), therefore, in the ejector nozzle a certain speed of water must be achieved, which results in the creation of a certain vacuum in the suction pipe and thus enables the mixing of a quantity of water from the return network with the water of the supply network. This amount of the mixed water then goes to the thermal consumer. If the pressure difference between the supply and return networks is low, in order to mix the return network water with the supply network water a pump must be used.

_{2}O) realize a mixing coefficient in the range u = 1.5 to 2.5.

_{3}= 15 mm and nozzle diameter d

_{1}= 10 mm, create a pressure difference of 39% higher than the non-diffuser ejector, respectively, pressure difference of Δ(Δp

_{s}/Δp

_{r}) = 0.16. This increase in the pressure change decreases by decreasing nozzle diameter d

_{1}or by increasing mixing chamber diameter d

_{3}.

_{3}. For illustration, the diffuser ejector with mixing chamber diameter d

_{3}= 15 mm and the nozzle diameter d

_{1}= 10 mm, creates an increase in the mixing coefficient of Δu = 0.85 higher than the non-diffuser ejector, while for the mixing chamber with diameter d

_{3}= 40 mm, with the same nozzle, the diffuser ejector creates a mixing coefficient for Δu = 1.75 higher than the non-diffuser ejector.

## 2. Materials and Methods

_{r}

_{2}. This stream of fluid creates a certain pressure in the (g

_{p}) pipe and consequently a quantity of water is absorbed from the return network of the heating system. This amount of water is introduced into the mixing chamber in Section 2-2 at speed W

_{n}

_{2}. The created mixture leaves the mixing chamber in Section 3-3, passes through the diffuser, and then is sent to the heating system with R (radiators).

_{s}/Δp

_{r}depends on the ratio of the cross sections of the components of the ejector, their velocity coefficients, as well as the mixing coefficient.

_{3}= 15 mm and the nozzles with diameters of d

_{1}= 4, 6, 8, and 10 mm is done after defining the ratios below:

_{3}= 15 mm is constructed using nozzles with diameters d

_{1}= 4, 6, 8, and 10 mm. This analysis was also done for mixing chambers with diameters d

_{3}= 20, 30, and 40 mm using the same nozzle diameters. The diagrams are constructed and presented in Figure 2, Figure 3, Figure 4 and Figure 5.

_{1}= 15 mm, by increasing the ratio of surfaces f

_{3}/f

_{r}

_{1}= 2.25 to the value f

_{3}/f

_{r}

_{1}= 14, the mixing coefficient increases from 1.25 to 4.2, which is realized with ejector nozzles with different diameters and there is a reduction in the ejector pressure difference from 0.57 to 0.12. The non-diffuser ejector with the same surface ratio f

_{3}/f

_{r}

_{1}creates a mixing coefficient from 0.4 to 2.3, while is noticed a lower pressure difference from 0.41 to 0.12.

_{3}= 20 mm, with the same nozzle diameters, are shown in Figure 3. For the mixing chamber with diameter d

_{3}= 20 mm, for the ratio f

_{3}/f

_{r}

_{1}= 4, the change in maximum pressure created by the diffuser ejector and non-ejector diffuser is 0.05 (15.15%).

_{3}= 30 mm, with the same nozzles, are shown in Figure 4.

_{3}= 30 mm, the difference of the maximum pressure created by the diffuser ejector and the non-diffuser ejector is greatly reduced up to the value 0.01 (5.9%). This pressure difference is quite low for higher values of the ratio f

_{3}/f

_{r}

_{1}, and especially for the mixing coefficient u < 1. In these conditions, the difference in the mixing coefficient u created by the diffuser ejector decreases, for the ratio of surfaces f

_{3}/f

_{r}

_{1}= 2.25 it is 2.8 while for the non-diffuser ejector it is 1.8.

_{3}= 40 mm, with the same nozzles, are shown in Figure 5. From the diagrams in Figure 2, Figure 3, Figure 4 and Figure 5, it can be seen that by increasing the diameter of the mixing chamber, the pressure difference in the ejector decreases and, consequently, the mixing coefficient of water from the return network increases.

_{3}/f

_{r}

_{1}and does not depend on the absolute value of these surfaces. This means that two ejectors with different dimensions can have the same surface ratio f

_{3}/fr

_{1}, respectively, the same characteristic. As the f

_{3}/fr

_{1}ratio increases, the mixing coefficient u increases but at the same time, the ejector effort decreases.

_{3}= 15, 20, 30, and 40 mm, respectively, for different ratios f

_{3}/fr

_{1}, are presented in Table 1.

_{3}/f

_{r}

_{1}, the value of the maximum pressure created by the diffuser ejector and the pressure created by the non-diffuser ejector is approximately equal. The change in pressure created by the ejector is more pronounced for lower values of the ratio f

_{3}/f

_{r}

_{1}, respectively, for higher values of the diameter of the ejector nozzle d

_{1}.

