Experimental testing of the heating performance of a rotor-type dissipative liquid heater

Abstract

The study focuses on the development of technology for volumetric noncontact liquid heating based on the dissipative liquid heating effect and realized in a high-gradient flow in the rotor–stator system of a hydrodynamic apparatus. In this paper, the heating performance of a prototype of a rotor-type dissipative liquid heater is studied, and the dynamics of several parameters, such as the heat power generated, the electrical power consumed and the efficiency factor, are defined. It is shown that the time evolution of the efficiency factor along with the other parameters displays a nonlinear character and depends on the flow pattern of the water–vapor system. It is found that the highest efficiency of the dissipative liquid heating of 91.6% is observed in the froth flow of the two-phase water–vapor system. In addition, potential industrial applications of the dissipative liquid heaters are discussed.

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Notes

  1. 1.

    Here, the multiplier factor \(\lambda\) represents a property of compressible fluids, similarly to the shear viscosity \(\mu\), and takes into account the energy dissipation due to the volume change of the fluid with finite velocity. It is defined as \(\lambda =-\frac{2}{3}\bullet \mu +{\mu }_{V}\), where \({\mu }_{V}\) is the bulk or volume viscosity of the fluid. The bulk viscosity \({\mu }_{V}\) plays a fundamental role in describing the fluid dynamics of two-phase flows, e.g., bubbly flows. It has also been found that the bulk viscosity of common fluids, such as water, has a higher value than the shear viscosity. For instance, it was reported in [26] that, at 15 °C, the bulk viscosity of water is 3.09·10–3 Pa·s versus the shear viscosity of 1.14·10–3 Pa·s. For more information on the bulk viscosity, we refer to the studies in [27, 28].

Abbreviations

\(a_{{\text{h}}}\) :

Sound velocity in the homogeneous water–vapor mixture (m/s)

\(a_{{\text{v}}}\) :

Sound velocity in the water vapor (m/s)

\(a_{{\text{w}}}\) :

Sound velocity in the water (m/s)

\(c_{{\text{P}}}^{{\text{s}}}\) :

Isobaric specific heat capacity of steel (J/kg K)

c P :

Isobaric specific heat capacity of water (J/kg K)

d :

Diameter of the cylindrical dimples (mm)

D :

External rotor diameter (mm)

E E :

Consumed electrical energy (J)

\(E_{{\text{E}}}^{{{\text{av}}}}\) :

Average value of the electrical energy consumed by the motor drive (active power) during the experiment (W h)

E H :

Generated heat (J)

H :

Depth of the cylindrical dimples (mm)

h :

Rotor width (mm)

I L :

Linear electrical current (A)

m :

Mass of the steel construction of the dissipative liquid heater (kg)

n :

Rotor mechanical speed/rotational speed (rpm)

P 1 :

Inlet gauge pressure (Pa)

P 2 :

Outlet gauge pressure (Pa)

P S :

Saturation water vapor pressure (Pa)

P St :

Static pressure in the annular flow (Pa)

Q :

Water volume flow rate (m3/h)

R :

Radius of the rotor (mm)

S a :

Surface area of the annulus (m2)

t 1 :

Inlet water temperature (°C)

t 2 :

Outlet water temperature (°C)

Δt S :

Temperature rise of the steel construction of the dissipative liquid heater (°C)

U av :

Average peripheral flow velocity in the annulus (m/s)

U L :

Linear electrical voltage (V)

U m :

Maximal peripheral velocity in the annulus (m/s)

\(U_{{{\text{av}}}}^{{\text{v}}}\) :

Average peripheral flow velocity of the vapor phase in the annulus (m/s)

\(U_{{{\text{av}}}}^{{\text{w}}}\) :

Average peripheral flow velocity of the liquid phase in the annulus (m/s)

V :

Annular volume (m3)

V av :

Average axial velocity in the annulus (m/s)

W DH :

Dissipation heat power (W)

W E :

Consumed electrical power (W)

W H :

Generated heat power (W)

α :

Bubble volume fraction

Δ:

Annular breadth (mm)

η :

Efficiency factor

μ :

Dynamic viscosity of the fluid (Pa s)

ν :

Kinematic viscosity of the fluid (m2/s)

ρ h :

Density of the homogeneous water–vapor mixture (kg/m3)

ρ v :

Density of the water vapor (kg/m3)

ρ w :

