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.

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 ΔW_E 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 ΔI_L is the total uncertainty of the linear electrical current measured, ΔU_L is the total uncertainty of the linear voltage measured.

Generated heat power

The uncertainty of the generated heat power ΔW_H 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, Δc_P 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 ΔW_H is the total uncertainty of the heat power calculated, ΔW_E 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.