_{3}increases, for the same diameter of the ejector nozzle, the ejector mixing coefficient increases and at the same time the ejector pressure decreases.

^{2}, and mixing coefficient u = 2.8, the calculations are given below:

_{3}= 0.0007065 m

^{2}.

_{1}= 8 mm.

_{r}

_{1}= 0.00005024 m

^{2}. The ratio f

_{3}/f

_{r}

_{1}is 14.0625.

_{s}= G

_{s}$\cdot $v

_{s}, follows:

_{3}/f

_{r}

_{1}= 14.06, respectively, f

_{r}

_{1}/f

_{3}= f

_{p}

_{3}= 0.0711, the characteristic of ejector is presented with curve number 3 and the same is given in Table 1.

_{A}= 0.015808 m

^{3}/s and pressure change (Δp

_{s})

_{A}= 199,272 N/m

^{2}.

_{s}

_{1}> S

_{s}, the water flow and the mixing coefficient of the ejector u in the heating system V

_{s}decrease while the pressure drop Δp

_{s}increases. These findings are seen from the diagram when the operation point changes from point A to point B.

_{s}

_{1}< Δp

_{s}. In this case, the operating point for network losses S

_{s}is point A

_{1}while it is point B

_{1}for network losses S

_{s}

_{1}> S

_{s}. In this case, the water flow in the system is decreased and so is the mixing coefficient u.

## 3. Results

_{3}/f

_{r}

_{1.}Therefore, the characteristic of the ejector does not depend on the absolute values of the surfaces of these sections. From the analysis of the equation of the ejector characteristic, it results that by increasing the ratio of surfaces f

_{3}/f

_{r}

_{1}, the coefficient of mixture u increases, and at the same time the pressure difference created by the ejector decreases.

_{1}= 15 mm, it is found that by increasing the ratio of surfaces f

_{3}/f

_{r}

_{1}= 2.25 to 14, the mixing coefficient increases from 1.25 to 4.2, while the ejector pressure difference decreases from 0.57 to 0.12. The same ejector with the same surface ratio f

_{3}/f

_{r}

_{1}, but without a diffuser, creates a mixing coefficient about 2–3 times lower than the ejector with a diffuser.

_{3}/f

_{r}

_{1}, the value of the maximum pressure created by the diffuser ejector and the pressure created by the non-diffuser ejector is approximately equal. The change in created pressure is more accentuated for lower values of the ratio f

_{3}/f

_{r}

_{1}, respectively, for higher values of the nozzle diameter d

_{1}.

_{3}/f

_{r}

_{1}= 2.25, which for the mixing chamber diameter of d

_{3}= 15 mm corresponds to the nozzle with a diameter of d

_{1}= 10 mm, the ratio change at the pressure created with the ejector with and without a diffuser is Δ(Δp

_{s}/Δp

_{r}) = (Δp

_{s}/Δp

_{r})

_{with diffuser}− (Δp

_{s}/Δp

_{r})

_{without diffuser}= 0.57 − 0.41 = 0.16.

_{3}increases, for the same diameter of the ejector nozzle, the ejector mixing coefficient u increases, and at the same time the ejector pressure decreases.

_{3}= 15 to 40 mm, and nozzles with diameters of 4, 6, 8, and 10 mm, create certain pressure change at the exit of the ejector. For the same nozzle, the pressure increase is higher for the ejector with the smaller mixing chamber diameter, which in this case of the study is d

_{3}= 15 mm, while this pressure increase is lower when the diameter of the nozzle is lowered or when the diameter of the mixing chamber increases. Ejectors with mixing chamber diameter d

_{3}= 15 mm and nozzle diameter d

_{1}= 10 mm, create a pressure difference of 39% higher than the non-diffuser ejector, respectively, a pressure difference of Δ(Δp

_{s}/Δp

_{r}) = 0.16. Diffuser and non-diffuser ejectors with a mixing chamber with a diameter of d

_{3}= 30 mm, with the same ratio of cross-sectional surfaces f

_{3}/f

_{r}

_{1}= 9, achieved with a nozzle diameter of d

_{1}= 10 mm, create a pressure difference of only Δ(Δp

_{s}/Δp

_{r}) = 0.01. When this nozzle is put in the ejector with the mixing chamber diameter d

_{3}= 40 mm, both types of ejectors realize the same pressure change, i.e., Δ(Δp

_{s}/Δp

_{r}) = 0. In this case, the diffuser ejector, compared to the non-diffuser ejector, with the same mixing chamber only increases the mixing coefficient u.