Water density (kg/m3)

τ :

Operating time (s)

ω :

Angular velocity (radian/s)

\({\text{Re}}_{{\text{a}}} = \frac{{2 \cdot \delta \cdot V_{{{\text{av}}}} }}{\nu }\) :

Reynolds number for the axial flow

\({\text{Ta}} = \frac{{\omega^{2} \cdot R \cdot \delta^{3} }}{{\nu^{2} }}\) :

Taylor number

AC:

Alternating current

CFD:

Computational fluid dynamics

LMTD:

Log-mean temperature difference

rpm:

Rotation per minute

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Acknowledgements

The authors would like to thank the administration of Shpola REM PJSC "Cherkasyoblenergo" (Ukraine) for permission to conduct our experiments and test the heating performance of the rotor-type dissipative liquid heater.

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Appendix: Measuring instrument description and uncertainty analysis

Appendix: Measuring instrument description and uncertainty analysis

Measuring instrument description

Description of the tools used for direct measurements of the hydraulic, thermal, and electrical parameters is presented in Table

Table 3 The measuring instruments and their characteristics

3.

Uncertainty analysis

The uncertainty analysis of the measured and calculated parameters was carried out based on the error propagation theory as described by Lee [38]. Table

Table 4 Uncertainty estimation of the measured parameters

4 contains total uncertainties of the measured parameters.

Consumed electrical power

The uncertainty of the consumed electrical power ΔWE can be found as follows:

$${\Delta }W_{{\text{E}}} = \left[ {\left( {\frac{{\partial W_{{\text{E}}} }}{{\partial I_{{\text{L}}} }} \cdot \Delta I_{{\text{L}}} } \right)^{2} + \left( {\frac{{\partial W_{{\text{E}}} }}{{\partial U_{{\text{L}}} }} \cdot \Delta U_{{\text{L}}} } \right)^{2} } \right]^{0.5} ,$$
(18)

where ΔIL is the total uncertainty of the linear electrical current measured, ΔUL is the total uncertainty of the linear voltage measured.

Generated heat power

The uncertainty of the generated heat power ΔWH can be calculated as given below:

$${\Delta }W_{{\text{H}}} = \left[ {\left( {\frac{{\partial W_{{\text{H}}} }}{\partial Q} \cdot \Delta Q} \right)^{2} + \left( {\frac{{\partial W_{{\text{H}}} }}{\partial \rho } \cdot \Delta \rho } \right)^{2} + \left( {\frac{{\partial W_{{\text{H}}} }}{{\partial c_{{\text{P}}} }} \cdot \Delta c_{P} } \right)^{2} + \left( {\frac{{\partial W_{{\text{H}}} }}{{\partial t_{2} }} \cdot \Delta t_{2} } \right)^{2} + \left( {\frac{{\partial W_{{\text{H}}} }}{{\partial t_{1} }} \cdot \Delta t_{1} } \right)^{2} } \right]^{0.5} ,$$
(19)

where ΔQ is the total uncertainty of the water volume flow rate measured, Δρ is the total uncertainty of the water density calculated, ΔcP is the total uncertainty of the water isobaric specific heat capacity calculated, Δt2 is the total uncertainty of the outlet water temperature measured, Δt1 is the total uncertainty of the inlet water temperature measured.

Efficiency factor

The uncertainty of the efficiency factor Δη can be estimated as follows:

$${\Delta }\eta = \left[ {\left( {\frac{\partial \eta }{{\partial W_{{\text{H}}} }} \cdot \Delta W_{{\text{H}}} } \right)^{2} + \left( {\frac{\partial \eta }{{\partial W_{{\text{E}}} }} \cdot \Delta W_{{\text{E}}} } \right)^{2} } \right]^{0.5} ,$$
(20)

where ΔWH is the total uncertainty of the heat power calculated, ΔWE is the total uncertainty of the electrical power calculated.

Table

Table 5 Uncertainty estimation of the calculated parameters

5 presents the total uncertainties of the calculated parameters.

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Bespalko, S., Halychyi, O., Yovchenko, A. et al. Experimental testing of the heating performance of a rotor-type dissipative liquid heater. Int J Energy Environ Eng 12, 39–54 (2021). https://doi.org/10.1007/s40095-020-00354-0

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Keyword

  • High-gradient
  • Annulus
  • Two-phase flow
  • Dissipation
  • Dissipative heating