_{3}, that in this case of the study is with diameter d

_{3}= 40 mm. For illustration, the diffuser ejector with a mixing chamber diameter of d

_{3}= 15 mm and the nozzle diameter of d

_{1}= 10 mm, creates an increase in the mixing coefficient of Δu = 0.85 higher than the ejector without a diffuser. Meanwhile, the diffuser ejector with a mixing chamber diameter of d

_{3}= 40 mm with the same nozzle, creates a mixture coefficient of 67.3% higher than the non-diffuser ejector.

_{3}/f

_{r}

_{1}, while the diffuser has less impact for low pressure ejectors.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Ejector connected to the heating system: 1-1—cross section of the nozzle; 2-2—cross section of mixing chamber entrance; 3-3—cross section of mixing chamber exit.

**Figure 2.**Diffuser ejector and non-diffuser ejector characteristics for with the mixing chamber diameter d

_{3}= 15 mm. The curves are given for the nozzle diameters d

_{1}= 4, 6, 8, and 10 mm. The values of the ratios for which the curves are constructed are f

_{p}

_{1}= 0.0711 (curve 1), f

_{p}

_{2}= 0.16 (curve 2), f

_{p}

_{3}= 0.2844 (curve 3), f

_{p}

_{4}= 0.444 (curve 4), respectively, f

_{v}

_{1}= 0.0765, f

_{v}

_{2}= 0.1905, f

_{v}

_{3}= 0.3975, f

_{v}

_{4}= 0.8.

**Figure 3.**Diffuser ejector and non-diffuser ejectors for the mixing chamber with diameter d

_{3}= 20 mm. The curves are given for the nozzle diameters d

_{1}= 4, 6, 8, and 10 mm. The values of the ratios for which the curves are constructed are f

_{p}

_{1}= 0.04 (curve 1), f

_{p}

_{2}= 0.09 (curve 2), f

_{p}

_{3}= 0.16 (curve 3), f

_{p}

_{4}= 0.25 (curve 4), respectively, f

_{v}

_{1}= 0.0416, f

_{v}

_{2}= 0.0989, f

_{v}

_{3}= 0.1904, f

_{v}

_{4}= 0.333.

**Figure 4.**Diffuser ejector and non-diffuser ejector characteristics with mixing chamber with diameter d

_{3}= 30 mm. The curves are given for the nozzle diameter d

_{1}= 4, 6, 8, and 10 mm. The values of the ratios for which the curves are constructed are f

_{p}

_{1}= 0.0177 (curve 1), f

_{p}

_{2}= 0.04 (curve 2), f

_{p}

_{3}= 0.0711 (curve 3), f

_{p}

_{4}= 0.1111 (curve 4), respectively, f

_{v}

_{1}= 0.0181, f

_{v}

_{2}= 0.0416, f

_{v}

_{3}= 0.0765, f

_{v}

_{4}= 0.0125.

**Figure 5.**Diffuser ejector and non-diffuser ejector characteristics with mixing chamber diameter d

_{3}= 40 mm. The curves are given for the nozzle diameter of d

_{1}= 4, 6, 8, and 10 mm. The values of the ratios for which the curves are constructed: f

_{p}

_{1}= 0.01 (curve 1), f

_{p}

_{2}= 0.0225 (curve 2), f

_{p}

_{3}= 0.04 (curve 3), f

_{p}

_{4}= 0.0625 (curve 4) respectively, f

_{v}

_{1}= 0.0101, f

_{v}

_{2}= 0.0230, f

_{v}

_{3}= 0.0416, f

_{v}

_{4}= 0.0666.

Mixing Chamber Diameter d_{3} | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

d_{3} = 15 | d_{3} = 20 | d_{3} = 30 | d_{3} = 40 | |||||||||||

$\frac{{\mathit{f}}_{3}}{{\mathit{f}}_{\mathit{r}1}}$ | u | $\frac{\mathsf{\Delta}{\mathit{p}}_{\mathit{s}}}{\mathsf{\Delta}{\mathit{p}}_{\mathit{r}}}$ | $\frac{{\mathit{f}}_{3}}{{\mathit{f}}_{\mathit{r}1}}$ | u | $\frac{\mathsf{\Delta}{\mathit{p}}_{\mathit{s}}}{\mathsf{\Delta}{\mathit{p}}_{\mathit{r}}}$ | $\frac{{\mathit{f}}_{3}}{{\mathit{f}}_{\mathit{r}1}}$ | u | $\frac{\mathsf{\Delta}{\mathit{p}}_{\mathit{s}}}{\mathsf{\Delta}{\mathit{p}}_{\mathit{r}}}$ | $\frac{{\mathit{f}}_{3}}{{\mathit{f}}_{\mathit{r}1}}$ | u | $\frac{\mathsf{\Delta}{\mathit{p}}_{\mathit{s}}}{\mathsf{\Delta}{\mathit{p}}_{\mathit{r}}}$ | |||

The diameter of ejector nozzle d_{1}, mm | Ejector with diffuser | 4 | 14 | 4.2 | 0.12 | 25 | >5 | 0.07 | 56.25 | >5 | 0.03 | 100 | >5 | 0.02 |

6 | 6.25 | 2.4 | 0.25 | 11.11 | 3.5 | 0.15 | 25 | >5 | 0.07 | 44.44 | >5 | 0.03 | ||

8 | 3.51 | 1.7 | 0.41 | 6.25 | 2.5 | 0.25 | 14.06 | 4.2 | 0.12 | 25 | >5 | 0.07 | ||

10 | 2.25 | 1.25 | 0.57 | 4.00 | 1.8 | 0.38 | 9.00 | 2.8 | 0.18 | 16 | 4.35 | 0.1 | ||

Ejector without diffuser | 4 | 14 | 2.3 | 0.12 | 25 | 3.4 | 0.07 | 56.25 | >5 | 0.03 | 100 | >5 | 0.02 | |

6 | 6.25 | 1.25 | 0.23 | 11.11 | 2.0 | 0.14 | 25 | 3.3 | 0.07 | 44.44 | 4.8 | 0.04 | ||

8 | 3.51 | 0.7 | 0.33 | 6.25 | 1.25 | 0.23 | 14.06 | 2.3 | 0.11 | 25 | 3.3 | 0.07 | ||

10 | 2.25 | 0.4 | 0.41 | 4.00 | 0.8 | 0.33 | 9.00 | 1.8 | 0.17 | 16 | 2.6 | 0.1 |

u | 0 | 1 | 2 | 2.8 | 3 |
---|---|---|---|---|---|

V_{s}, m^{3}/s | 0.00416 | 0.00832 | 0.01248 | 0.015808 | 0.01664 |

f(u,f_{3}/fr_{1}) = Δp_{s}/Δp_{r} | 0.125 | 0.116 | 0.0913 | 0.052461 | 0.0518 |

Δp_{s} = f(u,f_{3}/f_{r1}), N/m^{2} | 474,810.38 | 440,624.03 | 346,801.5 | 199,272 | 196,761.42 |

Δp_{s} = f(S_{s},V_{s}), N/m^{2} | 13,800 | 55,200 | 124,200 | 199,272 | 260,800 |

Symbol | Units | Explanation |
---|---|---|

G_{r}, G_{n} | kg/s | water flow through the nozzle and the water that is injected |

G_{s} = G_{r} + G_{n} | kg/s | total amount of water in the heating system |

u = G_{n}/G_{r} | - | mixing coefficient |

W_{r}_{2}, W_{n}_{2}, W_{3} | m/s | the speed of the working water at the entrance of the mixing chamber, the speed of the water in the injection pipe and the speed of the mixed water in section (3-3) |

${f}_{r1},{f}_{3}$ | m^{2} | surface of the cross section of the nozzle and of the mixing chamber |

f_{n}_{2}= f_{3} − f_{r}_{1} | m^{2} | surface of the cross section of the water stream injected into the mixing chamber |

${p}_{r},{p}_{n},{p}_{s}$ | Pa | pressure of water in the nozzle entrance, injectable water and mixed water |

$\Delta {p}_{s}={p}_{s}-{p}_{n}$ | Pa | change in pressure created by the ejector |

$\Delta {p}_{r}={p}_{r}-{p}_{n}$ | Pa | difference between the pressure in the nozzle and the water injection pipe |

v_{r}, v_{n}, v | m^{3}/kg | specific volumes of water at the outlet of the nozzle, in the injection pipe and water at the exit of the mixing room |

$\rho $ | kg/m^{3} | water density |

${\phi}_{1}$$=$0.95 | _ | speed coefficient of nozzle |

${\phi}_{2}$$=$0.975 | _ | speed coefficient of mixing chamber |

${\phi}_{3}$$=$0.90 | _ | speed coefficient of diffuser |

${\phi}_{4}$$=$0.925 | _ | speed coefficient of injection pipe |

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**MDPI and ACS Style**

Krasniqi Alidema, D.; Krasniqi, M.; Filkoski, R.V.; Krasniqi, F.
Analysis of the Working Characteristics of the Ejector in the Water Heating System. *Energies* **2022**, *15*, 2025.
https://doi.org/10.3390/en15062025

**AMA Style**

Krasniqi Alidema D, Krasniqi M, Filkoski RV, Krasniqi F.
Analysis of the Working Characteristics of the Ejector in the Water Heating System. *Energies*. 2022; 15(6):2025.
https://doi.org/10.3390/en15062025

**Chicago/Turabian Style**

Krasniqi Alidema, Drenusha, Marigona Krasniqi, Risto V. Filkoski, and Fejzullah Krasniqi.
2022. "Analysis of the Working Characteristics of the Ejector in the Water Heating System" *Energies* 15, no. 6: 2025.
https://doi.org/10.3390/en15062025